Direct Calculation of the Free Energy Using Reduced Boltzmann Factors: Application to Lennard-Jones Fluids and Square-Well Fluids

Abstract

Reduced Boltzmann factors have been introduced and averaged for the direct calculation of free energy during a single molecular dynamics or Monte Carlo simulation. Very stable results have been obtained for the excess free energies of the Lennard-Jones fluids and the square-well fluids at high densities. The free energies and entropies of chemical and biological systems are very important thermodynamic properties related to the direction of spontaneous change. A number of methods for the calculation of the free energy and entropy has been proposed with rapid progress in the field of computer simulations. 1-3 It is very important to compute the free energy and entropy at high densities because a number of chemical and biological processes occur in the highdensity region. However, it has been difficult to make these calculations directly from computer simulations. Recently a fluctuating cell model 4 using the Metropolis algorithm 5 for the generation of the constant NVT ensemble was proposed, although its application is limited to high-density phases of two-dimensional hard dumbbells. Although it is actually impossible to calculate the free energies directly from the averages of the Boltzmann factors owing to large fluctuations, 1 the fluctuation problem can be eased considerably by the multicanonical ensemble method 6 or the multiensemble sampling method. 7 On the other hand, a practical method using the canonical ensemble average of effective acceptance ratios (the EAR method) was proposed for the direct calculation of the free energy. 8 In the EAR method, large fluctuations according to the evaluation of the excess entropy can be reduced considerably by using the effective acceptance ratio, which is expressed as