Vector spherical harmonics: Concepts and applications to the single centre expansion method Original Research Article

In this paper the basic formulation of the Vector Spherical Harmonics (VSH) is recalled from the literature and the details on the various notations clarified. By means of compact definitions of differential operators in terms of VSH, a new formulation for the gradient and Laplacian of a generic Single Centre Expanded (SCE) function is developed. The new formulae are so derived to be directly computable and implementable in numerical codes to face problems in atomic and molecular physics. A set of numerical computations have been carried out to assess the proposed formulae where the behaviour of the gradient and Laplacian of the electron density and static potential of the water molecule is exploited in detail within the SCE framework of reference.