Tensor decomposition in potential energy surface representations

Abstract

In order to reduce the operation count in vibration correlation methods, e.g., vibrational configuration interaction (VCI) theory, a tensor decomposition approach has been applied to the analytical representations of multidimensional potential energy surfaces (PESs). It is shown that a decomposition of the coefficients within the individual n-mode coupling terms in a multimode expansion of the PES is feasible and allows for convenient contractions of one-dimensional integrals with these newly determined factor matrices. Deviations in the final VCI frequencies of a set of small molecules were found to be negligible once the rank of the factors matrices is chosen appropriately. Recommendations for meaningful ranks are provided and different algorithms are discussed.

MULTIMODE Calculations of Vibrational Spectroscopy and 1d Interconformer Tunneling Dynamics in Glycine Using a Full-Dimensional Potential Energy Surface

“…This representation has been used for nearly 20 years by a number of research groups; a sample of these are refs , , , and − . It continues to be actively used in a variety of applications and theoretical developments. − In MULTIMODE the maximum value of n is 6.…”

On the synergy of matrix-isolation infrared spectroscopy and vibrational configuration interaction computations

“…The multimode PES is usually truncated after three-mode or four-mode potentials. Furthermore, the PES can be represented in an analytic form by the fitting of polynomials or b-splines [45,46]. This analytic form enables transforming the PES from one isotopologue to another.…”

“…Numerous developments in quantum chemistry promise an economical and flexible, yet, accurate access to ab initio local PESs of polyatomic molecules [40][41][42][43][44][45][46][47][48], for which the design of global PESs would be too cumbersome and expensive. The MOLPRO software package [49] comprises a versatile and flexible computational environment for VSCF/VCI calculations.…”

Tensor-decomposed vibrational coupled-cluster theory: Enabling large-scale, highly accurate vibrational-structure calculations

“…[38][39][40][41][42][43][44][45] It has been applied to VCC calculations 24,25 and later to other types of vibrational-structure calculations [46][47][48] as well as for fitting PESs. 49,50 In our previous work of Refs. 24 and 25, we showed the perspectives of representing the VCC wave function in terms of CP tensors and that sufficient accuracy could be obtained.…”