Electronic Interaction Anisotropy between Atoms in Arbitrary Angular Momentum States

Abstract

A general tensorial expansion for the interaction potential between two atoms in arbitrary angular momentum states is derived and the relations between the expansion coefficients and the Born -Oppenheimer potentials of the diatomic molecule are obtained. It is demonstrated that a complete expansion of the interaction potential must employ tensors that are invariant under the inversion of the coordinate system, and the expansion in terms of conventional spherical harmonics is not adequate for the case of two atoms in states with nonzero electronic orbital angular momenta. The concept of the interaction anisotropy between two open-shell atoms is introduced. The correctness of the formalism is demonstrated by the example of two atoms in P states. Quantum chemistry calculations give an electronic interaction potential between two atoms in the molecule-fixed coordinate system. Collisions of atoms are described in the laboratoryfixed coordinate system and atomic collision theories are based on transformation relations between the molecule-fixed and space-fixed wave functions. The complexity of the wave function transformations often conceals the role of the electronic interaction potential in determining the dynamics of inelastic atomic collisions. It is desirable, therefore, to have a spacefixed representation of the electronic interaction potential which would allow for an analysis of collision mechanisms. Such potential forms would reflect the anisotropy of atom-atom interaction and provide simple techniques for the evaluation of the interaction potential matrix in a space-fixed basis of wave functions. Callaway and Bauer 1 suggested that the interaction between an atom in a P state and a closed-shell atom can be represented by an effective potential of the form