Calculation of Global, High-Dimensional Potential Energy Surface Fits in Sum-of-Products Form Using Monte-Carlo Methods

Abstract

We have implemented a Monte-Carlo version of the well-known potfit algorithm. With potfit one can transform high-dimensional potential energy surfaces sampled on a grid into a sum-of-products form. More precisely, an fth order general tensor can be transformed into Tucker form. Using Monte-Carlo methods we avoid high-dimensional integrals that are needed to obtain optimal fits and simultaneously introduce importance sampling. The Tucker form is well suited for further use within the Heidelberg MCTDH package for solving the time-dependent as well as the time-independent Schrödinger equation of molecular systems. We demonstrate the power of the Monte-Carlo potfit algorithm by globally fitting the 15-dimensional potential energy surface of the Zundel cation (H₅O$_2^+$) and subsequently calculating the lowest vibrational eigenstates of the molecule.