Interaction in Molecules Between Rotation and Slightly Anisotropic Oscillations

Abstract

The problem of the interaction between rotation and oscillation in two dimensionally slightly anisotropic molecules is considered quantum mechanically on the basis of model rotating only about an axis normal to the plane in which the oscillations take place. The energy of the molecule in the ground state becomes (h/2)(v₁+v₂)+K²h²/8π²A while for the upper states the energies are ${\mathrm{E=h(\nu }}_1{\mathrm{+\nu }}_2{\mathrm{)+(K}}^2{\mathrm{+\zeta }}^2{\mathrm{)h}}^2{\text{/8π}}^2{\text{A±((Δν/2)}}^2{\text{+(Kh/4π}}^2{\mathrm{A)}}^2{\zeta }^2{)}^{\frac{1}{2}}$ , where ζ is a quantity depending upon the normal coordinates which in general is not an integer. The selection rules are such as to enhance the intensities of the set of lines in the sides of the two bands adjacent to each other at the expense of the set of lines in the sides of the bands farthest away from each other. The spacings between rotational lines of the first set converge rapidly toward a limiting value of (1‐ζ)h/4π²A, while for the other set the spacings approach a value (1+ζ)h/4π²A.