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  • 1
    Electronic Resource
    Electronic Resource
    Outer-sphere electron transfer in polar solvents: Quantum scaling of strongly interacting systems (1993)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 99 (1993), S. 969-978 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The spin–boson Hamiltonian model is used to study electron transfer (ET) reactions of strongly interacting systems in polar solvents in the limit of fast dielectric relaxation of the solvent. The spectrum of polarization modes consists of low frequency modes which are treated classically, and high frequency modes which are treated quantum mechanically. A general explicit formula for the rate valid in all orders of perturbation theory in electronic coupling is derived. The rate formula is applicable in a wide range of parameters, including the inverted region of the reaction where the quantum tunneling corrections give the main contribution to the rate. It is found that the quantum degrees of freedom can be effectively eliminated from the model by renormalizing the electronic coupling matrix element. This renormalization results in the following scaling property of the electron transfer systems: a system containing both classical and quantum degrees of freedom is equivalent to a system of lower dimensionality, containing only classical degrees of freedom, with renormalized electronic coupling matrix element. An explicit formula for the renormalization is obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.465310
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  • 2
    Electronic Resource
    Electronic Resource
    Quantum effects in electron transfer reactions with strong electronic coupling (1994)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 101 (1994), S. 9354-9365 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A new complex centroid reaction coordinate method is used to study electron transfer systems with strong electronic coupling. Formal analogy between current problem and the Ising model of one-dimensional spin system is used to develop a useful approximation for the partition function of electron transfer system in all orders of perturbation theory and when quantum effects are present. The reactions in the inverted region are discussed. The range of applicability of the usual nonadiabatic theory is re-examined. It is concluded that quantum solvent modes can effectively reduce electronic coupling in such a way that a nonadiabatic behavior can sometimes be induced in conventionally strongly coupled systems. Such an induced quantum nonadiabaticity is demonstrated in a numerical calculation. © 1994 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.468444
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  • 3
    Electronic Resource
    Electronic Resource
    Tunneling currents in electron transfer reaction in proteins. II. Calculation of electronic superexchange matrix element and tunneling currents using nonorthogonal basis sets (1996)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 105 (1996), S. 10819-10829 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: In this paper we further develop the concept of interatomic tunneling currents [A.A. Stuchebrukhov, J. Chem. Phys. 104, 8424 (1996)] for the description of long-range electron tunneling in proteins. Here we discuss a formulation of the theory for the case when nonorthogonality of the atomic basis set of the medium propagating electron is explicitly taken into account. This method provides an effective computational scheme for an exact, i.e., nonperturbative, evaluation (in one-electron approximation) of the superexchange electron tunneling matrix element, and allows one to determine which regions in the protein matrix are important for the tunneling process. The theory is applied for calculation of tunneling currents and the electronic matrix element in His126-Ru-modified blue copper protein azurin from a recent experimental work of Gray and co-workers. Analysis of interatomic currents reveals a nontrivial structure of the tunneling flow between donor and acceptor in the intervening protein medium in this system. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.472890
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  • 4
    Electronic Resource
    Electronic Resource
    Tunneling currents in electron transfer reactions in proteins (1996)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 104 (1996), S. 8424-8432 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A new theoretical method for the analysis of the superexchange coupling and localization of electron tunneling pathways in long distance electron transfer reactions is introduced. The new method allows one to examine spatial distribution of microscopic quantum mechanical tunneling currents flowing through individual atoms, or to evaluate the relative probability that the tunneling electron will pass through an individual atom, in the intervening medium between donor and acceptor in the course of an electron transfer reaction. It is shown how the interatomic tunneling currents introduced in this paper can be calculated using methods of quantum chemistry. The method provides a rigorous theoretical framework for the description of the tunneling process in long-range electron transfer reactions in proteins. The relation of the present theory of tunneling currents to the theory of pathways of Beratan and Onuchic is discussed. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.471592
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  • 5
    Electronic Resource
    Electronic Resource
    Tunneling currents in long-distance electron transfer reactions. IV. Many-electron formulation. Nonorthogonal atomic basis sets and Mulliken population analysis (1998)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 108 (1998), S. 8510-8520 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: In this paper we further develop the formulation of the method of tunneling currents for the description of the tunneling transition in long-distance bridge-mediated electron transfer reactions introduced in our previous work [A. A. Stuchebrukhov, J. Chem. Phys. 104, 8424 (1996); 105, 10819 (1996)]. Here we present a full many-election treatment of the problem in the case when the atomic basis set employed for the description of the medium is nonorthogonal. In this formulation we introduce many-electron Mulliken population operator and derive a set of kinetic equations describing evolution of different atomic states during the tunneling transition. The analysis of the kinetic equations naturally leads then to a concept of electron density fluxes, or currents, between atoms of the medium propagating the tunneling electron. Explicit formulas expressing interatomic tunneling currents in terms of the coefficients of expansion of molecular orbitals of donor and acceptor diabatic electronic states in the atomic basis set are derived. Specific effects due many-electron nature of the system and non-orthogonality (overlaps) of the atomic states are discussed. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.476280
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  • 6
    Electronic Resource
    Electronic Resource
    Tunneling currents in long-distance electron transfer reactions. III. Many-electron formulation (1998)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 108 (1998), S. 8499-8509 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Many-electron formulation of the method of interatomic tunneling currents introduced in our earlier work [J. Chem. Phys. 104, 8424 (1996); 105, 10819 (1996)] for the description of long-range electron tunneling in large molecules such as proteins or DNA is proposed. The tunneling currents can be used both for calculation of the tunneling matrix element and for the description of the spatial distribution of tunneling pathways at the atomic level of resolution. It is shown that the tunneling currents can be expressed as a matrix element of a certain (current) operator evaluated between two diabatic nonorthogonal one- or multideterminant wave functions of the initial and final states of the electrons in the system. These states can be found in the standard ground state energy minimization calculations. Explicit expressions for the currents in terms of the atomic basis functions and the transformation matrices to molecular orbitals of the donor and acceptor states are given. Thus, the proposed theory provides a method that allows ordinary electronic structure calculations to be utilized for studies of tunneling dynamics in many-electron systems. All electron–electron interactions are included in the expressions for currents at the Hartree–Fock level, so that electron polarization effects arising due to interaction of the tunneling electron and other electrons in the system are taken into account in such a description. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.476279
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  • 7
    Electronic Resource
    Electronic Resource
    New expression for the effective transfer matrix element in long-range electron transfer reactions (1998)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 109 (1998), S. 4960-4970 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A new expression for the effective transfer matrix element, TDA, in long-range electron transfer is derived. This expression corrects the second-order perturbation theory estimate by accounting for an infinite number of terms in the perturbation expansion. The correction factors measure the extent of delocalization of the diabatic donor and acceptor states. A simple procedure is devised to adjust the molecule to its transition state, which is the point of avoided crossing of the energies of the adiabatic states. The new expression is used to compute the half-splitting in these eigenenergies, which equals TDA, without recourse to diagonalization. When checked against direct diagonalization for a truncated model of a ruthenium-modified azurin protein, this method located the point of avoided crossing and produced an estimate of the energy half-splitting which agreed with the result of diagonalization with exceptional accuracy. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.477107
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  • 8
    Electronic Resource
    Electronic Resource
    Tunneling currents in proteins: Nonorthogonal atomic basis sets and Mulliken population analysis (1997)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 107 (1997), S. 6495-6498 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A rigorous kinetic justification is given of the expression for interatomic tunneling currents introduced in our earlier work [Stuchebrukhov, J. Chem. Phys. 105, 10819 (1996)] for the analysis of long-distance electron transfer reactions when a nonorthogonal atomic basis set is used for the description of the medium intervening between donor and acceptor. The analysis is based on the kinetic equations describing the evolution of the Mulliken populations of the atomic states in the medium during the tunneling transition of a long-distance electron transfer reaction. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.474308
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  • 9
    Electronic Resource
    Electronic Resource
    Effect of quantum modes in biological electron transfer reactions: A useful approximation for the harmonic model with frequency change and Duchinsky rotation (2000)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 112 (2000), S. 9015-9024 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Although general theory of quantum effects in nonadiabatic electron transfer (ET) reactions based on spin-boson Hamiltonian is well known, its application to problems of biological interest is hampered by the amount of computational work needed to map the details of the real system onto the parameters of the model. In this paper we propose a new formulation of theory of quantum effects which remedies many defects of the usual approach. In the harmonic approximation an exact expression for the rate of electron transfer has long been known that includes effects of frequency change and Duchinsky rotation (mixing) of vibrational modes of donor and acceptor complexes. This expression, however, is not suitable for practical applications due to its complexity. We have developed an exceptionally accurate approximation that is capable of capturing all details of real redox systems typical for biological problems, yet simple enough to be practical. The approximation is based on the well-known Jortner expression for the quantum rate. We describe a method for calculation of the parameters of the Jortner model, average quantum frequency and average excitation number, which are usually treated as adjustable parameters, and in our case are calculated by ab initio quantum chemistry methods. The model is tested against the exact result. We also have tested another useful approximation, which is as good as the first one, however, in a limited region around maximum of ET rate. In this approximation the rate constant has the same form as the semiclassical Marcus expression, except that instead of one reorganization energy λ, it contains two λ's. We show how these parameters can be calculated for realistic systems. Examples of such calculations are presented for a novel electron transfer between tryptophan and tyrosine, which was discovered recently in photolyase, a DNA repair enzyme, and some other biological systems. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.481513
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  • 10
    Electronic Resource
    Electronic Resource
    Concerted electron and proton transfer: Transition from nonadiabatic to adiabatic proton tunneling (2000)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 113 (2000), S. 10438-10450 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A concerted electron–proton transfer reaction is discussed, in which proton tunneling occurs simultaneously with electronic transition. It is assumed that the potential in which the proton moves is formed by two electronic states, which in the absence of their interaction would cross in the region between the two minima of the proton adiabatic potential. The proton tunneling between the two wells is, therefore, coupled to a switch between the two electronic states. The later occurs only when the proton is in the tunneling region under the barrier. A simple analytical expression for the tunneling matrix element TDA is derived, which is uniformly correct for small and large values of the electronic coupling. For small electronic coupling our expression coincides with that obtained in the nonadiabatic theory of proton-coupled electron transfer reactions. For large electronic coupling the expression is reduced to that obtained in the Born–Oppenheimer approximation. The transition from nonadiabatic to adiabatic tunneling is governed by the magnitude of the Landau–Zener parameter defined for the tunneling process. The obtained result is discussed in the context of the proton tunneling time. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1323723
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