Atom-centered symmetry functions for constructing high-dimensional neural network potentials

Modelling ultrafast dynamics at a conical intersection with regularized diabatic states: An approach based on multiplicative neural networks

The UNited RESidue (UNRES) model of polypeptide chains is a coarse-grained model in which each amino-acid residue is reduced to two interaction sites, namely, a united peptide group (p) located halfway between the two neighboring α-carbon atoms (Cαs), which serve only as geometrical points, and a united side chain (SC) attached to the respective Cα. Owing to this simplification, millisecond molecular dynamics simulations of large systems can be performed. While UNRES predicts overall folds well, it reproduces the details of local chain conformation with lower accuracy. Recently, we implemented new knowledge-based torsional potentials (Krupa et al. J. Chem. Theory Comput. 2013, 9, 4620–4632) that depend on the virtual-bond dihedral angles involving side chains: Cα···Cα···Cα···SC (τ(1)), SC···Cα···Cα···Cα (τ(2)), and SC···Cα···Cα···SC (τ(3)) in the UNRES force field. These potentials resulted in significant improvement of the simulated structures, especially in the loop regions. In this work, we introduce the physics-based counterparts of these potentials, which we derived from the all-atom energy surfaces of terminally blocked amino-acid residues by Boltzmann integration over the angles λ(1) and λ(2) for rotation about the Cα···Cα virtual-bond angles and over the side-chain angles χ. The energy surfaces were, in turn, calculated by using the semiempirical AM1 method of molecular quantum mechanics. Entropy contribution was evaluated with use of the harmonic approximation from Hessian matrices. One-dimensional Fourier series in the respective virtual-bond-dihedral angles were fitted to the calculated potentials, and these expressions have been implemented in the UNRES force field. Basic calibration of the UNRES force field with the new potentials was carried out with eight training proteins, by selecting the optimal weight of the new energy terms and reducing the weight of the regular torsional terms. The force field was subsequently benchmarked with a set of 22 proteins not used in the calibration. The new potentials result in a decrease of the root-mean-square deviation of the average conformation from the respective experimental structure by 0.86 Å on average; however, improvement of up to 5 Å was observed for some proteins.

We developed a high-dimensional neural network potential (NNP) to describe the structural and energetic properties of borophene deposited on silver. This NNP has the accuracy of density functional theory (DFT) calculations while achieving computational speedups of several orders of magnitude, allowing the study of extensive structures that may reveal intriguing moiré patterns or surface corrugations. We describe an efficient approach to constructing the training data set using an iterative technique known as the "adaptive learning approach". The developed NNP is able to produce, with excellent agreement, the structure, energy, and forces obtained at the DFT level. Finally, the calculated stability of various borophene polymorphs, including those not initially included in the training data set, shows better stabilization for ν ∼ 0.1 hole density, and in particular for the allotrope α . The stability of borophene on the metal surface is shown to depend on its orientation, implying structural corrugation patterns that can be observed only from long-time simulations on extended systems. The NNP also demonstrates its ability to simulate vibrational densities of states and produce realistic structures with simulated STM images closely matching the experimental ones.

Machine learning approaches have been promising in constructing high-dimensional potential energy surfaces (PESs) for molecules and materials. Neural networks (NNs) are one of the most popular such tools because of its simplicity and efficiency. The training algorithm for NNs becomes essential to achieve a fast and accurate fit with numerous data. The Levenberg-Marquardt (LM) algorithm has been recognized as one of the fastest and robust algorithms to train medium sized NNs and widely applied in recent NN based high quality PESs. However, when the number of ab initio data becomes large, the efficiency of LM is limited, making the training time consuming. Extreme learning machine (ELM) is a recently proposed algorithm which determines the weights and biases of a single hidden layer NN by a linear solution and is thus extremely fast. It, however, does not produce sufficiently small fitting error because of its random nature. Taking advantages of both algorithms, we report a generalized hybrid algorithm in training multilayer NNs. Tests on H+H2 and CH4+Ni(111) systems demonstrate the much higher efficiency of this hybrid algorithm (ELM-LM) over the original LM. We expect that ELM-LM will find its widespread applications in building up high-dimensional NN based PESs.

In silico property prediction based on density functional theory (DFT) is increasingly performed for crystalline materials. Whether quantitative agreement with experiment can be achieved with current methods is often an unresolved question, and may require detailed examination of physical effects such as electron correlation, reciprocal space sampling, phonon anharmonicity, and nuclear quantum effects (NQE), among others. In this work, we attempt first-principles equation of state prediction for the crystalline materials ScF3 and CaZrF6, which are known to exhibit negative thermal expansion (NTE) over a broad temperature range. We develop neural network (NN) potentials for both ScF3 and CaZrF6 trained to extensive DFT data, and conduct direct molecular dynamics prediction of the equation(s) of state over a broad temperature/pressure range. The NN potentials serve as surrogates of the DFT Hamiltonian with enhanced computational efficiency allowing for simulations with larger supercells and inclusion of NQE utilizing path integral approaches. The conclusion of the study is mixed: while some equation of state behavior is predicted in semiquantitative agreement with experiment, the pressure-induced softening phenomenon observed for ScF3 is not captured in our simulations. We show that NQE have a moderate effect on NTE at low temperature but does not significantly contribute to equation of state predictions at increasing temperature. Overall, while the NN potentials are valuable for property prediction of these NTE (and related) materials, we infer that a higher level of electron correlation, beyond the generalized gradient approximation density functional employed here, is necessary for achieving quantitative agreement with experiment.

Modeling palladium surfaces with density functional theory, neural networks and molecular dynamics

Machine learned potentials based on artificial neural networks are becoming a popular tool to define an effective energy model for complex systems, either incorporating electronic structure effects at the atomistic resolution, or effectively renormalizing part of the atomistic degrees of freedom at a coarse-grained resolution. One main criticism regarding neural network potentials is that their inferred energy is less interpretable than in traditional approaches, which use simpler and more transparent functional forms. Here we address this problem by extending tools recently proposed in the nascent field of explainable artificial intelligence to coarse-grained potentials based on graph neural networks. With these tools, neural network potentials can be practically decomposed into n-body interactions, providing a human understandable interpretation without compromising predictive power. We demonstrate the approach on three different coarse-grained systems including two fluids (methane and water) and the protein NTL9. The obtained interpretations suggest that well-trained neural network potentials learn physical interactions, which are consistent with fundamental principles.

Artificial neural networks represent an accurate and efficient tool to construct high-dimensional potential-energy surfaces based on first-principles data. However, so far the main drawback of this method has been the limitation to a single atomic species. We present a generalization to compounds of arbitrary chemical composition, which now enables simulations of a wide range of systems containing large numbers of atoms. The required incorporation of long-range interactions is achieved by combining the numerical accuracy of neural networks with an electrostatic term based on environment-dependent charges. Using zinc oxide as a benchmark system we show that the neural network potential-energy surface is in excellent agreement with density-functional theory reference calculations, while the evaluation is many orders of magnitude faster.

Implementing a neural network interatomic model with performance portability for emerging exascale architectures

Many drug molecules contain biaryl fragments, resulting in a torsional barrier corresponding to rotation around the bond linking the aryls. The potential energy surfaces of these torsions vary significantly because of steric and electronic effects, ultimately affecting the relative stability of the molecular conformations in the protein-bound and solution states. Simulations of protein-ligand binding require accurate computational models to represent the intramolecular interactions to provide accurate predictions of the structure and dynamics of binding. In this article, we compare four force fields [generalized AMBER force field (GAFF), open force field (OpenFF), CHARMM general force field (CGenFF), optimized potentials for liquid simulations (OPLS)] and two neural network potentials (ANI-2x and ANI-1ccx) for their ability to predict the torsional potential energy surfaces of 88 biaryls extracted from drug fragments. The root mean square deviation (rmsd) over the full potential energy surface and the mean absolute deviation of the torsion rotational barrier height (MADB) relative to high-level ab initio reference data (CCSD(T1)*) were used as the measure of accuracy. Uncertainties in these metrics due to the composition of the data set were estimated using bootstrap analysis. In comparison to high-level ab initio data, ANI-1ccx was most accurate for predicting the barrier height (rmsd: 0.5 ± 0.0 kcal/mol, MADB: 0.8 ± 0.1 kcal/mol), followed closely by ANI-2x (rmsd: 0.5 ± 0.0 kcal/mol, MADB: 1.0 ± 0.2 kcal/mol), then CGenFF (rmsd: 0.8 ± 0.1 kcal/mol, MADB: 1.3 ± 0.1 kcal/mol) and OpenFF (rmsd: 0.7 ± 0.1 kcal/mol, MADB: 1.3 ± 0.1 kcal/mol), then GAFF (rmsd: 1.2 ± 0.2 kcal/mol, MADB: 2.6 ± 0.5 kcal/mol), and finally OPLS (rmsd: 3.6 ± 0.3 kcal/mol, MADB: 3.6 ± 0.3 kcal/mol). Significantly, the neural network potentials (NNPs) are systematically more accurate and more reliable than any of the force fields. As a practical example, the NNP/molecular mechanics method was used to simulate the isomerization of ozanimod, a drug used for multiple sclerosis. Multinanosecond molecular dynamics (MD) simulations in an explicit aqueous solvent were performed, as well as umbrella sampling and adaptive biasing force-enhanced sampling techniques. The rate constant for this isomerization calculated using transition state theory was 4.30 × 10-1 ns-1, which is consistent with direct MD simulations.

We construct a full-dimensional ab initio neural network potential energy surface (PES) for the isomerization system of the formic acid dimer (FAD). This is based upon ab initio calculations using the DLPNO-CCSD(T) approach with the aug-cc-pVTZ basis set, performed at over 14000 symmetry-unique geometries. An accurate fit to the obtained energies is generated using a general neural network fitting procedure combined with the fundamental invariant method, and the overall energy-weighted root-mean-square fitting error is about 6.4 cm-1. Using this PES, we present a multidimensional quantum dynamics study on tunneling splittings with an efficient theoretical scheme developed by our group. The ground-state tunneling splitting of FAD calculated with a four-mode coupled method is in good agreement with the most recent experimental measurements. The PES can be applied for further dynamics studies. The effectiveness of the present scheme for constructing a high-dimensional PES is demonstrated, and this scheme is expected to be feasible for larger molecular systems.

A new potential energy surface (PES) and dynamical study of the reactive process of H2CO + OH toward the formation of HCO + H2O and HCOOH + H are presented. In this work, a source of spurious long range interactions in symmetry adapted neural network (NN) schemes is identified, which prevents their direct application for low temperature dynamical studies. For this reason, a partition of the PES into a diabatic matrix plus a NN many-body term has been used, fitted with a novel artificial neural network scheme that prevents spurious asymptotic interactions. Quasi-classical trajectory (QCT) and ring polymer molecular dynamics (RPMD) studies have been carried on this PES to evaluate the rate constant temperature dependence for the different reactive processes, showing good agreement with the available experimental data. Of special interest is the analysis of the previously identified trapping mechanism in the RPMD study, which can be attributed to spurious resonances associated with excitations of the normal modes of the ring polymer.

The Co3O4spinel is an important material in oxidation catalysis. Its properties under catalytic conditions, i.e. at finite temperatures, can be studied by molecular dynamics simulations, which critically depend on an accurate description of the atomic interactions. Due to the high complexity of Co3O4, which is related to the presence of multiple oxidation states of the cobalt ions, to dateab initiomethods have been essentially the only way to reliably capture the underlying potential energy surface, while more efficient atomistic potentials are very challenging to construct. Consequently, the accessible length and time scales of computer simulations of systems containing Co3O4are still severely limited. Rapid advances in the development of modern machine learning potentials (MLPs) trained on electronic structure data now make it possible to bridge this gap. In this work, we employ a high-dimensional neural network potential (HDNNP) to construct a MLP for bulk Co3O4spinel based on density functional theory calculations. After a careful validation of the potential, we compute various structural, vibrational, and dynamical properties of the Co3O4spinel with a particular focus on its temperature-dependent behavior, including the thermal expansion coefficient.

The search of ground-state structures (GSSs) of gold (Au) clusters is a formidable challenge due to the complexity of potential energy surface (PES). In this work, we have built a high-dimensional artificial neural network (ANN) potential to describe the PES of Au20 clusters. The ANN potential is trained through learning the GSS search process of Au20 by the combination of density functional theory (DFT) method and genetic algorithm. The root mean square errors of energy and force are 7.72 meV atom−1 and 217.02 meV Å−1, respectively. As a result, it can find the lowest-energy structure (LES) of Au20 clusters that is consistent with previous results. Furthermore, the scalability test shows that it can predict the energy of smaller size Au16–19 clusters with errors less than 22.85 meV atom−1, and for larger size Au21–25 clusters, the errors are below 36.94 meV atom−1. Extra attention should be paid to its accuracy for Au21–25 clusters. Applying the ANN to search the GSSs of Au16–25, we discover two new structures of Au16 and Au21 that are not reported before and several candidate LESs of Au16–18. In summary, this work proves that an ANN potential trained for specific size clusters could reproduce the GSS search process by DFT and be applied in the GSS search of smaller size clusters nearby. Therefore, we claim that building ANN potential based on DFT data is one of the most promising ways to effectively accelerate the GSS pre-screening of clusters.

An accurate description of reactive scattering of molecules on metal surfaces often requires the modeling of energy transfer between the molecule and the surface phonons. Although ab initio molecular dynamics (AIMD) can describe this energy transfer, AIMD is at present untractable for reactions with reaction probabilities smaller than 1%. Here, we show that it is possible to use a neural network potential to describe a polyatomic molecule reacting on a mobile metal surface with considerably reduced computational effort compared to AIMD. The highly activated reaction of CHD3 on Cu(111) is used as a test case for this method. It is observed that the reaction probability is influenced considerably by dynamical effects such as the bobsled effect and surface recoil. A special dynamical effect for CHD3 + Cu(111) is that a higher vibrational efficacy is obtained for two quanta in the CH stretch mode than for a single quantum.