Efficient multidimensional free energy calculations for ab initio molecular dynamics using classical bias potentials

We present a method for calculating multidimensional free energy surfaces within the limited time scale of a first-principles molecular dynamics scheme. The sampling efficiency is enhanced using selected terms of a classical force field as a bias potential. This simple procedure yields a very substantial increase in sampling accuracy while retaining the high quality of the underlying ab initio potential surface and can thus be used for a parameter free calculation of free energy surfaces. The success of the method is demonstrated by the applications to two gas phase molecules, ethane and peroxynitrous acid, as test case systems. A statistical analysis of the results shows that the entire free energy landscape is well converged within a 40 ps simulation at 500 K, even for a system with barriers as high as 15 kcal/mol.