Correlation between the intensities of vibrational overtone transitions and the repulsive branch of the molecular potential

Abstract

Energy levels εn and n←0 vibrational overtone transition intensities for a distorted Morse potential (DMP) and a linear dipole moment function are calculated, and then are treated as “observed” quantities. The values of (εn−ε0)/n vs n fall on a straight line very closely. A linear least-squares fit provides an effective anharmonicity parameter (xe)eff which is then used to construct an “effective” Morse potential (EMP). The EMP closely follows the DMP near equilibrium but declines in the far repulsive and attractive regions. The intensities calculated for the EMP systematically overestimate or underestimate the DMP intensities, depending on whether the repulsive branch of the EMP above the dissociation limit runs over or under that of the DMP, respectively, and the discrepancies rapidly increase with the overtone number. This effect of the repulsive branch is further investigated quantitatively by comparing the steepness of the repulsive potential β calculated directly from the potential curve with its value found from the rate of the intensities falloff with the overtone energy. It is shown that these two β values coincide with each other in a wide range of parameters, as predicted by the quasiclassical theory. A semiempirical potential for hydroxyl radical is tested for the occurrence of the effect of the repulsive branch. The EMP and RKR potentials are simulated, and the latter is fitted with a kth-order polynomial, k=6–12. In all cases the energy levels and lower overtone intensities are reproduced with a high precision, but the higher overtone intensities are accurate only when the repulsive branch of the fitting function is close enough to that of the original semiempirical potential. An interpolation/extrapolation procedure commonly used to represent the RKR potential is also discussed.