Efficient generation of sum-of-products representations of high-dimensional potential energy surfaces based on multimode expansions
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J. Chem. Phys. 144 (11): 114114 (2016)

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.
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