Cubic anharmonic potential constants from vibration–rotation interaction constants. Application to carbonyl sulphide and hydrogen cyanide molecules

Abstract

The vibration–rotation interaction constants α which connect the rotational constants of a molecule in different vibrational states through B_v=B_e–Σα_s(V_s+g_s/2) provide a route to cubic anharmonic potential constants. If the 3 α's are available for two isotopic species of a linear triatomic molecule it is possible in principle to determine all the cubic potential constants. The procedure which is developed has been applied to the carbonyl sulphide and to hydrogen cyanide molecules. Harmonic force constants and Coriolis constants were evaluated in order to determine the harmonic and Coriolis contributions to each α. The following values were obtained. [graphic omitted] For both OCS and HCN anharmonicity makes the major contribution to the α's. The following cubic constants K_ss′s′ in the potential function in terms of the internal co-ordinates have been obtained. [graphic omitted] The cubic constants k_ss′s″ in the potential function expressed in terms of the normal co-ordinates are found to be as follows (× 10^–47 g.^–½ cm.^–1 sec.^–2) [graphic omitted]