The variation of molecular properties with vibration-rotation

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 … v_N ) 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 P_e ⁽⁰⁾ is the value of the property at equilibrium, P ^{J _τ} , A_i ^{J _τ} and B_ij 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|Π_α ²|J _τ⟩ where Π_α denotes the rotational angular momentum about a principal axis of rotation.