Vibrationhyphen;Rotation Energies of Planar ZXY2Molecules Part II. The Quantumhyphen;Mechanical Hamiltonian and the Energy Values

摘要

Nielsen's treatment of the vibration‐rotation energies of a general polyatomic molecule is applied to the planarZXY2molecular model. Due to the low symmetry of the model, the vibrational modes are non‐degenerate, and, if the frequencies are well separated in their values, Nielsen's general formulation can be applied directly. For this case the elements of the secular equation are evaluated to include all the first‐ and second‐order terms in the Hamiltonian. With the view of applying the theory to the analysis of the fundamental bands of formaldehyde, the effect of an approximate degeneracy between a pair of perpendicular vibrations, of symmetry typesB1andB2, respectively, is considered. For this case, the vibration‐rotation energies of the states giving rise to the fundamental bands are investigated to the first order of approximation. It is shown how, by a modification of Nielsen's general treatment, the secular equations can be set up with little difficulty to include all the first‐order terms in the Hamiltonian. The secular equations for values ofJ= 0, 1, 2, 3, 4 are given explicitly.