SIMPLE ANALYSIS OF NOISE AND HYSTERESIS IN (SLOW-GROWTH) FREE-ENERGY SIMULATIONS

The errors in the results of free energy simulations by molecular dynamics are analyzed in terms of fluctuations of a simple model with use of the diffusion equation. Mean square deviation, E, and hysteresis, H, for the slow-growth method are related to relaxation time and width of an (assumed Gaussian) distribution in configuration space. Both E and H are found to be inversely proportional to the length of the simulations, with E = HkT. Results for a simple system (conversion of two hydrogen atoms to methyl groups in the alanine dipeptide in a periodic box of water molecules) are found to agree well with the results of this theory. Relaxation time and distribution width estimated from computed fluctuations are found to be good predictors of E and H. Application to dynamic estimation of window size in free energy perturbation simulations is suggested in detail.