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  • 1
    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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  • 2
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 99 (1993), S. 523-532 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We present two new methods for molecular dynamics simulations based on general Hartree–Fock (GHF) theory. The first method involves approximating ab initio STO-3G matrix elements with fitting functions to enable faster computation of the energy and forces for molecular dynamics simulations. The implementation of this method includes a frozen-core approximation. The second method involves developing semiempirical potentials by reparametrizing the fitting functions obtained in the first method to fit experimental data. This second method enables us to reproduce experimental quantities with only the computational effort of an STO-3G calculation. We successfully applied both of these methods in conjunction with the Car–Parrinello ab initio molecular dynamics method to the geometry optimization of lithium clusters, cationic and neutral, of up to five atoms.
    Type of Medium: Electronic Resource
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  • 3
    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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  • 4
    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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  • 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
    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
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 105 (1996), S. 2236-2246 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We present the new method "multiconfigurational molecular dynamics with quantum transitions'' (MC-MDQT) for the simulation of processes involving multiple proton transfer reactions. MC-MDQT is a mixed quantum/classical molecular dynamics method that allows the quantum mechanical treatment of the nuclear motion of multiple hydrogen atoms and accurately describes branching processes (i.e., processes involving multiple channels or pathways). MC-MDQT is based on the surface hopping method MDQT, which has already been applied to single proton transfer reactions in solution, where the nuclear motion of only the hydrogen atom being transferred is treated quantum mechanically. The direct extension of MDQT to multiple proton transfer reactions, where many hydrogen atoms must be treated quantum mechanically, is not computationally practical. In MC-MDQT a multiconfigurational self-consistent-field method is combined with MDQT to allow the quantum mechanical treatment of multiple hydrogen atoms while still including the significant correlation. The adiabatic states are expanded in a basis set of single configurations, which are products of one-particle states calculated using effective Hamiltonians derived from the occupied adiabatic state. Thus the one-particle states and the multiconfigurational adiabatic states must be calculated self-consistently. Both the MC-MDQT and the full basis set expansion MDQT methods are applied to a model system comprised of two quantum protons moving in double well potentials and one classical harmonic solvent degree of freedom. The results show that MC-MDQT incorporates the significant correlation and accurately describes branching processes. The MC-MDQT method is also used to study model systems comprised of three quantum protons and one classical solvent degree of freedom. © 1996 American Institute of Physics.
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  • 8
    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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  • 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 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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