Fitting the derivative surfaces for full-dimensional interaction potentials†

Abstract

A new three-dimensional analytical representation of the interaction energy surface of the atom–diatom van der Waals complex is derived following the recently proposed derivative approach [P. Jankowski, J. Chem. Phys. 121, 1655 (2004)]. The method assumes the validity of the truncated Taylor expansion of the full-dimensional surface with respect to intramolecular coordinates. The expansion coefficients depend solely on intermolecular coordinates. With the second-order expansion the effective full-dimensional surface for the atom–diatom complex is generated from three low-dimensional surfaces. Each of these surfaces can be fitted separately to the numerical values of the derivatives defining the coefficients of the expansion. The formulae representing the surfaces of the first and second derivatives have been derived and are presented. The Ar–HF complex has been used for the numerical tests. The interaction energy and its derivatives were calculated on the grid of points using the coupled-cluster supermolecular method with single, double and non-iterative triple excitations, combined with the extrapolation to the basis set limit. The proposed analytical form of the potential was fitted and the features of the resulting surfaces are discussed. The two-dimensional surfaces, which build up the three-dimensional interaction energy surface, have different anisotropy properties, and the most pronounced anisotropy is observed for the surface representing the second derivative. The fit is formed to offer very high accuracy of the representation of the ab initio data. †Dedicated to Professor A. J. Sadlej on the occasion of his 65th birthday.