Many-Body Permutationally Invariant Polynomial Neural Network Potential Energy Surface for N₄

Abstract

A potential energy surface (PES) for high-energy collisions between nitrogen molecules is useful for modeling chemical dynamics in shock waves and plasmas. In the present work, we fit the many-body (MB) component of the ground-state PES of N 4 to an analytic function using neural networks (NNs) with permutationally invariant polynomials (PIPs). The fitting dataset of the N 4 system is an extension of one used previously, extended with 4859 new CASPT2 points and 13 new CCSD(T) points to reach a total of 21 406 points. The MB-PIP-NN fit required a very complete coverage of the geometry domain in order to get a physical fit, and we devised several tactical steps to achieve this, including trajectory calculations, the comparison of the NN fit with PIP fits with mixed-exponential Gaussian bond order variables, and searching geometry regions with sparse data coverage. With these efforts, the final dataset is more suitable for a NN fit. The energy range of the dataset is much wider than those used in other systems previously fitted by NNs, and there are more rugged surface regions than usual due to locally avoided crossings. The performance of the new MB-PIP-NN fit is compared to that of another new fit to the same data by least-squares methods not employing NNs, and the mean unsigned deviation from the electronic structure calculations is reduced by a factor of 3, although the computing time to calculate a force for a trajectory calculation is larger by an order of magnitude. The accuracy achievable with the NN fit for this difficult system is very impressive, and we anticipate that the NN method can give useful fits to difficult cases that cannot be achieved by more conventional methods.

Neural network potential energy surface for the low temperature ring polymer molecular dynamics of the H2CO + OH reaction

“…This was solved by removing some of the polynomials that connect the fragments asymptotically in what is called "Purified Basis." 58 An equivalent solution was recently proposed by Li et al 59 to be used in the fit of many-body (MB) terms with PIP-NN by removing those PIPs relating unconnected distances.…”

Advances and New Challenges to Bimolecular Reaction Dynamics Theory

“…We note that such techniques have led to accurate reactive PESs for large (up to nine atoms) systems with multiple product arrangement channels, − allowing dynamic investigations of not just overall reactivity but also detailed information on product branching. An extension based on many-body expansion was recently proposed, which may have some advantages over the fitting of the full PES. A challenge is to extend such high-fidelity representation of PESs to reactive systems with more than 10 atoms, for which some progress has already been made. ,, To this end, the AtNN method is very attractive because it can in principle be employed for fitting PESs of large polyatomic systems with exact symmetry properties and high fitting accuracy.…”

Neural Network Potential Energy Surfaces for Small Molecules and Reactions

“…As computing power and the availability of software have progressed, NN-based PES fitting methods have become increasingly popular and are widely used and continue to be improved in current literature. ,,− This is true also for machine learning methods in computational chemistry and physics in general. They have made it possible to tackle some outstanding problems in computational chemistry, ,, such as exchange-correlation − and kinetic energy ,,, functional development, solution of the Schrödinger equation, − and prediction of properties without solving the Schrödinger equation − that require even more powerful hardware and software resources than PES fitting, and in addition, manpower with interdisciplinary knowledge.…”