Interactions between Molecules in the Statistical Treatment of Real Gases. II. Derivation of van der Waals Interactions

The current perturbation theory for classical real gases, which views interaction energies between pairs, triplets, etc., of molecules, given in advance, as a perturbation to the ideal‐gas behavior, is replaced by a systematic perturbation expansion in terms of the Coulomb interaction between the electrons and nuclei in the different molecules and the intramolecular correlations of these particles in the isolated molecules. The latter refer to correlations at different imaginary times $\mathrm{t\hspace{0.17em}=\hspace{0.17em}-\hspace{0.17em}i\tau }$ , where $\text{0\hspace{0.17em}≤\hspace{0.17em}τ\hspace{0.17em}≤\hspace{0.17em}β}$ with $\text{β\hspace{0.17em}=\hspace{0.17em}1\hspace{0.17em}/\hspace{0.17em}kT}$ the reciprocal temperature. The Fourier transform of the pair correlation, expressed as a function of $\tau$ , is directly related to the susceptibility of the molecule at imaginary frequencies. In the expansion of the grand partition function the terms containing only particle pair correlations represent the contributions of molecular interactions due to the familiar additive and nonadditive van der Waals forces.