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

A potential energy surface 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 potential energy surface of N4 to an analytic function using neural networks (NNs) with permutationally invariant polynomials (PIP). The fitting data set of the N4 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 neural network fit with permutationally invariant polynomial fits with mixed exponential-Gaussian bond order variables, and searching geometry regions with loose data coverage. With these efforts, the final data set is more suitable for a neural-network fit. The energy range of the data set is much wider than those used in other systems previously fitted by neural networks, and there are more rugged surface regions than usual due to locally avoided crossings. The performance of new MB-PIP-NN fit is compared to another new fit to the same data by least-squares methods not employing neural networks, and the mean unsigned deviation from the electronic structure calculations is reduced by a factor three, although the computing time to calculate a force for a trajectory calculation is larger by an order of magnitude. The accuracy achievable with the neural network fit for this difficult system is very impressive, and we anticipate that the neural network method can give useful fits to difficult cases that cannot be achieved by more conventional methods.