Pair-Correlation Effects in a System of Coupled Rotators

Abstract

Orientational transitions in systems of coupled molecular rotators have previously been treated by methods that take account of pair-correlation effects, but only in the case of molecules with axial symmetry coupled by forces that do not depend on the direction of the line of centers between molecules. The theory is here generalized to the case of direction-dependent couplings. The resulting integral equations are treated by expanding in powers of Tb/T and 1/z, where Tb is the branching temperature of the ordered solution under consideration, and z is the number of next neighbors to which a molecule is coupled. The zero-order solution of the problem is related to the solution in the internal-field approximation. The first-order correction for pair-correlation effects is determined by an integral equation. The theory is applied to the James—Keenan model of solid methane, for which the integral equation is easily solved. Inclusion of the first-order pair-correlation correction increases the estimated octopole moment of methane by some 10% over that derived by the internal field method, to 0.55×10—24 electron·cm3. The effect of pair correlations on the orientational distribution of the molecules is discussed on the basis of this theory. The calculations on solid methane are of illustrative value only, since the small moment of inertia of even CD4 makes quantum effects important, whereas the present theory is based on classical statistical mechanics.