ReaxFF molecular dynamics of graphene oxide/NaCl aqueous solution interfaces

In this work, the interaction of NaCl aqueous solution with graphene (G), graphene oxide (GO), and graphite oxide (GTO) is studied using the ReaxFF module of Amsterdam Modeling Suite (AMS) software. We consider four models using the NaCl aqueous solution, containing a graphene sheet (G), a single sheet of GO with epoxide and hydroxyl groups on its surface, 4 layers of GO to model GTO, and a bulk NaCl solution as a reference. The structural and dynamical properties of G, GO, and GTO were quantified by analyzing the functional groups, radial distribution functions, density profiles and diffusivities of water and ions. Due to the reactive force field, the systems underwent spontaneous modification of surface functional groups during the first 750 ps after which the structure stabilizes (the energy stabilizes in less than 400 ps). Pristine graphene in contact with the NaCl solution formed hydroxyl groups on the edges, i.e., converted to partially reduced graphene oxide. The epoxy groups (Oe) on the initial GO were rather unstable, leading to a reduction of their number, however, there was an increase in the number of hydroxyl groups (Oh), mainly at the edges. The interactions of NaCl with the carbon-based sheets are rather weak, including GO and GTO which are decorated with numerous functional groups. Diffusion coefficients of water agree with the available data, but discrepancies in Na+ and Cl- diffusivity compared to other references underscore the need for further development in the dynamic parameters of the reactive force field used. In essence, our research provides specific data previously unreported, laying a foundation for advancing water desalination system design. The study's novelty lies in its realistic approach to graphene/graphene oxide modification, comprehensive characterization, and the application of the reactive force field to explore the graphene oxide-NaCl aqueous interface, contributing to the development of a practical membrane system for water desalination.

Semi-Empirical Shadow Molecular Dynamics: A PyTorch Implementation

Extended Lagrangian Born-Oppenheimer molecular dynamics (XL-BOMD) in its most recent shadow potential energy version has been implemented in the semiempirical PyTorch-based software PySeQM. The implementation includes finite electronic temperatures, canonical density matrix perturbation theory, and an adaptive Krylov subspace approximation for the integration of the electronic equations of motion within the XL-BOMB approach (KSA-XL-BOMD). The PyTorch implementation leverages the use of GPU and machine learning hardware accelerators for the simulations. The new XL-BOMD formulation allows studying more challenging chemical systems with charge instabilities and low electronic energy gaps. The current public release of PySeQM continues our development of modular architecture for large-scale simulations employing semi-empirical quantum-mechanical treatment. Applied to molecular dynamics, simulation of 840 carbon atoms, one integration time step executes in 4 s on a single Nvidia RTX A6000 GPU.

Shadow energy functionals and potentials in Born-Oppenheimer molecular dynamics

In Born-Oppenheimer molecular dynamics (BOMD) simulations based on the density functional theory (DFT), the potential energy and the interatomic forces are calculated from an electronic ground state density that is determined by an iterative self-consistent field optimization procedure, which, in practice, never is fully converged. The calculated energies and forces are, therefore, only approximate, which may lead to an unphysical energy drift and instabilities. Here, we discuss an alternative shadow BOMD approach that is based on backward error analysis. Instead of calculating approximate solutions for an underlying exact regular Born-Oppenheimer potential, we do the opposite. Instead, we calculate the exact electron density, energies, and forces, but for an underlying approximate shadow Born-Oppenheimer potential energy surface. In this way, the calculated forces are conservative with respect to the approximate shadow potential and generate accurate molecular trajectories with long-term energy stabilities. We show how such shadow Born-Oppenheimer potentials can be constructed at different levels of accuracy as a function of the integration time step, δt, from the constrained minimization of a sequence of systematically improvable, but approximate, shadow energy density functionals. For each energy functional, there is a corresponding ground state Born-Oppenheimer potential. These pairs of shadow energy functionals and potentials are higher-level generalizations of the original "zeroth-level" shadow energy functionals and potentials used in extended Lagrangian BOMD [Niklasson, Eur. Phys. J. B 94, 164 (2021)]. The proposed shadow energy functionals and potentials are useful only within this extended dynamical framework, where also the electronic degrees of freedom are propagated as dynamical field variables together with the atomic positions and velocities. The theory is quite general and can be applied to MD simulations using approximate DFT, Hartree-Fock, or semi-empirical methods, as well as to coarse-grained flexible charge models.

M-Chem: a Modular Software Package for Molecular Simulation that Spans Scientific Domains

We present a new software package called M-Chem that is designed from scratch in C++ and parallelized on shared-memory multi-core architectures to facilitate efficient molecular simulations. Currently, M-Chem is a fast molecular dynamics (MD) engine that supports the evaluation of energies and forces from two-body to many-body all-atom potentials, reactive force fields, coarse-grained models, combined quantum mechanics molecular mechanics (QM/MM) models, and external force drivers from machine learning, augmented by algorithms that are focused on gains in computational simulation times. M-Chem also includes a range of standard simulation capabilities including thermostats, barostats, multi-timestepping, and periodic cells, as well as newer methods such as fast extended Lagrangians and high quality electrostatic potential generation. At present M-Chem is a developer friendly environment in which we encourage new software contributors from diverse fields to build their algorithms, models, and methods in our modular framework. The long-term objective of M-Chem is to create an interdisciplinary platform for computational methods with applications ranging from biomolecular simulations, reactive chemistry, to materials research.

Using atomic charges to model molecular polarization

We review different models for introducing electric polarization in force fields, with special focus on methods where polarization is modelled at the atomic charge level. While electric polarization has been included in several force fields, the common approach has been to focus on atomic dipole polarizability. Several approaches allow modelling electric polarization by using charge-flow between charge sites instead, but this has been less exploited, despite that atomic charges and charge-flow is expected to be more important than atomic dipoles and dipole polarizability. A number of challenges are required to be solved for charge-flow models to be incorporated into polarizable force fields, for example how to parameterize the models and how to make them computational efficient.

Water in an External Electric Field: Comparing Charge Distribution Methods Using ReaxFF Simulations

The growing interest in the effects of external electric fields on reactive processes requires predictive methods that can reach longer length and time scales than quantum mechanical simulations. Recently, many studies have included electric fields in ReaxFF, a widely used reactive molecular dynamics method. In the case of modeling an external electric field, the charge distribution method used in ReaxFF is critical. The most common charge distribution method used in previous studies of electric fields is the charge equilibration (QEq) method, which assumes that the system is a contiguous conductor and that charge transfer can occur across any distance. In contrast, many systems of interest are insulators or semiconductors, and long-distance charge transfer should not occur in response to a small difference in potential. This study focuses on the limitations of the QEq method in the context of water in an external electric field. We demonstrate that QEq can predict unphysical charge distributions and exhibits properties that do not converge as a function of system size. Furthermore, we show that electric fields within the recently developed atom-condensed Kohn-Sham density functional theory (DFT) approximated to the second-order (ACKS2) approach address the major limitations of electric fields in QEq. With ACKS2, we observe more physical charge distributions and properties that converge as a function of system size. We do not suggest that ACKS2 is perfect in all circumstances but rather show specific cases where it addresses the major shortcomings of QEq in the context of an external electric field.

Quantum-Based Molecular Dynamics Simulations Using Tensor Cores

Tensor cores, along with tensor processing units, represent a new form of hardware acceleration specifically designed for deep neural network calculations in artificial intelligence applications. Tensor cores provide extraordinary computational speed and energy efficiency but with the caveat that they were designed for tensor contractions (matrix-matrix multiplications) using only low-precision floating-point operations. Despite this perceived limitation, we demonstrate how tensor cores can be applied with high efficiency to the challenging and numerically sensitive problem of quantum-based Born-Oppenheimer molecular dynamics, which requires highly accurate electronic structure optimizations and conservative force evaluations. The interatomic forces are calculated on-the-fly from an electronic structure that is obtained from a generalized deep neural network, where the computational structure naturally takes advantage of the exceptional processing power of the tensor cores and allows for high performance in excess of 100 Tflops on a single Nvidia A100 GPU. Stable molecular dynamics trajectories are generated using the framework of extended Lagrangian Born-Oppenheimer molecular dynamics, which combines computational efficiency with long-term stability, even when using approximate charge relaxations and force evaluations that are limited in accuracy by the numerically noisy conditions caused by the low-precision tensor core floating-point operations. A canonical ensemble simulation scheme is also presented, where the additional numerical noise in the calculated forces is absorbed into a Langevin-like dynamics.

Recent Advances for Improving the Accuracy, Transferability, and Efficiency of Reactive Force Fields

Reactive force fields provide an affordable model for simulating chemical reactions at a fraction of the cost of quantum mechanical approaches. However, classically accounting for chemical reactivity often comes at the expense of accuracy and transferability, while computational cost is still large relative to nonreactive force fields. In this Perspective, we summarize recent efforts for improving the performance of reactive force fields in these three areas with a focus on the ReaxFF theoretical model. To improve accuracy, we describe recent reformulations of charge equilibration schemes to overcome unphysical long-range charge transfer, new ReaxFF models that account for explicit electrons, and corrections for energy conservation issues of the ReaxFF model. To enhance transferability we also highlight new advances to include explicit treatment of electrons in the ReaxFF and hybrid nonreactive/reactive simulations that make it possible to model charge transfer, redox chemistry, and large systems such as reverse micelles within the framework of a reactive force field. To address the computational cost, we review recent work in extended Lagrangian schemes and matrix preconditioners for accelerating the charge equilibration method component of ReaxFF and improvements in its software performance in LAMMPS.

Extended Lagrangian Born-Oppenheimer molecular dynamics for orbital-free density-functional theory and polarizable charge equilibration models

Extended Lagrangian Born-Oppenheimer molecular dynamics (XL-BOMD) [A. M. N. Niklasson, Phys. Rev. Lett. 100, 123004 (2008)] is formulated for orbital-free Hohenberg-Kohn density-functional theory and for charge equilibration and polarizable force-field models that can be derived from the same orbital-free framework. The purpose is to introduce the most recent features of orbital-based XL-BOMD to molecular dynamics simulations based on charge equilibration and polarizable force-field models. These features include a metric tensor generalization of the extended harmonic potential, preconditioners, and the ability to use only a single Coulomb summation to determine the fully equilibrated charges and the interatomic forces in each time step for the shadow Born-Oppenheimer potential energy surface. The orbital-free formulation has a charge-dependent, short-range energy term that is separate from long-range Coulomb interactions. This enables local parameterizations of the short-range energy term, while the long-range electrostatic interactions can be treated separately. The theory is illustrated for molecular dynamics simulations of an atomistic system described by a charge equilibration model with periodic boundary conditions. The system of linear equations that determines the equilibrated charges and the forces is diagonal, and only a single Ewald summation is needed in each time step. The simulations exhibit the same features in accuracy, convergence, and stability as are expected from orbital-based XL-BOMD.

Stochastic Constrained Extended System Dynamics for Solving Charge Equilibration Models

We present a new stochastic extended Lagrangian molecular dynamics solution to charge equilibration that eliminates self-consistent field (SCF) calculations, thus eliminating the computational bottleneck in solving the charge distribution with standard SCF solvers. By formulating both charges and chemical potential as latent variables and introducing a holonomic constraint that satisfies charge conservation, the SC-XLMD method accurately reproduces thermodynamic, dynamic, and structural properties within the framework of ReaxFF for a bulk water system and highly reactive RDX molecules simulated at high temperature. The SC-XLMD method shows excellent computational performance and is available in the publicly available LAMMPS package.

C-GeM: Coarse-Grained Electron Model for Predicting the Electrostatic Potential in Molecules

We have developed a new coarse-grained electron model, C-GeM, in which atoms are represented by a positive core and an electron shell described by Gaussian charge distributions, with the interaction energy between the core and shell reflecting the electronegativity of a given atomic element. By minimizing the electronic shell positions in the field of atomic core positions, the model can provide accurate electrostatic properties of molecules and their interactions. We have tested the performance of the C-GeM model for a set of molecules containing H, C, O, and Cl atoms to show that it can predict the electrostatic potential with high accuracy, and correctly describe the dissociation of HCl into ionic fragments in solution and to neutral atoms in the gas phase. The resulting C-GeM approach offers many advantages over expensive ab initio methods and reactive force field charge equilibration methodologies: it can rapidly predict the electrostatic potential surfaces of molecules, molecules dissociate into integer charge fragments so that redox reactions are easily described, there is no unphysical long-range charge transfer, it can account for out-of-plane polarization, and charges are not required to be centered on atoms, thereby accounting for electrostatic features such as sigma holes.