The variation of molecular properties with vibration-rotation

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Abstract
Molecular properties depend on the state of rotation and vibration. As a result of recent experimental developments such a dependence has been detected by several techniques for a variety of molecular properties of a large number of compounds. By expanding the property P as a power series in the reduced normal coordinates it is possible to derive an expression relating P to the state of rotation and vibration. In the present paper this is done for an asymmetric rotor molecule in a vibrational state (v 1 v 2 … vN ) and a rotational state (J τ). Terms in the expansion of P up to those quartic in the reduced normal coordinates are taken into account. The expression is of the form where Pe (0) is the value of the property at equilibrium, P J τ , Ai J τ and Bij depend on the parameters describing the potential energy surface and the property surface, and a superscript J τ denotes a dependence on rotational state through the quantities ⟨J τ|Πα 2|J τ⟩ where Πα denotes the rotational angular momentum about a principal axis of rotation.