Product representation of potential energy surfaces

Abstract

The recently proposed scheme for representing multidimensional potential energy surfaces as a linear combination of products of one-dimensional functions is extended. The extensions prove to be important if one proceeds to higher dimensions. An iteration procedure is introduced which can further improve the representation. The product representation of potential energy surfaces is especially well suited to be employed within the framework of the multiconfiguration time-dependent Hartree (MCTDH) approximation. The potential representation scheme cannot only be used to represent given analytical potential energy surfaces, but also to interpolate multidimensional surfaces on given, e.g. ab initio, product grid points. The product representation method is applied to the three-dimensional S1 electronic surface of NOCl and to a six-dimensional model Coulomb potential. To check the quality of the NOCl surface representation, the photoabsorption spectrum for an excitation from the S0 to the S1 surface is computed. Weight functions are shown to be easily implemented and, in the case of the NOCl surface, allow a substantial reduction of the number of required expansion coefficients. Exploiting the underlying symmetries of the potential under consideration can further reduce the computational effort, as is shown in the example of the Coulomb potential. Finally, the NOCl S1 potential surface defined on 616 ab initio points is interpolated, as an example for the product interpolation scheme.