Mathematical and Computational Methods in Quantum Chemistry

Low Rank Approximation-Based Quadrature for Fast Evaluation of Quantum Chemistry Integrals

Prashant Rai

Sandia National Laboratories

: A new method based on low rank tensor decomposition for fast evaluation of high dimensional integrals in quantum chemistry is proposed. The integrand is first approximated in a suitable low rank canonical tensor subset with only a few integrand evaluations using classical alternating least squares. This allows representation of a high dimensional integrand function as sum of products of low dimensional functions. In the second step, low dimensional Gauss-Hermite quadrature rule is used to integrate this low rank representation thus avoiding the curse of dimensionality. Numerical tests on water and formaldehyde molecule demonstrate the accuracy of this method using very few samples as compared to Monte Carlo and its variants.