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Typically, electronically (vibrationally) adiabatic refers to reactions occurring in the electronic (vibrational) ground state, whereas electronically (vibrationally) nonadiabatic refers to reactions involving excited electronic (vibrational) states. The adiabatic limit corresponds to strong coupling and the non-adiabatic limit corresponds to weak coupling between the charge-transfer states.
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37
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0042706987
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The nonadiabatic rate is a sum of products of a prefactor and an exponential of a free-energy barrier, where the summation is over all relevant reactant and product quantum states. The prefactor differs in the adiabatic and nonadiabatic limits. For nonadiabatic electron and hydrogen-transfer reactions, the prefactor includes the coupling matrix element between the reactant and product wave functions, which determines the tunneling probability.
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38
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0041705365
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The assumption of a single reaction coordinate may not be appropriate for all types of reactions (e.g., multiple charge-transfer reactions). Furthermore, the choice of reaction coordinate is not unique. In some descriptions, the transition state is a saddle point on the coordinate potential energy surface, and the collective reaction coordinate corresponds to the minimum energy path from the transition state to the reactant and product. In alternative descriptions, the transition state is not necessarily a saddle point on the coordinate potential energy surface. For example, the collective reaction coordinate for charge-transfer reactions can be defined as the difference in the energies of two charge-transfer states interacting with the environment, and the transition state corresponds to the configuration at which this energy reaction coordinate is zero (39, 64, 71, 74).
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note
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For a two-state model of electron transfer, the electron is localized on the donor for state 1 and on the acceptor for state 2. For the analogous two-state model of hydrogen transfer, the hydrogen vibrational wave function is localized near the donor for state 1 and near the acceptor for state 2. The motion of the heavy nuclei leads to a configuration for which the two states are degenerate. For hydrogen-transfer reactions, the hydrogen may tunnel at this degenerate configuration. If the vibrational ground state is above the hydrogen-transfer barrier, or this barrier is zero, the reaction is not called "tunneling" but is still quantum mechanical in nature.
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76
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0042706986
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note
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Simulation approaches in which a tunneling "correction" is included in the prefactor (65, 117, 118) are useful for certain hydrogen-transfer systems but may be problematic in other regimes (67). An alternative approach (64) includes nuclear quantum mechanical effects for the calculation of the free-energy barrier, as well as for the calculation of the transmission coefficient prefactor. In this approach, the transition-state theory rate constant represents the adiabatic rate, and the transmission coefficient accounts for nonadiabatic effects as well as dynamical barrier recrossings. In this case (64), the transmission coefficient is between zero and unity, whereas tunneling corrections (65, 117, 118) introduce a prefactor that may be greater than unity.
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77
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0041705363
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note
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These two effects are not rigorously separable in the enzyme reaction, and many enzyme motions contribute to both types of effects. Moreover, there is not a one-to-one correspondence between these two effects and the free-energy barrier and transmission coefficient.
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80
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0042205868
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note
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For hydrogen-transfer reactions, the hydrogen donor-acceptor vibrational mode can be either included in the collective reaction coordinate representing the reorganization of the environment in Fig. 4 (64) or treated separately from the other motions in the enzyme system (66). The equilibrium, thermally averaged value of the donor-acceptor distance has been shown to change substantially along the collective reaction coordinate for hydrogen-transfer reactions (59, 61).
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81
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90
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0043208130
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note
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Note that the network of coupled motions identified from the simulations is most likely not complete or unique, and the analysis is unable to differentiate between motions playing an active role in catalysis and motions responding to alterations caused by catalysis. Moreover, the details of this network may depend on the potential energy surface and sampling procedure implemented in the simulations.
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122
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S.J.B. acknowledges funding from NIH grants GM13306 and GM24129. S.H.-S. acknowledges funding from NIH grant GM56207 and NSF grant CHE-0096357. We also thank Yolanda Small and James Watney for creating the figures.
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