The Calculation of Perturbation Energies in Vibrating Rotating Polyatomic Molecules

Abstract

An account is presented of the calculation of the purely vibrational contribution to the eigenvalues of the vibration‐rotation Hamiltonian of a polyatomic molecule. Special attention is given to the expansion of the quantum‐mechanical Hamiltonian; and to the results of the contact transformation of the Hamiltonian which simplifies the calculation of the second‐order energy corrections. The results of the transformation theory have been presented in the form of tables. For each type of perturbation term which appears in the first‐order Hamiltonian it is possible to obtain the second‐order energy corrections by inspection. This procedure eliminates the need for applying the transformation to each specific problem. The use of these results is illustrated by working out in considerable detail the case of the X₂YZ₂ tetrahedrally symmetric molecular model.