Ab initio QM/MM simulation with proper sampling: First principle calculations of the free energy of the autodissociation of water in aqueous solution

Quantum mechanical calculations of activation free energies of chemical reactions in condensed phases present a major challenge for computational chemistry. On one hand, it is important to use high-level ab initio methods to obtain reliable results. On the other hand, it is essential to perform sufficient configurational sampling to obtain meaningful free energies. Although the advance of quantum mechanical/molecular mechanics (QM/MM) approaches has made this problem tractable, it still requires an enormous amount of computer time. The present work advances several strategies that allow one to perform practical ab initio QM/MM calculations of free energy profiles in solutions and proteins. The basic idea is the use of a simple reference potential for the ab initio calculations (e.g., Bentzien; et al. J. Phys. Chem. B 1998, 102, 2293). One version of this approach evaluates the free energy of transfer from the reference potential to the ab initio potential by a single step free energy perturbation (FEP) approach. A new version evaluates this free energy by the linear response approximation (LRA), which involves running trajectories on both the reference and the ab initio potentials. The performance of both approaches is examined by calculating the potential of mean force for the autodissociation reaction of water in solution. It is found that the LRA approach allows one to obtain reasonable results even in cases where the ab initio and reference potentials are significantly different. The present work also explores options for increasing the size of the quantum mechanical region. Here it is shown that the constrained DFT (CDFT) method provides a promising strategy. Finally, the general issue of modeling the autodissociation reaction by quantum mechanical approaches is briefly considered. It is pointed out that the use of the empirical valence bond (EVB) approach in the sampling process should provide a way for evaluating the elusive nonequilibrium solvation effect.