Increasing the Efficiency of Free Energy Calculations Using Parallel Tempering and Histogram Reweighting

Free energy calculations from molecular simulations using thermodynamic integration or free energy perturbation require long simulation times to achieve sufficient precision. If entropic and enthalpic components of the free energy are desired, then the computational requirements are larger still. Here we present how parallel tempering (PT) Monte Carlo and weighted histogram analysis method (WHAM) can be used to improve the efficiency of free energy calculations. For both methods, which can be used separately or together, simulations at more than one temperature are performed. The same additional temperatures are often used to determine entropy changes. The results, for the aqueous solvation of n-butane and methane, show noticeable improvement in the precision of the free energy and entropy changes. The PT and WHAM methods can give similar error bars as conventional molecular dynamics in half the simulation time. The methods offer an efficient procedure for calculating free energy, entropy, and enthalpy changes in which free energy calculations are performed in parallel for a small number of closely spaced temperatures (for example, as here, at three temperatures:  298 K and 298 ± 15 K), and WHAM is used to enhance the data at each temperature.