Vector spherical harmonics: Concepts and applications to the single centre expansion method (Q1592212)

In this paper some compact definitions of differential operators in terms of vector spherical harmonics are used to express by means of dot product of a radial and an angular part, computable formulae for relevant molecular quantities in the area of computational chemical physics, within the Single Centre Expansion (SCE) framework [for further aspects of this model, see \textit{F. A. Gianturco}, \textit{R. R. Lucchese} and \textit{N. Sanna}, J. Chem. Phys. 104 (17), 6482 (1996), J. Phys. B: At. Mol. Opt. Phys. 32, 2181 (1999)]. Trough this SCE numerical procedure, directly computable formulae of the gradient and Laplacian operators are developed which can be also used to describe molecular properties depending on first and second derivatives with respect to spherical coordinates. Some numerical formulations in real cases computations are treated.