A low rank approach to approximate high dimensional potential energy surfaces

What is it about?

This article proposes a new technique to approximate potential energy surfaces of arbitrary molecules by sampling it at few geometric configurations. We make use of the fact that although potential energy surfaces can be high dimensional, they can be well approximated as a small sum of products of one-dimensional functions. This is known as the low-rank structure and uses methods based on tensor decomposition. The form of approximation renders the potential energy surface easy to integrate for calculating energy and frequency corrections.

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Why is it important?

Potential energy surfaces are ubiquitous in quantum chemistry. The method potentially generates an accurate functional form of high dimensional potential surfaces with very few energy evaluation and attempts to beat the curse of dimensionality. The paper explains involved mathematical ideas of tensor approximation in an easy-to-follow way.