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A theoretical study of proton-coupled electron transfer (PCET) in the radical anionic thymine−acrylamide complex is presented. This study is based on a multistate continuum theory, in which the solute is represented by a multistate valence bond model, the solvent is described by a dielectric continuum, and the transferring hydrogen nucleus is represented by a quantum mechanical wave function. In this application, the ground and excited electronic states are calculated with the complete active space self-consistent-field (CASSCF) method, the electronic coupling for the electron transfer reaction is calculated with the generalized Mulliken−Hush method, and the solvation properties are calculated with the frequency-resolved cavity model. The influence of neighboring DNA base pairs is determined by studying solvated DNA−acrylamide models in addition to the solvated thymine−acrylamide complex. The calculations indicate that the final product corresponds to single electron transfer (ET) for the solvated thymine−acrylamide complex but to a net PCET reaction for the solvated DNA−acrylamide complex. This difference is due to a decrease in solvent accessibility in the presence of DNA, which alters the relative free energies of the ET and PCET product states. Thus, the balance between ET and PCET in the DNA−acrylamide system is highly sensitive to the solvation properties of the system.

Mixed quantum/classical molecular dynamics simulations of the hydride transfer reaction catalyzed by dihydrofolate reductase are presented. The nuclear quantum effects such as zero point energy and hydrogen tunneling, as well as the motion of the entire solvated enzyme, are included during the generation of the free energy profiles and the real-time dynamical trajectories. The calculated deuterium kinetic isotope effect agrees with the experimental value. The simulations elucidate the fundamental nature of the nuclear quantum effects and provide evidence of hydrogen tunneling in the direction along the donor−acceptor axis. The transmission coefficient was found to be 0.80 for hydrogen and 0.85 for deuterium, indicating the significance of dynamical barrier recrossings. Nonadiabatic transitions among the vibrational states were observed but did not strongly affect the transmission coefficient. A study of motions involving residues conserved over 36 diverse species from Escherichia coli to human implies that motions of residues both in the active site and distal to the active site impact the free energy of activation and the degree of barrier recrossing. This analysis resulted in the characterization of a network of coupled promoting motions that extends throughout the protein and involves motions spanning femtosecond to millisecond time scales. This type of network has broad implications for protein engineering and drug design.

A new approach for the molecular dynamics simulation of proton-coupled electron transfer reactions in solution is presented. The solute is represented by a four-state valence bond model, and the solvent is described by explicit solvent molecules. The nuclear quantum effects of the transferring hydrogen are incorporated with a procedure based on a series of purely classical molecular dynamics simulations. The resulting mixed electronic/vibrational free energy surfaces depend on two solvent reaction coordinates corresponding to electron and proton transfer. This approach is shown to be equivalent to adiabatic mixed quantum/classical molecular dynamics, in which the nuclear quantum effects are included during the simulation, under well-defined, physically reasonable conditions. The results of the application of this approach to a model system are compared to those from a previous study based on a dielectric continuum treatment of the solvent. In addition, specific molecular motions of the solvent associated with proton-coupled electron transfer are identified, and solvent configurations that couple the proton and electron transfer reactions are characterized. This methodology may be implemented using commercial molecular dynamics software packages with little or no modification to the existing programs.

This Account presents a theoretical formulation for proton-coupled electron transfer reactions. The active electrons and transferring protons are treated quantum mechanically, and the free energy surfaces are obtained as functions of collective solvent coordinates corresponding to the proton and electron transfer reactions. Rate expressions have been derived in the relevant limits, and methodology for including the dynamical effects of the solvent and protein has been developed. This theoretical framework allows predictions of rates, mechanisms, and kinetic isotope effects for proton-coupled electron transfer reactions.

This paper presents a comprehensive theoretical study of model systems directed at predicting the effects of solute and solvent properties on the rates, mechanisms, and kinetic isotope effects for proton-coupled electron transfer (PCET) reactions. These studies are based on a multistate continuum theory in which the solute is described with a multistate valence bond model, the solvent is represented as a dielectric continuum, and the active electrons and transferring protons are treated quantum mechanically. This theoretical formulation is capable of describing a range of mechanisms, including single electron transfer and sequential or concerted EPT mechanisms in which both an electron and a proton are transferred. The probability of the EPT mechanism is predicted to increase as (1) the electron donor−acceptor distance is decreased, (2) the proton donor−acceptor distance is decreased, (3) the proton transfer reaction becomes more exothermic, (4) the electron transfer reaction becomes more endothermic (in the normal Marcus region), (5) the temperature decreases, (6) the solvent polarity decreases, and (7) the size of the electron donor and acceptor increases. The rates are predicted to increase with respect to these properties in a similar manner, with the exception that the rates will increase as the temperature increases and as the electron transfer reaction becomes more exothermic in the normal Marcus region. The kinetic isotope effects are predicted to increase as the probability of the EPT mechanism increases and as the localization and the distance between the reactant and product proton vibrational wave functions increase. Unusually strong kinetic isotope effects may be observed due to strong coupling between the transferring electron and proton. These theoretical studies elucidate the fundamental principles of PCET reactions and provide predictions that can be tested experimentally.

This paper presents an application of a computational approach combining electronic structure methods with the calculation of hydrogen vibrational wavefunctions. This application is directed at elucidating the nature of the nuclear quantum mechanical effects in the oxidation of benzyl alcohol catalyzed by liver alcohol dehydrogenase (LADH). The hydride transfer from the benzyl alcohol substrate to the NAD⁺ cofactor is described by a 148-atom model of the active site. The hydride potential energy curves and the associated hydrogen vibrational wavefunctions are calculated for structures along minimum energy paths and straight-line reaction paths obtained from electronic structure calculations at the semiempirical PM3 and ab initio RHF/3-21G levels. The results indicate that, for these levels of theory, the hydride transfer is adiabatic and hydrogen tunneling does not play a critical role along the minimum energy path. In contrast, nonadiabatic effects and hydrogen tunneling are shown to be important along the more relevant straight-line reaction paths. The secondary hydrogens were found to be significantly coupled to the transferring hydride near the transition state. In addition, the puckering of the NAD⁺ ring was found to be a dominant contribution to the reaction coordinate near the transition state. Further from the transition state, the reaction coordinate is a mixture of many heavy-atom modes, including the donor−acceptor distance and the distance between the substrate and the neighboring zinc and serine residue. These results imply that hydrogen tunneling in LADH is strongly impacted by the puckering of the NAD⁺ ring (which modulates the asymmetry of the hydride potential energy curve) and the distance between the donor and acceptor carbons (which modulates the barrier of the hydride potential energy curve).

The solvent effects for a Claisen rearrangement and a Diels−Alder reaction are investigated. Electronic structure methods are used to generate the frequencies, couplings, and curvatures along the minimum energy paths for these reactions in the gas phase and in the presence of two water molecules. The geometries and charge distributions along the minimum energy paths are analyzed to determine the structural and electrostatic roles of the water molecules. Reactive flux molecular dynamics methods based on a reaction path Hamiltonian are used to calculate the dynamical transmission coefficients, which account for recrossings of the transition state. The transmission coefficients for the Claisen rearrangement are nearly unity both in the gas phase and in the presence of two water molecules. The transmission coefficients for the Diels−Alder reaction are 0.95 and 0.89 in the gas phase and in the presence of two water molecules, respectively. These differences in the transmission coefficients are explained in terms of the locations and magnitudes of the curvature peaks along the reaction path, as well as the shape of the potential energy along the reaction coordinate near the transition state. Analysis of the dynamical trajectories provides insight into the dynamical role of the water molecules and elucidates possible reaction mechanisms.

This paper addresses the issue of internal consistency in the molecular dynamics with quantum transitions (MDQT) surface hopping method. The MDQT method is based on Tully's fewest switches algorithm, which is designed to ensure that the fraction of trajectories on each surface is equivalent to the corresponding average quantum probability determined by coherent propagation of the quantum amplitudes. For many systems, however, this internal consistency is not maintained. Two reasons for this discrepancy are the existence of classically forbidden transitions and the divergence of the independent trajectories. This paper presents a modified MDQT method that improves the internal consistency. The classically forbidden switches are eliminated by utilizing modified velocities for the integration of the quantum amplitudes, and the difficulties due to divergent trajectories are alleviated by removing the coherence of the quantum amplitudes when each trajectory leaves a nonadiabatic coupling region. The standard and modified MDQT methods are compared to fully quantum calculations for a classic model for ultrafast electronic relaxation (i.e., a two-state three-mode model of the conically intersecting S1 and S2 excited states of pyrazine). The standard MDQT calculations exhibit significant discrepancies between the fraction of trajectories in each state and the corresponding average quantum probability. The modified MDQT method leads to remarkable internal consistency for this model system.

In this paper, the multiconfigurational molecular dynamics with quantum transitions (MC-MDQT) method is used to simulate the nonequilibrium real-time quantum dynamics of proton transport along water chains in the presence of solvating water molecules. The model system consists of a protonated chain of three water molecules and two additional solvating water molecules hydrogen-bonded to each end of the chain. Nonequilibrium initial configurations are generated with an extra proton stabilized on one end of the water chain, and proton transport along the chain is induced by variations in the hydrogen-bonding distances between the solvating water molecules and the ends of the chain. These simulations indicate that solvation and hydrogen bonding significantly impact the proton-transport process and that quantum effects such as hydrogen tunneling and nonadiabatic transitions play an important role. Moreover, this model system exhibits a wide range of mechanisms, including both concerted and sequential double proton transfer, both strongly and weakly coupled double proton transfer, and both adiabatic and nonadiabatic pathways. The MC-MDQT approach provides a clear physical framework for interpreting and analyzing these different types of mechanisms.

This paper presents a new augmented molecular mechanical potential that incorporates significant quantum mechanical effects for proton and hydride transfer reactions in solution and in enzymes. The solvent is treated explicitly, specified covalent bonds in the solute are allowed to break and form, and the charge distribution of the solute is allowed to vary smoothly from that of the reactant to that of the product during the reaction. Moreover, in order to incorporate changes in bond order and hybridization, an efficient constraint dynamics method is combined with switching functions to smoothly vary the structure of the complex from the reactant to the product structure during the reaction. This new methodology is applied to model nicotinamide adenine dinucleotide (NADH) hydride transfer reactions, in particular to the oxidation of ethanol by the NAD⁺ analog 1-methyl-nicotinamide in acetonitrile and in water. Both cis and trans orientations of the NADH amide sidearm and both protonated and deprotonated forms of the substrate are studied. The structures and charge distributions of the model complexes are obtained from ab initio gas phase geometry optimizations at the Hartree−Fock 6-31G* level and are utilized to parametrize the potential energy surface. Classical free energy curves in both acetonitrile and water are calculated in order to illustrate the solvent effects on the energy gap between the reactant and the product states. The radial distribution functions between the solute and the water molecules together with the orientational distributions of the hydration shell water molecules are also calculated in order to elucidate the nature and extent of hydrogen bonding between the solvent and the solute.

This article presents the methodology we have developed for the simulation of hydrogen transfer reactions, including multiple proton transfer and proton-coupled electron transfer reactions. The central method discussed is molecular dynamics with quantum transitions (MDQT), which is a mixed quantum/classical surface hopping method that incorporates nonadiabatic transitions between the proton vibrational and/or electronic states. The advantages of MDQT are that it accurately describes branching processes (i.e., processes involving multiple pathways), is valid in the adiabatic and nonadiabatic limits and the intermediate regime, and provides real-time dynamical information. The multiconfigurational MDQT (MC-MDQT) method combines MDQT with an MC-SCF formulation of the vibrational modes for the simulation of processes involving multiple quantum modes (e.g., for multiple proton transfer reactions). MC-MDQT incorporates the significant correlation between the quantum modes in a computationally practical way and has been applied to proton transport along water chains. The EV-MDQT method incorporates transitions between mixed electronic/proton vibrational adiabatic states, which are calculated in a way that removes the standard double adiabatic aproximation. EV-MDQT has been applied to model proton-coupled electron transfer reactions. These new developments allow the simulation of a wide range of biologically and chemically important hydrogen transfer processes.