An effective fragment model is developed to treat solvent effects on chemical properties andreactions. The solvent, which might consist of discrete water molecules, protein, or othermaterial, is treated explicitly using a model potential that incorporates electrostatics,polarization, and exchange repulsion effects. The solute, which one can most generally envision as including some number of solvent molecules as well, is treated in a fully ab initio manner, using an appropriate level of electronic structure theory. In addition to the fragment model itself, formulae are presented that permit the determination of analytic energy gradients and, therefore, numerically determined energy second derivatives (hessians) for the complete system. Initial tests of the model for the water dimer and water-formamide are in good agreement with fully abinitio calculations. An effective fragment model is developed to treat solvent effects on chemical properties and reactions. The solvent, which might consist of discrete water molecules, protein, or other material, is treated explicitly using a model potential that incorporates electrostatics, polarization, and exchange repulsion effects. The solute, which one can most generally envision as including some number of solvent molecules as well, is treated in a fully ab initio manner, using an appropriate level of electronic structure theory. In addition to the fragment model itself, formulae are presented that permit the determination of analytic energy gradients and, therefore, numerically determined energy second derivatives ͑hessians͒ for the complete system. Initial tests of the model for the water dimer and water-formamide are in good agreement with fully ab initio calculations.

The nuclear-electronic orbital ͑NEO͒ method for the calculation of mixed nuclear-electronic wave functions is presented. Both electronic and nuclear molecular orbitals are expressed as linear combinations of Gaussian basis functions. In the NEO-HF ͑Hartree-Fock͒ method, the energy corresponding to the single-configurational mixed nuclear-electronic wave function is minimized with respect to the molecular orbitals. Multiconfigurational approaches are implemented to include significant correlation effects. In the NEO-CI ͑configuration interaction͒ method, the energy corresponding to the multiconfigurational mixed nuclear-electronic wave function is minimized with respect to the CI coefficients. In the NEO-MCSCF ͑multiconfigurational self-consistent-field͒ method, the energy is minimized with respect to the molecular orbitals as well as the CI coefficients. Analytic gradient expressions are presented for NEO-HF and NEO-MCSCF. These analytic gradients allow the variational optimization of the centers of the nuclear basis functions. They also enable the location and characterization of geometry stationary points and the generation of minimum energy paths and dynamic reaction paths. The advantages of the NEO approach are that nuclear quantum effects are incorporated during the electronic structure calculation, the Born-Oppenheimer separation of electrons and nuclei is avoided, excited vibrational-electronic states may be calculated, and its accuracy may be improved systematically. Initial applications are presented to illustrate the computational feasibility and accuracy of this approach.

The quantum dynamics of the hydride transfer reaction catalyzed by liver alcohol dehydrogenase (LADH) are studied with real-time dynamical simulations including the motion of the entire solvated enzyme. The electronic quantum effects are incorporated with an empirical valence bond potential, and the nuclear quantum effects of the transferring hydrogen are incorporated with a mixed quantum/classical molecular dynamics method in which the transferring hydrogen nucleus is represented by a three-dimensional vibrational wave function. The equilibrium transition state theory rate constants are determined from the adiabatic quantum free energy profiles, which include the free energy of the zero point motion for the transferring nucleus. The nonequilibrium dynamical effects are determined by calculating the transmission coefficients with a reactive flux scheme based on real-time molecular dynamics with quantum transitions (MDQT) surface hopping trajectories. The values of nearly unity for these transmission coefficients imply that nonequilibrium dynamical effects such as barrier recrossings are not dominant for this reaction. The calculated deuterium and tritium kinetic isotope effects for the overall rate agree with experimental results. These simulations elucidate the fundamental nature of the nuclear quantum effects and provide evidence of hydrogen tunneling in the direction along the donor-acceptor axis. An analysis of the geometrical parameters during the equilibrium and nonequilibrium simulations provides insight into the relation between specific enzyme motions and enzyme activity. The donor-acceptor distance, the catalytic zinc-substrate oxygen distance, and the coenzyme (NAD(+)/NADH) ring angles are found to strongly impact the activation free energy barrier, while the donor-acceptor distance and one of the coenzyme ring angles are found to be correlated to the degree of barrier recrossing. The distance between VAL-203 and the reactive center is found to significantly impact the activation free energy but not the degree of barrier recrossing. This result indicates that the experimentally observed effect of mutating VAL-203 on the enzyme activity is due to the alteration of the equilibrium free energy difference between the transition state and the reactant rather than nonequilibrium dynamical factors. The promoting motion of VAL-203 is characterized in terms of steric interactions involving THR-178 and the coenzyme.

A hybrid approach for simulating proton and hydride transfer reactions in enzymes is presented. The electronic quantum effects are incorporated with an empirical valence bond approach. The nuclear quantum effects of the transferring hydrogen are included with a mixed quantum/classical molecular dynamics method in which the hydrogen nucleus is described as a multidimensional vibrational wave function. The free energy profiles are obtained as functions of a collective reaction coordinate. A perturbation formula is derived to incorporate the vibrationally adiabatic nuclear quantum effects into the free energy profiles. The dynamical effects are studied with the molecular dynamics with quantum transitions (MDQT) surface hopping method, which incorporates nonadiabatic transitions among the adiabatic hydrogen vibrational states. The MDQT method is combined with a reactive flux approach to calculate the transmission coefficient and to investigate the real-time dynamics of reactive trajectories. This hybrid approach includes nuclear quantum effects such as zero point energy, hydrogen tunneling, and excited vibrational states, as well as the dynamics of the complete enzyme and solvent. The nuclear quantum effects are incorporated during the generation of the free energy profiles and dynamical trajectories rather than subsequently added as corrections. Moreover, this methodology provides detailed mechanistic information at the molecular level and allows the calculation of rates and kinetic isotope effects. An initial application of this approach to the enzyme liver alcohol dehydrogenase is also presented.

In this paper we present computational studies directed at elucidating the mechanism of the oxidation of benzyl alcohol by liver alcohol dehydrogenase (LADH). This enzyme reaction involves a hydride transfer from the alcohol substrate to the nicotinamide adenine dinucleotide coenzyme and a proton relay that deprotonates the alcohol substrate. Electronic structure calculations at various levels of theory were performed on a 148-atom model of the active site, and classical molecular dynamics simulations were performed on the entire solvated LADH dimer. These calculations support the hypothesis that alcohol deprotonation occurs prior to the hydride transfer step and that the alcohol deprotonation facilitates the hydride transfer by lowering the barrier for hydride transfer. In this postulated mechanism, the alcohol deprotonation leads to a zinc-bound alkoxide ion, and the subsequent hydride transfer leads to the benzaldehyde product. The calculations indicate that the zinc-bound alkoxide forms a strong hydrogen bond to Ser48 and that hydride transfer is accompanied by a weakening of this hydrogen bond. The results also suggest that the barrier to hydride transfer is lowered by the electrostatic interaction between the substrate alkoxide oxygen and the zinc counterion in the active site. The interaction of the alkoxide oxygen lone pair orbitals with the zinc competes with the formation of the double bond required for the aldehyde product, resulting in an earlier, more alcohol-like transition state and thus a lower activation energy barrier. In addition, the interaction between the alkoxide oxygen and the zinc restricts the dynamical motion of the substrate, decreasing the average donor-acceptor distance for hydride transfer and hence lowering the activation energy barrier.