Theory of Long-Range Interatomic Forces. II. First-Order Interaction Energies in the Uncoupled Representation

Abstract

General methods are developed to calculate the matrix elements between two arbitrary states and for any multipole order. The results are expressed in terms of generalized hypergeometric functions. Some delta conditions in the formula for the electrostatic potential allow substantial factorization of the secular determinant. A device called the interaction diagram is introduced to facilitate the ordering of the secular determinant and the classification of the resulting molecular states. The theory is first applied to systems in which spin-orbit effects are neglected. The energy curves between an alkali atom in the ground state and an alkali atom in the first and second excited states, two alkali atoms in the first excited state, and an alkali atom in the first and another in the second excited state are calculated. In the last case, where some matrix elements consist of more than one multipole term, the competition of multipoles leads to energy curves which have maxima and minima in first order. It is also shown that for the interaction between atoms in excited states the resonance forces are less dominant while configuration interactions and the forces obtained from simple product state functions become more and more important.