On the overtone-combination spectra of XY2 molecules

Abstract

It is well known that overtone and combination features in the infrared spectra of YXY molecules arise from several different effects: (1) anharmonicity in the individual stretch and bend motions; (2) nonlinear dependence of the electronic-ground-state dipole moment (μ) on the stretch and bend displacements (r, ?, and ϑ); and (3) coupling of stretches and bend via nonseparable terms in the many-dimensional potential energy (V). In order to unambiguously sort out these contributions it is necessary to know the r, ?, and ϑ dependence of both μ and V from which follow the vibrational eigenstates, line positions, and oscillator strengths. In this paper we discuss general criteria for separability of the nuclear potential energy with respect to stretch and bend motions. Preference for ’’local’’ versus ’’normal’’ coordinates is shown to derive from the atomic mass differences and bonding types. The infrared spectrum of the HOH molecule is treated in detail, since a great deal of information is already available concerning its V (r, ?, ϑ) and μ (r, ?, ϑ). First we obtain the vibrational eigenstates and use them to study the breakdown of separability with increasing energy. Then we compare the relative intensities of neighboring overtone and combination states and account for them in terms of ’’electrical’’ (μ) and ’’vibrational’’ (V) anharmonicity.