Using Multi-Dimensional Smolyak Interpolation to Make a Sum-of-Products-Potential
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Authors
Avila, Gustavo
Carrington, Tucker Jr
Date
2015-07-27
Type
journal article
Language
en
Keyword
Energy Surfaces , Sum-of-Products , SOP , Multidimensional Integrals , Quadrature
Alternative Title
Abstract
We propose a new method for obtaining potential energy surfaces in sum-of-products (SOP) form.
If the number of terms is small enough, a SOP potential surface significantly reduces the cost
of quantum dynamics calculations by obviating the need to do multidimensional integrals by
quadrature. The method is based on a Smolyak interpolation technique and uses polynomial-like
or spectral basis functions and 1D Lagrange-type functions. When written in terms of the basis
functions from which the Lagrange-type functions are built, the Smolyak interpolant has only a
modest number of terms. The ideas are tested for HONO (nitrous acid).