Statistical mechanics of pendular molecules

Abstract

When molecules are subjected to an external electric field, static or radiative, the interaction with either permanent or induced dipole moments creates pendular eigenstates, directional superpositions or hybrids of the field-free rotational states. These hybrids reflect the anisotropy of the interaction; for a linear molecule this is proportional to cos θ for a permanent dipole and to cos² θ for an induced dipole, with θ the angle between the molecular axis and the field direction. In the weak-field regime, the molecular axis tumbles through 360°, but in the strong-field limit it is confined to harmonic librations about the field direction. Here we treat the statistical mechanics of pendular states of linear molecules, either polar (with a permanent dipole moment μ) or nonpolar but polarizable (with a polarizability anisotropy Δα contributing to an induced dipole moment). The partition function and the thermodynamic properties and other ensemble averages can be specified by two reduced variables involving μ or Δα, the field strength, rotational constant, and temperature. A simple approximation due to Pitzer enables the partition function to be cast in terms of the classical result with quantum corrections derived from the harmonic librator limit. This provides explicit analytic formulas which permit thermodynamic properties to be evaluated to good accuracy without computing energy levels and state sums. We also evaluate the average orientation or alignment of the molecular dipoles and examine field-induced shifts of chemical equilibria.