Efficient ab initio free energy calculations by classically assisted trajectory sampling

A method for efficiently performing ab initio free energy calculations based on coupling constant thermodynamic integration is demonstrated. By the use of Boltzmann-weighted sums over states generated from a classical ensemble, the free energy difference between the classical and ab initio ensembles is readily available without the need for time-consuming integration over molecular dynamics trajectories. Convergence and errors in this scheme are discussed and characterised in terms of a quantity representing the degree of misfit between the classical and ab initio systems. Smaller but still substantial efficiency gains over molecular dynamics are also demonstrated for the calculation of average properties such as pressure and total energy for systems in equilibrium.