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  • 1
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 115 (2001), S. 285-296 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: This paper presents a theoretical formulation for electron transfer coupled to the motion of multiple protons. This theory is applied to proton-coupled electron transfer (PCET) through amidinium–carboxylate salt bridges, where the electron transfer reaction is coupled to the motion of two protons at the proton transfer interface. The rate for the donor–(amidinium–carboxylate)–acceptor system is found to be substantially slower than the rate for the switched interface donor–(carboxylate–amidinium)–acceptor system. This trend is consistent with experimental data for photoinduced PCET in analogous systems. The calculations indicate that this difference in rates is due mainly to the opposite dipole moments at the proton transfer interfaces for the two systems, leading to an endothermic reaction for the donor–(amidinium–carboxylate)–acceptor system and an exothermic reaction for the donor–(carboxylate–amidinium)–acceptor system. The deuterium kinetic isotope effects are found to be moderate (i.e., kH/kD〈3) for both types of systems. These moderate kinetic isotope effects are due to the dominance of vibrationally excited product states, leading to significant overlap between the reactant and product proton vibrational wave functions. © 2001 American Institute of Physics.
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  • 2
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 113 (2000), S. 2385-2396 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: This paper presents a derivation of rate expressions for nonadiabatic proton-coupled electron transfer (PCET) reactions in solution. The derivation is based on a multistate continuum theory in which the solvent is described by a dielectric continuum, the solute is represented by a multistate valence bond model, and the transferring proton(s) are treated quantum mechanically. In this formulation, a PCET reaction is described as a transition between two sets of diabatic free energy surfaces associated with the two electron transfer states. For PCET reactions involving the transfer of one electron and one proton, these mixed electronic/proton vibrational free energy surfaces are functions of two scalar solvent coordinates corresponding to electron and proton transfer. The Golden Rule is applied to these two-dimensional free energy surfaces in conjunction with a series of well-defined approximations. The contributions from intramolecular solute modes are also included. The final rate expression is similar in form to the standard rate expression for nonadiabatic single electron transfer, but the reorganization energies, equilibrium free energy differences, and couplings are defined in terms of the two-dimensional free energy surfaces. The practical implementation of this rate expression and the calculation of the input quantities are also discussed. © 2000 American Institute of Physics.
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  • 3
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 113 (2000), S. 5214-5227 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The Fourier Grid Hamiltonian Multiconfigurational Self-Consistent-Field (FGH-MCSCF) method for calculating vibrational wavefunctions is presented. This method is designed to calculate multidimensional hydrogen nuclear wavefunctions for use in mixed quantum/classical molecular dynamics simulations of hydrogen transfer reactions. The FGH-MCSCF approach combines a MCSCF variational method, which describes the vibrational wavefunctions as linear combinations of configurations that are products of one-dimensional wavefunctions, with a Fourier grid method that represents the one-dimensional wavefunctions directly on a grid. In this method a full configuration interaction calculation is carried out in a truncated one-dimensional wavefunction space [analogous to complete active space self-consistent-field (CASSCF) in electronic structure theory]. A state-averaged approach is implemented to obtain a set of orthogonal multidimensional vibrational wavefunctions. The advantages of the FGH-MCSCF method are that it eliminates the costly calculation of multidimensional integrals, treats the entire range of the hydrogen coordinates without bias, avoids the expensive diagonalization of large matrices, and accurately describes ground and excited state hydrogen vibrational wavefunctions. This paper presents the derivation of the FGH-MCSCF method, as well as a series of test calculations on systems comparing its performance with exact diagonalization schemes. © 2000 American Institute of Physics.
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  • 4
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: 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. © 2001 American Institute of Physics.
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  • 5
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 101 (1994), S. 4657-4667 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We apply "molecular dynamics with quantum transitions'' (MDQT), a surface-hopping method previously used only for electronic transitions, to proton transfer in solution, where the quantum particle is an atom. We use full classical mechanical molecular dynamics for the heavy atom degrees of freedom, including the solvent molecules, and treat the hydrogen motion quantum mechanically. We identify new obstacles that arise in this application of MDQT and present methods for overcoming them. We implement these new methods to demonstrate that application of MDQT to proton transfer in solution is computationally feasible and appears capable of accurately incorporating quantum mechanical phenomena such as tunneling and isotope effects. As an initial application of the method, we employ a model used previously by Azzouz and Borgis to represent the proton transfer reaction AH–B(large-closed-square)A−–H+B in liquid methyl chloride, where the AH–B complex corresponds to a typical phenol–amine complex. We have chosen this model, in part, because it exhibits both adiabatic and diabatic behavior, thereby offering a stringent test of the theory. MDQT proves capable of treating both limits, as well as the intermediate regime. Up to four quantum states were included in this simulation, and the method can easily be extended to include additional excited states, so it can be applied to a wide range of processes, such as photoassisted tunneling. In addition, this method is not perturbative, so trajectories can be continued after the barrier is crossed to follow the subsequent dynamics.
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  • 6
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 103 (1995), S. 8528-8537 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Classical transition state theory (TST) provides the rigorous basis for the application of molecular dynamics (MD) to infrequent events, i.e., reactions that are slow due to a high energy barrier. The TST rate is simply the equilibrium flux through a surface that divides reactants from products. In order to apply MD to infrequent events, corrections to the TST rate that account for recrossings of the dividing surface are computed by starting trajectories at the dividing surface and integrating them backward and forward in time. Both classical TST and conventional MD invoke the adiabatic approximation, i.e., the assumption that nuclear motion evolves on a single potential energy surface. Many chemical rate processes involve multiple potential energy surfaces, however, and a number of "surface-hopping'' MD methods have been developed in order to incorporate nonadiabatic transitions among the potential energy surfaces. In this paper we generalize TST to processes involving multiple potential energy surfaces. This provides the framework for a new method for MD simulation of infrequent events for reactions that evolve on multiple potential energy surfaces. We show how this method can be applied rigorously even in conjunction with phase-coherent surface-hopping methods, where the probability of switching potential energy surfaces depends on the history of the trajectory, so integrating trajectories backward to calculate the recrossing correction is problematic. We illustrate this new method by applying it in conjunction with the "molecular dynamics with quantum transitions'' (MDQT) surface-hopping method to a one-dimensional two-state barrier crossing problem. © 1995 American Institute of Physics.
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  • 7
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 101 (1994), S. 375-393 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We present a general formulation of the Hartree–Fock–Roothaan method of electronic structure calculations for systems subject to periodic boundary conditions and apply this method to crystals. The derivation of the method does not involve any divergent or conditionally convergent infinite series. The final result for the Hartree–Fock energy per unit cell consists of only absolutely convergent series and can be written in a form whose structure is almost identical to that for the nonperiodic Hartree–Fock energy. A Fock matrix that consists of only absolutely convergent series is also defined. An important feature of the method is that the Ewald potential, which has been used in the past to eliminate divergences in series involving the expectation value of the Coulomb interaction, is introduced in a physically reasonable way at an early stage of the formulation of the quantum mechanical problem. In the final result, the Ewald potential is used not only to express the Coulomb energy, but also to express the exchange energy as an absolutely convergent series, thereby eliminating the problem of slow convergence, or lack of convergence, of the series for the exchange energy. The numerical implementation of this method, which is not discussed in this paper, requires calculation of standard one- and two-electron matrix elements of the electronic kinetic energy and the Coulomb interaction, as well as certain easily calculated moments of basis function overlap charge densities. No integrals involving matrix elements of the Ewald potential between basis functions are required for evaluation of either the energy or the Fock matrix. Instead, Ewald interactions must be evaluated only for point multipoles. The methods used here to formulate the Hartree–Fock problem can be extended to formulate Møller–Plesset perturbation theory and coupled cluster theory for crystals.
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  • 8
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 111 (1999), S. 4672-4687 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: In this article we present a multistate continuum theory for multiple charge transfer reactions such as proton-coupled electron transfer and multiple proton transfer reactions. The solute is described with a multistate valence bond model, the solvent is represented as a dielectric continuum, and the transferring protons are treated quantum mechanically. This theory provides adiabatic free energy surfaces that depend on a set of scalar solvent variables corresponding to the individual charge transfer reactions. Thus this theory is a multidimensional analog of standard Marcus theory for single charge transfer reactions. For processes involving significant inner-sphere (i.e., solute) reorganization, the effects of solute intramolecular vibrations can be incorporated into the adiabatic free energy surfaces. The input quantities required for this theory are gas phase valence bond matrix elements fit to standard quantum chemistry calculations and solvent reorganization energy matrix elements calculated with standard continuum electrostatic methods. The goal of this theory is to provide insight into the underlying fundamental physical principles dictating the mechanisms and rates of multiple charge transfer reactions. © 1999 American Institute of Physics.
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  • 9
    Electronic Resource
    Electronic Resource
    s.l. : American Chemical Society
    The @journal of physical chemistry 〈Washington, DC〉 99 (1995), S. 5793-5797 
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Physics
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  • 10
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 109 (1998), S. 7051-7063 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Numerical tests are presented for a method that combines the time-dependent self-consistent-field (TDSCF) method with the reaction path Hamiltonian (RPH) derived by Miller, Handy, and Adams [J. Chem. Phys. 72, 99 (1980)]. The theoretical basis for this TDSCF-RPH method was presented in a previous paper. The equations of motion were derived for three different cases: (1) zero coupling matrix (i.e., zero reaction path curvature and zero coupling between the normal modes); (2) zero reaction path curvature and nonzero coupling between the normal modes; and (3) zero coupling between the normal modes and nonzero but small reaction path curvature. For these three cases the dynamics can always be reduced to a one-dimensional numerical time propagation of the reaction coordinate. In this paper the TDSCF-RPH methodology for all three cases is tested by comparing the TDSCF-RPH dynamics to exact quantum dynamics based on the exact Hamiltonian for simple model systems. The remarkable agreement indicates that the TDSCF-RPH method could be useful for the calculation of the real-time quantum dynamics of a wide range of chemical reactions involving polyatomic molecules. © 1998 American Institute of Physics.
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