The transformation of multi-dimensional potential energy surfaces (PESs) from a grid-based multi- mode representation to an analytical one is a standard procedure in quantum chemical programs. Within the framework of linear least squares fitting, a simple and highly efficient algorithm is presented, which relies on a direct product representation of the PES and a repeated use of Kronecker products. It shows the same scalings in computational cost and memory require- ments as the potfit approach. In comparison to customary linear least squares fitting algorithms, this corresponds to a speed-up and memory saving by several orders of magnitude. Different fitting bases are tested, namely, polynomials, B-splines, and distributed Gaussians. Benchmark calculations are provided for the PESs of a set of small molecules.
%0 Journal Article
%1 ISI:000373384100017
%A Ziegler, Benjamin
%A Rauhut, Guntram
%D 2016
%J J. Chem. Phys.
%K chemie imported from:alexanderdenzel rauhut theoretische stuttgart theochem
%N 11
%P 114114
%R 10.1063/1.4943985
%T Efficient generation of sum-of-products representations of high-dimensional potential energy surfaces based on multimode expansions
%U http://dx.doi.org/10.1063/1.4943985
%V 144
%X The transformation of multi-dimensional potential energy surfaces (PESs) from a grid-based multi- mode representation to an analytical one is a standard procedure in quantum chemical programs. Within the framework of linear least squares fitting, a simple and highly efficient algorithm is presented, which relies on a direct product representation of the PES and a repeated use of Kronecker products. It shows the same scalings in computational cost and memory require- ments as the potfit approach. In comparison to customary linear least squares fitting algorithms, this corresponds to a speed-up and memory saving by several orders of magnitude. Different fitting bases are tested, namely, polynomials, B-splines, and distributed Gaussians. Benchmark calculations are provided for the PESs of a set of small molecules.
%@ 1041031041
@article{ISI:000373384100017,
abstract = {The transformation of multi-dimensional potential energy surfaces (PESs) from a grid-based multi- mode representation to an analytical one is a standard procedure in quantum chemical programs. Within the framework of linear least squares fitting, a simple and highly efficient algorithm is presented, which relies on a direct product representation of the PES and a repeated use of Kronecker products. It shows the same scalings in computational cost and memory require- ments as the potfit approach. In comparison to customary linear least squares fitting algorithms, this corresponds to a speed-up and memory saving by several orders of magnitude. Different fitting bases are tested, namely, polynomials, B-splines, and distributed Gaussians. Benchmark calculations are provided for the PESs of a set of small molecules.},
added-at = {2019-02-15T17:47:57.000+0100},
author = {Ziegler, Benjamin and Rauhut, Guntram},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/246c3f7347dd0facae3b6a09acfdacf04/theochem},
doi = {10.1063/1.4943985},
interhash = {2b3e3dede54ddd660ba9b554d56993b9},
intrahash = {46c3f7347dd0facae3b6a09acfdacf04},
isbn = {1041031041},
issn = {00219606},
journal = {J. Chem. Phys.},
keywords = {chemie imported from:alexanderdenzel rauhut theoretische stuttgart theochem},
number = 11,
pages = 114114,
timestamp = {2019-02-15T16:47:57.000+0100},
title = {{Efficient generation of sum-of-products representations of high-dimensional potential energy surfaces based on multimode expansions}},
url = {http://dx.doi.org/10.1063/1.4943985},
volume = 144,
year = 2016
}
