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  • 1
    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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  • 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
    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
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 99 (1993), S. 1901-1913 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The general Hartree–Fock (GHF) method is a quantum mechanical method for electronic structure calculations that uses a single determinantal wave function with no restrictions on the one-electron orbitals other than orthonormality and the use of a specific basis set. The more familiar restricted Hartree–Fock (RHF) and unrestricted Hartree–Fock (UHF) methods can be regarded as special cases of the GHF method in which additional restrictions are imposed on the occupied orbitals. We propose that the GHF method is very suitable as an electronic structure method to be incorporated into computer simulations that combine the calculation of the Born–Oppenheimer ground state surface with the simulation of the motion of the nuclei on that surface. In particular, for many problems of interest there is only a single GHF minimum of the energy, and the GHF wave function is a continuous function of nuclear positions. The RHF and UHF methods, in comparison, typically have a multiplicity of local minima with curve crossings that generate a discontinuous behavior of the ground electronic state wave function as a function of nuclear positions. In this paper, we use energy minimization techniques to identify and characterize the UHF and GHF electronic minima at fixed nuclear positions for three model systems. The results verify the above assertions and suggest that the GHF method would be more suitable than the RHF or UHF methods for computer simulations.
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  • 5
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    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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  • 6
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    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 110 (1999), S. 11166-11175 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: This paper presents a comparison of surface hopping and mean field approaches for simulating proton transfer reactions. In these mixed quantum/classical simulations, the transferring proton(s) are treated quantum mechanically, while the remaining nuclei are treated classically. The surface hopping method used for these calculations is the molecular dynamics with quantum transitions (MDQT) method based on Tully's fewest switches algorithm. In addition, this paper describes a modified MDQT method (denoted MDQT*) that eliminates classically forbidden transitions to promote consistency between the quantum probabilities and the fraction of trajectories in each adiabatic state. The MDQT, MDQT*, mean field, and fully quantum dynamical methods are applied to one-dimensional model single and double proton transfer reactions. Both the MDQT and MDQT* calculations agree remarkably well with the fully quantum dynamical calculations, while the mean field calculations exhibit qualitatively incorrect behavior. © 1999 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 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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  • 8
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    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 108 (1998), S. 7085-7099 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: 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)] is proposed. This TDSCF-RPH method allows the calculation of the real-time quantum dynamics of chemical reactions involving polyatomic molecules. When both the coupling between the normal modes and the curvature are zero, the dynamics of an F-dimensional system is shown to reduce to a one-dimensional numerical time propagation. When the reaction path curvature is zero and the coupling between the normal modes is non-zero, the dynamics is shown to still reduce to a one-dimensional problem for a specific choice of initial wavepacket (which can have an arbitrary component for the reaction coordinate), but F coupled one-dimensional equations of motion must be propagated for a general initial wavepacket (unless the RPH is transformed to the diabatic representation). When the coupling between the normal modes is zero and the reaction path curvature is non-zero but small, the dynamics is shown to reduce to a one-dimensional numerical time propagation for an arbitrary initial wavepacket. The derivations of the equations of motion for these cases are presented in this paper, and numerical tests are presented in a separate paper. © 1998 American Institute of Physics.
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  • 9
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 107 (1997), S. 5727-5739 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Photoinduced proton-coupled electron transfer is investigated for a minimal model consisting of three coupled degrees of freedom that represent an electron, a proton, and a collective solvent coordinate. Altering the parameters in this model generates a wide range of proton-coupled electron transfer (PCET) dynamics. Four different models are presented in this paper. Three of these models represent sequential mechanisms and one represents a concerted mechanism. The adiabatic potential energy curves as a function of solvent coordinate and the corresponding two-dimensional wave functions, which depend on both the proton and the electron coordinates, are calculated in order to study the possible mechanisms of photoinduced PCET. The surface hopping method "molecular dynamics with quantum transitions" (MDQT), which incorporates nonadiabatic transitions between adiabatic quantum states, is utilized to simulate the dynamics of photoinitiated PCET for two of these model systems. In this application of MDQT the proton and electron coordinates are treated quantum mechanically, and the solvent coordinate is treated classically. A relatively large number (e.g., 11) of mixed proton/electron adiabatic states are included in the MDQT simulations. The reaction is initiated on the electronically excited state, and many different dynamical pathways to lower energy stable states are observed. Nonadiabatic effects are shown to play an essential role in determining the rates and mechanisms of photoinduced PCET reactions. This paper differs from previous studies of PCET reactions in that it presents real-time nonadiabatic molecular dynamics simulations of model PCET reactions initiated on an electronically excited state. © 1997 American Institute of Physics.
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  • 10
    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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