ESTIMATION OF ERRORS IN FREE-ENERGY CALCULATIONS DUE TO THE LAG BETWEEN THE HAMILTONIAN AND THE SYSTEM CONFIGURATION

In molecular dynamics and Monte Carlo calculations a system does not immediately equilibrate to a change in the Hamiltonian, so that there is a time lag or a configuration number lag in the response of the system. These lags cause errors in free energy calculations. Two methods of measuring these "time lags" are proposed. The first method is based on Onsager's fluctuation regression hypothesis and the measurement of the fluctuations in dE/d-lambda. The second method is from a measurement of the hysteresis in slow-growth calculations. Both methods indicate that time lags are between 0.04 and 0.2 ps for typical systems. For time lags showing a single-exponential decay, it is shown that the average of the forward and reverse runs provides a very accurate estimate of the free energy for typical experimental curves provided that the system is equilibrated before starting the reverse run. Programming lambda in a nonlinear fashion in order to make DELTA-G a linear function of time is not a generally helpful procedure and is sometimes less accurate than a linear change of lambda with time. By use of a simple model of the time lags, the free energy perturbation runs can be used to measure the time lags, estimate the errors caused by these time lags, and correct the results for the errors. A generalization of Onsager's fluctuation regression hypothesis allows the calculation of configuration number lags in Monte Carlo runs from the observed fluctuations in dE/d-lambda.