On the dipole moment distribution of rigid symmetric rotors

The properties of dipolar molecules in electric fields have been studied for a long time. Their description often requires extensive numerical simulations, and only a limited number of analytically solvable models are known so far. Here, we derive an expression for the dipole probability density function of polar rigid symmetric rotors in the limit of high rotational temperatures and low electric field strengths, starting from the moment sequence of the probability distribution. Deviations of the distribution due to the non-spherical shape of the rotors are discussed in detail. In addition, it is demonstrated that there is a general connection between the average dipole moment of a thermal ensemble of rigid rotors in the high-temperature limit and the average dipole moment of an ensemble adiabatically entering the electric field.