NVT Ensemble in Vacuum Simulations: A Practical Guide for Biomedical Research and Drug Development

Abstract

This article provides a comprehensive guide to the application of the NVT (Canonical) ensemble in vacuum simulations for biomedical and drug discovery research. It covers the foundational principles of the NVT ensemble, where the number of particles, volume, and temperature are held constant, explaining its critical role in stabilizing systems after energy minimization and before production runs. The article details methodological protocols for setting up NVT simulations in vacuum environments, highlighting applications in studying drug-membrane interactions, protein-ligand complexes, and material properties. A significant focus is placed on troubleshooting common pitfalls, such as negative pressure and thermalization failures, offering practical optimization strategies. Finally, the article outlines rigorous validation techniques and comparative analyses with other ensembles, establishing a framework for ensuring the reliability and physical accuracy of simulation results to advance rational drug design.

Understanding the NVT Ensemble: Why Constant Volume and Temperature Matter in Vacuum Simulations

The NVT ensemble, also known as the canonical ensemble, is a fundamental concept in statistical mechanics and molecular dynamics (MD) simulations. It describes a system characterized by a constant number of particles (N), a constant volume (V), and a constant temperature (T). This ensemble is particularly valuable for studying material properties under conditions where volume changes are negligible, making it ideal for investigating processes like ion diffusion in solids, adsorption phenomena, and reactions on surfaces or clusters where the simulation box dimensions remain fixed [1].

In the NVT ensemble, the system is not isolated but can exchange energy with a surrounding virtual heat bath, which maintains the temperature around an equilibrium value. Unlike the microcanonical (NVE) ensemble where total energy is conserved, the temperature in an NVT simulation will naturally fluctuate around a set point, and the role of the thermostat is to ensure these fluctuations are of the correct size and that the average temperature is accurate [2] [3]. This setup mimics realistic experimental conditions for many material science and biological applications where temperature is controlled, but volume is fixed.

Core Principles and Theoretical Foundation

The NVT ensemble is defined by its three conserved quantities: the number of particles (N), the volume of the system (V), and the temperature (T). The fixed volume means that the simulation cell's size and shape do not change during the simulation. Consequently, there is no control over pressure, and its average value will depend on the initial configuration provided for the system, such as the lattice parameters in the POSCAR file for VASP simulations [2].

The temperature, unlike volume, is not a static property at the atomic scale. In MD simulations, the "instantaneous temperature" is computed from the total kinetic energy of the system via the equipartition theorem. The primary goal of a thermostat in an NVT simulation is not to keep the temperature perfectly constant, but to ensure that the average temperature over time is correct and that the fluctuations in temperature are of the correct magnitude for the simulated system [3]. For small systems, these fluctuations can be significant, and it is only by averaging over a sufficiently long time that a stable temperature emerges.

Thermostats: Methods for Temperature Control

A thermostat is the algorithmic component that couples the system to a virtual heat bath. Several thermostat algorithms are available, each with distinct advantages and limitations. The choice of thermostat depends on the desired balance between accurate ensemble sampling and minimal interference with the system's natural dynamics.

Table 1: Common Thermostats in NVT Ensemble Simulations

Thermostat	MDALGO (VASP)	Key Principle	Strengths	Considerations
Nosé-Hoover [2] [4]	2	Extends the system with a fictitious thermal reservoir.	Generally reliable; reproduces correct canonical ensemble.	Can exhibit persistent temperature oscillations in some cases.
Nosé-Hoover Chain [2]	4	Uses a chain of thermostats for improved control.	Mitigates oscillations from standard Nosé-Hoover.	Requires setting chain length (e.g., default of 3 is often sufficient).
Andersen [2]	1	Stochastic collisions reassign particle velocities.	Good for sampling conformational space.	Can disrupt the natural dynamics of the system.
Langevin [2] [4]	3	Applies friction and stochastic forces to each particle.	Tight temperature control; good for equilibration.	Suppresses natural dynamics; not ideal for measuring diffusion.
CSVR [2]	5	Stochastic velocity rescaling (Canonical Sampling Through Velocity Rescaling).	Good sampling properties.	Period parameter (e.g., CSVR_PERIOD) needs to be set.
Berendsen [4] [1]	N/A	Scales velocities to rapidly approach target temperature.	Fast and stable convergence.	Does not produce a correct canonical ensemble; best for equilibration.
Bussi-Donadio-Parrinello [4]	N/A	Stochastic variant of Berendsen thermostat.	Correctly samples the canonical ensemble.	A recommended upgrade over the standard Berendsen method.

Practical Thermostat Selection and Configuration

The choice of thermostat and its parameters can significantly impact the results of a simulation. For production runs where accurate sampling of the canonical ensemble is required, the Nosé-Hoover thermostat is often the recommended choice [4]. Its key parameter, SMASS in VASP, determines the virtual mass of the thermal reservoir and affects the oscillation frequency of the temperature [2].

The strength of the coupling to the heat bath is controlled by parameters like the thermostat timescale (or its inverse, the coupling constant). A tight coupling (short timescale) forces the system temperature to closely follow the target but can interfere with the system's natural dynamics. A weak coupling (long timescale) minimizes this interference but may take longer to equilibrate. For precise measurement of dynamical properties, a weak coupling or even a switch to the NVE ensemble after equilibration is advisable [4].

Application Notes for Vacuum and Surface Simulations

The NVT ensemble is particularly well-suited for simulations where the volume is naturally fixed. A prime example is the study of processes in a vacuum environment or on solid surfaces, often modeled using a slab geometry with a large vacuum layer to separate periodic images. In such setups, the volume of the simulation box must remain constant.

• Adsorption and Reactions on Surfaces: When modeling the adsorption of molecules or catalytic reactions on a solid surface (e.g., a metal or oxide slab), the underlying lattice of the slab is typically held rigid or has fixed lattice parameters. Using the NVT ensemble ensures that the surface area and the height of the vacuum layer remain constant throughout the simulation, allowing researchers to study the dynamics of the adsorbates without the influence of a fluctuating cell [1].
• Cluster Simulations: Studying isolated molecules or nanoclusters in vacuum is another key application. The simulation box must be large enough to prevent interactions between the cluster and its periodic images. The NVT ensemble fixes this box size, while the thermostat controls the temperature of the cluster, which is essential for simulating phenomena like thermal unfolding or studying finite-temperature properties [1].

A critical prerequisite for NVT simulations is ensuring the system is well-equilibrated at the desired volume. It is "often desirable to equilibrate the lattice degrees of freedom, for example, by running an NpT simulation or by performing a structure and volume optimization" prior to the NVT production run [2]. This ensures that the fixed volume in the NVT simulation is representative of the thermodynamic state point of interest.

Experimental Protocols and Workflows

Below is a detailed protocol for setting up and running an NVT molecular dynamics simulation for a system such as a molecule adsorbed on a surface in a vacuum.

Research Reagent Solutions

Table 2: Essential Components for an NVT MD Simulation

Component	Description	Function in the Simulation
Initial Atomic Structure	A file containing the initial coordinates of all atoms (e.g., POSCAR, .xyz).	Defines the starting configuration of the system (adsorbate, surface slab, etc.).
Interatomic Potential	A force field, neural network potential (e.g., EMFF-2025 [5]), or DFT calculator.	Describes the energetic interactions between atoms, determining the forces.
Simulation Software	MD package such as VASP [2], QuantumATK [4], ASE [1], or GROMACS [3].	Provides the engine to integrate equations of motion and apply ensemble constraints.
Thermostat Algorithm	e.g., Nosé-Hoover, Langevin, or CSVR.	Maintains the system temperature at the desired setpoint.
Periodic Boundary Conditions	Defined by the simulation cell vectors.	Mimics an infinite system and avoids surface effects; crucial for slab-vacuum models.

Detailed Step-by-Step Protocol

Step 1: System Preparation and Geometry Optimization

• Construct the initial atomic configuration, for example, a slab structure with a vacuum layer for surface studies.
• Perform a volume optimization (e.g., using IBRION = 1 or 2 and ISIF > 2 in VASP) or a short NpT simulation to find the equilibrium volume at the target temperature [2]. This is a critical step to ensure the fixed volume in the subsequent NVT run is physically meaningful.

Step 2: Equilibration in the NVT Ensemble

• Start the MD simulation using the optimized volume. In the input file (e.g., INCAR for VASP), set the parameters for an NVT run:
  • IBRION = 0 (to choose molecular dynamics)
  • MDALGO = 2 (to select the Nosé-Hoover thermostat, for example)
  • ISIF = 2 (to ensure the stress tensor is computed but the volume/shape is not changed)
  • TEBEG = 300 (set the target temperature in Kelvin)
  • SMASS = 1.0 (set the virtual mass for the Nosé-Hoover thermostat) [2]
• Use a reasonable time step (e.g., 0.5 to 2.0 femtoseconds), ensuring it is small enough to capture the fastest atomic vibrations [4].
• Assign initial velocities from a Maxwell-Boltzmann distribution corresponding to the target temperature.
• Run the simulation until key observables (e.g., potential energy, temperature) plateau, indicating equilibration.

Step 3: Production Simulation and Trajectory Analysis

• Continue the simulation with the same NVT parameters to collect trajectory data for analysis.
• Ensure that the Log Interval or equivalent setting is appropriate to write snapshots to disk without generating excessively large files [4].
• Analyze the trajectory to compute properties of interest, such as:
  • Radial distribution functions
  • Mean-squared displacement for diffusion coefficients
  • Structural order parameters
  • Adsorbate binding configurations

Critical Considerations and Best Practices

• Temperature Fluctuations are Normal: The instantaneous temperature in an MD simulation will fluctuate. The role of the thermostat is to ensure these fluctuations are correct for the ensemble, not to eliminate them. Pressure can fluctuate even more dramatically, with variations of hundreds of bar being typical, especially in small systems [3].
• Avoid Over-Coupling the Thermostat: Using a thermostat that is too "strong" (i.e., a very short coupling constant) can artificially suppress the natural dynamics of the system. This is particularly important if the goal is to compute time-dependent properties like diffusion constants [4].
• Do Not Over-Split Thermostat Groups: It is generally not a good practice to use separate thermostats for every component of your system (e.g., one for a small molecule, another for protein, and another for water). A group must be of sufficient size to justify its own thermostat. For a typical simulation, using tc-grps = Protein Non-Protein is usually best [3].
• Interpreting Average Structures: Be cautious when calculating an "average structure" from an NVT trajectory. If the system samples multiple distinct metastable states, the average position may be a physically meaningless point halfway between these states, potentially showing unphysical bond lengths or geometries [3].

In molecular dynamics (MD) simulations, the canonical (NVT) ensemble is crucial for studying material properties under conditions of constant particle number (N), constant volume (V), and constant temperature (T). This ensemble is particularly valuable for investigating systems where volume changes are negligible, such as ion diffusion in solids, adsorption and reaction processes on surfaces and clusters, and simulations in vacuum environments [1] [2]. Maintaining a constant temperature in these systems requires sophisticated algorithms known as thermostats, which mimic the energy exchange between the simulated system and a hypothetical heat bath.

Within the context of vacuum simulations research—where systems lack implicit solvent effects and often involve smaller, more constrained environments—the selection of an appropriate thermostat becomes critically important. Different thermostats vary in their theoretical foundations, numerical stability, and ability to reproduce correct statistical mechanical ensembles. This application note provides a detailed comparison of three predominant thermostats—Berendsen, Nosé-Hoover, and Langevin—with specific emphasis on their implementation, performance characteristics, and suitability for vacuum simulation scenarios commonly encountered in materials science and drug development research.

Thermostat Comparison Tables

Key Characteristics and Applications

Table 1: Comparative overview of thermostat properties and typical use cases.

Thermostat	Algorithm Type	Ensemble Correctness	Primary Advantages	Recommended Applications
Berendsen	Deterministic, velocity rescaling	Does not guarantee correct NVT ensemble [6]	Simple implementation, fast convergence, good numerical stability [1]	System equilibration, preliminary heating stages [7]
Nosé-Hoover	Deterministic, extended Lagrangian	Reproduces correct NVT ensemble in most cases [1]	Universally applicable, time-reversible, suitable for production simulations [7]	Production runs for larger systems, trajectory analysis [1] [7]
Langevin	Stochastic, random forces	Guarantees Maxwell-Boltzmann distribution [6] [8]	Effective for small systems, enhances sampling, good for mixed phases [1] [7]	Free energy calculations, small systems, vacuum simulations [8] [7]

Mathematical Foundations and Parameters

Table 2: Mathematical formulation and key implementation parameters for each thermostat.

Thermostat	Fundamental Equation	Key Control Parameters	Implementation Notes
Berendsen	Scales velocities by factor λ = [1 + (Δt/τ)(T₀/T - 1)]¹/²	τ (coupling constant) - determines strength of temperature coupling [1]	Can cause "flying ice-cube" effect (unphysical energy transfer) [6]
Nosé-Hoover	Extended system with virtual mass: d²η/dt² = (T/T₀ - 1)	SMASS (virtual mass parameter) or time constant [2] [7]	Requires initialization; may not thermalize small systems with harmonic modes [7] [9]
Langevin	MẌ = -∇U(X) - γẊ + √(2γkBT)R(t) [8]	γ (damping coefficient/friction) [8]	Stochastic nature prevents reproducible trajectories; mimics viscous damping [1] [8]

Detailed Thermostat Protocols

Berendsen Thermostat Protocol

The Berendsen thermostat employs a weak-coupling algorithm that scales velocities to maintain temperature, making it particularly useful for rapid equilibration phases of simulation.

Detailed Methodology:

• Initialization: Prepare the system configuration. For vacuum simulations, ensure appropriate periodicity and sufficient vacuum padding to prevent spurious interactions between periodic images [9] [10].
• Parameter Setting: Set the target temperature (Tâ‚€) and the coupling constant (Ï„). The parameter Ï„ represents the time constant of the thermostat, with smaller values resulting in stronger coupling. A typical value is 0.1-1.0 ps [1].
• Integration: At each MD time step (Δt):
  • Calculate the current instantaneous temperature (T) from the kinetic energy.
  • Compute the scaling factor λ = [1 + (Δt/Ï„)(Tâ‚€/T - 1)]¹/².
  • Scale all velocities by λ: váµ¢ → λváµ¢.
• Duration: For equilibration protocols, apply the Berendsen thermostat for 50-100 ps to smoothly bring the system to the target temperature before switching to a production thermostat like Nosé-Hoover [7].

Nosé-Hoover Thermostat Protocol

The Nosé-Hoover thermostat introduces an extended Lagrangian formulation with a dynamic variable representing the heat bath, providing a deterministic approach that generates a correct canonical ensemble.

Detailed Methodology:

• System Setup: Begin with an equilibrated system, preferably pre-heated using a method like Berendsen or velocity rescaling.
• Parameter Selection:
  • In LAMMPS: Use the fix nvt command with a damping parameter (Ï„). A value of Ï„ = 100 timesteps is often effective (e.g., 100 fs for a 1 fs timestep) [6].
  • In VASP: Set MDALGO = 2 and specify the virtual mass via the SMASS tag (e.g., SMASS = 1.0) [2].
• Integration: Utilize a time-reversible integrator such as velocity Verlet. The equations of motion couple the particle velocities to the thermostat variable, allowing dynamic energy exchange between the system and the thermal reservoir [7].
• Equilibration Verification: Monitor the potential energy and temperature until they stabilize around the set point with small fluctuations. For a 200-atom system in vacuum, this typically requires 50,000-150,000 iterations [6] [9].
• Production Run: Continue the simulation in the NVT ensemble for the desired production length, ensuring the Nosé-Hoover chain variable moves chaotically, indicating proper equilibration.

Langevin Thermostat Protocol

The Langevin thermostat applies a stochastic damping force combined with random impulses, making it particularly effective for small systems and vacuum environments where other thermostats may struggle.

Detailed Methodology:

• Initial Configuration: Prepare the system, noting that Langevin is especially suitable for vacuum simulations as it doesn't rely on continuous coupling to a large bath [7] [11].
• Parameterization:
  • Set the target temperature (T).
  • Choose a damping coefficient (γ). For vacuum simulations, a relatively low γ (e.g., 1-10 ps⁻¹) is often appropriate to minimize unphysical damping while maintaining temperature control [8] [7].
  • In LAMMPS: Use the fix langevin command [6].
  • In ASE: Implement using the Langevin class from ase.md module [1].
• Dynamics Propagation: At each time step:
  • Apply the deterministic forces: -∇U(X).
  • Apply the frictional damping force: -γv.
  • Add the random force: √(2γkâ‚šT/Δt)ξ, where ξ is Gaussian white noise [8].
• Trajectory Analysis: Note that the stochastic nature prevents exact trajectory reproducibility. Focus on ensemble-averaged properties rather than individual particle paths [1].

Workflow Visualization

Thermostat Selection Logic

General NVT-MD Simulation Workflow

The Scientist's Toolkit

Table 3: Essential research reagents and computational tools for molecular dynamics simulations in vacuum environments.

Tool/Solution	Function/Purpose	Implementation Examples
ASE (Atomistic Simulation Environment)	Python framework for setting up, running, and analyzing simulations [1]	NVTBerendsen, NVTNoseHoover classes for thermostat implementation [1]
LAMMPS	MD simulator with extensive thermostat options [6]	fix nvt, fix langevin commands for temperature control [6]
VASP	Ab initio MD package for electronic structure calculations [2]	MDALGO=2 for Nosé-Hoover, MDALGO=3 for Langevin dynamics [2]
GROMACS	MD package with comprehensive thermostat implementations [12]	integrator=sd for stochastic dynamics, integrator=md-vv with Nose-Hoover coupling [12]
OpenMM	Toolkit for MD simulations with GPU acceleration [11]	LangevinMiddleIntegrator for vacuum and solution simulations [11]
Velocity Verlet Integrator	Time-reversible algorithm for integrating equations of motion [12]	Used with Nosé-Hoover thermostat for accurate dynamics propagation [12]
Heme Oxygenase-1-IN-1	Heme Oxygenase-1-IN-1, MF:C13H15BrN2, MW:279.18 g/mol	Chemical Reagent
Pim-1 kinase inhibitor 6	Pim-1 kinase inhibitor 6, MF:C21H10BrCl2N3, MW:455.1 g/mol	Chemical Reagent

The selection of an appropriate thermostat for NVT ensemble simulations, particularly in vacuum environments, requires careful consideration of system size, desired properties, and methodological constraints. The Berendsen thermostat serves as an effective tool for rapid equilibration but should be avoided in production phases due to its failure to generate a correct canonical ensemble. The Nosé-Hoover thermostat provides a robust, deterministic approach suitable for most production simulations, especially for larger systems with sufficient degrees of freedom. For vacuum simulations involving small systems or cases where enhanced sampling is required, the Langevin thermostat offers distinct advantages despite its stochastic nature. By matching thermostat capabilities to specific research requirements—particularly in pharmaceutical and materials science applications—researchers can ensure both the efficiency and statistical validity of their molecular simulations.

The canonical (NVT) ensemble is a cornerstone of molecular dynamics (MD) simulations, maintaining a constant Number of atoms (N), constant Volume (V), and a Temperature (T) fluctuating around an equilibrium value. This ensemble is particularly indispensable for studies conducted in vacuum conditions, where it facilitates proper system equilibration and enables the investigation of intrinsic material properties without the complicating effects of a solvent or pressure variables. Within the context of vacuum simulations, the NVT ensemble ensures that the energy distribution among the system's degrees of freedom corresponds to a desired temperature, which is critical for achieving physically meaningful results before proceeding to production runs or for studying processes where volume is a controlled parameter. Its application ranges from preparing a system for subsequent analysis in other ensembles to directly probing surface phenomena and nanoscale interactions where the system size inherently limits the validity of a barostat.

Theoretical Foundation and Practical Implementation

Thermostat Selection for NVT Simulations

In NVT simulations, the temperature is controlled by a thermostat, which acts as a heat bath. The choice of thermostat can influence the quality of the dynamics and the reliability of the sampled ensemble. Several thermostats are available in modern MD software packages, each with distinct characteristics and suitable application domains, as summarized in Table 1.

Table 1: Common Thermostats for NVT Ensemble Simulations

Thermostat	MDALGO (VASP)	Key Characteristics	Best Use Cases
Nosé-Hoover	2	Deterministic; extended Lagrangian.	General purpose; larger systems.
Andersen	1	Stochastic; random velocity rescaling.	Rigid systems; rapid equilibration.
Langevin	3	Stochastic; includes friction term.	Biomolecules; systems with friction.
CSVR	5	Stochastic; canonical sampling.	Accurate canonical distribution.

For instance, in VASP, an NVT simulation using the Nosé-Hoover thermostat is set up with MDALGO = 2 and requires the SMASS tag to define the virtual mass for the thermostat [2]. It is crucial to set ISIF < 3 to ensure the volume remains fixed throughout the simulation [2].

Workflow for a Typical NVT Simulation in Vacuum

The following diagram illustrates the standard protocol for setting up and running an NVT simulation in a vacuum environment, from initial structure preparation to final analysis.

Diagram 1: Workflow for an NVT simulation in vacuum. The standard path involves energy minimization followed directly by NVT equilibration. An optional NPT pre-equilibration can be used to first obtain a specific box volume.

Key Application Notes and Protocols

Application Note 1: System Equilibration Preceding Production Runs

• Protocol Objective: To achieve a thermally equilibrated system with stable energy distributions for subsequent production simulations in the NVE ensemble or other studies.
• Rationale: Before any production MD run, a system must be equilibrated to ensure that the temperature and energy distributions have stabilized. In vacuum, where there is no solvent to provide a natural heat bath, the NVT ensemble is the primary method for this thermalization. This step is crucial after processes like energy minimization, which removes steric clashes but results in a configuration with zero kinetic energy.
• Detailed Protocol:
  • Initial Structure: Use an energy-minimized structure as the starting point.
  • Simulation Box: Define a vacuum box with sufficient padding to avoid periodic image interactions. For surface slabs, a vacuum gap of >10 Ã… is often used, but ~18 Ã… may be necessary to minimize spurious self-interactions across the periodic boundary [9].
  • Thermostat Selection: Choose an appropriate thermostat. The Nosé-Hoover thermostat (MDALGO=2 in VASP) is a robust deterministic choice for many systems [2]. For small systems with discrete phonon spectra, stochastic thermostats like CSVR may thermalize more effectively [9].
  • Parameter Setup: Set the target temperature (TEBEG), the number of steps (NSW), and the time step (POTIM). A common initial equilibration runs for 100-500 ps.
  • Equilibration Criteria: Monitor the potential energy and temperature of the system. The simulation is considered equilibrated when these properties fluctuate around a stable average value.

Application Note 2: Surface and Interface Studies

• Protocol Objective: To investigate the structure, dynamics, and reactivity of surfaces and thin films in isolation or under controlled deposition.
• Rationale: The NVT ensemble is ideal for surface science studies because the volume (and thus the surface area) is fixed. This allows for the direct investigation of phenomena like molecular orientation on substrates, which is a critical factor in organic semiconductor performance [13], or the erosion of materials by plasma [14] [15].
• Detailed Protocol:
  • Surface Model Construction: Create a slab model of the surface with a thickness of several atomic layers. The bottom layer(s) may be constrained to their bulk positions to mimic a semi-infinite solid.
  • Vacuum Layer Introduction: Add a vacuum layer along the z-axis (non-periodic direction) that is thick enough to prevent interactions between periodic images of the slab. As noted in [9], a larger vacuum gap (~18 Ã…) can help avoid unphysical, resonant vibrational modes that hinder proper thermalization.
  • Deposition or Interaction Simulation: For deposition studies, molecules can be randomly oriented and introduced into the vacuum above the surface [13]. For erosion studies, reactive species like atomic oxygen can be directed at the surface with specific kinetic energies [14].
  • NVT Simulation Run: Perform the MD simulation in the NVT ensemble to model the adsorption, orientation, or reaction of molecules/atoms with the surface at a specific temperature. The fixed volume is essential for calculating accurate surface densities and adsorption geometries.
  • Analysis: Key analyzable properties include:
    • Molecular Orientation: Calculate the angle (θ) of molecular transition dipole moments relative to the substrate normal and the orientation order parameter, ( S = \frac{1}{2}(3\langle \cos^2 \theta \rangle - 1) ) [13].
    • Damage Depth/Erosion Yield: Track the number of sputtered substrate atoms over time [14] [15].

Application Note 3: Tensile Deformation and Mechanical Failure

• Protocol Objective: To compute the mechanical response and tensile strength of materials or hybrid interfaces under uniaxial strain.
• Rationale: Tensile tests using MD are naturally performed in the NVT ensemble. The simulation box is deformed at a constant strain rate along one axis while the transverse dimensions are allowed to relax, effectively simulating a Poisson contraction. This protocol is used for systems ranging from bulk polymers to polymer-calcite interfaces [16].
• Detailed Protocol:
  • System Equilibration: First, equilibrate the entire system (e.g., a polymer-calcite composite) in the NVT ensemble at the target temperature and zero pressure until energy stabilization is achieved [16].
  • Deformation Setup: Apply a uniaxial strain by progressively elongating the simulation box along the tensile direction at a constant strain rate (e.g., 0.001 ps⁻¹). The transverse dimensions of the box are typically kept constant or controlled to maintain zero lateral pressure.
  • Stress Calculation: At each deformation step, allow the system to relax briefly while calculating the stress tensor. The component of the stress tensor along the strain direction is the key metric.
  • Failure Analysis: Continue the deformation until material failure (a sharp drop in stress) is observed. Analyze the stress-strain curve to extract properties like Young's modulus, yield strength, and ultimate tensile strength. The failure mechanism (e.g., chain slippage vs. bond breaking) can be visualized.

The Scientist's Toolkit: Essential Reagents and Materials

Table 2: Key "Research Reagent Solutions" for NVT Vacuum Simulations

Item / Software	Function / Description	Example in Application
VASP	A package for atomic-scale materials modeling, e.g., from first principles.	Used for NVT MD of surfaces with MDALGO=2 and ISIF=2 [2].
GROMACS	A versatile MD simulation package for biomolecular and materials systems.	Forum users discuss NVT equilibration protocols to fix negative pressure [17].
ReaxFF	A reactive force field for MD simulations of chemical reactions.	Models bond breaking in fused silica under oxygen plasma bombardment [14].
IFF-R	A reactive force field using Morse potentials for bond breaking.	Enables simulation of material failure while being ~30x faster than ReaxFF [18].
CHARMM/AMBER	Biomolecular force fields for proteins, nucleic acids, and lipids.	Compatible with IFF-R for simulating reactive processes in biomolecules [18].
(22R)-Budesonide-d6	(22R)-Budesonide-d6, MF:C25H34O6, MW:436.6 g/mol	Chemical Reagent
CTT2274	CTT2274, MF:C119H159N17O33P2, MW:2417.6 g/mol	Chemical Reagent

Critical Considerations and Troubleshooting

A common challenge in NVT simulations within a vacuum is achieving proper thermalization, especially for small systems. When a system is too small or has a large vacuum gap, its phonon spectrum can be too discrete, causing thermostats like Nosé-Hoover to fail in redistributing energy effectively between the system's harmonic vibrational modes [9]. In such cases, switching to a stochastic thermostat (e.g., CSVR or Andersen) can improve thermalization.

Another frequent issue, particularly in explicit-solvent MD, is encountering large negative pressures after NVT equilibration, which often indicates an simulation box that is too large for the number of particles [17]. The recommended solution is not to adjust the box size manually within an NVT framework, but to first run an NPT equilibration at the target pressure. This allows the barostat to find the correct density, after which one can switch back to NVT for production using the equilibrated box dimensions [17].

The canonical (NVT) ensemble, which maintains a constant Number of atoms (N), constant Volume (V), and constant Temperature (T), serves as a critical bridge between energy minimization and production simulations in molecular dynamics. This equilibration phase allows a system to achieve a thermally stable state consistent with a target temperature while preserving the system volume. Within vacuum simulation research, particularly for systems with explicit vacuum interfaces (e.g., vacuum/surfactant/water systems), NVT equilibration plays a specialized role by permitting energy redistribution and thermal stabilization without altering the simulation box dimensions [19] [1]. This is especially vital for studies of surface phenomena, adsorption, and biomolecular conformations in diluted or interfacial environments where maintaining a specific geometry and volume is paramount. The process effectively prepares the system for subsequent isothermal-isobaric (NPT) ensemble simulations or for production runs where volume control remains essential, such as in simulating ion diffusion in solids or reactions on slab-structured surfaces and clusters [1].

Theoretical Foundations of NVT Equilibration

Following energy minimization, which relieves steepest gradients and steric clashes, a system possesses minimal potential energy but lacks appropriate kinetic energy and a physically realistic distribution of velocities. The NVT equilibration phase addresses this by coupling the system to a thermostat, a computational algorithm designed to maintain the target temperature. Several thermostat methods are commonly implemented, each with distinct advantages and limitations for vacuum simulation research [1].

Table 1: Comparison of Common Thermostat Methods in NVT Simulations

Thermostat Method	Theoretical Basis	Advantages	Limitations	Suitability for Vacuum Simulations
Berendsen [1]	Scales velocities uniformly towards a target temperature with an exponential decay.	Simple, fast convergence.	Produces unphysical velocity distributions; does not generate a correct canonical ensemble.	Good for initial, rapid equilibration but not for production.
Nosé-Hoover [1]	Introduces an extended Lagrangian with a fictitious variable representing a heat bath.	Reproduces the correct canonical ensemble; widely applicable.	Can exhibit non-ergodic behavior for small or stiff systems.	Excellent for most systems, including vacuum interfaces.
Langevin [1]	Applies random and frictional forces to individual atoms.	Good for mixed phases and dissipative systems; controls temperature locally.	Trajectories are not deterministic (not reproducible).	Ideal for solvated systems and preventing "flying ice cube" effect.

The core challenge during NVT equilibration, especially in systems with vacuum interfaces or large density variations, is achieving thermal stability without inducing artificial density artifacts. The fixed volume constraint means that if the initial solvation density is incorrect, the system cannot adjust to reach the proper equilibrium density for the given temperature, potentially leading to the formation of vacuum bubbles or empty regions as water molecules coalesce [19] [20]. This phenomenon is a classic manifestation of surface tension at work in a fixed volume [20].

Detailed Experimental Protocol for NVT Equilibration

This protocol is designed for a complex interface system, such as vacuum/surfactant/water/surfactant/vacuum, using the GROMACS simulation package, a standard in biomolecular simulations [19] [21].

System Setup Preceding NVT

• Construct the Molecular Assembly: Build the initial configuration, placing surfactants at the desired interface with vacuum layers.
• Energy Minimization: Run a steepest descent or conjugate gradient minimization to remove any steric clashes and achieve a minimum energy configuration. A sample GROMACS MDP file configuration is provided below.

• Initial Velocity Generation: Assign initial velocities from a Maxwell-Boltzmann distribution at the target temperature (e.g., 294.15 K) at the beginning of the NVT equilibration [19].

NVT Equilibration Parameters

The following configuration outlines key parameters for a successful NVT equilibration run in GROMACS, incorporating lessons from common pitfalls [19].

Workflow and Decision Logic

The following diagram illustrates the logical workflow for NVT equilibration and the subsequent steps based on the outcome, which is critical for avoiding instability.

Troubleshooting Common NVT Equilibration Artifacts

A frequently encountered issue in interface and vacuum simulations is the formation of holes or bubbles within the solvent region during NVT equilibration [19] [20]. These are not errors but a physical consequence of the fixed volume constraint and an initially suboptimal solvent density.

• Symptom: Empty regions or voids appear in the solvent (e.g., water) region in the output trajectory, while the overall box size remains unchanged.
• Root Cause: The NVT ensemble fixes the volume. If the initial solvation step placed too few solvent molecules in the box to achieve the correct density for the target temperature, or if strong positional restraints prevent the system from relaxing, the solvent will naturally coalesce due to cohesive forces, leaving behind vacuum bubbles [19] [20]. As one expert notes, "It’s NVT, so the box is not changing, and once you turn on the dynamics... the water molecules are going to 'stick' to each other" [19].
• Solutions:
  • Proceed to NPT: The most straightforward solution is to continue with NPT equilibration, which allows the box size to adjust and the density to relax to its correct equilibrium value, thereby collapsing the bubbles [19] [20].
  • Modify Restraints: Overly strong or extensive positional restraints can frustrate the system. Running a short NPT equilibration without position restraints on key molecules (e.g., surfactants) can allow the system to find a natural density before applying restraints for subsequent steps [19].
  • Improved System Preparation: Equilibrate a pure solvent box first to its correct density in NPT. Then, use this pre-equilibrated solvent when solvating the solute (e.g., surfactant/protein) system. This ensures a much better starting density [19].
  • Alternative Solvation: Manually add more solvent molecules to the dry system to compensate for the underestimated density, taking care not to insert them too close to the solutes of interest [20].

Another common warning encountered after NVT, when proceeding to NPT, is "Pressure scaling more than 1%". This strongly indicates that the system density from the NVT phase is far from equilibrium, and the pressure coupling must work aggressively to correct it. Using a robust barostat like C-rescale is recommended in such cases [19].

Research Applications and Case Studies

NVT equilibration is a foundational step across numerous research domains. The following table summarizes key applications and the specific role of NVT in each context.

Table 2: Research Applications of NVT Equilibration in Vacuum and Interface Studies

Field of Study	System Description	Role & Importance of NVT Equilibration	Key Findings Enabled
Protein Thermal Stability [21]	Wild-type vs. mutant BrCas12b protein (apo form).	To equilibrate the system at ambient and elevated temperatures (e.g., 300K, 400K) before analyzing unfolding.	Revealed increased flexibility in the PAM-interacting domain of the mutant at high temperatures, providing insights for CRISPR-based diagnostic design.
Peptide Mutational Analysis [22]	Neuropeptide Y (NPY) and its tyrosine-to-phenylalanine mutants.	To thermally stabilize the system post-minimization for subsequent production runs analyzing hairpin stability.	Uncovered unusually large increases in melting temperatures (ΔTm ~20-30°C) in mutants, linked to enhanced self-association into hexamers.
Surface Science & Catalysis [1]	Adsorption and reactions on slab-structured surfaces or clusters.	To maintain a constant surface area and volume while bringing the system to the reaction temperature.	Enables the study of reaction mechanisms and binding energies on well-defined surfaces without volume fluctuations.
Interface Systems [19]	Vacuum/Surfactant/Water/Surfactant/Vacuum.	To achieve thermal stability for the entire system while keeping the interface geometry and vacuum layer sizes fixed.	Allows the study of surfactant behavior at interfaces before allowing the box volume to relax in a subsequent NPT step.

The Scientist's Toolkit: Essential Research Reagents and Software

Table 3: Essential Tools for NVT Simulations in Biomolecular Research

Tool Name	Category	Function in NVT Equilibration
GROMACS [19] [21]	MD Software Suite	A high-performance molecular dynamics package used to perform energy minimization, NVT/NPT equilibration, and production simulations.
CHARMM36m [21]	Force Field	Provides parameters for the potential energy function, defining bonded and non-bonded interactions for proteins, lipids, and nucleic acids.
TIP3P [21]	Water Model	A rigid, three-site model for water molecules that is commonly used with the CHARMM force field for solvating systems.
V-Rescale Thermostat [19] [21]	Algorithm	A modified Berendsen thermostat that provides a correct canonical ensemble by stochastic rescaling of kinetic energy.
LINCS [21]	Algorithm	Constrains bond lengths to hydrogen atoms, allowing for a longer time step (e.g., 2 fs) during the simulation.
Particle Mesh Ewald (PME) [21]	Algorithm	Handles long-range electrostatic interactions accurately in systems with periodic boundary conditions.
Position Restraints [19]	Simulation Technique	Used to restrain heavy atoms of solutes (e.g., proteins, surfactants) to their initial positions, allowing the solvent to relax around them.
CU-T12-9	CU-T12-9, MF:C17H13F3N4O2, MW:362.31 g/mol	Chemical Reagent
Palmitoylglycine-d31	Palmitoylglycine-d31, MF:C18H35NO3, MW:344.7 g/mol	Chemical Reagent

Implementing NVT Vacuum Simulations: Protocols for Drug Discovery and Biomolecular Research

In molecular dynamics (MD) simulations, the canonical (NVT) ensemble, which maintains a constant Number of particles, Volume, and Temperature, serves as a critical bridge between energy-minimized structures and production simulations. This ensemble is particularly crucial in vacuum simulations research, where it allows the system to reach the desired temperature and stabilize its kinetic energy distribution without the complicating factors of pressure coupling. For drug development professionals, proper NVT equilibration ensures that simulated protein-ligand complexes or small molecules in solvent-free environments have achieved thermal stability before proceeding to advanced sampling or production runs, thereby providing more reliable data for binding affinity predictions or conformational analysis.

Theoretical foundations of NVT MD involve integrating Newton's equations of motion while controlling temperature using specialized algorithms. As described in MD theory, the simulation "generates successive configurations of a given molecular system, by integrating the classical laws of motion as described by Newton" [23]. The temperature is maintained through thermostats that scale velocities or couple the system to an external heat bath, with the NVT ensemble being "applied when the volume change is negligible for the target system" [1]. In the context of vacuum simulations, this is particularly relevant as the absence of solvent reduces system complexity while maintaining control over thermal fluctuations.

Theoretical Framework: NVT Ensemble and Thermostat Selection

The NVT ensemble, also known as the canonical ensemble, represents a fundamental statistical mechanical distribution where the number of particles, system volume, and temperature remain constant. This ensemble is ideally suited for systems where volume changes are negligible, such as solid-state materials, confined systems, or vacuum simulations where periodic boundary conditions may not be applied [1]. In drug discovery applications, NVT equilibration is frequently employed for systems where maintaining a specific density is not the primary concern, but controlling temperature is essential for replicating experimental conditions or preparing the system for subsequent simulation stages.

Several thermostat algorithms are available for maintaining constant temperature in MD simulations, each with distinct advantages and limitations:

• Berendsen Thermostat: Provides exponential relaxation of the system temperature toward the desired value with good numerical stability. It uniformly scales atomic velocities, which can sometimes suppress natural temperature fluctuations [24] [1].
• Nosé-Hoover Chains (NHC): Extends the Nosé-Hoover thermostat with multiple thermostats coupled in series, typically producing more correct canonical sampling compared to Berendsen. The tdamp parameter (Ï„â‚œ) determines the first thermostat mass as Q = NₑᵣₑₑkBTₛₑₜτₜ², where Ï„â‚œ corresponds to the period of characteristic oscillations [24].
• Langevin Dynamics: Applies random forces and friction to individual atoms, providing good temperature control even for heterogeneous systems. However, its stochastic nature makes trajectories non-reproducible, limiting its use for precise pathway analysis [1].

For vacuum simulations of biomolecular systems, the Nosé-Hoover Chains thermostat often provides the best balance between accurate sampling and numerical stability, particularly for well-equilibrated systems where natural temperature fluctuations are important.

Experimental Protocol: Step-by-Step Workflow

System Preparation and Energy Minimization

Before initiating NVT equilibration, proper system preparation and energy minimization are essential to remove steric clashes and unrealistic geometries that could destabilize the dynamics.

• Initial Structure Preparation: Obtain or generate the initial molecular structure. For proteins, this may involve downloading from the RCSB PDB, ensuring proper protonation states, and removing crystallographic waters and heteroatoms unless specifically relevant to the study [23]. For small molecules or drug-like compounds, ensure proper geometry optimization and assignment of partial charges compatible with your chosen force field.

• Force Field Selection: Choose an appropriate force field for your system. For biomolecular simulations, widely used options include AMBER, CHARMM, GROMOS, and OPLS. The AMBER99SB-ILDN force field is frequently recommended for proteins as it "reproduces fairly well experimental data" [23]. For drug-like molecules containing elements H, C, N, O, F, S, Cl, and P, recent neural network potentials such as DPA-2-Drug can provide "chemical accuracy compared to our reference DFT calculations" while being computationally efficient [25].

• Vacuum Environment Setup: For vacuum simulations, simply place your molecule in a sufficiently large box to prevent periodic images from interacting. Alternatively, disable periodic boundary conditions entirely if your MD engine supports non-periodic simulations.

• Energy Minimization: Perform steepest descent or conjugate gradient minimization to relax the structure:

  • Step 1: Apply position restraints on heavy atoms and minimize for 500-1000 steps to relax hydrogen atoms and resolve minor clashes.
  • Step 2: Perform full-system minimization without restraints for 1000-5000 steps or until the maximum force falls below a reasonable threshold (typically 100-1000 kJ/mol/nm depending on system size and required precision).

NVT Equilibration Parameters and Procedure

Once the system is properly minimized, proceed with NVT equilibration to bring the system to the desired temperature.

• Temperature Coupling:

  • Set the reference temperature appropriate for your study (typically 300-310 K for biological systems).
  • For the Berendsen thermostat, set tau_t (temperature damping constant) to 0.1-1.0 ps. This parameter "determines the relaxation time" for temperature coupling [24].
  • For Nosé-Hoover Chains, the characteristic oscillation period is typically set to a similar range (0.1-1.0 ps).

• Integration Parameters:

  • Set the integration time step to 1-2 femtoseconds, which is "large enough to sample significant dynamics but not as large as to cause problems during the calculations" [23].
  • For hydrogen-heavy systems, consider using constrained algorithms such as LINCS or SHAKE to allow for a 2-fs time step.

• Initial Velocity Generation:

  • Assign random velocities from a Maxwell-Boltzmann distribution corresponding to the target temperature.
  • Use different random seeds for replicate simulations to ensure sampling of different initial conditions.

• Simulation Duration:

  • Run the NVT equilibration for a sufficient duration to achieve temperature stabilization. "Typically, 50-100 ps should be sufficient. If the desired temperature has not been achieved or has not yet stabilized, additional time will be required" [26].
  • For larger systems or more complex biomolecules, longer equilibration times may be necessary.

• Monitoring and Validation:

  • Monitor the temperature, potential energy, and root-mean-square deviation (RMSD) throughout the equilibration.
  • The "running average of the temperature of the system should reach a plateau at the desired value" [26] before considering the equilibration complete.
  • Check that the potential energy has stabilized and that structural RMSD has reached a plateau, indicating the system has adapted to the simulation temperature.

The following workflow diagram illustrates the complete process from system preparation through NVT equilibration:

Key Parameters and Research Reagent Solutions

Critical NVT Equilibration Parameters

Table 1: Essential Parameters for NVT Equilibration in Vacuum Simulations

Parameter	Recommended Setting	Technical Description	Impact on Simulation
Ensemble	NVT (Canonical)	Constant Number of particles, Volume, Temperature	Allows system to reach target temperature while maintaining fixed density
Thermostat	Nosé-Hoover Chains (NHC) or Berendsen	Algorithm for temperature control	NHC provides better canonical sampling; Berendsen has faster stabilization
Target Temperature	300-310 K (biological)	Reference temperature for coupling	Should match experimental conditions or desired simulation state
Temperature Coupling Constant (τₜ)	0.1-1.0 ps	Relaxation time for temperature coupling	Shorter values provide tighter control but may affect dynamics
Integration Time Step	1-2 fs	Interval for solving equations of motion	2 fs possible with hydrogen constraints; affects simulation stability
Simulation Duration	50-100 ps (minimum)	Time for temperature stabilization	"Typically, 50-100 ps should be sufficient" [26]
Velocity Generation	Maxwell-Boltzmann distribution	Initial atomic velocities	"Set the momenta corresponding to the given temperature" [1]

Research Reagent Solutions

Table 2: Essential Computational Tools for NVT Equilibration

Tool Category	Specific Examples	Function in NVT Protocol
MD Simulation Software	GROMACS, AMBER, NAMD, LAMMPS	Performs the actual dynamics calculations and integration of equations of motion
Thermostat Algorithms	Berendsen, Nosé-Hoover Chains, Langevin	Maintains constant temperature during simulation
Force Fields	AMBER99SB-ILDN, CHARMM36, DPA-2-Drug (NN potential)	Defines potential energy function and parameters for molecular interactions
Analysis Tools	GROMACS analysis suite, VMD, MDAnalysis	Processes trajectories to assess equilibration progress and system properties
Visualization Software	PyMOL, VMD, Chimera	Provides structural insight and validation of simulation behavior
Neural Network Potentials	ANI-2x, DPA-2-Drug	Offers "QM accuracy at a limited computational cost" for drug-like molecules [25]

Troubleshooting and Quality Control

Common Issues and Solutions

Even with careful preparation, NVT equilibration may encounter issues that require intervention:

• Temperature Instability: If the system temperature fails to stabilize or exhibits large oscillations, check for incomplete energy minimization, increase the temperature coupling constant (Ï„â‚œ), or extend the equilibration duration. For systems with disparate time scales, consider using the "separate damping for translational, rotational, and vibrational degrees of freedom" by setting imdmet=1 and itdmet=7 in ReaxFF implementations [24].

• System Drift: In vacuum simulations, the entire molecule may drift due to non-zero total momentum. Apply center-of-mass motion removal every step to prevent this artifact.

• Insufficient Equilibration: If the system has not reached the target temperature or stabilized after the planned duration, simply "run the NVT equilibration step again by providing the input data from the previous NVT equilibration step" [26].

Validation Metrics

Before proceeding from NVT equilibration to production simulations, verify the following quality control metrics:

• Temperature Stability: The instantaneous temperature should fluctuate around the target value with a running average that has reached a stable plateau. "The plots are automatically generated and saved when the job is finished" showing "the evolution of the system's temperature over simulation time" [26].

• Energy Equilibration: Both potential and total energy should reach stable values with fluctuations consistent with the canonical ensemble.

• Structural Stability: The root-mean-square deviation (RMSD) of atomic positions relative to the minimized structure should plateau, indicating the system has adapted to the simulation temperature without undergoing large conformational changes.

The following decision diagram guides the selection of appropriate thermostat algorithms based on system characteristics:

Applications in Drug Discovery and Vacuum Simulations

The NVT equilibration protocol finds particular utility in structure-based drug design, where it helps prepare systems for subsequent molecular dynamics analyses. Recent studies have demonstrated that "molecular dynamics simulations evaluated using RMSD, RMSF, Rg, and SASA analysis, revealed that compounds significantly influenced the structural stability of the αβIII-tubulin heterodimer compared to the apo form" [27]. Similarly, in antibiotic resistance research, "MD simulations, trajectory analyses, including root-mean-square deviation (RMSD), root-mean-square fluctuation (RMSF), and hydrogen bond monitoring, confirmed the structural stability" of drug-protein complexes [28].

For vacuum simulations specifically, NVT equilibration provides a controlled environment to study intrinsic molecular properties without solvent effects. This is particularly valuable for:

• Gas-Phase Molecular Properties: Studying conformational preferences and energy landscapes of drug-like molecules without solvent interference.
• Protein-Ligand Complex Pre-screening: Rapid assessment of binding stability before committing to more expensive solvated simulations.
• Nanomaterial Characterization: Investigating the thermal stability of drug delivery nanoparticles or nanostructures.

When performing multiple simulations for statistical analysis, "you'd probably be much better off doing 9 separate NVT runs (with different seeds of course) and using the last conformation of each one" rather than sampling multiple frames from a single trajectory [29]. This approach ensures proper equilibration for each replicate and provides better sampling of initial conditions.

By following this comprehensive protocol, researchers can ensure proper thermal equilibration of their systems, providing a solid foundation for subsequent production simulations and reliable scientific conclusions in drug discovery applications.

The development of therapeutics against the Ebola virus (EBOV) represents a critical frontier in infectious disease research. EBOV causes severe hemorrhagic fever with high mortality rates, and the development of effective antiviral drugs remains a pressing global health challenge [30]. A key stage in the virus's life cycle is its entry into the host cell, a process mediated by the viral glycoprotein (GP) that culminates in the fusion of the viral envelope with the endosomal membrane [31] [32]. Disrupting this entry mechanism offers a promising strategy for antiviral intervention.

The process of membrane permeation and fusion is highly dynamic and occurs within the specific chemical environment of the late endosome, characterized by acidic pH, the presence of calcium ions (Ca²⁺), and unique anionic phospholipids [32]. Experimental observation of these molecular-scale events is exceptionally difficult. Consequently, molecular dynamics (MD) simulations have emerged as an indispensable tool for probing the biophysical details of drug-target interactions and the fusion process, providing insights that are often inaccessible to laboratory experiments alone. This application note details the integration of MD simulation methodologies, particularly within the NVT (constant Number of particles, Volume, and Temperature) ensemble, to study the permeation of promising anti-EBOV therapeutic candidates and their mechanism of action.

Scientific Background

Ebola Virus Entry and the Glycoprotein as a Drug Target

The Ebola virus glycoprotein (GP) is the sole viral protein responsible for mediating host cell attachment and entry. GP is a trimer composed of GP1 and GP2 subunits; GP1 facilitates receptor binding, while GP2 drives the membrane fusion process [31] [32]. Viral entry occurs via macropinocytosis, after which the virus is trafficked to the late endosome. Here, the chemical environment—acidic pH and elevated Ca²⁺ levels—triggers essential conformational changes in GP, leading to the insertion of its fusion loop into the endosomal membrane and subsequent fusion [32]. Key mutations in GP, such as the epidemic variant A82V, have been shown to increase fusion loop dynamics and enhance viral infectivity [31]. This makes the GP-membrane interaction a prime target for small-molecule inhibitors.

The Role of the Endosomal Environment

The late endosome provides a specific chemical milieu that regulates GP conformation and membrane binding. Critical factors include:

• Acidic pH: Promotes global conformational changes in GP, repositioning the fusion loop and making it available for membrane insertion [32].
• Calcium Ions (Ca²⁺): Interact with anionic residues in the fusion loop, promoting local conformational changes and electrostatic interactions with anionic phospholipids in the target membrane [32].
• Anionic Lipids: The late endosomal membrane is rich in phosphatidylserine (PS) and bis(monoacylglycero)phosphate (BMP). BMP, in particular, is critical for determining the Ca²⁺-dependence of the GP-membrane interaction [32].

Table 1: Key Environmental Factors in the Late Endosome Affecting EBOV GP

Factor	Role in Viral Entry	Experimental/Simulation Insight
Acidic pH	Triggers conformational changes in GP	smFRET imaging shows low pH repositions the fusion loop [32]
Ca²⁺ Ions	Mediates GP-membrane electrostatic interaction	Mutagenesis of residues D522/E540 disrupts Ca²⁺ binding and membrane interaction [32]
BMP Lipid	Enhances Ca²⁺-dependent membrane binding	Fluorescence Correlation Spectroscopy (FCS) shows BMP is critical for efficient GP-membrane interaction [32]

Computational Methodologies

MD simulations model the physical movements of atoms and molecules over time. The NVT ensemble, also known as the canonical ensemble, is a fundamental computational condition wherein the number of atoms (N), the volume of the simulation box (V), and the temperature (T) are kept constant. This is particularly useful for studying system behavior at a stabilized temperature, such as biomolecular conformational changes or ligand-protein interactions under controlled conditions.

Key Simulation Approaches

Several advanced MD techniques are employed to study membrane permeation and drug binding:

• Equilibrium MD (EMD): Used to study system behavior at equilibrium, such as the stability of a drug-protein complex. Simulations are often run for hundreds of nanoseconds to ensure robustness [30].
• Non-Equilibrium MD (NEMD): Applied to study transport phenomena, such as the permeation of solvents or ions through membranes. Boundary-driven (BD-NEMD) and moving wall (MW-NEMD) are common approaches for simulating pressure-driven flow [33].
• Enhanced Sampling Methods: Techniques such as calculating the Potential of Mean Force (PMF) are used to determine the free energy landscape and identify energy barriers for processes like membrane translocation [33].

Case Study: Simulating Anti-EBOV Inhibitors

Promising Therapeutic Candidates

Recent computational studies have identified several small molecules as promising EBOV inhibitors. A comprehensive in silico evaluation of six compounds—Latrunculin A, LJ001, CA-074, CA-074Me, U18666A, and Apilimod—identified CA-074 as a leading candidate [30]. CA-074 exhibits a strong binding affinity to Cathepsin B (-40.87 kcal/mol), a host cysteine protease crucial for Ebola virus entry.

Table 2: In Silico Profiles of Selected Anti-EBOV Inhibitors [30]

Compound	Primary Target	Docking Score (kcal/mol)	Key ADMET Properties
CA-074	Cathepsin B	-40.87	Fulfills Lipinski/Veber rules; no hERG inhibition/mutagenicity
Apilimod	Not Specified	Data Not Provided	Data Not Provided
LJ001	Viral Entry	Data Not Provided	Data Not Provided
U18666A	Not Specified	Data Not Provided	Data Not Provided

Other research has focused on designing novel entry inhibitors. Optimization of diarylsulfide hits led to diarylamine derivatives with confirmed antiviral activity against replicative EBOV and significantly improved metabolic stability. These compounds target the EBOV glycoprotein (GP), with residue Y517 in GP2 being critical for their biological activity [34].

Simulation Workflow for Drug-Membrane Permeation

The following diagram illustrates the integrated computational workflow for evaluating anti-EBOV therapeutics, from candidate identification to assessing membrane interaction and binding.

Diagram Title: Workflow for Simulating Anti-EBOV Therapeutics

Protocol: Simulating Inhibitor Binding to Ebola GP

This protocol outlines the key steps for simulating the interaction between a small-molecule inhibitor and the Ebola virus glycoprotein, a target for entry inhibitors [34] [32].

1. System Setup and Preparation

• Protein Preparation: Obtain the 3D structure of the EBOV GP trimer from a database like the Protein Data Bank (e.g., PDB ID 4M0Q for VP24 protein [35]). Remove crystallographic water molecules and heteroatoms. Add missing hydrogen atoms and assign protonation states to residues appropriate for the late endosomal pH using a tool like the H++ server [35].
• Ligand Preparation: Obtain the 3D structure of the small-molecule inhibitor (e.g., a diarylamine derivative [34] or CA-074 [30]). Perform geometry optimization and assign partial atomic charges using quantum chemical methods or force field tools.
• Membrane Modeling: Construct a model late endosomal membrane containing anionic lipids such as Phosphatidylserine (PS) and Bis(monoacylglycero)phosphate (BMP) using membrane builder tools (e.g., in CHARMM-GUI) [32].
• Solvation and Ionization: Place the protein-ligand complex or the membrane system in a simulation box filled with explicit water molecules (e.g., TIP3P model). Add ions (Na⁺, Cl⁻) to neutralize the system's charge and to achieve a physiologically relevant salt concentration (e.g., 0.15 M). Include Ca²⁺ ions to model the endosomal environment [32].

2. Molecular Dynamics Simulation (NVT Ensemble)

• Energy Minimization: Run a steepest descent or conjugate gradient algorithm to remove any steric clashes and bad contacts in the initial system, typically for 5,000-50,000 steps.
• System Equilibration: Gradually heat the system to the target temperature (e.g., 310 K) over 100-500 ps while applying positional restraints to the protein and ligand heavy atoms. Use a thermostat (e.g., Nosé-Hoover, Berendsen) to maintain temperature. This step allows the solvent and ions to relax around the solute.
• Production Run: Run an NVT simulation for a duration sufficient to observe the phenomenon of interest (e.g., 100-300 ns [30] [35]). Use a time step of 2 fs. Constrain bonds involving hydrogen atoms using algorithms like LINCS or SHAKE. Calculate long-range electrostatic interactions using the Particle Mesh Ewald (PME) method.

3. Analysis of Trajectory and Binding

• Binding Affinity: Calculate the binding free energy using methods such as Molecular Mechanics/Poisson-Boltzmann Surface Area (MM/PBSA) or Linear Interaction Energy (LIE).
• Intermolecular Interactions: Analyze hydrogen bonds, hydrophobic contacts, and salt bridges formed between the inhibitor and key GP residues (e.g., Y517, T519, E100, D522 [34]).
• Structural Stability: Monitor the Root Mean Square Deviation (RMSD) of the protein backbone and the ligand to assess the stability of the complex throughout the simulation.
• Fusion Loop Dynamics: Calculate the Root Mean Square Fluctuation (RMSF) of the GP fusion loop residues to understand the effect of the inhibitor on the mobility of this critical functional region [31].

The Scientist's Toolkit

Table 3: Essential Research Reagents and Computational Tools

Item/Solution	Function/Description	Application in EBOV Research
CHARMM36 Force Field	A set of parameters for simulating biomolecules (proteins, lipids, nucleic acids).	Provides accurate energy calculations for EBOV GP and membrane interactions [36] [32].
GROMACS	A software package for performing MD simulations.	Used for high-throughput simulation of drug-protein binding and membrane permeation [30].
AutoDock Vina	A program for molecular docking and virtual screening.	Predicts binding poses and affinity of small molecules to EBOV targets like GP or VP24 [35].
BMP Lipid	Bis(monoacylglycero)phosphate, a late endosome-specific anionic lipid.	Critical component in model membranes for studying Ca²⁺-dependent GP-membrane binding [32].
LigDream	A deep learning-based tool for de novo molecular design.	Generates novel molecular scaffolds based on a parent compound (e.g., BCX4430) for anti-EBOV drug discovery [35].
HJC0350	HJC0350, MF:C15H19NO2S, MW:277.4 g/mol	Chemical Reagent
JT001 sodium	JT001 sodium, MF:C19H21N4NaO4S, MW:424.5 g/mol	Chemical Reagent

Molecular dynamics simulations provide a powerful framework for investigating the permeation and mechanism of anti-Ebola therapeutics. By employing NVT ensembles and other advanced computational methods, researchers can unravel the complex interactions between drug candidates, the viral glycoprotein, and the endosomal membrane at an atomic level. The insights gained from these simulations, such as the critical role of the endosomal environment and the identification of key residues like Y517 in GP [34] and the pH-sensing mechanisms [32], are invaluable for rational drug design. This integrated computational approach accelerates the identification and optimization of potent EBOV entry inhibitors, paving the way for more effective treatments against Ebola virus disease.

Analyzing Protein-Ligand Complex Stability in Vacuum-like Environments

The analysis of protein-ligand complex stability in vacuum-like environments represents a specialized niche in computational biophysics, providing critical insights into the intrinsic thermodynamic and kinetic properties of molecular interactions absent solvent effects. Such environments, typically created through implicit solvent models or gas-phase simulations, are methodologically framed within the NVT (canonical) ensemble, which maintains a constant number of particles (N), volume (V), and temperature (T). This approach is particularly valuable for isolating the fundamental interaction energetics between proteins and ligands without the complicating effects of explicit water molecules [37]. The controlled conditions enable researchers to probe the essential physics of binding, including conformational stability, interaction fingerprints, and the free energy landscape, which might otherwise be obscured by bulk solvent fluctuations [38] [39].

While full physiological relevance requires eventual transition to explicit solvent models, vacuum-like analyses serve as an important methodological foundation for understanding binding mechanisms, facilitating rapid screening in drug design, and providing benchmark data for force field validation. This application note details the experimental protocols, computational methodologies, and analytical frameworks required to conduct such investigations effectively.

Theoretical Background

NVT Ensemble in Vacuum-like Simulations

The NVT ensemble is characterized by a constant number of atoms (N), a fixed simulation volume (V), and a regulated temperature (T). In the context of vacuum-like protein-ligand simulations, this ensemble enables the study of the system's intrinsic behavior by effectively removing the extensive thermodynamic bath of explicit water molecules. Temperature control is typically maintained using algorithms such as the Langevin thermostat, which adds friction and random forces to mimic collisions with a heat bath [37]. This is particularly crucial in vacuum simulations where the absence of solvent can lead to inadequate energy redistribution.

The theoretical foundation rests on statistical mechanics, where the NVT ensemble samples configurations according to the Boltzmann distribution. This allows for the calculation of equilibrium properties relevant to protein-ligand stability, such as binding free energies and conformational entropies, albeit in a simplified environment that highlights the direct molecular interactions.

Key Stability Metrics in Vacuum-like Conditions

In the absence of solvent, the assessment of protein-ligand complex stability relies on a different set of metrics than those used in explicit solvent simulations:

• Interaction Fingerprints: A qualitative scoring function based on the conservation of non-covalent interactions (e.g., hydrogen bonds, hydrophobic contacts, ionic interactions) between the protein and ligand throughout the simulation trajectory. The loss of these interactions indicates decreasing stability [37].
• Free Energy Landscape (FEL): Constructed from simulation data to visualize the relationship between system conformation and free energy. FEL analysis reveals low-energy basins corresponding to stable states and the energy barriers between them, providing insight into conformational stability and transitions [40].
• Root Mean Square Deviation (RMSD): Measures the average atomic displacement of the protein or ligand relative to a reference structure. Lower RMSD values suggest greater structural integrity and complex stability under vacuum-like conditions [40].
• Constraint Forces: In constrained molecular dynamics, the mean constraint force required to maintain a specific protein-ligand distance is integrated to obtain the potential of mean force (PMF), which is a direct measure of the free energy profile along the chosen reaction coordinate [38].

Table 1: Key Stability Metrics and Their Significance in Vacuum-like Analyses

Metric	Description	Information Provided
Interaction Fingerprints	Conservation of native non-covalent contacts	Qualitative binding mode stability [37]
Free Energy Landscape (FEL)	Conformational distribution mapped to free energy	Identifies stable states and transition pathways [40]
RMSD	Atomic displacement from reference structure	Overall structural integrity of the complex [40]
Constraint Forces	Mean force along a reaction coordinate	Free energy profile for binding/unbinding [38]

Computational Protocols

System Preparation and Minimization

The initial setup of the protein-ligand system is a critical step that determines the reliability of subsequent simulations.

• Structure Retrieval and Preparation: Obtain three-dimensional coordinates of the protein-ligand complex from the Protein Data Bank (PDB). Using a molecular modeling suite like Molecular Operating Environment (MOE), process the structure by assigning the highest occupancy conformations to alternates, rebuilding missing loops via homology modeling, and correcting any discrepancies between the primary sequence and tertiary structure. Remove all non-protein and non-ligand atoms, except for crystallographic water molecules within 4.5 Ã… of the ligand, which may be crucial for specific interactions [37].
• Protonation State Assignment: Employ a tool like "Protonate3D" in MOE to add missing hydrogen atoms and determine the most probable protonation states of titratable residues at the desired pH (typically 7.4). The ligand's protonation state should also be assigned, considering the most abundant protomer at the simulation pH and any specific interaction networks within the binding pocket that might favor an alternative state [37].
• Parameter and Topology Generation: Parameterize protein atoms using a force field such as ff14SB. For the ligand, use the General Amber Force Field (GAFF). Partial atomic charges for the ligand should be assigned using the AM1-BCC method [37].
• Energy Minimization: Subject the prepared system to energy minimization using a conjugate-gradient algorithm (e.g., for 500 steps) to remove atomic clashes, bad contacts, and unrealistically high potential energy, resulting in a stable starting structure for dynamics [37].

Thermal Titration Molecular Dynamics (TTMD)

The TTMD protocol provides a qualitative yet robust method for assessing the relative stability of protein-ligand complexes by challenging them with increasing thermal stress.

• Equilibration: Before production runs, equilibrate the minimized system in two stages. First, perform a short simulation (e.g., 0.1 ns) in the NVT ensemble with harmonic positional restraints (5 kcal mol⁻¹ Å⁻²) on both protein and ligand atoms. Second, conduct a longer simulation (e.g., 0.5 ns) in the NPT ensemble, applying restraints only to the ligand and protein backbone to allow side-chain relaxation [37].
• Production Simulations: Launch a series of independent MD simulations in the NVT ensemble using the equilibrated structure as the starting point. Each simulation in the series should be performed at a progressively increasing temperature (e.g., 310 K, 350 K, 400 K, 450 K, 500 K). Maintain a constant temperature for each run using a Langevin thermostat. Use an integration timestep of 2 fs and constrain bonds involving hydrogen atoms with an algorithm like M-SHAKE [37].
• Trajectory Analysis: For each temperature trajectory, calculate the interaction fingerprints between the protein and ligand at regular intervals. The stability of the complex is qualitatively estimated by the temperature at which the native binding mode (i.e., the pattern of specific non-covalent interactions) is lost. Complexes that retain their native interaction fingerprints at higher temperatures are deemed more stable [37].

Constrained MD for Unbinding Pathways

This protocol uses a geometric constraint to force the dissociation of the ligand and compute the associated free energy profile.

• Reaction Coordinate (RC) Selection: Choose a suitable RC that describes the unbinding pathway. A common and often effective choice is the distance between the centers of mass (COM) of the ligand and the protein binding pocket [38].
• Constrained Simulation: Apply a holonomic constraint to the chosen RC during an MD simulation. To map the unbinding process, perform either a "slow-growth" simulation where the constraint value is gradually changed, or a series of simulations at fixed values of the RC spanning from the bound state to the fully dissociated state [38].
• Mean Force and PMF Calculation: In the fixed-distance approach, the mean constraint force is recorded at each RC value. The Potential of Mean Force (PMF), which is equivalent to the free energy profile along the RC, is obtained by integrating the mean force over the distance: ΔG(R) = -∫ dR. This profile reveals energy barriers and stable intermediate states along the dissociation path [38].
• Kinetic Parameter Estimation: The free energy barrier extracted from the PMF (ΔG‡) can be used within the framework of transition state theory to estimate the dissociation rate constant: koff = (kB T / h) exp(-ΔG‡ / k_B T). A higher barrier corresponds to a slower dissociation rate and a longer complex residence time [38].

The following diagram illustrates the core workflow for setting up and running these vacuum-like stability simulations.

Free Energy Landscape (FEL) Analysis

This protocol analyzes simulation trajectories to construct a Free Energy Landscape, revealing the conformational stability of the complex.

• Collective Variable (CV) Selection: Choose one or two Collective Variables that capture the essential motions related to stability or binding. Common choices include the Root Mean Square Deviation (RMSD) of the protein-ligand interface, radius of gyration (Rg), or number of native contacts [40].
• Trajectory Projection: Project the entire MD trajectory onto the chosen CVs. For each frame of the simulation, calculate the values of the CVs.
• Landscape Construction: Create a 2D histogram of the CVs from the trajectory data. Convert this population histogram into a free energy landscape using the relation: ΔG(X) = -k_B T ln P(X), where P(X) is the probability distribution along the CVs. The resulting landscape will show basins (low free energy, stable states) and barriers (high free energy, unstable transitions) [40].
• Conformational Cluster Analysis: Identify and extract representative structures from the major free energy basins. Analyzing these structures provides atomic-level insight into the stable conformations of the protein-ligand complex and the structural changes associated with instability or dissociation [40].

The Scientist's Toolkit: Research Reagent Solutions

Table 2: Essential Software and Computational Tools for Vacuum-like Simulations

Tool/Reagent	Function/Description	Application Note
Molecular Operating Environment (MOE)	Integrated software for structure preparation, protonation, and molecular modeling [37].	Used for pre-processing PDB files, assigning protonation states at pH 7.4, and loop modeling.
AMBER Tools & ff14SB/GAFF	Suite for generating force field parameters and system topologies [37].	ff14SB for proteins; General Amber Force Field (GAFF) for ligands; AM1-BCC for ligand partial charges.
Visual Molecular Dynamics (VMD)	Molecular visualization and trajectory analysis program [37].	Used for system setup, solvation (implicit solvent in vacuum-like sims), and visualization of results.
Langevin Thermostat	Algorithm for temperature control in NVT simulations [37].	Critical for maintaining constant temperature in the absence of a solvent bath for heat exchange.
AutoDock 4.0	Molecular docking package for predicting binding modes [40].	Used for initial placement of ligands into the binding site prior to detailed stability analysis.
Interaction Fingerprint (IFP)	A scoring function based on conserved non-covalent contacts [37].	Qualitative metric for binding mode stability in Thermal Titration MD (TTMD) simulations.
UNC9994	UNC9994, MF:C21H22Cl2N2OS, MW:421.4 g/mol	Chemical Reagent
DK2403	DK2403, MF:C19H17ClN4O2, MW:368.8 g/mol	Chemical Reagent

Data Analysis & Interpretation

Quantitative Data from Case Studies

The following table summarizes key quantitative findings and parameters from relevant studies that inform the analysis of complex stability.

Table 3: Summary of Quantitative Data from Methodological and Application Studies

System / Method	Key Measured Parameters	Results / Implications for Stability
Insulin-Phenol Complex [38]	Constrained MD (COM distance as RC), Free Energy Profile.	Calculated equilibrium constant and friction-corrected rates agreed well with experimental data, validating the constrained MD approach for studying unbinding.
TTMD Protocol Validation [37]	Discrimination between high-affinity (nM) and low-affinity (μM) ligands based on interaction fingerprint persistence across temperatures.	TTMD successfully distinguished ligand affinity classes, proving useful as a screening tool for complex stability under thermal stress.
CCoAOMT-CCoA Complex [40]	Free Energy Landscape (FEL), Conformational Cluster Analysis, Hydrogen Bonding.	Identified key stabilizing residues (e.g., Y188, D218 forming H-bonds); showed structure becomes more compact upon substrate binding.
Finite-Size Electrostatic Corrections [41]	Charging free energy errors for a +1e ligand with charged protein (up to 17.1 kJ mol⁻¹).	Proposed analytical correction scheme to eliminate box-size dependence, crucial for accurate free energy calculations in periodic systems.

Visualization of Stability Analysis Logic

The logical process for interpreting simulation data to arrive at a conclusion about complex stability is outlined below.

Concluding Remarks

The protocols outlined in this application note provide a robust framework for analyzing protein-ligand complex stability under vacuum-like conditions using the NVT ensemble. The combination of Thermal Titration MD (TTMD) for qualitative ranking, constrained MD for detailed unbinding pathway and free energy analysis, and Free Energy Landscape (FEL) construction for conformational stability offers a multi-faceted approach to the problem. These methods are particularly powerful for isolating the intrinsic protein-ligand interaction energetics and for medium-throughput computational screening in early-stage drug discovery.

It is crucial to recognize that these vacuum-like simulations represent a foundational step. For full physiological relevance, the most promising candidates or mechanistic hypotheses generated from these studies must be validated using more computationally expensive explicit solvent simulations and, ultimately, experimental assays. The strength of this approach lies in its ability to efficiently provide deep mechanistic insights and reliable relative stability rankings, forming a critical component of a multi-scale research strategy in structural biology and rational drug design.

The heat treatment of wood is an advanced processing method that enhances dimensional stability and decay resistance [42] [43]. This process, typically conducted at temperatures ranging from 160°C to 230°C (approximately 433 K to 503 K), induces significant changes in the chemical composition and supramolecular structure of wood, particularly in its primary structural component: cellulose [44]. The choice of heat treatment medium—whether vacuum, nitrogen, or air—profoundly influences the resulting material properties, with vacuum environments demonstrating particular promise for preserving mechanical performance [42] [44].

Molecular dynamics (MD) simulation has emerged as a powerful technique for investigating these structural changes at the atomic level, providing insights that are challenging to obtain through experimental methods alone [42]. By employing computational models, researchers can precisely control environmental conditions and observe molecular behavior across a range of temperatures, offering a microscopic perspective on macroscopic property changes [42]. This application note explores how MD simulations, particularly within the NVT (canonical) and NPT (isothermal-isobaric) ensembles, have advanced our understanding of cellulose behavior during thermal treatment under various atmospheres.

Key Findings from Simulation Studies

Comparative Performance of Heat Treatment Media

Recent molecular dynamics studies have systematically compared the effects of different thermal treatment environments on cellulose structure and properties. The simulations reveal that the heat treatment medium significantly influences hydrogen bonding, structural stability, and mechanical performance.

Table 1: Comparison of Cellulose Properties Under Different Heat Treatment Conditions

Treatment Medium	Optimal Temperature Range	Key Mechanical Properties	Structural Characteristics	Hydrogen Bonding
Vacuum	463-503 K	Higher Young's modulus and shear modulus; Maximum E and G at 463 K	Enhanced structural stability; Stabilized mean square displacement	Increased number of intra-chain hydrogen bonds
Nitrogen	443-483 K	Moderate mechanical properties; Maximum E and G at 443 K	Cellular characteristics decrease then increase with temperature	Intermediate hydrogen bonding preservation
Air	423-503 K	Lower mechanical properties; Progressive degradation with temperature	Reduced structural stability	Fewer hydrogen bonds maintained

Simulations demonstrate that vacuum heat treatment most effectively enhances the structural stability of single-chain cellulose by increasing the number of hydrogen bonds within the cellulose chain and stabilizing the mean square displacement [42]. The Young's modulus and shear modulus consistently remain higher for the vacuum model across all temperatures studied, while the Poisson's ratio shows an opposite trend [42].

The mechanical properties of cellulose under different treatment media exhibit distinct temperature dependencies. For vacuum-treated cellulose, properties initially increase and then decrease with rising temperature, peaking at approximately 450 K [44]. This optimal performance point correlates strongly with hydrogen bond connectivity and the thermal motion of molecular chains [44].

Hydrogen Bonding and Structural Transformations

Hydrogen bonding plays a crucial role in determining cellulose behavior during thermal treatment. Simulations tracking hydrogen bond count under different conditions reveal that:

• The number of hydrogen bonds in cellulose decreases as temperature increases across all media [42]
• Vacuum environment better preserves hydrogen bonding networks compared to nitrogen and air atmospheres [42]
• Hydrogen bond stability directly correlates with improved mechanical performance, particularly in vacuum treatments [44]

Table 2: Temperature-Dependent Mechanical Properties of Cellulose in Vacuum Environment

Temperature (K)	Young's Modulus (GPa)	Shear Modulus (GPa)	Poisson's Ratio	Mechanical Status
430	Moderate	Moderate	Moderate	Below optimum
450	Maximum	Maximum	Minimum	Optimal performance
470	Decreasing	Decreasing	Increasing	Post-optimal
490	Lower	Lower	Higher	Significant decline
510	Lowest	Lowest	Highest	Substantial degradation

Beyond mechanical properties, thermal exposure induces significant conformational changes in cellulose chains. Studies on cellulose nanofibers (CNFs) at 190°C for 5 hours revealed that glucopyranose rings undergo partial dehydration, resulting in enol formation and altered dihedral angles ranging from ±27° to ±139° after thermal exposure [45]. These structural transformations directly impact the material's macroscopic behavior and performance characteristics.

Experimental Protocols

Model Construction and Simulation Workflow

The following protocol outlines the standard methodology for simulating cellulose heat treatment using molecular dynamics approaches, based on established procedures in the field [42] [43] [44].

Simulation Workflow for Cellulose Heat Treatment Studies

Model Construction

• Cellulose Chain Generation: Build a single cellulose chain with a degree of polymerization (DP) of 20, representing the amorphous region of cellulose Iβ [42] [44]. The selection of DP=20 is based on established protocols where this chain length provides results consistent with experimental observations while maintaining computational efficiency [44].

• Treatment Media Setup: Construct three distinct model environments:

  • Vacuum-Cellulose: Pure cellulose system without additional molecules [42]
  • Nitrogen-Cellulose: System containing 20 nitrogen molecules with the cellulose chain [43]
  • Air-Cellulose: System containing 16 nitrogen and 4 oxygen molecules with the cellulose chain [43]

• Simulation Cell Preparation: Place the cellulose chain and treatment media molecules in a periodic cubic cell with target density of 1.5 g/cm³ and approximate dimensions of 19.6 × 19.6 × 19.6 ų [43] [44].

Dynamics Simulation

• Force Field Selection: Apply the Polymer Consistent Force Field (PCFF), which has demonstrated strong performance for organic compounds and carbohydrate systems [43] [44].

• Geometric Optimization: Perform energy minimization using the smart algorithm for 5,000 steps to reach a local energy minimum [43].

• System Relaxation (NVT Ensemble): Conduct initial dynamic relaxation at 300 K for 1 ns in the canonical ensemble (NVT) using the Nosé thermostat [43] [44]. Parameters:

  • Timestep: 1 fs
  • Total simulation length: 1 ns
  • Output frame frequency: Every 5,000 steps
  • Temperature control: Nosé method [43]

• Production Simulation (NPT Ensemble): Execute the main simulation in the isothermal-isobaric ensemble (NPT) across the target temperature range (423-503 K) for 1 ns [42] [44]. Parameters:

  • Pressure control: Berendsen method [43] [44]
  • Pressure: 2×10⁻⁵ GPa [44]
  • Timestep: 1 fs
  • Total simulation time: 1 ns
  • Temperature points: 423 K, 443 K, 463 K, 483 K, 503 K [42]

• System Equilibrium Validation: Confirm system equilibrium by monitoring energy fluctuations, ensuring they remain within ±10% during the final 200 ps of simulation [43].

Analysis Methods

The following analytical approaches should be employed to extract meaningful data from the simulations:

• Energy Analysis: Track potential, kinetic, and non-bond energy components throughout the simulation to monitor system stability [43].

• Mechanical Properties Calculation: Compute elastic constants (Young's modulus, shear modulus, Poisson's ratio) using stress-strain relationships derived from simulation trajectories [42] [43].

• Hydrogen Bonding Analysis: Quantify hydrogen bond formation and stability using geometric criteria (donor-acceptor distance < 3.5 Ã…, angle > 120°) [42].

• Mean Square Displacement (MSD): Calculate MSD to evaluate molecular mobility and diffusion characteristics under different treatment conditions [42].

• Structural Parameters: Monitor cell parameters, density variations, and conformational changes throughout the thermal treatment process [42] [45].

The Scientist's Toolkit

Table 3: Essential Research Reagents and Computational Tools for Cellulose Simulations

Item	Function/Description	Application Notes
Materials Studio	Molecular modeling software suite	Primary simulation environment; Versions 8.0-2020 used [42] [43] [44]
Forcite Module	Classical molecular mechanics tool	Used for geometric optimization, dynamics calculations, and mechanical properties computation [43] [44]
Amorphous Cell Module	Construction of 3D periodic structures	Creates amorphous polymer models for cellulose chain construction [44]
PCFF Force Field	Polymer Consistent Force Field	Specialized for organic compounds and carbohydrates; parameters optimized for cellulose [43] [44]
Cellulose Iβ Model	Natural cellulose allomorph	Represents the most prevalent form of cellulose in nature [42]
Nosé Thermostat	Temperature control algorithm	Maintains constant temperature during NVT simulations [43]
Berendsen Barostat	Pressure control algorithm	Maintains constant pressure during NPT simulations [43] [44]
AR453588	AR453588, MF:C25H25N7O2S2, MW:519.6 g/mol	Chemical Reagent
YMU1	YMU1, MF:C17H22N4O4S, MW:378.4 g/mol	Chemical Reagent

Visualization and Analysis Techniques

Effective analysis of simulation results requires specialized visualization approaches to interpret the complex data generated. The following diagram illustrates the key analysis pathways and their relationships:

Analysis Pathways for Simulation Data

Molecular dynamics simulations of cellulose heat treatment provide invaluable insights into the atom-level mechanisms governing material property changes. The evidence consistently demonstrates that vacuum environments offer superior preservation of cellulose's mechanical properties compared to nitrogen and air atmospheres, with optimal performance observed at specific temperature ranges (450-463 K). These findings align with experimental observations that vacuum heat treatment minimizes degradation of wood's mechanical characteristics [44].

The protocols outlined herein establish a robust framework for investigating thermal treatment processes using computational methods. By employing standardized approaches to model construction, simulation parameters, and analysis techniques, researchers can generate comparable, reproducible data to advance our understanding of cellulose behavior under thermal stress. These methods not only provide explanations for macroscopic experimental observations but also predict optimal processing conditions for enhancing material performance in industrial applications.

Solving Common NVT Vacuum Simulation Problems: A Troubleshooting Guide

In molecular dynamics (MD) simulations conducted within the NVT (canonical) ensemble, the maintenance of system stability is a primary concern, particularly when simulating under vacuum conditions. A frequently encountered yet often overlooked source of instability is the phenomenon of negative internal pressure, which can lead to unphysical system collapse. This application note examines the critical relationship between simulation box size and the emergence of negative pressure, providing researchers with practical methodologies to identify, prevent, and correct this issue within the broader context of vacuum simulation research. The insights presented are particularly relevant for drug development professionals employing MD for structure-based drug discovery, where accurate simulation of protein-ligand complexes in various environments is essential [46].

The Negative Pressure Phenomenon in NVT Ensembles

In MD simulations, the NVT ensemble maintains a constant Number of particles (N), Volume (V), and Temperature (T), allowing the system to exchange energy with a thermostat but not volume with its surroundings [4]. Under these conditions, the internal pressure becomes a dependent variable, fluctuating in response to interatomic forces and the available space within the fixed simulation volume.

Negative internal pressure develops when the chosen simulation volume is too large relative to the natural equilibrium density of the system at the simulated temperature. This creates an effective "tension" within the system, as intermolecular forces attempt to pull the system inward against the fixed boundary conditions [47]. In vacuum simulations, where periodic boundary conditions are still typically employed, this effect can be particularly pronounced due to the absence of surrounding solvent molecules that would normally provide counterbalancing positive pressure components.

The manifestation of negative pressure is not merely a numerical artifact but can correspond to physical instabilities. As demonstrated in collagen fibril simulations, internal stresses can develop and persist at specific hydration levels, with lateral stresses becoming null at a hydration level of approximately 0.78 g/g, while significant longitudinal stress of about 210 MPa remains [47]. This highlights how internal stress conditions are highly sensitive to system composition and environmental factors.

Quantitative Assessment of Box Size Effects

Pressure-System Size Relationship

Table 1: Characteristic Pressure Values Observed Under Different Box Sizing Conditions

Box Size Ratio (V/Vâ‚€)	Pressure Range (bar)	System Stability	Observed Structural Effects
0.8-0.9	+100 to +300	High	Minimal structural deformation
0.9-1.0	+10 to +100	Stable	No significant distortion
1.0-1.1	-50 to +10	Marginally stable	Slight compaction possible
1.1-1.3	-200 to -50	Unstable	Significant collapse likely
>1.3	< -200	Highly unstable	Rapid structural degradation

Vâ‚€ represents the optimal equilibrium volume at the target temperature and pressure.

The data in Table 1 demonstrates that box sizes exceeding 10% above the optimal volume (V/Vâ‚€ > 1.1) typically result in significant negative pressure conditions that compromise system integrity. This relationship was quantitatively validated in microfibril simulations where internal stress components followed nonlinear trends with changing environmental conditions [47].

System-Specific Factors Influencing Pressure

Table 2: System Properties Affecting Sensitivity to Negative Pressure

System Characteristic	Effect on Pressure Sensitivity	Typical Value Range	Remediation Approach
Temperature	Inverse relationship with pressure magnitude	290-330 K [47]	Adjust initial velocity distribution
Composition Complexity	Increased variability in pressure fluctuations	~20,000 complexes [46]	Enhanced sampling protocols
Force Field Selection	Significant impact on absolute pressure values	CHARMM36m, OPLS-AA [47]	Parameter refinement
Hydration Level	Direct relationship with pressure state transition	0.6-1.25 g/g [47]	Precise hydration control

The selection of force field parameters notably influences observed pressure values, with different force fields yielding variations in the hydration level required to achieve zero lateral pressure by as many as 500 water molecules in collagen microfibril simulations [47].

Experimental Protocols for Box Size Optimization

Initial System Equilibration Protocol

Objective: Establish stable initial configuration minimizing pressure artifacts. Duration: 300-500 ps for most systems [48].

• Energy Minimization

  • Perform steepest descent minimization (10,000 steps) followed by conjugate gradient minimization (10,000 steps) to remove high-energy atomic clashes [49].
  • Apply Particle Mesh Ewald (PME) electrostatics with 10Ã… real-space cutoff [49].

• Temperature Equilibration

  • Conduct NVT equilibration for 360 ps while gradually heating system from 0K to target temperature (typically 300K) in 50K increments [49].
  • Use Langevin dynamics with collision frequency of 2 ps⁻¹ for temperature coupling [49].

• Volume Relaxation (if transitioning from NPT)

  • Execute NPT equilibration at target temperature and pressure (1 atm) for 300 ps [49].
  • Employ Berendsen barostat with reference pressure of 1 bar for gentle pressure coupling [49].

• Stability Verification

  • Monitor potential energy, temperature, and density for convergence.
  • Check pressure tensor components for systematic deviations.

Negative Pressure Identification and Remediation Protocol

Objective: Detect and correct developing negative pressure conditions during NVT simulations.

• Pressure Monitoring

  • Record pressure tensor components at minimum 100-200 step intervals.
  • Calculate mean and standard deviation over 10-20 ps windows.

• Negative Pressure Threshold Detection

  • Flag systematic negative pressure values below -50 bar.
  • Identify consistent negative diagonal elements in pressure tensor.

• Box Size Adjustment Procedure

  • If negative pressure persists beyond initial equilibration, restart with scaled volume.
  • Apply volume scaling factor of 0.95-0.98 to gradually approach optimal volume.
  • For extreme cases (> -200 bar), reduce volume by 10-15% and re-equilibrate.

• Alternative Remediation Strategies

  • Increase system temperature by 10-20K to enhance molecular motion (if scientifically justified).
  • Re-evaluate initial structure preparation and solvation procedures.
  • Consider force field modifications if systematic errors are suspected.

The Scientist's Toolkit: Essential Research Reagents and Materials

Table 3: Critical Software Tools and Computational Resources for Vacuum MD Simulations

Tool/Resource	Function	Application Context
GROMACS [50]	Molecular dynamics simulation package	Primary engine for MD simulations with advanced constraint algorithms
AMBER [49]	Molecular dynamics software	Specialized for biomolecular simulations with advanced force fields
GAFF (General AMBER Force Field) [49]	Force field parameterization	Provides parameters for small organic molecules in drug discovery contexts
Python 3.11 with LangChain [51]	AI-agent framework development	Enables automation of simulation workflows through multi-agent systems
AlphaFold-Metainference [52]	Structural ensemble prediction	Generates accurate starting structures for proteins, including disordered regions
DynaMate [51]	Multi-agent framework	Automates setup, execution, and analysis of molecular simulations
QUICK [49]	Quantum chemistry engine	Enables QM/MM calculations for more accurate electronic structure treatment
Materials Studio [42]	Molecular modeling environment	Provides specialized modules for polymer and materials simulations
LY-2584702 hydrochloride	LY-2584702 hydrochloride, MF:C21H20ClF4N7, MW:481.9 g/mol	Chemical Reagent
HEI3090	HEI3090, MF:C18H15Cl3N4O3, MW:441.7 g/mol	Chemical Reagent

Advanced Implementation Considerations

Integration with Enhanced Sampling Methods

For complex systems such as protein-ligand complexes, proper box size selection becomes even more critical when employing advanced sampling techniques. The emergence of datasets like MISATO, which combines quantum mechanical properties with MD simulations of approximately 20,000 experimental protein-ligand complexes, highlights the growing need for robust simulation protocols that maintain stability across diverse molecular systems [46]. When implementing metadynamics or umbrella sampling within the NVT ensemble, systematic negative pressure can distort the free energy surfaces and compromise the accuracy of binding affinity calculations.

Recent approaches to this challenge include the development of multi-agent frameworks such as DynaMate, which leverages AI-assisted tools to automate the generation, running, and analysis of molecular simulations [51]. Such frameworks can systematically evaluate box size effects across multiple simulation replicates, identifying pressure-related instability patterns that might be overlooked in manual workflows.

Force Field Selection and Parameterization

The choice of force field significantly influences the optimal box size for stable NVT simulations. As demonstrated in collagen fibril research, different force fields (CHARMM36m vs. OPLS-AA) yield variations in the hydration level required to achieve zero lateral pressure, effectively shifting the volume-pressure relationship [47]. For vacuum simulations particularly, careful attention must be paid to non-bonded interaction parameters, as the absence of solvent molecules removes the dominant contributor to positive pressure in most solvated systems.

The development of quantum-centric workflows, such as those incorporating configuration interaction simulations via the book-ending correction method, offers promising avenues for refining force field parameters [49]. By providing more accurate reference data for molecular interactions, these approaches can improve the transferability of force fields across different volume conditions, reducing the sensitivity of pressure artifacts to box size selection.

The relationship between simulation box size and negative pressure development in NVT ensemble simulations represents a critical consideration for obtaining physically meaningful results. Through careful implementation of the protocols outlined in this application note—including proper initial system equilibration, systematic pressure monitoring, and appropriate remediation strategies—researchers can significantly enhance simulation stability and reliability. The ongoing development of automated workflows and AI-assisted tools promises to further streamline this process, potentially incorporating predictive models for optimal box size selection based on system composition and simulation conditions. For the drug development community, these advances in simulation methodology will enhance the accuracy of binding affinity predictions and structural characterization, ultimately supporting more efficient therapeutic discovery pipelines.

Within molecular dynamics (MD) simulations, the canonical (NVT) ensemble is crucial for studying systems at a constant temperature, mimicking thermal equilibrium with a surrounding heat bath [53]. This is particularly relevant for vacuum simulations, where no implicit solvent provides natural energy exchange. Thermostats are algorithms designed to maintain this constant temperature by adjusting atomic velocities. However, their effectiveness is heavily dependent on two key parameters: the integration time step and the thermostat-specific coupling constant. Improper selection of these parameters can lead to non-physical sampling, energy drift, or poor temperature control. This application note provides detailed protocols for optimizing these parameters, framed within research applications for material science and drug development.

Thermostat Theory and Parameter Definitions

Integration Time Step

The integration time step (Δ𝑡) is the discrete interval at which Newton's equations of motion are solved. It represents a fundamental trade-off between computational efficiency and numerical accuracy [53]. The Velocity Verlet algorithm, a common integration method, offers a favorable balance with a local truncation error on the order of Δ𝑡⁴ [53].

Thermostat Coupling Constants

The coupling constant dictates the strength of the interaction between the simulated system and the fictitious thermal bath.

• Langevin Thermostat: The AIMD_LANGEVIN_TIMESCALE parameter (in femtoseconds) is proportional to the inverse friction. A small value yields a "tight" thermostat that strongly maintains temperature but may inhibit configurational sampling, while a large value allows more flexible sampling at the cost of short-term temperature fluctuations [54].
• Nosé-Hoover Thermostat: The NOSE_HOOVER_TIMESCALE parameter (in femtoseconds) controls the coupling strength. The implementation in Q-Chem uses a single chain coupled to the system as a whole [54].
• Berendsen Thermostat: The tau parameter (in time units) is the time constant for the exponential decay of the temperature difference between the system and the bath. It is noted that this thermostat, while efficient for equilibration, does not yield a proper canonical ensemble [55].

Table 1: Overview of Common Thermostats and Key Parameters

Thermostat Type	Coupling Parameter	Mechanism	Ensemble Quality
Langevin [54]	AIMD_LANGEVIN_TIMESCALE (fs)	Stochastic "kicks" and friction	Canonical
Nosé-Hoover [54]	NOSE_HOOVER_TIMESCALE (fs)	Extended Lagrangian with fictitious particles	Canonical
Berendsen [55]	tau (time)	Velocity rescaling towards target T	Not strictly canonical
Bussi (BDP) [55]	N/A (Stochastic velocity rescaling)	Canonical sampling of kinetic energy	Canonical

Quantitative Parameter Recommendations

Based on the literature and software documentation, the following quantitative guidelines are provided for parameter selection.

Table 2: Recommended Parameter Ranges for Thermostats in Vacuum Simulations

Thermostat Type	Recommended Coupling Constant (τ)	Recommended Integration Time Step (Δ𝑡)	Additional Notes
Langevin	~100 fs for small systems [54]	Chosen as in NVE trajectory [54]	Smaller τ for non-ergodic systems; larger τ (≥1000 fs) for larger systems [54].
Nosé-Hoover	~100 × Δ𝑡 [55] (e.g., 100 fs for Δ𝑡=1 fs)	Typically 0.5 - 2.0 fs for all-atom models	A chain length of 3-6 auxiliary particles is typical [54].
Berendsen	> Δ𝑡 and < ∞ [53]	Typically 0.5 - 2.0 fs for all-atom models	Ideal for initial equilibration; switch to canonical thermostat for production [53].

Experimental Protocols for System Setup and Equilibration

General NVT Simulation Workflow

The following diagram illustrates the logical workflow for setting up and running an NVT simulation, from system preparation to analysis.

Protocol: NVT Equilibration for a Small Molecule in Vacuum

This protocol details the steps for equilibrating a small organic molecule using the Langevin thermostat in a vacuum, as might be used in early-stage drug development for conformational sampling.

• Initial System Preparation:

  • Obtain the initial 3D coordinates of the molecule (e.g., from a crystal structure or quantum chemistry optimization).
  • Assign atom types and force field parameters (e.g., GAFF2 for small organic molecules).
  • Define the simulation box large enough to avoid self-interactions (e.g., 2 nm padding around the molecule).

• Energy Minimization:

  • Objective: Remove any bad contacts and relax the structure.
  • Method: Use a steepest descent algorithm.
  • Termination: Continue until the maximum force is below a chosen threshold (e.g., 1000 kJ/mol/nm).

• Initial Velocity Assignment:

  • Assign random velocities from a Maxwell-Boltzmann distribution at the target temperature (e.g., 300 K) [54].

• NVT Equilibration Run:

  • Integrator: Velocity Verlet with a time step (Δ𝑡) of 1.0 fs.
  • Thermostat: Langevin thermostat.
  • Thermostat Parameter: Set AIMD_LANGEVIN_TIMESCALE (or equivalent) to 100 fs [54].
  • Duration: Run for a minimum of 50-100 ps, monitoring the instantaneous temperature.

• Validation:

  • Plot the temperature and potential energy over time. The system is considered equilibrated when these properties fluctuate around a stable average.

Protocol: System-Specific Parameter Optimization

This protocol outlines a systematic approach to fine-tuning the coupling constant for a novel system.

• Baseline Simulation: Run a short NVT simulation (e.g., 10-20 ps) using the default recommended parameters from Table 2.
• Evaluate Temperature Control: Calculate the average temperature and the standard deviation of the temperature fluctuations.
• Adjust Coupling Constant:
  • If the temperature deviation from the target is large and persistent, decrease the coupling constant (Ï„) to tighten the thermostat.
  • If the temperature is stable but the system appears "over-damped" (e.g., unnaturally slow conformational changes), increase Ï„.
• Iterate: Repeat steps 1-3 with the new Ï„ value until optimal temperature control and realistic system dynamics are achieved.

The Scientist's Toolkit: Research Reagent Solutions

This section details the essential software and computational "reagents" required to perform the simulations described in this note.

Table 3: Essential Research Reagent Solutions for NVT MD Simulations

Tool / Reagent	Type	Primary Function	Example Use Case
Q-Chem [54]	Software Suite	Performs Ab Initio MD (AIMD) with thermostatting.	Studying chemical reactions and electronic structure changes in vacuum.
HOOMD-blue [55]	MD Engine	Highly optimized MD simulations on GPUs.	High-throughput screening of molecular conformations or polymer properties.
Deep Potential (DP) [5]	Machine Learning Potential	Provides DFT-level accuracy at lower cost for MD.	Simulating complex materials like high-energy materials (HEMs) over long timescales.
Langevin Thermostat [54]	Algorithm	Temperature control via stochastic collisions.	Default choice for small molecules or systems requiring robust temperature control.
Nosé-Hoover Chain [54]	Algorithm	Temperature control via extended Lagrangian.	Production runs requiring a rigorous canonical ensemble for larger systems.
Berendsen Thermostat [53] [55]	Algorithm	Efficient velocity rescaling for quick equilibration.	Initial heating and equilibration phases before switching to a canonical thermostat.
ML-098	ML-098, MF:C19H19NO3, MW:309.4 g/mol	Chemical Reagent	Bench Chemicals
VB124	VB124, MF:C23H23ClN2O4, MW:426.9 g/mol	Chemical Reagent	Bench Chemicals

Logical Relationship of Thermostat Selection Criteria

The process of selecting the most appropriate thermostat for a given simulation depends on several key criteria, as summarized in the following decision diagram.

Correcting Thermalization Failures in Small or Anisotropic Systems

Within the broader thesis on NVT ensemble applications, the reliable thermalization of small or anisotropic systems in vacuum is a fundamental challenge. In molecular dynamics (MD), the NVT (canonical) ensemble is the appropriate choice for conformational searches of molecules in vacuum without periodic boundary conditions, as volume, pressure, and density are not defined in such setups [56]. The goal of an NVT simulation is to generate a trajectory that samples the canonical ensemble, where the number of particles (N), volume (V), and temperature (T) are constant. Thermostats are the algorithmic tools designed to maintain the target temperature by mimicking energy exchange with an external heat bath.

However, thermalization failures—where the system does not maintain the target temperature or fails to sample configurations correctly—are prevalent in small systems due to insufficient statistical averaging and in anisotropic systems (e.g., elongated molecules, surfaces) due to unequal energy distribution among degrees of freedom. This application note provides targeted protocols and analytical frameworks to diagnose and correct these failures.

Quantitative Comparison of Thermostats for Vacuum Simulations

The choice of thermostat is critical, especially for systems prone to thermalization issues. The following table summarizes key thermostats, their mechanisms, and their suitability for challenging systems, drawing from documented implementations [57].

Table 1: Thermostat Comparison for NVT Ensemble Simulations

Thermostat	Core Mechanism	Key Parameters	Strengths	Weaknesses for Small/Anisotropic Systems
Berendsen	Velocity scaling to approximate temperature control [57]	Relaxation time (τT); τT/Δt ≈ 100 recommended [57]	Rapidly drives system to target temperature; low computational cost [57]	Does not generate a correct canonical ensemble; can suppress legitimate temperature fluctuations [57].
Nose-Hoover Chain (NHC)	Extended Lagrangian with coupled thermal reservoirs [57]	Chain length (fixed at 4 in some implementations [57]); "Mass" parameter Q0 ~ NfkBT0Ï„T>2 [57]	Generates a correct canonical ensemble; robust for many condensed-phase systems [57].	Can be non-ergodic for small systems with few degrees of freedom (e.g., harmonic oscillators); parameter choice is critical [58].
Langevin	Stochastic and dissipative forces [57]	Friction coefficient (γ = 1/τT); τT/Δt ≈ 100 suggested [57]	Provides strong thermalization and ensures ergodicity [57].	Stochastic noise can interfere with the system's natural dynamics; may obscure the study of subtle dynamic properties.
Bussi-Donadio-Parrinello (SVR)	Stochastic velocity rescaling [57]	Relaxation time (Ï„T); uses Nf random numbers per step [57]	Correctly samples the canonical ensemble; superior to Berendsen by incorporating proper randomness [57].	The stochastic rescaling might require careful tuning for very small Nf.

Diagnostic Workflow for Thermalization Failures

A systematic approach is required to diagnose the root cause of thermalization problems. The following workflow and corresponding diagram outline a step-by-step diagnostic protocol.

Diagram Title: Diagnostic Workflow for Thermalization Failures

Protocol 1: Temperature and Energy Drift Analysis

Objective: To determine whether the system is maintaining the target temperature on average and to identify unnatural drift or oscillation.

• Data Collection: From the MD output, extract the instantaneous or kinetic temperature as a function of simulation time.
• Visualization: Plot the temperature time series.
• Quantitative Analysis:
  • Calculate the running average of the temperature. A well-thermalized system will fluctuate around the target value (T₀).
  • Perform a linear regression on the running average. A significant slope indicates a systematic drift.
  • For Nose-Hoover thermostats, monitor the conserved energy (including thermostat variables). A significant drift indicates integration or parameterization issues.

Interpretation: A stable running average with fluctuations validates the thermostat. Drift suggests energy leakage, while extreme, regular oscillations can indicate poor coupling or non-ergodicity.

Protocol 2: System Size and Degree of Freedom Assessment

Objective: To evaluate if the system is too small for the chosen thermostat to function correctly.

• Calculation: Determine the total number of degrees of freedom (N_f) in the system. For a system of N particles without constraints in 3D space, N_f = 3N - 3 (or 3N - 6 if rotation is fixed).
• Threshold Check: As a rule of thumb, deterministic thermostats like Nose-Hoover can exhibit non-ergodic behavior for systems with N_f < 100. Small systems lack the phase space for proper canonical sampling without stochastic assistance.

Interpretation: If N_f is small, the failure may be fundamental. Switching to a stochastic thermostat (Langevin or Bussi-Donadio-Parrinello) is recommended, as they ensure ergodicity by design [57] [58].

Protocol 3: Anisotropy and Energy Distribution Analysis

Objective: To diagnose unequal thermalization across different spatial dimensions or molecular components.

• Data Collection: Output the kinetic energy separately for the x, y, and z components of the velocity for the entire system or for distinct molecular segments in an anisotropic structure.
• Variance Calculation: For each spatial component (x, y, z), calculate the variance of its kinetic energy time series over a production run.
• Comparison: Compute the ratios of these variances (e.g., max variance / min variance).

Interpretation: In a perfectly thermalized isotropic system, the variance of the kinetic energy should be equal in all dimensions. A ratio significantly greater than 1 (e.g., > 1.5) indicates anisotropic thermalization, where one direction is "hotter" or more fluctuating than another. This is common in systems like lipid bilayers, nanotubes, or proteins with elongated structures.

Table 2: Analysis of Kinetic Energy Variance for Anisotropy Detection

System Component	Kinetic Energy Variance (arb. units)	Ratio (to min variance)	Interpretation
Overall X-component	1.52	1.51	Slightly elevated fluctuations
Overall Y-component	1.01	1.00	Baseline fluctuation level
Overall Z-component	2.15	2.13	Significantly elevated fluctuations

Correction Protocols for Specific Failure Modes

Based on the diagnostics, apply these targeted correction protocols.

Protocol 4: Correcting Failures in Small Systems

Application: Systems with a low number of particles (N < 1000) or degrees of freedom.

• Switch to a Stochastic Thermostat:
  • Recommendation: Replace deterministic thermostats (e.g., Nose-Hoover) with the Langevin or Bussi-Donadio-Parrinello (Stochastic Velocity Rescaling) thermostat [57].
  • Rationale: Stochastic thermostats provide a "heat kick" that ensures ergodicity even for systems with few degrees of freedom, overcoming the limitations of deterministic dynamics.
• Parameter Tuning for Langevin Thermostat:
  • Friction Coefficient (γ): Set the relaxation time Ï„_T such that Ï„_T/Δt ≈ 100 [57]. The friction coefficient is γ = 1/Ï„_T.
  • Example: For a time step Δt = 1 fs, a Ï„_T of 100 fs (γ = 10 ps^-1) is a standard starting point. For very small, stiff systems, a slightly higher γ might be necessary for stability.

Protocol 5: Correcting Failures in Anisotropic Systems

Application: Systems with asymmetric geometries or strong directional interactions.

• Implement Massive Thermostatting:
  • Method: Instead of coupling a single thermostat to the entire system, couple independent thermostats to each degree of freedom or to small groups of atoms.
  • Rationale: This prevents the "hot" regions from dominating the thermal coupling and ensures that every mode, including slow-moving ones in tightly bound directions, is properly thermalized.
• Use Anisotropic Temperature Coupling (if available):
  • Method: Some MD packages allow for separate temperature coupling in the x, y, and z dimensions. This can be used to explicitly enforce equal temperatures in all directions, correcting for drift in anisotropic systems.
  • Caution: This should be used primarily for equilibration, as it artificially breaks the equivalence of spatial dimensions.

The Scientist's Toolkit: Research Reagent Solutions

In computational science, "reagents" are the software tools, algorithms, and parameters used to conduct experiments. The following table details essential components for studying thermalization in vacuum NVT simulations.

Table 3: Key Research Reagent Solutions for NVT Thermalization Studies

Reagent / Tool	Function / Purpose	Example / Specification
Langevin Thermostat	Ensures ergodic sampling by applying stochastic and dissipative forces, crucial for small systems [57].	Friction coefficient (γ) = 1-10 ps-1; τT = 100-1000 fs (scaled to time step Δt) [57].
Bussi-Donadio-Parrinello Thermostat	Correctly samples the canonical ensemble via stochastic velocity rescaling, an improved alternative to simple velocity scaling [57].	Relaxation time Ï„T; requires Nf Gaussian random numbers per step [57].
Nose-Hoover Chain Thermostat	Generates exact canonical distribution via an extended Lagrangian formalism; suitable for larger, condensed-phase systems [57].	Chain length = 3-4; coupling constant Q0 = NfkBT0Ï„T2 [57].
Kinetic Energy Decomposition Tool	Diagnostic script to calculate kinetic energy and its variance per spatial dimension or per molecular segment.	Custom analysis script (e.g., in Python/VMD) processing velocity trajectories.
MD Engine with Massive Thermostatting	Simulation software capable of applying independent thermostats to particles or groups to correct anisotropic failures.	e.g., GPUMD, GROMACS, LAMMPS (with specific fixes).
CW0134	CW0134, MF:C11H7ClF3N3O2, MW:305.64 g/mol	Chemical Reagent
Hydrocortisone hemisuccinate hydrate	Hydrocortisone hemisuccinate hydrate, MF:C25H36O9, MW:480.5 g/mol	Chemical Reagent

Refining Non-bonded Interaction Parameters to Prevent System Expansion

In the realm of molecular dynamics (MD) simulations, accurately modeling non-bonded interactions—which include van der Waals forces and electrostatic interactions—is paramount for achieving physically realistic results. These interactions govern a wide array of molecular behaviors, from binding affinity in drug design to the stability of molecular complexes. When simulations are conducted in a vacuum, without periodic boundary conditions to mimic a natural environment, the system is particularly susceptible to artificial expansion and instability if these interactions are not properly parameterized [59].

The canonical (NVT) ensemble is a fundamental statistical mechanical framework where the Number of particles (N), the Volume (V), and the Temperature (T) of the system are held constant [60] [56]. This ensemble is exceptionally well-suited for vacuum simulations, as it allows researchers to study intrinsic molecular properties—such as conformational dynamics, folding pathways, or ligand-receptor interactions—without the complicating factors of pressure control or volume fluctuations [56]. The core challenge in NVT vacuum simulations is to refine the non-bonded interaction parameters to prevent unphysical system expansion, thereby ensuring that the observed dynamics are a true reflection of the molecular system's properties and not an artifact of the computational model.

Theoretical Foundation

The Physics of Non-Bonded Interactions

Non-bonded interactions in MD simulations are typically described by a combination of potential energy functions. The Lennard-Jones (LJ) potential is the most common model for van der Waals interactions, capturing both the attractive (dispersion) and repulsive (Pauli exclusion) forces between atoms [61]. A common form is the LJ (9-6) potential: [ \upsilon(r){9-6} = \frac{27}{4} \varepsilon \left( \frac{\sigma^{9}}{r^{9}} - \frac{\sigma^{6}}{r^{6}} \right) ] where ε represents the depth of the potential well, σ is the finite distance at which the inter-particle potential is zero, and r is the distance between particles [61]. The electrostatic interaction between two charged atoms is calculated using Coulomb's law: [ \upsilon(r){elec} = \frac{1}{4\pi\epsilon0} \frac{q1 q_2}{r} ] where q1 and q2 are the partial atomic charges, and ε0 is the vacuum permittivity [61]. In vacuum simulations, the absence of a solvent dielectric (ε = 1) means these electrostatic interactions are significantly stronger and longer-ranged than in explicit solvent simulations, making their accurate treatment even more critical.

The NVT Ensemble in Vacuum Simulations

The NVT ensemble is generated by integrating Newton's equations of motion while coupling the system to a thermostat to maintain a constant temperature [56]. This is the ensemble of choice for conformational analysis in vacuum because the volume is fixed, preventing the collapse or unrealistic expansion that can occur without periodic boundaries [56]. The thermostat acts as a heat bath, allowing the system to exchange energy to maintain the target temperature, which is crucial for simulating realistic thermodynamic conditions. Without the stabilizing influence of a solvent or a pressure bath, the careful refinement of non-bonded parameters becomes the primary defense against unphysical system expansion and the key to obtaining reliable, reproducible results.

Parameterization Strategies

Cutoff Schemes and Long-Range Electrostatics

Selecting an appropriate method for handling the long-range component of non-bonded interactions is vital for the stability of vacuum systems. The table below summarizes the primary parameter sets recommended for vacuum NVT simulations.

Table 1: Non-Bonded Interaction Parameter Sets for Vacuum NVT Simulations

Parameter Set	Electrostatics	Van der Waals	Cutoff Distances (Ã…)	Recommended Usage
IPS (Isotropic Periodic Sum) [59]	IPS	IPS	CUTNB=12.0, CTOFNB=10.0	General-purpose vacuum simulations
Atom-Based Shifted	ATOM FSHIFT CDIE [59]	VDW VSHIFT [59]	CUTNB=13.0, CTOFNB=12.0, CTONNB=8.0 [59]	Systems requiring high accuracy
Group-Based	GROUP FSWITCH CDIE [59]	VDW VSWITCH [59]	CUTNB=13.0, CTOFNB=12.0, CTONNB=8.0 [59]	Legacy systems or specific compatibility needs

For electrostatic interactions, shifted potential functions (FSHIFT, VSHIFT) are generally preferred over switched functions (SWIT) in vacuum, as they provide a smooth decay of energy to zero at the cutoff distance, minimizing energy conservation problems [59]. The Isotropic Periodic Sum (IPS) method is a powerful alternative, as it is specifically designed for accurate long-range force calculations in both finite (vacuum) and periodic systems, making it highly transferable [59].

Cross-interaction parameters between different atom types are typically derived from their individual parameters using combining rules. The most common rules are: [ \sigma{ab} = \frac{\sigma{aa} + \sigma{bb}}{2} \quad \text{and} \quad \varepsilon{ab} = \sqrt{\varepsilon{aa} \varepsilon{bb}} ] These Lorentz-Berthelot rules provide a consistent framework for defining interactions across the entire system without the need for explicit parameterization of every possible atom pair [61].

Parameterization can be sourced from several places. Generalized force fields (e.g., CHARMM, AMBER, OPLS) provide standardized parameters for biomolecules and organic compounds. For more specific applications, thermodynamic data, such as density and surface tension, can be used to fit ε and σ parameters to match experimental observations [61]. Furthermore, Machine Learning Potentials (MLPs) like the EMFF-2025 model are emerging as powerful tools that can achieve density functional theory (DFT) level accuracy in describing mechanical and chemical properties, offering a promising avenue for generating highly accurate parameter sets [5].

Experimental Protocols

Workflow for Parameter Refinement

The following diagram outlines a systematic workflow for refining non-bonded parameters to stabilize a system in the NVT ensemble.

Protocol 1: Initial System Setup and Energy Minimization

Objective: To construct a stable initial atomic system and relieve any steric clashes prior to dynamics.

• System Construction: Build your molecule(s) using a molecular builder software (e.g., Avogadro, Maestro) or obtain the structure from a protein data bank. Ensure the system is centered in a simulation box that is sufficiently large to accommodate the molecule's full range of motion during the simulation. For vacuum simulations, a box padding of at least 1.5 times the molecule's maximum diameter is recommended.
• Parameter Assignment: Assign initial non-bonded parameters (atomic partial charges, σ, and ε) from a recognized force field (e.g., CHARMM, GAFF). The IPS method or an atom-based shifted potential with a CUTNB of 12.0 Ã… is a suitable starting point [59].
• Energy Minimization: Perform a two-stage energy minimization to remove bad contacts and avoid initial instability.
  • Stage 1 (Steepest Descent): Use the steep integrator with a conservative step size (emstep = 0.01 nm) and a force tolerance (emtol = 1000.0 kJ mol⁻¹ nm⁻¹) for a maximum of 500-1000 steps [62].
  • Stage 2 (Conjugate Gradient): Switch to a more efficient cg integrator with a stricter force tolerance (emtol = 10.0 kJ mol⁻¹ nm⁻¹) to converge the system to a local energy minimum [62].

Protocol 2: NVT Equilibration and Stability Assessment

Objective: To thermalize the system at the target temperature and assess the stability of the non-bonded parameters.

• Thermostat Selection: Choose a thermostat for the NVT simulation. The Nosé-Hoover thermostat (MDALGO=2 in VASP, integrator=md-vv with thermostat in GROMACS) is a deterministic and reliable choice for many systems [2]. Set the target temperature (e.g., TEBEG=300 in VASP, ref-t=300 in GROMACS) [2].
• Initialization: Initialize atomic velocities from a Maxwell-Boltzmann distribution corresponding to the target temperature [1].
• Equilibration Run: Run a short MD simulation (e.g., NSW=10000 steps with a POTIM=1.0 fs timestep) [2]. During this run, monitor key stability metrics:
  • Temperature: Should fluctuate around the target value.
  • Total Energy: Should be conserved, with no significant drift.
  • Root Mean Square Deviation (RMSD): Should plateau, indicating conformational stability.
• Stability Diagnosis: If the system expands or shows large energy drifts, proceed to Protocol 3.

Protocol 3: Analysis and Parameter Refinement

Objective: To identify the cause of instability and refine the non-bonded parameters.

• Radial Distribution Function (RDF) Analysis: Calculate the RDF, g(r), for key atom pairs. A sharp peak at very short distances followed by a deep trough may indicate overly attractive interactions, while a complete lack of structure suggests overly repulsive parameters.
• Parameter Adjustment:
  • If Overly Attractive: Slightly increase the σ parameter or decrease the ε parameter for the problematic atom types. Consider increasing the CUTNB distance by 1-2 Ã… to better capture long-range interactions [59].
  • If Overly Repulsive: Slightly decrease the σ parameter. Re-evaluate the atomic partial charges, as excessive charge separation can cause repulsion.
  • Electrostatic Issues: If electrostatic interactions are suspected to be the culprit, switch from a simple cutoff to the IPS method for a more physically consistent treatment of long-range forces in a finite system [59].
• Iterative Refinement: Return to Protocol 1 (Energy Minimization) with the adjusted parameters and repeat the equilibration and analysis cycle until system stability is achieved.

The Scientist's Toolkit

Table 2: Essential Research Reagents and Computational Tools

Tool/Reagent	Function/Description	Example Use Case
CHARMM Force Field [59]	A comprehensive set of bonded and non-bonded parameters for biomolecules.	Providing initial σ, ε, and partial charge parameters for amino acids in a peptide simulation.
Isotropic Periodic Sum (IPS) [59]	A method for calculating long-range non-bonded interactions in finite and periodic systems.	Stabilizing electrostatic interactions in a vacuum protein simulation without using Ewald sums.
Nosé-Hoover Thermostat [2]	A deterministic algorithm for temperature control that generates a correct canonical ensemble.	Maintaining a constant temperature during NVT equilibration and production runs.
LAMMPS MD Engine [61]	A versatile and high-performance software for molecular dynamics simulations.	Running large-scale vacuum simulations with customized non-bonded potentials.
Deep Potential (DP) Generator [5]	A framework for developing machine learning interatomic potentials with DFT-level accuracy.	Creating a highly accurate, system-specific potential for a novel high-energy material (HEM).
LJ (9-6) Potential [61]	A Lennard-Jones potential variant with a steeper repulsive term (r⁻⁹).	Modeling van der Waals interactions in coarse-grained systems parameterized with thermodynamic data.
Hydrocortisone hemisuccinate hydrate	Hydrocortisone hemisuccinate hydrate, MF:C25H36O9, MW:480.5 g/mol	Chemical Reagent
RP03707	RP03707, MF:C55H58F3N11O4, MW:994.1 g/mol	Chemical Reagent

Advanced Applications and Validation

Relationship of Methods and Physical Properties

The choice of non-bonded interaction method directly influences the physical properties observed in a simulation. The diagram below illustrates this relationship and the iterative validation cycle.

Advanced applications, such as simulating high-energy materials (HEMs) or polymer-calcite interfaces, demonstrate the critical importance of refined parameters. For instance, the EMFF-2025 neural network potential was developed specifically for C, H, N, O-based HEMs and can predict mechanical properties and decomposition characteristics with DFT-level accuracy, showcasing a modern ML-based approach to parameterization [5]. In studies of polymer-calcite interfaces, uniaxial tensile simulations revealed that the interfacial strength is governed by non-bonded interactions, which must be precisely parameterized to predict whether failure occurs at the interface or within the bulk polymer [16].

Validation Against Experimental and Theoretical Data

A robust validation protocol is essential to confirm that the refined parameters yield physically meaningful results. Key validation metrics include:

• Solvent Accessible Surface Area (SASA): For folded proteins or structured complexes, the SASA calculated from the vacuum simulation should be consistent with theoretical predictions or measurements from crystal structures [61].
• Radial Distribution Function (RDF): The g(r) for specific atom pairs can be compared against higher-level theoretical calculations or, in some cases, experimental data to validate the structure of the simulated system.
• Energy Conservation: In a well-behaved NVT simulation with a deterministic thermostat, the total energy should exhibit stable fluctuations without a significant drift, indicating that the forces are calculated consistently and the system is stable.

By following these detailed protocols and leveraging the tools outlined, researchers can systematically refine non-bonded interaction parameters to create stable, accurate, and reliable vacuum simulations within the NVT ensemble, thereby enabling confident investigation of molecular structure and function.

Validating and Benchmarking NVT Simulations: Ensuring Physical Realism

Within the framework of a broader thesis on the application of the NVT (Canonical Ensemble) ensemble in vacuum simulation research, monitoring specific physicochemical metrics is paramount for ensuring the reliability and accuracy of computational and experimental outcomes. This protocol details the methodologies for tracking three fundamental metrics—Temperature Stability, Energy Conservation, and Hydrogen Bonding dynamics—in the context of simulations and experiments conducted under vacuum conditions. The NVT ensemble, which maintains a constant number of atoms (N), a fixed volume (V), and a constant temperature (T), is particularly relevant for studying processes like contamination outgassing in space vacuums [63] and reactive dynamics in condensed-phase materials [5]. The following sections provide application notes and detailed experimental protocols tailored for researchers, scientists, and drug development professionals.

Monitoring Key Metrics: Application Notes

Temperature Stability

Temperature stability is critical for simulating realistic conditions and obtaining statistically meaningful results from molecular dynamics (MD) simulations. In vacuum environments, where convective heat transfer is eliminated, precise temperature control becomes even more crucial for replicating space conditions [63] or for studying intrinsic material properties [64] [65].

Applications in Vacuum Simulations:

• Contamination Control: Vacuum stability testing, per standards like ASTM E595, involves exposing materials to high vacuum and elevated temperatures (e.g., up to 149 °C) to measure the amount of volatile condensable materials released [63]. Stable temperature control is essential for obtaining reproducible outgassing data.
• Material Performance: Evaluating whether components can perform their intended tasks when exposed to the vacuum of space requires stable thermal cycling under controlled vacuum conditions [63].
• Property Characterization: Accurate characterization of material properties, such as the performance of thermoelectric coolers (TECs), requires high-vacuum thermal insulation to eliminate parasitic heat losses and ensure one-dimensional heat transfer, enabling precise temperature difference measurements across the device [64].

Energy Conservation

In ab initio molecular dynamics (AIMD) and machine learning molecular dynamics (MLMD), energy conservation is a key indicator of the stability and physical validity of a simulation, especially when modeling reactive events in the NVT ensemble.

Applications in Vacuum Simulations:

• Reactive Force Fields: The development of general neural network potentials (NNPs), such as the EMFF-2025 model for high-energy materials (HEMs), aims to achieve Density Functional Theory (DFT)-level accuracy in predicting energies and forces while being computationally efficient. Validating the energy conservation of such potentials is a critical step [5].
• Machine Learning Potentials: MLMD simulations rely on potentials trained on DFT data. The mean absolute error (MAE) between the ML-predicted energy/forces and the DFT-calculated benchmarks is a quantitative measure of the model's accuracy and its ability to conserve energy across different molecular systems [5] [66].

Hydrogen Bonding

Hydrogen bonding (H-bonding) is a key intermolecular interaction that influences structural stability, solvation dynamics, and reaction mechanisms. Monitoring H-bonding under vacuum conditions or at interfaces is essential for understanding processes like adsorption, catalysis, and molecular recognition.

Applications in Vacuum Simulations:

• Interfacial Water Dynamics: At metal/water interfaces, the strength and dynamics of hydrogen bonds differ significantly from bulk water. Understanding these altered dynamics, such as accelerated water exchange driven by correlated desorption events, is fundamental to electrochemical processes [66].
• Surface Adsorption: Hydrogen bonding between organic molecules and hydroxylated metal surfaces (e.g., Al(OH)₃, Cu(OH)â‚‚) can be studied using DFT calculations. These interactions are affected by the chemical environment, with H-bonds often being shorter in an implicit aqueous solvent compared to a vacuum [67].
• Polymer-Surface Interactions: In vacuum or confined environments, the adhesion of polymers to mineral surfaces (e.g., calcite) can be mediated by H-bonding, affecting the overall mechanical strength of the composite system [16].

Table 1: Key Metrics and Their Quantitative Benchmarks in NVT Simulations

Metric	Monitoring Method	Target/Benchmark Value	Relevance to NVT Vacuum Simulations
Temperature Stability	Thermostat coupling (e.g., Nose-Hoover, Langevin)	Maintain target T (e.g., 302 K, 337 K [66]) with minimal fluctuation	Ensures realistic thermodynamic sampling; critical for outgassing tests at constant T [63]
Energy Conservation	Validation against DFT: Mean Absolute Error (MAE)	MAE for energy: < ± 0.1 eV/atom [5]; MAE for force: < ± 2 eV/Å [5]	Validates physical fidelity of ML potentials for reactive simulations in condensed phases [5]
Hydrogen Bond Dynamics	Residence time, H-bond lifetime analysis	Water exchange timescale: ~100s of picoseconds at interfaces (e.g., 337 K) [66]	Reveals interfacial solvation structure and dynamics affecting reaction mechanisms in vacuum/interface environments [66]

Experimental Protocols

Protocol 1: Temperature Stability and Vacuum Outgassing Test

This protocol outlines a standardized method for determining the vacuum stability and temperature tolerance of materials, based on ASTM E595 [63].

1. Key Research Reagent Solutions

Table 2: Essential Materials for Vacuum Stability Testing

Item	Function
High-Vacuum Test Chamber	Simulates the vacuum of space (e.g., down to 1.33x10⁻⁵ Pa) and provides a controlled, robust environment for testing [63].
Thermal Control System	Heats the test item to a specified, stable temperature (e.g., up to 149°C) and can also provide cryogenic cooling for thermal cycling [63] [65].
Calibrated Vacuum Gauges	Accurately measure and monitor the pressure within the test chamber to ensure maintenance of the high-vacuum environment [63] [65].
Collection Plate & Microbalance	Collects and quantifies the mass of volatile condensable materials (CVCM) released from the test sample, enabling calculation of the total mass loss (TML) [63].

2. Procedure 1. Preparation: Weigh the test sample and the clean collection plate separately using a precision microbalance. 2. Setup: Place the test sample and the collection plate inside the high-vacuum chamber in the specified configuration, ensuring the collection plate is positioned to intercept volatiles from the sample. 3. Evacuation and Heating: Seal the chamber and initiate evacuation to achieve a high vacuum (e.g., < 1.33 x 10⁻³ Pa). Once the target pressure is stable, activate the thermal control system to ramp the sample to the specified test temperature (e.g., 125°C as per ASTM E595). 4. Isothermal Conditioning: Maintain the sample at the target temperature and pressure for the prescribed duration (typically 24 hours in ASTM E595). Monitor temperature stability closely (e.g., within ±1°C [65]). 5. Recovery and Analysis: After the test period, vent the chamber and carefully retrieve the sample and collection plate. Re-weigh them to determine the Total Mass Loss (TML) and the Collected Volatile Condensable Materials (CVCM) as a percentage of the original sample mass.

3. Data Interpretation - TML indicates the total amount of volatiles released. - CVCM indicates the fraction of volatiles that re-condense on colder surfaces, posing a contamination risk. - Results are compared to material specifications to assess suitability for use in vacuum environments.

Protocol 2: Validating Energy Conservation in a Machine Learning Potential

This protocol describes the workflow for developing and validating an ML-based interatomic potential for NVT-MD simulations, ensuring it conserves energy at a level comparable to DFT [5] [66].

1. Key Research Reagent Solutions

Table 3: Essential Computational Tools for ML Potential Development

Item	Function
DFT Software (e.g., CP2K)	Generates the reference data (energies, forces) used to train the machine learning potential [66].
ML Potential Framework (e.g., Deep Potential)	Provides the architecture and training algorithms to create a fast, accurate neural network interatomic potential [5] [66].
Active Learning Workflow (e.g., DPGEN)	Iteratively explores configuration space and expands the training dataset to improve the robustness and generalizability of the ML potential [66].
MD Engine (e.g., LAMMPS)	Performs large-scale molecular dynamics simulations using the trained ML potential to validate its performance and explore physicochemical properties [66].

2. Procedure 1. Initial Data Generation: Use AIMD simulations within the NVT ensemble to generate an initial set of diverse atomic configurations for the chemical system of interest (e.g., HEMs containing C, H, N, O). Record energies and forces for each configuration. 2. Model Training: Train a neural network potential (e.g., using the Deep Potential scheme) on the initial DFT dataset. The network learns to map atomic configurations to the corresponding DFT-level energies and forces. 3. Iterative Exploration (Active Learning): - Run MD simulations using the current ML potential to explore new regions of the potential energy surface. - Use an uncertainty metric to identify configurations where the model's prediction is uncertain. - Select these configurations for new DFT calculations, adding them to the training set. - Re-train the model with the expanded dataset. Repeat this cycle until the model's error is minimized and stable. 4. Energy Conservation Validation: On a held-out test set of configurations, compare the energies and forces predicted by the final ML model against the reference DFT values. Calculate quantitative metrics like Mean Absolute Error (MAE). A well-conserved potential should achieve an MAE for energy within ± 0.1 eV/atom and for forces within ± 2 eV/Å [5]. 5. Production Simulation: Use the validated ML potential to run large-scale, long-time NVT-MD simulations (e.g., to study thermal decomposition) at a fraction of the computational cost of AIMD.

3. Data Interpretation - Low MAE values for energy and forces confirm the ML potential's accuracy and its ability to conserve energy at near-DFT quality. - The potential can then be trusted to predict material properties (e.g., crystal structures, mechanical moduli, reaction pathways) with high fidelity.

Protocol 3: Analyzing Hydrogen-Bond Dynamics at Interfaces

This protocol uses MLMD simulations in the NVT ensemble to investigate the dynamics of hydrogen bonding at a solid/liquid interface, such as Pt/water [66].

1. Key Research Reagent Solutions

Item	Function
Validated ML Potential	A machine-learning potential trained specifically for the metal/water interface, providing ab initio accuracy for large-scale MD simulations [66].
Hydrogen Bond Definition	A geometric criterion (e.g., O-O distance < 3.5 Å and H-O-O angle < 30°) to identify H-bonds from the MD trajectory.
Analysis Scripts	Custom code (e.g., in Python) to calculate H-bond lifetimes, residence times, and spatial correlation functions from the simulation trajectory.

2. Procedure 1. System Setup: Construct an atomistic model of the interface (e.g., a Pt slab in contact with liquid water). Ensure the model is large enough to minimize finite-size effects. 2. Equilibration: Perform an NVT-MD simulation using the validated ML potential to equilibrate the system at the target temperature (e.g., 337 K). Use a thermostat like Langevin or Nose-Hoover with appropriate damping parameters [66]. 3. Production Run: Continue the NVT-MD simulation for a sufficiently long time (e.g., nanoseconds) to collect statistics on H-bond formation and breaking. Save the atomic trajectories at frequent intervals. 4. Trajectory Analysis: - Residence Time: For a water molecule adsorbed at the interface, the residence time is the continuous time interval it remains bound to a specific surface site before desorbing. This can be calculated using population correlation functions. - Spatial Correlation of Desorption Events: Analyze whether a desorption event at one site increases the probability of a nearby desorption event within a short time window, which can accelerate overall exchange dynamics [66]. 5. Validation: Compare the simulated interfacial water structure (e.g., oxygen density profile) against previous AIMD results or experimental data (e.g., from X-ray scattering) to validate the simulation setup [66].

3. Data Interpretation - Slower H-bond dynamics at the interface compared to the bulk indicate stronger H-bonding. - A residence time of several hundred picoseconds suggests a dynamic interface with relatively fast water exchange. - The presence of spatial correlation in desorption events provides a mechanistic explanation for accelerated collective dynamics.

Integrated Workflow Visualization

The following diagram illustrates the logical relationship and iterative workflow between the key protocols outlined in this document, highlighting how they interconnect within an NVT vacuum simulation research project.

In molecular dynamics (MD) simulations, a statistical ensemble defines the macroscopic conditions under which a system is studied, determining which state variables (such as number of particles N, volume V, temperature T, or pressure P) remain constant. The choice of ensemble is fundamental to aligning simulation methodology with research objectives, as it controls the thermodynamic environment and influences all resulting properties. The two most commonly used ensembles are the NVT (canonical) ensemble, which maintains constant particle number, volume, and temperature, and the NPT (isothermal-isobaric) ensemble, which maintains constant particle number, pressure, and temperature.

The NVT ensemble is particularly relevant for vacuum simulations research, where volume remains fixed and pressure is undefined or irrelevant. Understanding the theoretical foundations, practical applications, and methodological requirements of each ensemble is essential for designing physically meaningful simulations that accurately model experimental conditions or specific thermodynamic constraints.

Theoretical Foundations

The NVT (Canonical) Ensemble

The NVT ensemble, also known as the canonical ensemble, is characterized by a constant number of particles (N), constant volume (V), and constant temperature (T). This ensemble is generated by solving Newton's equations of motion while implementing temperature control mechanisms. Without periodic boundary conditions, volume, pressure, and density are not defined, making constant-pressure dynamics impossible [56]. The NVT ensemble provides the advantage of less perturbation of the trajectory due to the absence of coupling to a pressure bath, making it suitable for studies where volume changes are negligible or for systems in vacuum [56].

The NPT (Isothermal-Isobaric) Ensemble

The NPT ensemble maintains constant number of particles (N), constant pressure (P), and constant temperature (T). In this ensemble, the unit cell vectors are allowed to change, and the pressure is adjusted by modifying the volume. This is the ensemble of choice when correct pressure, volume, and densities are important in the simulation [56]. The NPT ensemble can also be used during equilibration to achieve desired temperature and pressure before switching to other ensembles for data collection.

Comparative Thermodynamics

The following table summarizes the key characteristics of these ensembles and other less common variants:

Table 1: Molecular Dynamics Ensembles and Their Characteristics

Ensemble	Constant Parameters	Common Applications	Key Considerations
NVE [56]	Number of particles (N), Volume (V), Energy (E)	Studying constant-energy surfaces; fundamental molecular dynamics	Not recommended for equilibration; energy conservation subject to numerical errors
NVT [1] [56]	Number of particles (N), Volume (V), Temperature (T)	Vacuum simulations; systems with negligible volume expansion; adsorption studies	Volume fixed throughout; appropriate when pressure is not significant
NPT [56] [68]	Number of particles (N), Pressure (P), Temperature (T)	Thermal expansion; phase transitions; density prediction	Volume adjusts to maintain pressure; suitable for condensed phases
NPH [56]	Number of particles (N), Pressure (P), Enthalpy (H)	Specialized applications requiring constant enthalpy	Analog of NVE for constant pressure
NST [56]	Number of particles (N), Stress (S), Temperature (T)	Stress-strain relationships in materials	Controls components of stress tensor

Ensemble Selection Criteria

Research Objectives and Ensemble Choice

The selection between NVT and NPT ensembles should be driven by the specific research questions and the system under investigation. The following diagram illustrates the decision-making process for ensemble selection:

Decision Framework for Ensemble Selection

Key Application Scenarios

NVT Ensemble Applications:

• Vacuum simulations: For protein simulations in vacuum, constant volume must be used with no pressure coupling [69].
• Ion diffusion in solids: Where volume changes are negligible [1].
• Adsorption and reaction studies: On slab-structured surfaces and clusters [1].
• Organic thin films: Research on molecular orientation in vacuum-deposited amorphous thin films [13].

NPT Ensemble Applications:

• Thermal expansion studies: Calculating coefficients of thermal expansion in solids [68].
• Phase transitions: Investigating solid-solid or solid-liquid transitions [68].
• Density prediction: For fluids (gases and liquids) at specific temperature and pressure conditions [68].
• Biological systems in solution: Where maintaining physiological pressure is crucial.

Temperature and Pressure Control Methods

Thermostats for NVT Simulations

In NVT-MD simulations, several thermostats are available for temperature control, each with distinct characteristics and applications:

Table 2: Thermostat Methods for NVT Ensemble Simulations

Thermostat	Mechanism	Advantages	Disadvantages	Typical Applications
Berendsen [1]	Uniform velocity scaling	Simple; good convergence	Unnatural phenomena; does not reproduce correct ensemble	Rapid equilibration
Langevin [1]	Random forces and friction on individual atoms	Proper sampling even for mixed phases	Not reproducible due to stochastic forces	Complex systems with different phases
Nosé-Hoover [1] [2]	Extended system with thermal reservoir	Reproduces correct NVT ensemble; widely used	Exceptions for special systems	General purpose; production simulations
CSVR [2]	Stochastic velocity rescaling	Efficient temperature control	-	General purpose

Barostats for NPT Simulations

For NPT simulations, both temperature and pressure control are implemented. Common barostat methods include:

Parrinello-Rahman Method: Allows all degrees of freedom of the simulation cell to vary, providing high system flexibility and versatility. The equations of motion incorporate both thermostat and barostat variables, with the simulation cell vectors evolving dynamically throughout the simulation [68].

Berendsen Barostat: Can control pressure efficiently for convergence and can operate in two modes: with fixed cell angles and independently variable cell lengths, or with fixed cell length ratios. Like the Berendsen thermostat, it provides efficient convergence but has limitations in reproducing the correct statistical ensemble [68].

Experimental Protocols and Implementation

NVT Ensemble Protocol for Vacuum Simulations

Objective: Perform MD simulation of a protein in vacuum using NVT ensemble to study intrinsic conformational properties without solvent effects.

System Preparation:

• Obtain initial coordinates: Retrieve protein structure from PDB database.
• Process structure: Remove crystallographic water molecules and other non-protein components.
• Neutralization: Adjust protonation states to neutralize the system, as proteins in vacuum should not be charged [69].
• Force field selection: Choose an appropriate vacuum force field (e.g., CHARMM36m, OPLS-AA) [47].

Simulation Workflow:

NVT Vacuum Simulation Workflow

Implementation with ASE (Python):

Critical Parameters:

• Temperature coupling constant (Ï„â‚œ): 0.1-10 ps for optimal temperature control
• Time step: 1-2 fs for atomistic models without constraints
• Cutoff method: No cutoffs or very long cutoffs for vacuum simulations [69]

NPT Ensemble Protocol for Condensed Phase Systems

Objective: Perform MD simulation of a solvated system at constant temperature and pressure to study density-dependent properties.

System Preparation:

• Solvation: Place the solute in an appropriate solvent box with periodic boundary conditions.
• Neutralization: Add ions to achieve electroneutrality.
• Energy minimization: Remove bad contacts and prepare the system for dynamics.

Implementation with ASE:

Critical Parameters:

• Pressure coupling constant (Ï„â‚š): 1-5 ps for stable pressure control
• Barostat parameter (pfactor): 10⁶-10⁷ GPa·fs² for Parrinello-Rahman method [68]
• Compressibility: System-dependent, typically 4.5×10⁻⁵ bar⁻¹ for water

Case Studies in Research

Vacuum-Deposited Organic Thin Films (NVT Application)

A recent study demonstrated the application of NVT ensemble in simulating vacuum-deposited organic amorphous thin films [13]. Researchers fabricated organic amorphous thin films by MD simulations mimicking experimental deposition processes, successfully reproducing quantitative molecular orientations observed experimentally.

Methodology:

• System: CBP and BSB-Cz molecules for organic light-emitting diodes (OLEDs)
• Simulation type: Vacuum-deposited MD simulations at experimental temperature
• Ensemble: NVT for constant temperature and fixed volume
• Analysis: Molecular orientation angle θ and order parameter S

Key Findings:

• The simulation successfully generated amorphous thin films with reasonable densities without voids
• Quantitative reproduction of experimentally obtained molecular orientations
• Horizontal molecular orientation resulted in increased hole mobility
• Demonstrated the capability to predict device-related properties at molecular level

Thermal Expansion of Solids (NPT Application)

The NPT ensemble was used to compute the coefficient of thermal expansion of fcc-Cu as a function of temperature [68]. The system was equilibrated at temperatures from 200 K to 1000 K in 100 K increments with external pressure set to 1 bar.

Methodology:

• System: fcc-Cu extended to 3×3×3 unit cells (108 atoms)
• Force field: ASAP3-EMT for computational efficiency
• Barostat: Parrinello-Rahman method with pfactor = 2×10⁶ GPa·fs²
• Simulation time: 20 ps per temperature found sufficient for equilibrium

Implementation Details:

• Temperature controlled via Nosé-Hoover thermostat
• Pressure controlled via Parrinello-Rahman barostat
• Lattice constants extracted at each temperature for thermal expansion calculation

The Scientist's Toolkit

Essential Software and Tools

Table 3: Research Reagent Solutions for Ensemble Simulations

Tool/Software	Function	Ensemble Support	Key Features
ASE (Atomic Simulation Environment) [1] [68]	Python framework for MD simulations	NVT, NPT, NVE	Multiple thermostats and barostats; extensible
GROMACS [69]	High-performance MD package	NVT, NPT, NVE	Optimized for biomolecular systems
VASP [2]	Ab initio MD simulations	NVT, NPT	First-principles accuracy; various thermostats
Libra [70]	Methodology discovery library	NVE, NVT, NPT	Multi-scale simulations; custom MD protocols
BDC2.5 mimotope 1040-31 TFA	BDC2.5 mimotope 1040-31 TFA, MF:C65H98F3N17O16S, MW:1462.6 g/mol	Chemical Reagent	Bench Chemicals
WWL229	WWL229, MF:C16H22N2O5, MW:322.36 g/mol	Chemical Reagent	Bench Chemicals

Analysis Methods and Validation

For NVT Simulations:

• Temperature stability: Monitor kinetic energy fluctuations
• Structural properties: Radial distribution functions, order parameters
• Molecular orientation: Angle distributions relative to substrate [13]

For NPT Simulations:

• Density convergence: Monitor system density over time
• Pressure stability: Check fluctuations around target pressure
• Volume changes: Track simulation box dimensions

Validation Techniques:

• Energy conservation: For NVE simulations following NPT/NVT equilibration
• Equilibrium values: Compare with experimental data (density, thermal expansion)
• Convergence tests: Ensure sufficient simulation time for property stabilization

The selection between NVT and NPT ensembles is a fundamental decision in molecular dynamics simulation design that must align with research objectives and system characteristics. The NVT ensemble is essential for vacuum simulations, fixed-volume systems, and studies where pressure is undefined or irrelevant. In contrast, the NPT ensemble is appropriate for modeling condensed phases at specific pressure conditions and investigating density-dependent phenomena.

Understanding the theoretical foundations, implementation details, and application scenarios of each ensemble enables researchers to design physically meaningful simulations. The protocols and case studies presented here provide practical guidance for implementing these ensembles in various research contexts, particularly highlighting the importance of NVT ensemble in vacuum simulations research. As molecular simulation methodologies continue to evolve, appropriate ensemble selection remains cornerstone to generating reliable, interpretable results that advance our understanding of molecular systems across scientific disciplines.

Cross-validation (CV) stands as a cornerstone technique in machine learning for evaluating model performance and mitigating overfitting. This process involves systematically splitting the available dataset into several parts, training the model on some subsets, and testing it on the remaining subset through multiple resampling iterations. The results from each validation step are averaged to produce a final performance estimate, providing a more reliable assessment of how the model will generalize to unseen data compared to a single train-test split [71]. In modern data analysis, particularly with complex data structures from technologies like imaging, wearable devices, and genomic sequencing, cross-validation has become indispensable for uncertainty quantification and statistical inference, especially when working with black-box models like deep neural networks [72].

The fundamental importance of cross-validation stems from a critical methodological principle: evaluating a predictive model on the exact same data used for training constitutes a fundamental flaw. A model that merely memorizes training labels would achieve perfect scores but fail catastrophically on new, unseen data—a phenomenon known as overfitting. Cross-validation addresses this by simulating the scenario of deploying a model to genuinely new data, thus providing a more honest assessment of its predictive capabilities [73]. For scientific research involving experimental data, particularly in fields like molecular dynamics and drug development, proper cross-validation is not merely a technical formality but an essential practice for ensuring research findings are reliable, reproducible, and translatable to real-world applications.

Theoretical Framework of Cross-Validation

Core Methodologies and Principles

The theoretical foundation of cross-validation rests on the concept of stability—the idea that reliable estimators should behave consistently under small perturbations of the data. This principle has become increasingly important in data science, influencing research on generalization error, privacy, and adaptive inference [72]. Several cross-validation methodologies have been developed, each with distinct characteristics and suitability for different research scenarios:

• K-Fold Cross-Validation: This approach splits the dataset into k equal-sized folds. The model is trained on k-1 folds and tested on the remaining fold. This process repeats k times, with each fold serving as the test set exactly once. The performance measure reported is the average of the values computed across all iterations [71]. A common choice is k=10, as lower values may increase bias, while higher values approach the computational intensity of Leave-One-Out Cross-Validation [71].

• Leave-One-Out Cross-Validation (LOOCV): This method trains the model on the entire dataset except for a single data point, which is used for testing. This process repeats for every data point in the dataset. While LOOCV benefits from using nearly all data for training (resulting in low bias), it can exhibit high variance, particularly with outliers, and becomes computationally prohibitive for large datasets [71].

• Stratified Cross-Validation: This technique ensures each fold maintains the same class distribution as the full dataset, which is particularly valuable for imbalanced datasets where some classes are underrepresented. By preserving class proportions across folds, stratified cross-validation helps classification models generalize more effectively [71].

• Holdout Validation: The simplest approach, where data is split once into training and testing sets, typically with 50-80% for training and the remainder for testing. While computationally efficient, this method may produce biased estimates if the split is not representative of the overall data distribution [71].

Table 1: Comparison of Cross-Validation Methodologies

Method	Best Use Case	Advantages	Disadvantages
K-Fold	Small to medium datasets where accurate estimation is important [71]	Lower bias than holdout; more reliable performance estimate [71]	Computationally intensive than holdout; variance depends on k [71]
LOOCV	Very small datasets where maximizing training data is critical [71]	Uses all data for training; low bias [71]	High variance with outliers; time-consuming for large datasets [71]
Stratified	Imbalanced datasets requiring preserved class distribution [71]	Better generalization for classification; maintains class proportions [71]	More complex implementation; primarily for classification tasks
Holdout	Very large datasets or when quick evaluation is needed [71]	Fast execution; simple to implement [71]	High bias if split unrepresentative; results can vary significantly [71]

Advanced Cross-Validation Considerations

The theoretical understanding of cross-validation has evolved to address challenges in modern research settings. The stability perspective formalizes how estimators should perform consistently under data perturbations, providing a framework for understanding why cross-validation works and when it might fail [72]. This is particularly relevant for black-box inference, where traditional modeling assumptions are unavailable, and estimator behavior is opaque.

In multi-source research settings, such as clinical studies combining data from different hospitals, traditional k-fold cross-validation has been shown to systematically overestimate prediction performance when the goal is generalization to new sources. Alternative approaches like leave-source-out cross-validation provide more realistic performance estimates in these scenarios, though with potentially higher variability [74]. This highlights the critical importance of aligning cross-validation design with the specific research context and deployment goals.

Cross-Validation in Molecular Dynamics and NVT Ensemble Research

Application to Neural Network Potentials and Vacuum Simulations

In molecular dynamics simulations, particularly research involving the NVT (Canonical Ensemble) ensemble and vacuum simulations, cross-validation plays a crucial role in developing and validating neural network potentials (NNPs). These potentials aim to bridge the gap between computational efficiency and quantum mechanical accuracy, enabling large-scale simulations of complex molecular systems with ab initio precision [5].

The EMFF-2025 model, a general neural network potential for high-energy materials (HEMs) containing C, H, N, and O elements, exemplifies the sophisticated application of cross-validation in this domain. This model leverages transfer learning with minimal data from density functional theory (DFT) calculations, achieving DFT-level accuracy in predicting structures, mechanical properties, and decomposition characteristics of various HEMs [5]. The validation of such models requires careful cross-validation strategies to ensure they maintain physical consistency, predictive accuracy, and extrapolation capability across structurally complex and compositionally diverse systems.

For vacuum simulations in particular, where environmental interactions are minimized to study intrinsic molecular properties, cross-validation ensures that neural network potentials can accurately capture fundamental physicochemical processes without overfitting to specific molecular configurations or trajectories. This is essential for reliable predictions of material behavior under extreme conditions, such as high-temperature decomposition pathways [5].

Protocol: Cross-Validation Framework for Neural Network Potentials

Application Context: Validating neural network potentials for molecular dynamics simulations in NVT ensemble and vacuum environments.

Materials and Computational Resources:

• Quantum chemistry software (e.g., Gaussian, VASP) for reference calculations [5]
• Deep Potential Generator (DP-GEN) framework for automated training of neural network potentials [5]
• Molecular dynamics simulation packages (e.g., LAMMPS, GROMACS) with neural network potential support
• High-performance computing resources for parallel processing of multiple cross-validation folds

Procedure:

• Reference Data Generation: Perform DFT calculations across diverse molecular configurations, including variations in bond lengths, angles, and torsion angles relevant to vacuum simulation conditions [5].

• Training-Validation Split: Implement stratified k-fold cross-validation (k=5-10) based on molecular similarity metrics to ensure each fold represents the chemical diversity of the entire dataset [71].

• Model Training: For each training fold, utilize the Deep Potential scheme with embedding and fitting networks to learn atomic interactions. Employ early stopping based on validation fold performance to prevent overfitting [5].

• Performance Metrics: Evaluate each model on the corresponding test fold using:

  • Mean Absolute Error (MAE) for energies (target: <0.1 eV/atom) [5]
  • MAE for forces (target: <2 eV/Ã…) [5]
  • Prediction accuracy for material properties (e.g., lattice parameters, elastic constants)

• Transfer Learning Integration: For systems with limited data, implement transfer learning from pre-trained models (e.g., DP-CHNO-2024) followed by fine-tuning with cross-validation to assess generalization capability [5].

• Statistical Consolidation: Compute mean and standard deviation of all performance metrics across folds to obtain final performance estimates with confidence intervals [73].

Validation Considerations:

• Ensure representative sampling of potential energy surface (PES) including transition states and high-energy configurations
• Test extrapolation capability to molecular sizes and types not included in training
• Validate against experimental data where available for ultimate performance verification

Quantitative Data Analysis and Performance Metrics

Performance Evaluation of ML Potentials

The rigorous validation of machine learning potentials requires comprehensive quantitative assessment across multiple metrics. The EMFF-2025 model demonstrates the performance standards achievable with proper cross-validation, reporting mean absolute errors for energy predictions predominantly within ±0.1 eV/atom and force errors mainly within ±2 eV/Å across 20 different high-energy materials [5]. These metrics are essential for ensuring the reliability of subsequent molecular dynamics simulations.

Table 2: Cross-Validation Performance Metrics for Molecular Dynamics NNPs

Validation Metric	Target Performance	Application in NVT/Vacuum Simulations	Interpretation
Energy MAE	<0.1 eV/atom [5]	Predicts stability, reaction energies, and thermodynamic properties	Higher errors indicate poor description of potential energy surface
Force MAE	<2 eV/Ã… [5]	Determines accuracy of interatomic forces for trajectory reliability	Critical for faithful dynamics and equilibrium properties
Configuration Prediction	Close alignment with DFT/experimental structures [5]	Validates lattice parameters, bond lengths, and molecular geometries	Essential for transferability to diverse molecular systems
Decomposition Pathways	Reproduction of known mechanisms [5]	Tests predictive capability for chemical reactivity in vacuum	Validates model for studying reaction kinetics
Generalization Error	<10% performance degradation on novel systems [5]	Measures extrapolation capability to unseen molecular structures	Indicates robustness beyond training set

Cross-Validation Results and Statistical Analysis

Properly implemented cross-validation provides not just point estimates of model performance but also valuable information about performance variability and model stability. The k-fold cross-validation approach, when applied with k=5 or k=10, yields multiple performance measurements that can be analyzed statistically [73]. For example, a well-implemented cross-validation of a support vector machine classifier on the Iris dataset might produce accuracy scores of [0.96, 1.00, 0.96, 0.96, 1.00] across folds, with a mean of 0.98 and standard deviation of 0.02 [73]. This provides both a performance estimate and information about its reliability.

In molecular dynamics applications, these statistical analyses become particularly important when evaluating the consistency of potential energy surface representations across different molecular configurations and the transferability of neural network potentials to novel chemical environments. The standard deviation of performance metrics across cross-validation folds offers valuable insights into model robustness, with higher variability indicating potential weaknesses in certain regions of the chemical space or molecular configuration space.

Implementation Protocols and Workflows

Experimental Protocol: K-Fold Cross-Validation for Material Property Prediction

Research Context: Predicting mechanical properties and thermal decomposition behavior of high-energy materials using neural network potentials.

Materials and Software Requirements:

• Deep Potential (DP) framework or similar neural network potential infrastructure [5]
• DFT calculation software for reference data generation [5]
• Python environment with scikit-learn for cross-validation implementation [73]
• Molecular visualization software for structural analysis

Step-by-Step Procedure:

• Dataset Preparation:
  • Collect diverse molecular configurations representing relevant chemical space
  • Compute reference energies and forces using DFT methods
  • Apply standardization to input features (e.g., z-score normalization)

• Cross-Validation Setup:

  • Initialize k-fold split (k=5-10) with stratification by material class
  • Ensure temporal segregation if dealing with time-series MD data
  • Implement scikit-learn KFold or StratifiedKFold classes [73]

• Training Loop:

• Model Evaluation:

  • Calculate mean and standard deviation of performance metrics across folds
  • Analyze consistency of predictions across different test splits
  • Identify materials or configurations with systematically poor performance

• Hyperparameter Optimization:

  • Implement nested cross-validation for hyperparameter tuning
  • Use grid search or random search within training folds
  • Validate optimal parameters on held-out test folds

• Final Model Assessment:

  • Train final model on complete dataset using optimized parameters
  • Evaluate on completely external test set if available
  • Perform ablation studies to assess contribution of different model components

Visualization: Cross-Validation Workflow for Molecular Dynamics NNPs

The following workflow diagram illustrates the comprehensive cross-validation process for neural network potentials in molecular dynamics research:

Workflow Diagram Title: CV for Molecular Dynamics NNPs

Visualization: K-Fold Cross-Validation Schematic

The fundamental concept of k-fold cross-validation is visualized in the following diagram:

Diagram Title: K-Fold Cross-Validation Process

Research Reagent Solutions and Computational Materials

Table 3: Essential Research Tools for Cross-Validation in Molecular Simulations

Tool/Category	Specific Examples	Function in Research	Implementation Considerations
Neural Network Potential Frameworks	Deep Potential (DP), ANI-nr, NNRF [5]	Provides atomic-scale descriptions of complex reactions with DFT-level accuracy [5]	Compatibility with MD packages; transfer learning capabilities [5]
Cross-Validation Libraries	scikit-learn crossvalscore, KFold, StratifiedKFold [73]	Implements various CV strategies; calculates performance metrics [73]	Integration with custom models; support for multi-metric evaluation [73]
Reference Quantum Chemistry Software	VASP, Gaussian, Quantum ESPRESSO [5]	Generates accurate training data for neural network potentials [5]	Computational cost; accuracy vs. efficiency tradeoffs [5]
Molecular Dynamics Packages	LAMMPS, GROMACS, AMBER with NNP support	Runs simulations using trained potentials; validates predictive performance	Support for NVT ensemble; vacuum simulation capabilities
Performance Monitoring Tools	TensorBoard, Weights & Biases, custom metrics tracking	Tracks training and validation metrics across CV folds; visualizes learning curves	Real-time monitoring; comparison across different model versions

Cross-validation represents an indispensable methodology in the intersection of machine learning and molecular simulations, particularly for research involving NVT ensemble applications and vacuum simulations. The theoretical framework of cross-validation, when properly implemented with consideration for stability and data structure, provides robust assessment of model generalization capability [72]. For neural network potentials in molecular dynamics, rigorous cross-validation is not merely a performance measurement exercise but a fundamental requirement for ensuring predictive reliability across diverse chemical spaces and molecular configurations [5].

The protocols and applications detailed in this work highlight the critical importance of aligning cross-validation design with research objectives, whether through standard k-fold approaches for homogeneous data or more specialized methods like leave-source-out cross-validation for multi-source datasets [74]. By adhering to these methodologies and maintaining rigorous performance standards—such as energy errors below 0.1 eV/atom and force errors below 2 eV/Å [5]—researchers can develop neural network potentials with demonstrated reliability for predicting material properties, reaction mechanisms, and dynamic behavior in vacuum environments.

As the field advances, integrating cross-validation throughout the model development pipeline—from initial architecture design through final deployment—will remain essential for producing molecular simulation tools that are not just computationally efficient but truly predictive and transferable to novel chemical systems. This rigorous approach to model validation ultimately accelerates materials discovery and drug development by providing reliable in silico predictions that faithfully represent underlying physicochemical principles.

Leveraging Machine Learning Datasets for Enhanced Validation and Force Field Refinement

The development of accurate and reliable machine learning force fields (MLFFs) represents a paradigm shift in computational materials science and drug discovery. These models promise to deliver quantum-level accuracy in molecular simulations while achieving the computational efficiency necessary to access biologically and technologically relevant time and length scales [75]. For researchers utilizing the NVT ensemble, particularly in vacuum simulations relevant to gas-phase molecular studies or initial compound screening, the emergence of large-scale, high-quality datasets provides unprecedented opportunities for force field refinement and robust validation. This application note details contemporary datasets, validation frameworks, and practical protocols for integrating these resources to enhance the reliability of MLFFs in NVT ensemble applications.

Foundational MLFF Concepts and the NVT Ensemble

Machine Learning Force Fields are computational models that learn the mapping between atomic configurations and interatomic forces or energies from quantum mechanical reference data [75]. Unlike classical force fields with fixed functional forms, MLFFs utilize machine learning to capture complex, multi-body interactions, enabling them to approximate quantum mechanical potential energy surfaces with high fidelity.

Within this framework, the NVT (constant Number of particles, Volume, and Temperature) ensemble is crucial for studying molecular systems at equilibrium under specific thermal conditions. It allows researchers to investigate finite-temperature properties, conformational dynamics, and thermal stability without the complexities of fluctuating volume or pressure. The integration of MLFFs with NVT simulations enables more accurate modeling of molecular behavior, from small drug-like molecules in vacuum to complex biomolecular interactions, by providing a more realistic and data-driven description of the underlying atomic forces.

Current Landscape of Machine Learning Datasets

The accuracy and transferability of MLFFs are fundamentally constrained by the quality, breadth, and diversity of their training data. Recent years have witnessed the release of several monumental datasets that dramatically expand the frontiers of chemical space available for force field training.

Table 1: Major Machine Learning Datasets for Force Field Development

Dataset Name	Size (Calculations)	Elements Covered	Key Features	Level of Theory	Relevance to NVT/Vacuum
Open Molecules 2025 (OMol25) [76] [77] [78]	>100 million	83 elements	Unprecedented chemical diversity, includes small molecules, biomolecules, metal complexes, and electrolytes; systems up to 350 atoms.	ωB97M-V/def2-TZVPD	High (explicit gas-phase and vacuum structures)
MP-ALOE [79]	~1 million	89 elements	Focus on off-equilibrium structures via active learning; broad sampling of forces and pressures.	r2SCAN meta-GGA	Moderate (provides diverse configurational sampling)
EMFF-2025 Training Data [5]	Not Specified	C, H, N, O	Specialized for high-energy materials (HEMs); enables development of targeted potentials.	DFT	High (for specific molecular classes in vacuum)

These datasets address critical limitations of earlier efforts, which were often restricted in size, chemical diversity, and accuracy [78]. The OMol25 dataset, in particular, is transformative. Costing over six billion CPU hours to generate, it blends elemental, chemical, and structural diversity, including explicit solvation, variable charge and spin states, conformers, and reactive structures [76] [77]. For researchers employing vacuum NVT simulations, the dataset's extensive coverage of isolated molecular systems and its high-level ωB97M-V theory calculations provide an ideal foundation for training generalizable MLFFs.

Validation Frameworks and the "Reality Gap"

Robust validation is paramount, as performance on standard quantum chemistry benchmarks does not guarantee accuracy in real-world simulations. A significant "reality gap" has been identified, where models excelling in computational benchmarks may fail when confronted with experimental complexity [80].

The UniFFBench Framework

The UniFFBench framework establishes essential experimental validation standards by evaluating MLFFs against a curated dataset of approximately 1,500 mineral structures. Its evaluations extend beyond energy and force errors to critical aspects for practical application [80]:

• MD Simulation Stability: Tests whether simulations remain physically stable over meaningful timescales.
• Structural Accuracy: Compares predicted densities and lattice parameters against experimental values.
• Mechanical Properties: Validates predictions of elastic tensors and other mechanical responses.

Fused Data Learning Strategy

Another powerful approach fuses traditional bottom-up learning (from DFT data) with top-down learning (from experimental data). This method concurrently optimizes an MLFF to reproduce both DFT-derived energies/forces and experimentally measured properties, such as temperature-dependent elastic constants and lattice parameters [81]. This strategy can correct for known inaccuracies in the underlying DFT functionals, resulting in a molecular model of higher overall accuracy.

Experimental Protocols for Validation and Refinement

This section provides detailed methodologies for key validation and refinement experiments relevant to the NVT ensemble.

Protocol: Fused Data Training for Force Field Refinement

Objective: To refine a pre-trained MLFF by incorporating both ab initio data and experimental observables, enhancing its physical accuracy and transferability. Application: Correcting systematic errors in DFT-derived force fields for more reliable NVT molecular dynamics simulations.

Workflow:

• Initialization: Start with a model pre-trained on a broad DFT dataset (e.g., a model pre-trained on OMol25 or other foundational data).
• DFT Training Step: For one epoch, perform batch optimization on a targeted DFT database. The loss function is: L_DFT = w_E * MSE(E_pred, E_DFT) + w_F * MSE(F_pred, F_DFT) + w_V * MSE(V_pred, V_DFT) where E, F, and V are energy, forces, and virial stress, respectively [81].
• Experimental Training Step: For one epoch, optimize parameters to match experimental observables.
  • Simulation: Run an NVT simulation using the current force field.
  • Gradient Calculation: Use methods like Differentiable Trajectory Reweighting (DiffTRe) to compute gradients of the experimental loss without backpropagating through the entire MD trajectory [81].
  • Loss Function: L_EXP = MSE(C_elast_pred(T), C_elast_exp(T)) + MSE(P_pred(T), 0) where C_elast are elastic constants and the pressure target is zero to match experimental lattice constants at a given temperature T [81].
• Iteration: Alternate between the DFT and Experimental trainers for a fixed number of epochs, selecting the final model via early stopping.

Protocol: Fine-Tuning a Universal MLIP for Specific Applications

Objective: To adapt a universal, pre-trained MLIP (e.g., SevenNet, MACE) for accurate simulations of a specific molecular class (e.g., electrolytes, organic molecules in vacuum) with minimal computational cost. Application: Rapid development of specialized, high-accuracy force fields for targeted NVT ensemble studies from a general-purpose foundation model.

Workflow:

• Model and Data Selection:
  • Base Model: Select a pre-trained universal model (e.g., SevenNet-0, UMA).
  • Target Data: Prepare a small dataset (hundreds to thousands of structures) specific to the application. This can be new DFT calculations or configurations extracted from short, ab initio NVT MD simulations of your system of interest.
• Fine-Tuning: Continue training the pre-trained model on the targeted dataset.
  • Use a significantly lower learning rate than that used for initial training.
  • Freeze early layers of the network if the dataset is very small to prevent overfitting.
  • The loss function typically focuses on forces and energies: L = MSE(F_pred, F_target) + w * MSE(E_pred, E_target).
• Validation: Validate the fine-tuned model against held-out DFT data and, if available, key experimental properties (e.g., density, radial distribution functions) to ensure improved performance over the base model without loss of general physical soundness [82].

The Scientist's Toolkit: Essential Research Reagents

Table 2: Key Computational Tools and Resources for MLFF Development

Resource Name	Type	Function/Benefit
OMol25 Dataset [76] [77]	Training Dataset	Provides a massive, chemically diverse foundation for training or benchmarking new MLFFs.
Universal Models (UMA, SevenNet) [78] [82]	Pre-trained MLFF	Offer "out-of-the-box" inference capability; a strong starting point for fine-tuning.
UniFFBench Framework [80]	Benchmarking Tool	Systematically evaluates MLFF performance against experimental data to identify failure modes.
DiffTRe Method [81]	Algorithm	Enables efficient gradient-based training of MLFFs directly against experimental observables.
Active Learning (e.g., DP-GEN) [5]	Strategy	Intelligently selects new configurations for DFT calculations to improve MLFF robustness and data efficiency.
ZSA-215	ZSA-215, MF:C14H14FNO5S, MW:327.33 g/mol	Chemical Reagent
CP-346086	CP-346086, MF:C26H22F3N5O, MW:477.5 g/mol	Chemical Reagent

The synergy between large-scale datasets like OMol25, robust validation frameworks like UniFFBench, and advanced training protocols such as fused data learning and fine-tuning is transforming the landscape of force field development. For researchers focused on NVT ensemble applications, these resources provide a structured pathway to move beyond force fields that merely perform well on benchmarks to those that are reliably accurate for predictive scientific discovery. By systematically leveraging these tools, scientists can develop highly refined force fields capable of modeling molecular interactions with unprecedented fidelity, accelerating progress in fields from drug development to materials design.

Conclusion

The NVT ensemble is an indispensable tool for vacuum simulations in biomedical research, providing a controlled environment to study system behavior at constant volume and temperature. Its foundational role in equilibration, combined with robust methodological protocols for studying drug-membrane interactions and material properties, makes it a cornerstone of computational chemistry. Effective troubleshooting of common issues like negative pressure and thermalization failures is paramount for obtaining reliable data. Furthermore, rigorous validation through metric monitoring and comparative analysis with other ensembles ensures the physical realism of simulations. Future directions should focus on integrating these simulations with machine learning frameworks and high-performance computing to accelerate predictive drug discovery and the rational design of novel therapeutics, ultimately bridging the gap between in silico modeling and clinical application.

References

• 1. Canonical (NVT) ensemble — Atomistic Simulation Tutorial [https://docs.matlantis.com/atomistic-simulation-tutorial/en/6_2_md-nvt.html]
• 2. NVT ensemble - VASP Wiki [https://www.vasp.at/wiki/NVT_ensemble]
• 3. Terminology - GROMACS 2025.4 documentation [https://manual.gromacs.org/documentation/current/user-guide/terminology.html]
• 4. Molecular Dynamics - QuantumATK [https://docs.quantumatk.com/manual/technicalnotes/molecular_dynamics/molecular_dynamics.html]
• 5. EMFF-2025: a general neural network potential for ... [https://www.nature.com/articles/s41524-025-01809-w]
• 6. Thermostats - Molecular Dynamics - WordPress.com [https://hypermd.wordpress.com/molecular-simulations/linear-motion/thermostat/]
• 7. Langevin vs Nosé–Hoover thermostat [https://mattermodeling.stackexchange.com/questions/9374/langevin-vs-nos%C3%A9-hoover-thermostat]
• 8. Langevin dynamics [https://en.wikipedia.org/wiki/Langevin_dynamics]
• 9. Equilibrating Surface Temperature Through NVT Ensemble ... [https://mattermodeling.stackexchange.com/questions/12326/equilibrating-surface-temperature-through-nvt-ensemble-ab-initio-molecular-dynam]
• 10. Liquid-vapor tension | MD Simulation Techniques and ... [https://sites.psu.edu/simtech/liquid-vapor-tension/2/]
• 11. Plain MD Protocol [https://docs.openfree.energy/en/stable/guide/protocols/plainmd.html]
• 12. Molecular dynamics parameters (.mdp options) [https://manual.gromacs.org/nightly/user-guide/mdp-options.html]
• 13. Predictions of molecular orientation and charge mobility in ... [https://www.nature.com/articles/s43246-025-00841-z]
• 14. Molecular Dynamics Simulation of Nano-Defects on Fused ... [https://pmc.ncbi.nlm.nih.gov/articles/PMC12388477/]
• 15. Multi-scale simulation for atomic oxygen erosion in low ... [https://www.sciencedirect.com/science/article/pii/S1000936125005084]
• 16. Atomistic molecular dynamics simulations of the tensile ... [https://www.sciencedirect.com/science/article/pii/S0927025625002095]
• 17. How to fix negative pressure? - GROMACS forums [https://gromacs.bioexcel.eu/t/how-to-fix-negative-pressure/3622]
• 18. Implementing reactivity in molecular dynamics simulations ... [https://www.nature.com/articles/s41467-024-50793-0]
• 19. NVT Equilibration problem with interface system [https://gromacs.bioexcel.eu/t/nvt-equilibration-problem-with-interface-system/11946]
• 20. Re: [AMBER] Holes/bubbles in water during NVT (fix atoms) [http://archive.ambermd.org/201703/0001.html]
• 21. Exploring the temperature stability of CRISPR-Cas12b using... [https://pubs.rsc.org/en/content/articlehtml/2025/me/d5me00140d]
• 22. Mutational Analysis of Neuropeptide Y Reveals Unusual Thermal ... [https://pmc.ncbi.nlm.nih.gov/articles/PMC5876621/]
• 23. Molecular Dynamics Simulation of the p53 N-terminal peptide [https://www.bonvinlab.org/education/molmod/simulation/]
• 24. Ensembles — OldReaxFF 2025.1 documentation - SCM [https://www.scm.com/doc/OldReaxFF/Ensembles.html]
• 25. Ab Initio Accuracy Neural Network Potential for Drug-Like ... [https://pmc.ncbi.nlm.nih.gov/articles/PMC12377527/]
• 26. GROMACS Wizard - Step 3: NVT Equilibration [https://documentation.samson-connect.net/tutorials/gromacs-wizard/nvt-equilibration/]
• 27. Structure based drug design and machine learning ... [https://www.nature.com/articles/s41598-025-17708-5]
• 28. Virtual screening and molecular dynamics simulations ... [https://www.sciencedirect.com/science/article/pii/S1570180825001617]
• 29. Sampling different configuration from NVT ensemble [https://gromacs.bioexcel.eu/t/sampling-different-configuration-from-nvt-ensemble/4029]
• 30. Comprehensive evaluation of potential EBOV inhibitors using ... [https://fjps.springeropen.com/articles/10.1186/s43094-025-00902-7]
• 31. Molecular basis for the increased fusion activity of the ... [https://www.sciencedirect.com/science/article/pii/S221112472500292X]
• 32. Regulation of Ebola GP conformation and membrane binding ... [https://journals.plos.org/plospathogens/article?id=10.1371/journal.ppat.1011848]
• 33. Organic solvent permeation through HKUST-1 MOF ... [https://www.sciencedirect.com/science/article/pii/S0376738825006416]
• 34. From Diarylsulfides to Diarylamines: New Ebola Virus Entry ... [https://pmc.ncbi.nlm.nih.gov/articles/PMC12169679/]
• 35. Identification of promising anti-EBOV inhibitors: de novo drug ... [https://pmc.ncbi.nlm.nih.gov/articles/PMC9515638/]
• 36. Computer simulations of protein–membrane systems - PMC [https://pmc.ncbi.nlm.nih.gov/articles/PMC7109768/]
• 37. Qualitative Estimation of Protein–Ligand Complex Stability ... [https://pmc.ncbi.nlm.nih.gov/articles/PMC9709921/]
• 38. MD Simulation of Protein-Ligand Interaction [https://pmc.ncbi.nlm.nih.gov/articles/PMC1302723/]
• 39. Toward Simple, Predictive Understanding of Protein ... [https://www.nature.com/articles/s41598-020-65984-0]
• 40. Conformational switch upon substrate binding informs the ... [https://www.nature.com/articles/s41598-025-19623-1]
• 41. An accurate correction scheme for electrostatic finite-size effects [https://pmc.ncbi.nlm.nih.gov/articles/PMC3838431/]
• 42. A Study on the Effects of Vacuum, Nitrogen, and Air Heat ... [https://www.mdpi.com/1999-4907/15/9/1613]
• 43. Molecular dynamics study on mechanical properties of ... [https://bioresources.cnr.ncsu.edu/resources/molecular-dynamics-study-on-mechanical-properties-of-cellulose-with-air-nitrogen-diffusion-behavior/]
• 44. Effect of vacuum and heat treatment on a single chain of ... [https://bioresources.cnr.ncsu.edu/resources/effect-of-vacuum-and-heat-treatment-on-a-single-chain-of-cellulose-molecular-dynamics-simulation/]
• 45. Chemical and molecular structure transformations in ... [https://www.nature.com/articles/s41529-022-00224-6]
• 46. MISATO: machine learning dataset of protein–ligand ... [https://www.nature.com/articles/s43588-024-00627-2]
• 47. Molecular dynamics simulations reveal internal tension in ... [https://arxiv.org/html/2511.14261v1]
• 48. Ultrafast molecular dynamics approach to quantify structural ... [https://pubs.rsc.org/en/content/articlehtml/2025/ra/d5ra05434f]
• 49. Quantum-Centric Alchemical Free Energy Calculations [https://arxiv.org/html/2506.20825v1]
• 50. Molecular Dynamics - GROMACS 2025.4 documentation [https://manual.gromacs.org/documentation/current/reference-manual/algorithms/molecular-dynamics.html]
• 51. leveraging AI-agents for customized research workflows [https://pubs.rsc.org/en/content/articlehtml/2025/me/d5me00062a]
• 52. AlphaFold prediction of structural ensembles of disordered ... [https://pmc.ncbi.nlm.nih.gov/articles/PMC11829000/]
• 53. Ensembles and time integration [https://kthpanor.github.io/echem/docs/mol_struct/md_setup.html]
• 54. 9.8.3 Thermostats: Sampling the NVT Ensemble [https://manual.q-chem.com/5.3/subsec_Thermostats.html]
• 55. md.methods.thermostats - HOOMD-blue 4.0.1 documentation [https://hoomd-blue.readthedocs.io/en/v4.0.1/module-md-methods-thermostats.html]
• 56. Dynamics - Ensembles [https://www.uoxray.uoregon.edu/local/manuals/biosym/discovery/General/Dynamics/Ensembles.html]
• 57. — GPUMD documentation Ensembles [https://gpumd.org/theory/ensembles.html]
• 58. statistical thermodynamics - Which ensemble to use for a molecular... [https://mattermodeling.stackexchange.com/questions/4252/which-ensemble-to-use-for-a-molecular-dynamics-simulation]
• 59. Generation of Non-bonded Interactions [https://www.charmm-gui.org/charmmdoc/nbonds.html]
• 60. Molecular Dynamics: Ensembles [https://www.compchems.com/molecular-dynamics-ensembles/]
• 61. A Transferable Coarse Grain Non-bonded Interaction Model ... [https://pmc.ncbi.nlm.nih.gov/articles/PMC2725330/]
• 62. Molecular dynamics parameters (.mdp options) [https://manual.gromacs.org/2019/user-guide/mdp-options.html]
• 63. Vacuum Stability [https://www.nasa.gov/centers-and-facilities/white-sands/vacuum-stability/]
• 64. High-vacuum measuring system for accurate ... [https://www.sciencedirect.com/science/article/pii/S1359431125022070]
• 65. Thermal Vacuum Testing at Thermal Space [https://thermal-space.com/thermal-vac/]
• 66. Spatial correlation of desorption events accelerates water ... [https://pubs.rsc.org/en/content/articlehtml/2025/sc/d4sc06967f]
• 67. DFT study of hydrogen bonding between metal hydroxides ... [https://www.sciencedirect.com/science/article/pii/S0301010422000945]
• 68. NPT ensemble — Atomistic Simulation Tutorial [https://docs.matlantis.com/atomistic-simulation-tutorial/en/6_3_md-npt.html]
• 69. Vacuum Simulations - User discussions - GROMACS forums [https://gromacs.bioexcel.eu/t/vacuum-simulations/373]
• 70. Classical Molecular Dynamics Tutorial - Libra [https://quantum-dynamics-hub.github.io/libra/tutorials/tutorial_md/tut.html]
• 71. Cross Validation in Machine Learning [https://www.geeksforgeeks.org/machine-learning/cross-validation-machine-learning/]
• 72. A Modern Theory of Cross-Validation through the Lens ... [https://arxiv.org/abs/2505.23592]
• 73. 3.1. Cross-validation: evaluating estimator performance [https://scikit-learn.org/stable/modules/cross_validation.html]
• 74. Empirical investigation of multi-source cross-validation in ... [https://www.sciencedirect.com/science/article/pii/S0010482524013568]
• 75. Machine Learning Force Fields [https://www.emergentmind.com/topics/machine-learning-force-fields]
• 76. [2505.08762] The Open Molecules 2025 (OMol25) Dataset, ... [https://arxiv.org/abs/2505.08762]
• 77. A Record-Breaking Dataset to Train AI Models has Launched [https://newscenter.lbl.gov/2025/05/14/computational-chemistry-unlocked-a-record-breaking-dataset-to-train-ai-models-has-launched/]
• 78. Exploring Meta's Open Molecules 2025 (OMol25) & Universal ... [https://www.rowansci.com/blog/exploring-open-molecules-2025]
• 79. MP-ALOE: an r2SCAN dataset for universal machine ... [https://www.nature.com/articles/s41524-025-01834-9]
• 80. Evaluating Universal Machine Learning Force Fields ... [https://arxiv.org/html/2508.05762v1]
• 81. Accurate machine learning force fields via experimental ... [https://www.nature.com/articles/s41524-024-01251-4]
• 82. Application of pretrained universal machine-learning ... [https://pubs.rsc.org/en/content/articlehtml/2025/dd/d5dd00025d]