Cost-Effective Method for Free-Energy Minimization in Complex Systems with Elaborated Ab Initio Potentials

Abstract

We describe a method to locate stationary points in the free-energy hypersurface of complex molecular systems using high-level correlated <i>ab initio</i> potentials. In this work, we assume a combined QM/MM description of the system although generalization to full <i>ab initio</i> potentials or other theoretical schemes is straightforward. The free-energy gradient (FEG) is obtained as the mean force acting on relevant nuclei using a dual level strategy. First, a statistical simulation is carried out using an appropriate, low-level quantum mechanical force-field. Free-energy perturbation (FEP) theory is then used to obtain the free-energy derivatives for the target, high-level quantum mechanical force-field. We show that this composite FEG-FEP approach is able to reproduce the results of a standard free-energy minimization procedure with high accuracy, while simultaneously allowing for a drastic reduction of both computational and wall-clock time. The method has been applied to study the structure of the water molecule in liquid water at the QCISD/aug-cc-pVTZ level of theory, using the sampling from QM/MM molecular dynamics simulations at the B3LYP/6-311+G­(d,p) level. The obtained values for the geometrical parameters and for the dipole moment of the water molecule are within the experimental error, and they also display an excellent agreement when compared to other theoretical estimations. The developed methodology represents therefore an important step toward the accurate determination of the mechanism, kinetics, and thermodynamic properties of processes in solution, in enzymes, and in other disordered chemical systems using state-of-the-art <i>ab initio</i> potentials