Ab initio potential-energy surfaces for complex, multichannel systems using modified novelty sampling and feedforward neural networks

Abstract

A neural network/trajectory approach is presented for the development of accurate potential-energy hypersurfaces that can be utilized to conduct ab initio molecular dynamics (AIMD) and Monte Carlo studies of gas-phase chemical reactions, nanometric cutting, and nanotribology, and of a variety of mechanical properties of importance in potential microelectromechanical systems applications. The method is sufficiently robust that it can be applied to a wide range of polyatomic systems. The overall method integrates ab initio electronic structure calculations with importance sampling techniques that permit the critical regions of configuration space to be determined. The computed ab initio energies and gradients are then accurately interpolated using neural networks (NN) rather than arbitrary parametrized analytical functional forms, moving interpolation or least-squares methods. The sampling method involves a tight integration of molecular dynamics calculations with neural networks that employ early stopping and regularization procedures to improve network performance and test for convergence. The procedure can be initiated using an empirical potential surface or direct dynamics. The accuracy and interpolation power of the method has been tested for two cases, the global potential surface for vinyl bromide undergoing unimolecular decomposition via four different reaction channels and nanometric cutting of silicon. The results show that the sampling methods permit the important regions of configuration space to be easily and rapidly identified, that convergence of the NN fit to the ab initio electronic structure database can be easily monitored, and that the interpolation accuracy of the NN fits is excellent, even for systems involving five atoms or more. The method permits a substantial computational speed and accuracy advantage over existing methods, is robust, and relatively easy to implement.

Principal component analysis for fermionic critical points

“…Neural networks have also been used in combination with QMC to provide information of quantum phase transitions [19][20][21] , topological states 22-25 , manybody localization 21,26 and entanglement properties 27 . Furthermore, neural networks are useful to fit functional forms for potential energy surfaces which are then used in subsequent simulations 28 . In contrast to the situations described above, where DQMC is applied to tight-binding Hamiltonians and the energy scales U, t, T, µ are unambiguously known, in these studies the network is used to avoid complicated and somewhat arbitrary fits to the functional form of the potential energy, allowing for more robust molecular dynamics simulations.…”

Communication: An accurate global potential energy surface for the OH + CO → H + CO2 reaction using neural networks

“…14 Over the past two decades, they have been applied to fit many high-dimensional PESs for isolated molecules and moleculesurface systems. [15][16][17][18][19][20][21][22][23] Recently, we reported a very accurate global PES for the H 2 +OH ↔ H 2 O+H reaction based on ∼17 000 ab initio points calculated at UCCSD(T)-F12/augcc-pVTZ level of theory. 24 Various tests revealed that the new surface is considerably more smooth and accurate than the existing YZCL2 and XXZ surfaces, 25,26 representing the best available potential energy surface for the OH 3 system.…”

“…17 Then we started to perform NN fitting and carried out extensive quasi classical trajectory (QCT) calculations on the fitted PES to generate more molecular configurations. New data points were selected from generated molecular configurations by using a selection scheme originally proposed by Behler,22,24 and had their ab initio energies calculated, added to the data set.…”

A Full-Dimensional Neural Network Potential-Energy Surface for Water Clusters up to the Hexamer

“…On the other hand, the total number of training structures should be as small as possible not only to avoid time-consuming reference calculations but also to keep the optimization process efficient. A systematic way to generate the training data for systems of arbitrary dimensionality is to employ MD tra-jectories to sample relevant configurations [28,57,76]. First, based on a set of initial training structures a preliminary NN potential is constructed and used to perform MD simulations.…”

“…NNs have been used for about two decades to construct PESs for a number of different systems and several reviews have been published [22][23][24][25]. Most of these NN potentials, however, are restricted to small molecules [26][27][28][29][30][31][32] or small molecules interacting with frozen metal surfaces [33][34][35][36][37][38]. Only a few potentials for higher-dimensional systems exist, which aim to describe the properties of solids [39,40].…”