Ab Initio QM/MM Simulation with Proper Sampling:  “First Principle” Calculations of the Free Energy of the Autodissociation of Water in Aqueous Solution

Abstract

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.

Perspective: Defining and quantifying the role of dynamics in enzyme catalysis

“…In this respect we like to point out that using QM/MM surface with energy minimization does not provide correct way of exploring activation barriers in enzymes. Although the sampling problem can be reduced by using reference potentials, [161][162][163][164] it seems to us that even at present the EVB is the most effective way of exploring catalytic effects in enzymes. The effectiveness of this approach, when it is calibrated on the energetics of the reference solution reaction (e.g., Ref.…”

Accurate frozen-density embedding potentials as a first step towards a subsystem description of covalent bonds

“…This strategy has, for instance, successfully been applied to model solvent effects on molecular properties 15,[17][18][19][20] and to account for environment effects on free energies in solution and in proteins. [21][22][23][24] Second, the FDE scheme can be used as a subsystem alternative to conventional KS-DFT calculations by iteratively exchanging the roles of the frozen and nonfrozen subsystems in the so-called freeze-and-thaw cycles. 25 This allows the frozen density to change, so that in principle it should be possible to obtain subsystem densities that add up to the correct total electron densities, even if the initial densities do not fulfill the required criteria.…”

Exact functional derivative of the nonadditive kinetic-energy bifunctional in the long-distance limit

“…7 It has further been successfully applied to model more complex environments, e.g., for describing induced circular dichroism in host-guest systems 8 or for free-energy calculations in protein environments. 9,10 Recently, Neugebauer has extended the FDE formalism to describe couplings between electronic transitions in different subsystems. 11 In addition, it has been extended by Carter and co-workers to embed a system of interest, which is described using wave function based ab initio methods, in an environment described by DFT.…”