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Multidimensional treatment of stochastic solvent dynamics in photoinduced proton-coupled electron transfer processes: Sequential, concerted, and complex branching mechanisms
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10.1063/1.3651083
/content/aip/journal/jcp/135/14/10.1063/1.3651083
http://aip.metastore.ingenta.com/content/aip/journal/jcp/135/14/10.1063/1.3651083

Figures

Image of FIG. 1.
FIG. 1.

Model systems for collinear PCET (Model I) and orthogonal PCET (Model II). The green balls denote the electron donor and acceptor sites, the blue balls denote the proton donor and acceptor sites, and the gray ball denotes the transferring hydrogen. The cavities constructed from overlapping spheres around the sites are also shown. These cavities are used for the FRCM calculations of the solvent reorganization energy matrix elements. The arrows below depict the direction of PT and ET in these model systems.

Image of FIG. 2.
FIG. 2.

Initial conditions used for the simulations. (a) Diabatic harmonic proton potentials, , for the 1a and 1b diabatic electronic states and the initial proton wavepacket following photoexcitation (at t = 0) for the initial conditions A (red) and B (blue). The proton vibrational wavepacket prior to photoexcitation (green) corresponds to the ground proton vibrational state in the electronic ground state (not shown). (b) Initial distributions for the solvent coordinates Z p and Z e for the initial conditions A (red) and B (blue) for the symmetric Model II. The contour plot schematically depicts the four diabatic vibronic free energy surfaces with minima indicated as 1a, 1b, 2a, and 2b. For both initial conditions, the distributions are centered at Z e = 0. The distributions are centered at the Z p value corresponding to the 1a/2a minima for initial condition A and the 1b/2b minima for initial condition B.

Image of FIG. 3.
FIG. 3.

Results for Model IA, the symmetric collinear PCET model system with initial condition A. (a) The time-dependent populations of the lowest two adiabatic vibronic states, , and the diabatic electronic states, (i = 1a, 1b, 2a, 2b), where the notation for these populations is slightly altered for convenience. (b) The time-dependent marginal distributions, P (solv)(Y p) and P (solv)(Y e), for the collective solvent coordinates Y p and Y e, corresponding predominantly to PT and ET, respectively. The darker blue corresponds to a greater value of the marginal distribution function. The values of the solvent coordinates corresponding to the 1a and 2b minima on the diabatic vibronic surfaces are indicated by dashed lines. (c) Snapshots of the distributions, , of the transformed solvent coordinates Z p and Z e in the lowest two adiabatic vibronic states along the trajectories. In the first snapshot, the minima of the ground adiabatic vibronic surface are labeled according to the dominant diabatic electronic state. See supplementary material for a movie of the time-dependent solvent distribution (Ref. 55).

Image of FIG. 4.
FIG. 4.

Results for Model IB, the symmetric collinear PCET model system with initial condition B. (a) The time-dependent populations of the lowest five adiabatic vibronic states, , and the diabatic electronic states, (i = 1a, 1b, 2a, 2b). (b) The time-dependent marginal distributions, P (solv)(Y p) and P (solv)(Y e), for the collective solvent coordinates Y p and Y e, corresponding predominantly to PT and ET, respectively. The darker blue corresponds to a greater value of the marginal distribution function. The values of the solvent coordinates corresponding to the 1a and 2b minima on the diabatic vibronic surfaces are indicated by dashed lines. (c) Snapshots of the distributions, , of the transformed solvent coordinates Z p and Z e in the lowest five adiabatic vibronic states along the trajectories. In the first snapshot, the minimum of the ground adiabatic vibronic surface is labeled according to the dominant diabatic electronic state. See supplementary material for a movie of the time-dependent solvent distribution (Ref. 55).

Image of FIG. 5.
FIG. 5.

Results for Model IA, the biased collinear PCET model system with initial condition A. (a) The time-dependent populations of the lowest five adiabatic vibronic states, , and the diabatic electronic states, (i = 1a, 1b, 2a, 2b). (b) The time-dependent marginal distributions, P (solv)(Y p) and P (solv)(Y e), for the collective solvent coordinates Y p and Y e, corresponding predominantly to PT and ET, respectively. The darker blue corresponds to a greater value of the marginal distribution function. The values of the solvent coordinates corresponding to the 1a, 2a, and 2b minima on the diabatic vibronic surfaces are indicated by dashed lines. (c) Snapshots of the distributions, , of the transformed solvent coordinates Z p and Z e in the lowest five adiabatic vibronic states along the trajectories. In the first snapshot, the minimum of the ground adiabatic vibronic surface is labeled according to the dominant diabatic electronic state. See supplementary material for a movie of the time-dependent solvent distribution (Ref. 55).

Image of FIG. 6.
FIG. 6.

Results for Model IIA, the symmetric orthogonal PCET model system with initial condition A. (a) The time-dependent populations of the lowest two adiabatic vibronic states, , and the diabatic electronic states, (i = 1a, 1b, 2a, 2b). (b) The time-dependent marginal distributions, P (solv)(Y p) and P (solv)(Y e), for the collective solvent coordinates Y p and Y e, corresponding predominantly to PT and ET, respectively. The darker blue corresponds to a greater value of the marginal distribution function. The values of the solvent coordinates corresponding to the 1a, 1b, 2a, and 2b minima on the diabatic vibronic surfaces are indicated by dashed lines. (c) Snapshots of the distributions, , of the transformed solvent coordinates Z p and Z e in the lowest two adiabatic vibronic states along the trajectories. In the first snapshot, the minima of the ground adiabatic vibronic surface are labeled according to the dominant diabatic electronic state. See supplementary material for a movie of the time-dependent solvent distribution (Ref. 55).

Image of FIG. 7.
FIG. 7.

Results for Model IIB, the symmetric orthogonal PCET model system with initial condition B. (a) The time-dependent populations of the lowest five adiabatic vibronic states, , and the diabatic electronic states, (i = 1a, 1b, 2a, 2b). (b) The time-dependent marginal distributions, P (solv)(Y p) and P (solv)(Y e), for the collective solvent coordinates Y p and Y e, corresponding predominantly to PT and ET, respectively. The darker blue corresponds to a greater value of the marginal distribution function. The values of the solvent coordinates corresponding to the 1a, 1b, 2a, and 2b minima on the diabatic vibronic surface are indicated by dashed lines. (c) Snapshots of the distributions, , of the transformed solvent coordinates Z p and Z e in the lowest five adiabatic vibronic states along the trajectories. In the first snapshot, the minima of the diabatic vibronic surfaces are labeled according to the dominant diabatic electronic state. See supplementary material for a movie of the time-dependent solvent distribution (Ref. 55).

Tables

Generic image for table
Table I.

Radii and charges for the model PCET systems. ET and PT donor sites are denoted De and Dp, respectively; ET and PT acceptor sites are denoted Ae and Ap, respectively; and the transferring proton is denoted H. All of the quantities in this table are used to calculate the solvent reorganization energy matrix elements, and the charges are used to calculate the electrostatic contributions to the gas phase potentials of the reaction complex.

Generic image for table
Table II.

Solvent reorganization energies, λPT and λET, for PT and ET reactions, respectively, and cross-reorganization energy γ for the model PCET systems studied in this paper. Quantities given in units of kcal/mol.

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/content/aip/journal/jcp/135/14/10.1063/1.3651083
2011-10-13
2014-04-19
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Multidimensional treatment of stochastic solvent dynamics in photoinduced proton-coupled electron transfer processes: Sequential, concerted, and complex branching mechanisms
http://aip.metastore.ingenta.com/content/aip/journal/jcp/135/14/10.1063/1.3651083
10.1063/1.3651083
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