STATISTICAL-MECHANICS OF PENDULAR MOLECULES

When molecules are subjected to an external electric held, static or r adiative, the interaction with either permanent or induced dipole mome nts creates pendular eigenstates, directional superpositions or hybrid s of the field-free rotational states. These hybrids reflect the aniso tropy of the interaction; for a linear molecule this is proportional t o cos theta for a permanent dipole and to cos(2) theta for an induced dipole, with theta the angle between the molecular axis and the held d irection. In the weak-field regime, the molecular axis tumbles through 360 degrees, but in the strong-field limit it is confined to harmonic librations about the held direction. Here we treat the statistical me chanics of pendular states of linear molecules, either polar (with a p ermanent dipole moment mu) or nonpolar but polarizable (with a polariz ability anisotropy Delta alpha contributing to an induced dipole momen t). The partition function and the thermodynamic properties and other ensemble averages can be specified by two reduced variables involving mu or Delta alpha, the held strength, rotational constant, and tempera ture. A simple approximation due to Fitter enables the partition funct ion to be cast in terms of the classical result with quantum correctio ns derived from the harmonic librator limit. This provides explicit an alytic formulas which permit thermodynamic properties to be evaluated to good accuracy without computing energy levels and state sums. We al so evaluate the average orientation or alignment of the molecular dipo les and examine held-induced shifts of chemical equilibria.