THE QUASI-GAUSSIAN ENTROPY THEORY - FREE-ENERGY CALCULATIONS BASED ONTHE POTENTIAL-ENERGY DISTRIBUTION FUNCTION

A new theory is presented for calculating the Helmholtz free energy ba sed on the potential energy distribution function. The usual expressio ns of free energy, internal energy and entropy involving the partition function are rephrased in terms of the potential energy distribution function, which must be a near Gaussian one, according to the central limit theorem. We obtained expressions for the free energy and entropy with respect to the ideal gas, in terms of the potential energy momen ts. These can be linked to the average potential energy and its deriva tives in temperature. Using thermodynamical relationships we also prod uce a general differential equation for the free energy as a function of temperature at fixed volume. In this paper we investigate possible exact and approximated solutions. The method was tested on a theoretic al model for a solid (classical harmonic solid) and some experimental liquids. The harmonic solid has an energy distribution, which can be d erived exactly from the theory. Experimental free energies of water an d methanol could be reproduced very well over a temperature range of m ore than 300 K. For water, where the appropriate experimental data wer e available, also the energy and heat capacity could be reproduced ver y well. (C) 1996 American Institute of Physics.