The mean squared force and mean squared torque in molecular liquids

Abstract

The mean squared force in a general molecular liquid is developed in terms of the spherical harmonic expansion of the interaction energy of two molecules. The convergence of this series is examined by calculating the mean squared force and the expansion coefficients in a molecular dynamics simulation. For site-site intermolecular potentials (ISM or interaction site models), the mean squared force can be calculated in terms of the angle-averaged site-site distribution functions (g _αγ(r _αγ ≡ g ₀₀₀ ^αγ(r _αγ). The mean squared torque for an ISM fluid can be calculated from a knowledge of g ₀₀₀ ^αγ(r _αγ) plus the angular correlations contained in the two higher harmonic coefficients, g ₁₀₀ ^αγ(r _αγ) and g ₂₀₀ ^αγ(r _αγ). These three coefficients are calculated in molecular dynamics simulations of ISM fluids representing liquid nitrogen and liquid chlorine and their usefulness in calculating the mean squared torque is demonstrated. The calculation of multipolar contributions to the thermodynamic and quasithermodynamic properties of ISM fluids is briefly discussed.