Toward transferable empirical valence bonds: Making classical force fields reactive.

The empirical valence bond technique allows classical force fields to model reactive processes. However, parametrization from experimental data or quantum mechanical calculations is required for each reaction present in the simulation. We show that the parameters present in the empirical valence bond method can be predicted using a neural network model and the SMILES strings describing a reaction. This removes the need for quantum calculations in the parametrization of the empirical valence bond technique. In doing so, we have taken the first steps toward defining a new procedure for enabling reactive atomistic simulations. This procedure would allow researchers to use existing classical force fields for reactive simulations, without performing additional quantum mechanical calculations.

The ONETEP linear-scaling density functional theory program.

We present an overview of the onetep program for linear-scaling density functional theory (DFT) calculations with large basis set (plane-wave) accuracy on parallel computers. The DFT energy is computed from the density matrix, which is constructed from spatially localized orbitals we call Non-orthogonal Generalized Wannier Functions (NGWFs), expressed in terms of periodic sinc (psinc) functions. During the calculation, both the density matrix and the NGWFs are optimized with localization constraints. By taking advantage of localization, onetep is able to perform calculations including thousands of atoms with computational effort, which scales linearly with the number or atoms. The code has a large and diverse range of capabilities, explored in this paper, including different boundary conditions, various exchange-correlation functionals (with and without exact exchange), finite electronic temperature methods for metallic systems, methods for strongly correlated systems, molecular dynamics, vibrational calculations, time-dependent DFT, electronic transport, core loss spectroscopy, implicit solvation, quantum mechanical (QM)/molecular mechanical and QM-in-QM embedding, density of states calculations, distributed multipole analysis, and methods for partitioning charges and interactions between fragments. Calculations with onetep provide unique insights into large and complex systems that require an accurate atomic-level description, ranging from biomolecular to chemical, to materials, and to physical problems, as we show with a small selection of illustrative examples. onetep has always aimed to be at the cutting edge of method and software developments, and it serves as a platform for developing new methods of electronic structure simulation. We therefore conclude by describing some of the challenges and directions for its future developments and applications.

QUBEKit: Automating the Derivation of Force Field Parameters from Quantum Mechanics.

Modern molecular mechanics force fields are widely used for modeling the dynamics and interactions of small organic molecules using libraries of transferable force field parameters. However, for molecules outside the training set, the parameters are potentially inaccurate and it may be preferable to derive molecule-specific parameters. Here we present an intuitive parameter derivation toolkit, QUBEKit (QUantum mechanical BEspoke Kit), which enables the automated generation of system-specific small molecule force field parameters directly from quantum mechanics. QUBEKit is written in python and combines bond, angle, torsion, charge, and Lennard-Jones parameter derivation methodologies alongside a method for deriving the positions and charges of off-center virtual sites from the partitioned quantum mechanical electron density. As a proof of concept, we have rederived a complete set of parameters for 109 small organic molecules and assessed the accuracy by comparing computed liquid properties with experiments. QUBEKit gives competitive results when compared to standard transferable force fields, with mean unsigned errors of 0.024 g/cm3, 0.79 kcal/mol, and 1.17 kcal/mol for the liquid density, heat of vaporization, and free energy of hydration, respectively. This indicates that the derived parameters are suitable for molecular modeling applications, including computer-aided drug design.

Machine Learning Potentials with the Iterative Boltzmann Inversion: Training to Experiment.

Methodologies for training machine learning potentials (MLPs) with quantum-mechanical simulation data have recently seen tremendous progress. Experimental data have a very different character than simulated data, and most MLP training procedures cannot be easily adapted to incorporate both types of data into the training process. We investigate a training procedure based on iterative Boltzmann inversion that produces a pair potential correction to an existing MLP using equilibrium radial distribution function data. By applying these corrections to an MLP for pure aluminum based on density functional theory, we observe that the resulting model largely addresses previous overstructuring in the melt phase. Interestingly, the corrected MLP also exhibits improved performance in predicting experimental diffusion constants, which are not included in the training procedure. The presented method does not require autodifferentiating through a molecular dynamics solver and does not make assumptions about the MLP architecture. Our results suggest a practical framework for incorporating experimental data into machine learning models to improve the accuracy of molecular dynamics simulations.

Machine learning of material properties: Predictive and interpretable multilinear models.

Machine learning models can provide fast and accurate predictions of material properties but often lack transparency. Interpretability techniques can be used with black box solutions, or alternatively, models can be created that are directly interpretable. We revisit material datasets used in several works and demonstrate that simple linear combinations of nonlinear basis functions can be created, which have comparable accuracy to the kernel and neural network approaches originally used. Linear solutions can accurately predict the bandgap and formation energy of transparent conducting oxides, the spin states for transition metal complexes, and the formation energy for elpasolite structures. We demonstrate how linear solutions can provide interpretable predictive models and highlight the new insights that can be found when a model can be directly understood from its coefficients and functional form. Furthermore, we discuss how to recognize when intrinsically interpretable solutions may be the best route to interpretability.

Linear Atomic Cluster Expansion Force Fields for Organic Molecules: Beyond RMSE.

We demonstrate that fast and accurate linear force fields can be built for molecules using the atomic cluster expansion (ACE) framework. The ACE models parametrize the potential energy surface in terms of body-ordered symmetric polynomials making the functional form reminiscent of traditional molecular mechanics force fields. We show that the four- or five-body ACE force fields improve on the accuracy of the empirical force fields by up to a factor of 10, reaching the accuracy typical of recently proposed machine-learning-based approaches. We not only show state of the art accuracy and speed on the widely used MD17 and ISO17 benchmark data sets, but we also go beyond RMSE by comparing a number of ML and empirical force fields to ACE on more important tasks such as normal-mode prediction, high-temperature molecular dynamics, dihedral torsional profile prediction, and even bond breaking. We also demonstrate the smoothness, transferability, and extrapolation capabilities of ACE on a new challenging benchmark data set comprised of a potential energy surface of a flexible druglike molecule.

Modelling flexible protein-ligand binding in p38α MAP kinase using the QUBE force field.

The quantum mechanical bespoke (QUBE) force field is used to retrospectively calculate the relative binding free energies of a series of 17 flexible inhibitors of p38α MAP kinase. The size and flexibility of the chosen molecules represent a stringent test of the derivation of force field parameters from quantum mechanics, and enhanced sampling is required to reduce the dependence of the results on the starting structure. Competitive accuracy with a widely-used biological force field is achieved, indicating that quantum mechanics derived force fields are approaching the accuracy required to provide guidance in prospective drug discovery campaigns.

Development and Validation of the Quantum Mechanical Bespoke Protein Force Field.

Molecular mechanics force field parameters for macromolecules, such as proteins, are traditionally fit to reproduce experimental properties of small molecules, and thus, they neglect system-specific polarization. In this paper, we introduce a complete protein force field that is designed to be compatible with the quantum mechanical bespoke (QUBE) force field by deriving nonbonded parameters directly from the electron density of the specific protein under study. The main backbone and sidechain protein torsional parameters are rederived in this work by fitting to quantum mechanical dihedral scans for compatibility with QUBE nonbonded parameters. Software is provided for the preparation of QUBE input files. The accuracy of the new force field, and the derived torsional parameters, is tested by comparing the conformational preferences of a range of peptides and proteins with experimental measurements. Accurate backbone and sidechain conformations are obtained in molecular dynamics simulations of dipeptides, with NMR J coupling errors comparable to the widely used OPLS force field. In simulations of five folded proteins, the secondary structure is generally retained, and the NMR J coupling errors are similar to standard transferable force fields, although some loss of the experimental structure is observed in certain regions of the proteins. With several avenues for further development, the use of system-specific nonbonded force field parameters is a promising approach for next-generation simulations of biological molecules.

Harmonic Force Constants for Molecular Mechanics Force Fields via Hessian Matrix Projection.

A modification to the Seminario method [ Int. J. Quantum Chem. 1996 , 60 , 1271 - 1277 ] is proposed, which derives accurate harmonic bond and angle molecular mechanics force field parameters directly from the quantum mechanical Hessian matrix. The new method reduces the average error in the reproduction of quantum mechanical normal-mode frequencies of a benchmark set of 70 molecules from 12.3% using the original method, to 6.3%. The modified Seminario method is fully automated, and all parameters are computed directly from quantum mechanical data, thereby avoiding interdependency between bond and angle parameters and other components of the force field. A complete set of bond and angle force field parameters for the 20 naturally occurring amino acids is also provided for use in the future development of protein force fields.