TorchMD-Net 2.0: Fast Neural Network Potentials for Molecular Simulations.

Achieving a balance between computational speed, prediction accuracy, and universal applicability in molecular simulations has been a persistent challenge. This paper presents substantial advancements in TorchMD-Net software, a pivotal step forward in the shift from conventional force fields to neural network-based potentials. The evolution of TorchMD-Net into a more comprehensive and versatile framework is highlighted, incorporating cutting-edge architectures such as TensorNet. This transformation is achieved through a modular design approach, encouraging customized applications within the scientific community. The most notable enhancement is a significant improvement in computational efficiency, achieving a very remarkable acceleration in the computation of energy and forces for TensorNet models, with performance gains ranging from 2× to 10× over previous, nonoptimized, iterations. Other enhancements include highly optimized neighbor search algorithms that support periodic boundary conditions and smooth integration with existing molecular dynamics frameworks. Additionally, the updated version introduces the capability to integrate physical priors, further enriching its application spectrum and utility in research. The software is available at https://github.com/torchmd/torchmd-net.

TorchMD-Net 2.0: Fast Neural Network Potentials for Molecular Simulations.

Achieving a balance between computational speed, prediction accuracy, and universal applicability in molecular simulations has been a persistent challenge. This paper presents substantial advancements in the TorchMD-Net software, a pivotal step forward in the shift from conventional force fields to neural network-based potentials. The evolution of TorchMD-Net into a more comprehensive and versatile framework is highlighted, incorporating cutting-edge architectures such as TensorNet. This transformation is achieved through a modular design approach, encouraging customized applications within the scientific community. The most notable enhancement is a significant improvement in computational efficiency, achieving a very remarkable acceleration in the computation of energy and forces for Tensor-Net models, with performance gains ranging from 2x to 10x over previous, non-optimized, iterations. Other enhancements include highly optimized neighbor search algorithms that support periodic boundary conditions and smooth integration with existing molecular dynamics frameworks. Additionally, the updated version introduces the capability to integrate physical priors, further enriching its application spectrum and utility in research. The software is available at https://github.com/torchmd/torchmd-net.

Enhancing Protein-Ligand Binding Affinity Predictions Using Neural Network Potentials.

This letter gives results on improving protein-ligand binding affinity predictions based on molecular dynamics simulations using machine learning potentials with a hybrid neural network potential and molecular mechanics methodology (NNP/MM). We compute relative binding free energies with the Alchemical Transfer Method and validate its performance against established benchmarks and find significant enhancements compared with conventional MM force fields like GAFF2.

Enhancing Protein-Ligand Binding Affinity Predictions using Neural Network Potentials.

This letter gives results on improving protein-ligand binding affinity predictions based on molecular dynamics simulations using machine learning potentials with a hybrid neural network potential and molecular mechanics methodology (NNP/MM). We compute relative binding free energies (RBFE) with the Alchemical Transfer Method (ATM) and validate its performance against established benchmarks and find significant enhancements compared to conventional MM force fields like GAFF2.

OpenMM 8: Molecular Dynamics Simulation with Machine Learning Potentials.

Machine learning plays an important and growing role in molecular simulation. The newest version of the OpenMM molecular dynamics toolkit introduces new features to support the use of machine learning potentials. Arbitrary PyTorch models can be added to a simulation and used to compute forces and energy. A higher-level interface allows users to easily model their molecules of interest with general purpose, pretrained potential functions. A collection of optimized CUDA kernels and custom PyTorch operations greatly improves the speed of simulations. We demonstrate these features in simulations of cyclin-dependent kinase 8 (CDK8) and the green fluorescent protein chromophore in water. Taken together, these features make it practical to use machine learning to improve the accuracy of simulations with only a modest increase in cost.

OpenMM 8: Molecular Dynamics Simulation with Machine Learning Potentials.

Machine learning plays an important and growing role in molecular simulation. The newest version of the OpenMM molecular dynamics toolkit introduces new features to support the use of machine learning potentials. Arbitrary PyTorch models can be added to a simulation and used to compute forces and energy. A higher-level interface allows users to easily model their molecules of interest with general purpose, pretrained potential functions. A collection of optimized CUDA kernels and custom PyTorch operations greatly improves the speed of simulations. We demonstrate these features on simulations of cyclin-dependent kinase 8 (CDK8) and the green fluorescent protein (GFP) chromophore in water. Taken together, these features make it practical to use machine learning to improve the accuracy of simulations at only a modest increase in cost.

NNP/MM: Accelerating Molecular Dynamics Simulations with Machine Learning Potentials and Molecular Mechanics.

Machine learning potentials have emerged as a means to enhance the accuracy of biomolecular simulations. However, their application is constrained by the significant computational cost arising from the vast number of parameters compared with traditional molecular mechanics. To tackle this issue, we introduce an optimized implementation of the hybrid method (NNP/MM), which combines a neural network potential (NNP) and molecular mechanics (MM). This approach models a portion of the system, such as a small molecule, using NNP while employing MM for the remaining system to boost efficiency. By conducting molecular dynamics (MD) simulations on various protein-ligand complexes and metadynamics (MTD) simulations on a ligand, we showcase the capabilities of our implementation of NNP/MM. It has enabled us to increase the simulation speed by ∼5 times and achieve a combined sampling of 1 µs for each complex, marking the longest simulations ever reported for this class of simulations.

Developing machine-learned potentials to simultaneously capture the dynamics of excess protons and hydroxide ions in classical and path integral simulations.

The transport of excess protons and hydroxide ions in water underlies numerous important chemical and biological processes. Accurately simulating the associated transport mechanisms ideally requires utilizing ab initio molecular dynamics simulations to model the bond breaking and formation involved in proton transfer and path-integral simulations to model the nuclear quantum effects relevant to light hydrogen atoms. These requirements result in a prohibitive computational cost, especially at the time and length scales needed to converge proton transport properties. Here, we present machine-learned potentials (MLPs) that can model both excess protons and hydroxide ions at the generalized gradient approximation and hybrid density functional theory levels of accuracy and use them to perform multiple nanoseconds of both classical and path-integral proton defect simulations at a fraction of the cost of the corresponding ab initio simulations. We show that the MLPs are able to reproduce ab initio trends and converge properties such as the diffusion coefficients of both excess protons and hydroxide ions. We use our multi-nanosecond simulations, which allow us to monitor large numbers of proton transfer events, to analyze the role of hypercoordination in the transport mechanism of the hydroxide ion and provide further evidence for the asymmetry in diffusion between excess protons and hydroxide ions.

Elucidating the Role of Hydrogen Bonding in the Optical Spectroscopy of the Solvated Green Fluorescent Protein Chromophore: Using Machine Learning to Establish the Importance of High-Level Electronic Structure.

Hydrogen bonding interactions with chromophores in chemical and biological environments play a key role in determining their electronic absorption and relaxation processes, which are manifested in their linear and multidimensional optical spectra. For chromophores in the condensed phase, the large number of atoms needed to simulate the environment has traditionally prohibited the use of high-level excited-state electronic structure methods. By leveraging transfer learning, we show how to construct machine-learned models to accurately predict the high-level excitation energies of a chromophore in solution from only 400 high-level calculations. We show that when the electronic excitations of the green fluorescent protein chromophore in water are treated using EOM-CCSD embedded in a DFT description of the solvent the optical spectrum is correctly captured and that this improvement arises from correctly treating the coupling of the electronic transition to electric fields, which leads to a larger response upon hydrogen bonding between the chromophore and water.

Electron transfer at electrode interfaces via a straightforward quasiclassical fermionic mapping approach.

Electron transfer at electrode interfaces to molecules in solution or at the electrode surface plays a vital role in numerous technological processes. However, treating these processes requires a unified and accurate treatment of the fermionic states of the electrode and their coupling to the molecule being oxidized or reduced in the electrochemical processes and, in turn, the way the molecular energy levels are modulated by the bosonic nuclear modes of the molecule and solvent. Here we present a physically transparent quasiclassical scheme to treat these electrochemical electron transfer processes in the presence of molecular vibrations by using an appropriately chosen mapping of the fermionic variables. We demonstrate that this approach, which is exact in the limit of non-interacting fermions in the absence of coupling to vibrations, is able to accurately capture the electron transfer dynamics from the electrode even when the process is coupled to vibrational motions in the regimes of weak coupling. This approach, thus, provides a scalable strategy to explicitly treat electron transfer from electrode interfaces in condensed-phase molecular systems.

A derivation of the conditions under which bosonic operators exactly capture fermionic structure and dynamics.

The dynamics of many-body fermionic systems are important in problems ranging from catalytic reactions at electrochemical surfaces to transport through nanojunctions and offer a prime target for quantum computing applications. Here, we derive the set of conditions under which fermionic operators can be exactly replaced by bosonic operators that render the problem amenable to a large toolbox of dynamical methods while still capturing the correct dynamics of n-body operators. Importantly, our analysis offers a simple guide on how one can exploit these simple maps to calculate nonequilibrium and equilibrium single- and multi-time correlation functions essential in describing transport and spectroscopy. We use this to rigorously analyze and delineate the applicability of simple yet effective Cartesian maps that have been shown to correctly capture the correct fermionic dynamics in select models of nanoscopic transport. We illustrate our analytical results with exact simulations of the resonant level model. Our work provides new insights as to when one can leverage the simplicity of bosonic maps to simulate the dynamics of many-electron systems, especially those where an atomistic representation of nuclear interactions becomes essential.

Building insightful, memory-enriched models to capture long-time biochemical processes from short-time simulations.

The ability to predict and understand complex molecular motions occurring over diverse timescales ranging from picoseconds to seconds and even hours in biological systems remains one of the largest challenges to chemical theory. Markov state models (MSMs), which provide a memoryless description of the transitions between different states of a biochemical system, have provided numerous important physically transparent insights into biological function. However, constructing these models often necessitates performing extremely long molecular simulations to converge the rates. Here, we show that by incorporating memory via the time-convolutionless generalized master equation (TCL-GME) one can build a theoretically transparent and physically intuitive memory-enriched model of biochemical processes with up to a three order of magnitude reduction in the simulation data required while also providing a higher temporal resolution. We derive the conditions under which the TCL-GME provides a more efficient means to capture slow dynamics than MSMs and rigorously prove when the two provide equally valid and efficient descriptions of the slow configurational dynamics. We further introduce a simple averaging procedure that enables our TCL-GME approach to quickly converge and accurately predict long-time dynamics even when parameterized with noisy reference data arising from short trajectories. We illustrate the advantages of the TCL-GME using alanine dipeptide, the human argonaute complex, and FiP35 WW domain.

An accurate and efficient Ehrenfest dynamics approach for calculating linear and nonlinear electronic spectra.

Linear and nonlinear electronic spectra provide an important tool to probe the absorption and transfer of electronic energy. Here, we introduce a pure state Ehrenfest approach to obtain accurate linear and nonlinear spectra that is applicable to systems with large numbers of excited states and complex chemical environments. We achieve this by representing the initial conditions as sums of pure states and unfolding multi-time correlation functions into the Schrödinger picture. By doing this, we show that one can obtain significant improvements in accuracy over the previously used projected Ehrenfest approach and that these benefits are particularly pronounced in cases where the initial condition is a coherence between excited states. While such initial conditions do not arise when calculating linear electronic spectra, they play a vital role in capturing multidimensional spectroscopies. We demonstrate the performance of our method by showing that it is able to quantitatively capture the exact linear, 2D electronic spectroscopy, and pump-probe spectra for a Frenkel exciton model in slow bath regimes and is even able to reproduce the main spectral features in fast bath regimes.

Data-Efficient Machine Learning Potentials from Transfer Learning of Periodic Correlated Electronic Structure Methods: Liquid Water at AFQMC, CCSD, and CCSD(T) Accuracy.

Obtaining the atomistic structure and dynamics of disordered condensed-phase systems from first-principles remains one of the forefront challenges of chemical theory. Here we exploit recent advances in periodic electronic structure and provide a data-efficient approach to obtain machine-learned condensed-phase potential energy surfaces using AFQMC, CCSD, and CCSD(T) from a very small number (≤200) of energies by leveraging a transfer learning scheme starting from lower-tier electronic structure methods. We demonstrate the effectiveness of this approach for liquid water by performing both classical and path integral molecular dynamics simulations on these machine-learned potential energy surfaces. By doing this, we uncover the interplay of dynamical electron correlation and nuclear quantum effects across the entire liquid range of water while providing a general strategy for efficiently utilizing periodic correlated electronic structure methods to explore disordered condensed-phase systems.

SPICE, A Dataset of Drug-like Molecules and Peptides for Training Machine Learning Potentials.

Machine learning potentials are an important tool for molecular simulation, but their development is held back by a shortage of high quality datasets to train them on. We describe the SPICE dataset, a new quantum chemistry dataset for training potentials relevant to simulating drug-like small molecules interacting with proteins. It contains over 1.1 million conformations for a diverse set of small molecules, dimers, dipeptides, and solvated amino acids. It includes 15 elements, charged and uncharged molecules, and a wide range of covalent and non-covalent interactions. It provides both forces and energies calculated at the ωB97M-D3(BJ)/def2-TZVPPD level of theory, along with other useful quantities such as multipole moments and bond orders. We train a set of machine learning potentials on it and demonstrate that they can achieve chemical accuracy across a broad region of chemical space. It can serve as a valuable resource for the creation of transferable, ready to use potential functions for use in molecular simulations.

2D spectroscopies from condensed phase dynamics: Accessing third-order response properties from equilibrium multi-time correlation functions.

The third-order response lies at the heart of simulating and interpreting nonlinear spectroscopies ranging from two-dimensional infrared (2D-IR) to 2D electronic (2D-ES), and 2D sum frequency generation (2D-SFG). The extra time and frequency dimensions in these spectroscopic techniques provide access to rich information on the electronic and vibrational states present, the coupling between them, and the resulting rates at which they exchange energy that are obscured in linear spectroscopy, particularly for condensed phase systems that usually contain many overlapping features. While the exact quantum expression for the third-order response is well established, it is incompatible with the methods that are practical for calculating the atomistic dynamics of large condensed phase systems. These methods, which include both classical mechanics and quantum dynamics methods that retain quantum statistical properties while obeying the symmetries of classical dynamics, such as LSC-IVR, centroid molecular dynamics, and Ring Polymer Molecular Dynamics (RPMD), naturally provide short-time approximations to the multi-time symmetrized Kubo transformed correlation function. Here, we show how the third-order response can be formulated in terms of equilibrium symmetrized Kubo transformed correlation functions. We demonstrate the utility and accuracy of our approach by showing how it can be used to obtain the third-order response of a series of model systems using both classical dynamics and RPMD. In particular, we show that this approach captures features such as anharmonically induced vertical splittings and peak shifts while providing a physically transparent framework for understanding multidimensional spectroscopies.

Optically Induced Anisotropy in Time-Resolved Scattering: Imaging Molecular-Scale Structure and Dynamics in Disordered Media with Experiment and Theory.

Time-resolved scattering experiments enable imaging of materials at the molecular scale with femtosecond time resolution. However, in disordered media they provide access to just one radial dimension thus limiting the study of orientational structure and dynamics. Here we introduce a rigorous and practical theoretical framework for predicting and interpreting experiments combining optically induced anisotropy and time-resolved scattering. Using impulsive nuclear Raman and ultrafast x-ray scattering experiments of chloroform and simulations, we demonstrate that this framework can accurately predict and elucidate both the spatial and temporal features of these experiments.

Solvent Organization and Electrostatics Tuned by Solute Electronic Structure: Amide versus Non-Amide Carbonyls.

The ability to exploit carbonyl groups to measure electric fields in enzymes and other complex reactive environments by using the vibrational Stark effect has inspired growing interest in how these fields can be measured, tuned, and ultimately designed. Previous studies have concentrated on the role of the solvent in tuning the fields exerted on the solute. Here, we explore instead the role of the solute electronic structure in modifying the local solvent organization and electric field exerted on the solute. By measuring the infrared absorption spectra of amide-containing molecules, as prototypical peptides, and contrasting them with non-amide carbonyls in a wide range of solvents, we show that these solutes experience notable differences in their frequency shifts in polar solvents. Using vibrational Stark spectroscopy and molecular dynamics simulations, we demonstrate that while some of these differences can be rationalized by using the distinct intrinsic Stark tuning rates of the solutes, the larger frequency shifts for amides and dimethylurea primarily result from the larger solvent electric fields experienced by their carbonyl groups. These larger fields arise due to their stronger p-π conjugation, which results in larger C═O bond dipole moments that further induce substantial solvent organization. Using electronic structure calculations, we decompose the electric fields into contributions from solvent molecules that are in the first solvation shell and those from the bulk and show that both of these contributions are significant and become larger with enhanced conjugation in solutes. These results show that structural modifications of a solute can be used to tune both the solvent organization and electrostatic environment, indicating the importance of a solute-centric paradigm in modulating and designing the electrostatic environment in condensed-phase chemical processes.

A two-directional vibrational probe reveals different electric field orientations in solution and an enzyme active site.

The catalytic power of an electric field depends on its magnitude and orientation with respect to the reactive chemical species. Understanding and designing new catalysts for electrostatic catalysis thus requires methods to measure the electric field orientation and magnitude at the molecular scale. We demonstrate that electric field orientations can be extracted using a two-directional vibrational probe by exploiting the vibrational Stark effect of both the C=O and C-D stretches of a deuterated aldehyde. Combining spectroscopy with molecular dynamics and electronic structure partitioning methods, we demonstrate that, despite distinct polarities, solvents act similarly in their preference for electrostatically stabilizing large bond dipoles at the expense of destabilizing small ones. In contrast, we find that for an active-site aldehyde inhibitor of liver alcohol dehydrogenase, the electric field orientation deviates markedly from that found in solvents, which provides direct evidence for the fundamental difference between the electrostatic environment of solvents and that of a preorganized enzyme active site.

Characterizing and Contrasting Structural Proton Transport Mechanisms in Azole Hydrogen Bond Networks Using Ab Initio Molecular Dynamics.

Imidazole and 1,2,3-triazole are promising hydrogen-bonded heterocycles that conduct protons via a structural mechanism and whose derivatives are present in systems ranging from biological proton channels to proton exchange membrane fuel cells. Here, we leverage multiple time-stepping to perform ab initio molecular dynamics of imidazole and 1,2,3-triazole at the nanosecond time scale. We show that despite the close structural similarities of these compounds, their proton diffusion constants vary by over an order of magnitude. Our simulations reveal the reasons for these differences in diffusion constants, which range from the degree of hydrogen-bonded chain linearity to the effect of the central nitrogen atom in 1,2,3-triazole on proton transport. In particular, we uncover evidence of two "blocking" mechanisms in 1,2,3-triazole, where covalent and hydrogen bonds formed by the central nitrogen atom limit the mobility of protons. Our simulations thus provide insights into the origins of the experimentally observed 10-fold difference in proton conductivity.