Maximum similarity orbitals for analysis of the electronic excited states

A new theoretical tool for analyzing the excited-state wave functions obtained from separate Hartree–Fock or configuration-interaction calculations on each state is proposed. Isopycnic transformations among the natural spin–orbitals of the ground and excited states yield the maximum similarity spin–orbitals (MSOs). These MSOs, which are a generalization of the method of corresponding spin–orbitals due to Amos and Hall, allow one to identify the initial and final spin–orbitals associated with the electronic excitation. The proposed formalism is equally valid in the cases of either identical or different geometries of the ground and excited states and makes it possible to assess magnitudes of the nuclear and electron relaxations accompanying the excitation. The methodology is illustrated using the example of the ROHF/6–31G** calculations on the keto and zwitterionic forms of the 3-hydroxypyrone molecule in their ground and two lowest-lying triplet excited states.