Explicitly Correlated MRCI-F12 Potential Energy Surfaces for Methane Fit with Several Permutation Invariant Schemes and Full-dimensional Vibrational Calculations


A data-set of nearly 100,000 symmetry unique multi-configurational ab initio points for methane were generated at the (AE)-MRCI-F12(Q)/CVQZ-F12 level, including energies beyond 30,000 cm-1 above the minimum and fit into potential energy surfaces (PESs) by several permutation invariant schemes. A multi-expansion interpolative fit combining interpolating moving least squares (IMLS) fitting and permutation invariant polynomials (PIP) was able to fit the complete data-set to a root-mean-square deviation of 1.0 cm-1 and thus was used to benchmark the other fitting methods. The other fitting methods include a single PIP expansion and two neural network (NN) based approaches, one of which combines NN with PIP. Full-dimensional variational vibrational calculations using a contracted-iterative method (and a Lanczos eigensolver) were used to assess the spectroscopic accuracy of the electronic structure method. The results show that the NN-based fitting approaches are able to fit the data-set remarkably accurately with the PIP-NN method producing levels in remarkably close agreement with the PIP-IMLS benchmark. The (AE)-MRCI-F12(Q)/CVQZ-F12 electronic structure method produces vibrational levels of near spectroscopic accuracy and a superb equilibrium geometry. The levels are systematically slightly too high, beginning at ~ 1-2 cm-1 above the fundamentals and becoming correspondingly higher for overtones. The PES is therefore suitable for small ab initio or empirical corrections and since it is based on a multi-reference method, can be extended to represent dynamically relevant dissociation channels.



Research Center/Lab(s)

Center for High Performance Computing Research

Keywords and Phrases

Calculations; Data flow analysis; Electronic structure; Iterative methods; Methane; Molecular physics; Neural networks; Potential energy; Potential energy surfaces; Quantum chemistry; Rate constants; Spectroscopy, Dissociation channels; Equilibrium geometries; Interpolating moving least squares; Invariant polynomials; Moving least squares; permutation invariant; Root mean square deviations; Vibrational calculations, Least squares approximations; methane; moving least squares; neural network; permutation invariant; potential energy surface; spectroscopy

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Article - Journal

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© 2015 Taylor & Francis Ltd., All rights reserved.

Publication Date

01 Jul 2015