Cluster Expansion Methods for Systems of Polar Molecules: Some Solvents and Dielectric Properties

Abstract

General methods are developed for evaluating Mayer cluster diagrams for systems of molecules with orientation-dependent forces. These methods are particularly useful for obtaining chain and ring contributions. Simplification occurs for ordinary two-body forces in the absence of external fields because of invariance under rotation of the two-body complex as a whole. Using these methods we adapt Mayer's rearrangement procedure to calculate the cluster expansion of the potential of the average force between two ionic or dipolar solute molecules that are immersed and fixed in a gas of dipolar molecules. The comparison of this potential with the corresponding macroscopic quantity leads to a cluster expansion for the dielectric constant of the dipolar gas.

The Structure of Simple Molecular Liquids

“…This procedure is quite simple, because the multipole expansion is in accordance with the expansion in eq. (2). In particular, in the nonoverlapping region the following relation holds[*, 'I1: where MI is the respective multipole moment (M, =dipole moment, M, = quadrupole moment, M3 = octupole moment, etc.).…”

“…In order to define a reference system one can separate u p ' in eq. (2) from the remaining terms. The respective pertubation theories for the pair correlation function have been treated up to second order[291.…”

“…An alternative choice of the reference system is obtained, if one replaces u in eq. (2) by the Boltzmann factor exp [ -u / k T ] =J The isotropic termfhm) can then be used again. One should note thatfmm' does not only depend on u r ' ; inspection of eq.…”

“…(2) follows from the fact that the well known[34-401 statistical mechanical expressions for thermodynamical quantities can be used separately for each term of the expansion. As example the configurational contribution to the internal energy might be mentioned.…”

“…There exist two possibilities: 1) application of different radiations (X-rays, neutrons and, recently, also electrons [521). 2) Use of different isotopes in neutron scattering experiments. In the latter case the coherent scattering lengths of the isotopes should differ markedly.…”