THE ORDERS OF MAGNITUDEOF THE VARIOUS CORRECTIONS TO THE VIBRATION-ROTATION ENERGIES OF POLYATOMICMOLECULES

Author Institution: Laboratoire de Chimie Physique, Faculte A des Sciences de Paris; Department of Physics and Astronomy, The Ohio State UniversityIt is customary in arriving at the vibration-rotation energiesof a molecule to expand the Hamiltonian in orders of magnitude $H = H_{0}+H_{1}+H_{2}+H_{3}+H_{4}+\cdots$ and then carry out a perturbation calculation to successive approximations. The manner in which the various operators have been grouped to form the Hamiltonian of successive orders zero, one, two, etc., has varied from one author to another and the results obtained for the vibration-rotation energiesdiffer somewhat in appearance. We have studied, systematically, to what order the various terms of the Hamiltonian contribute: (a) when the rotational quantum numbers J and K are small (as is generally the case in the transitions observed in the microwave region) and (b) when J and K take large values (as is generally the case when one considers the rotational structure of bands in the infrared, the visible and the ultraviolet). This study refers to the elements which are diagonal and nondiagonal with respect to K, $l_{s},l_{s},\ldots$ and permits the classification of the different terms figuring in the expression for the energy $E_{n\nu}$, or in the expression for the frequencies, $\nu$, corresponding to transitions of a given type (the relative importance of various terms may be different in $E_n \nu$, and in $\nu$ according to their order of magnitude