Approach to the description of atoms using hyperspherical coordinates

Abstract

We formulate and develop an expansion of N‐electron atomic wavefunctions in hyperspherical coordinates. The expansion basis is a complete set of functions of 3N − 1 angle variables which describe the relative configuration of the electrons. The system is scaled in size by one extensive variable, the hyperradius r. All angular momentum and Pauli antisymmetry properties of the system are contained in the hyperspherical basis. A new, total angular momentum, antisymmetry‐adapted basis is derived and used to construct an expansion of the total electronic wavefunction which has all of these properties term by term. These basis functions are called configurational normal modes and provide a new element of atomic structure to replace the electron orbital. Several methods of implementing calculations with this expansion are discussed.