The overall classical transmission coefficient as a function of the reduced friction for the model proton transfer system coupled to a dissipative bath at . The results were obtained with the plateau reactive flux method (triangles) and Keck’s reactive flux method (squares). The results obtained previously with the plateau reactive flux method by Topaler and Makri (Ref. 34) are shown as circles. The Kramers-Grote-Hynes transmission coefficient (Refs. 96 and 97) (dashed line) and the Pollak-Grabert-Hänggi turnover theory (Ref. 98) (solid line) are also shown. The equations for these theories and the corresponding data were obtained from Ref. 34.
The proton potential energy curves averaged over (a) reactant bath configurations and (b) transition state bath configurations. The results are shown for the following values of the reduced friction : 1.0 (solid), 1.5 (dashed), 3.0 (dotted), and 4.5 (dot-dashed).
The average proton potential energy curves shown in Fig. 2 and the corresponding proton vibrational states for (left) and (right). The proton potentials averaged over reactant bath configurations are shown on the top, and the proton potentials averaged over transition state bath configurations are shown on the bottom.
The potential of mean force , where , for the following values of the reduced friction : 1.0 (solid), 1.5 (dashed), 3.0 (dotted), and 4.5 (dot-dashed).
Schematic illustration of a proton transfer reaction in the condensed phase. The proton potential energy curves and the corresponding ground and excited vibrational states are depicted. The solid and dashed lines represent the occupied and unoccupied adiabatic vibrational states, respectively. Initially the reactant well is stabilized, and the proton is in the ground state localized in the reactant well. Fluctuations of the environment lead to a symmetric double well potential, and the proton vibrational wave functions are delocalized over the reactant and product wells. Further fluctuations stabilize the product well. In the adiabatic pathway, the system remains in the ground state and the proton becomes localized in the product well. In the nonadiabatic pathway, the system switches to the excited vibrational state and the proton remains localized in the reactant well.
Analysis of a representative nonadiabatic MDQT trajectory. The reaction coordinate , the quantum probabilities and the vibrational state energies for (solid) and (dashed), and the nonadiabatic coupling between the lowest two vibrational states are depicted as functions of time. For clarity, only the portion of the trajectory near the dividing surface (i.e., near time ) is shown. This trajectory exhibits two nonadiabatic transitions from the ground state to the first excited state at and and two nonadiabatic transitions from the first excited state down to the ground state at and . These nonadiabatic transitions lead to a recrossing that prevents the reaction.
The overall transmission coefficient as a function of the reduced friction for the model proton transfer system coupled to a dissipative bath at . The hybrid quantum/classical reactive flux approach results (filled circles) and the numerically exact results obtained by Topaler and Makri (Ref. 34) (open circles) are shown. The Wolynes transmission factor (Ref. 99) from quantum Grote-Hynes theory (Ref. 96) (dotted line) and the quantum turnover theories due to Hänggi et al. (Refs. 35 and 100) (solid line) and to Rips and Pollak (Ref. 101) (dashed line) are also shown. The equations for these theories and the corresponding data were obtained from Ref. 34.
The values for the TST rate constant , the two factors comprising the TST rate constant, the transmission coefficient , and the overall transmission coefficient for four different friction values. The first factor comprising the TST rate constant is and the second factor is . The TST rate constant is given in Eq. (25), the transmission coefficient is given in Eq. (24), and the overall transmission coefficient is defined in Eq. (9).
Article metrics loading...
Full text loading...