Reformulation and extension of Wigner-Witmer and Mulliken's correlation rules for the spin and orbital states of diatomic molecules upon dissociation

Abstract

Projection operator technique and angular momentum coupling methods are used to construct the eigenfunctions of diatomic molecular states in terms of the eigenfunctions of separate atomic states. The resulting eigenfunctions of the molecular term manifolds contain correct and compatible permutation symmetry and continuous group as well as point group symmetry pertinent to the molecule. These eigenfunctions will, in contrast to molecular orbital description, give the correct states of the atomic dissociation products required in chemical reactions and collisional energy transfer. In the above construction, we elucidate the correlation principle that dictates the nonexistence of two incompatible symmetries for certain states and allows for certain symmetries of the molecular term manifold to arise from given atomic multiplet states. The qualitative aspects of the newly derived correlation rules in simple mathematical language are shown to agree with the early works of Wigner-Witmer and Mulliken. These rules are then extended to treat ionic molecular states arising from atomic ions and radicals of variable charge and number of electrons but of the same element. Such ions may be important in ion-molecule reactions and in mass spectrometry studies. The extension as well as quantitative application of the new procedure devised are illustrated by constructing explicitly the eigenfunctions, in Slater determinant forms, of the molecular states that arise from different combinations of 0 (3Pg2, 1Dg, 1Sg), O+ ( 4SU, 2Du, 2P u), and O+ (2PU) which have not been considered by early workers. These combinations are shown to exhibit charge-exchange degeneracy in parallel to excitation exchange degeneracy in the study of exciton states.