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Direct simulation of proton-coupled electron transfer across multiple regimes
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10.1063/1.4797462
/content/aip/journal/jcp/138/13/10.1063/1.4797462
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/13/10.1063/1.4797462

Figures

Image of FIG. 1.
FIG. 1.

(a) Schematic illustration of a co-linear PCET reaction, where De/Dp and Ae/Ap are the respective donor and acceptor for the electron/proton. (b) Schematic illustration of sequential and concerted PCET reaction mechanisms, indicating the rate constants for the individual charge transfer processes. The sequential mechanism proceeds along the horizontal and vertical edges of the schematic, whereas the concerted mechanism proceeds along the diagonal.

Image of FIG. 2.
FIG. 2.

Reactive RPMD trajectories reveal distinct concerted (red), sequential PT-ET (purple), and sequential ET-PT (orange) reaction mechanisms for PCET in System 1. The trajectories are projected onto the FE surface in the electron bead-count coordinate, f b, and the proton centroid coordinate, , with contour lines indicating FE increments of 2 kcal/mol.

Image of FIG. 3.
FIG. 3.

(a) The 1D FE profile in the electron bead-count coordinate, F(f b), utilized in the RPMD rate calculation for the concerted PCET reaction. (b) The corresponding transmission coefficient for the concerted PCET reaction. (c) The 1D FE profile in the electron bead-count coordinate, F SET(f b), utilized in the RPMD rate calculation for the ET reactions prior to PT in the sequential PCET mechanism. (d) The corresponding forward (red) and reverse (blue) transmission coefficients for the ET reactions prior to PT. (e) The 1D FE profile in the proton centroid coordinate, , utilized in the RPMD rate calculation for the PT reactions prior to ET in the sequential PCET mechanism. (f) The corresponding forward (red) and reverse (blue) transmission coefficients for the PT reactions prior to ET. All FE profiles are plotted in kcal/mol.

Image of FIG. 4.
FIG. 4.

(a) Reactive RPMD trajectories (red) and the average over the ensemble of reactive trajectories (yellow) for the concerted PCET reaction in System 1 reveal a Marcus-type solvent-gating mechanism indicated by the black arrows. The trajectories are projected onto the FE surface in the electron bead-count coordinate, f b, and the solvent position coordinate, q s, with contour lines indicating FE increments of 2 kcal/mol. The regions corresponding to the concerted PCET reactant (OU), product (RP), and dividing surface (DS) are indicated. (b) Illustration of the mechanism for concerted PCET. The left panels present the vibronic diabatic free energy surfaces along the solvent coordinate; the red dot indicates the solvent configuration associated with the OU, RP, and DS regions indicated in (a). The right panels present the double-well potential that is experienced by the electron in the OU, RP, and DS regions, as well as the ring-polymer configuration in the electron position coordinate at the corresponding points along a typical reactive trajectory. (c) The combined dipole for the transferring particles in the ensemble of reactive RPMD trajectories, d ep(t) (black), as well as the individual components from the transferring electron, d e (red), and the transferring proton, d p (blue), for the concerted PCET reaction in System 1.

Image of FIG. 5.
FIG. 5.

(a) ET reaction rates as a function of the temperature-reduced electronic coupling, obtained using RPMD (red), the non-adiabatic rate expression for ET (Eq. (22) , black), and the adiabatic rate expression for ET (Eq. (15) , blue) for Systems 4a-4g. (b) and (c) At left, the electron position as a function of the ring-polymer bead index for (b) System 4a (log (βV ET) = −2.98) and (c) System 4g (log (βV ET) = 1.32); at right, a schematic illustration of the corresponding double-well potentials that are experienced by the transferring electron at the dividing surface, as well as the ring-polymer configurations in the electron position coordinate. The orange and purple stripes indicate the positions of the electron donor and acceptor sites, respectively. (d) The fraction of ring-polymer configurations at the dividing surface for ET that contain either a single kink-pair (black) or multiple kink-pairs (red) as a function of the temperature-reduced electronic coupling.

Image of FIG. 6.
FIG. 6.

(a) Concerted PCET reaction rates as a function of the temperature-reduced electronic coupling, obtained using RPMD (red), the fully non-adiabatic rate expression (Eq. (19) , black) and the partially adiabatic rate expression (Eq. (16) , blue) for Systems 2a-2f. (b)–(d) At left, the electron position as a function of the ring-polymer bead index for (b) System 2a (log (βV ET) = −2.28), (c) System 2d (log (βV ET) = 0.72), and (d) System 2f (log (βV ET) = 2.02); at right, a schematic illustration of the corresponding potentials that are experienced by the transferring electron at the dividing surface, as well as the ring-polymer configurations in the electron position coordinate. The orange, purple, and green stripes indicate the positions of the electron donor site, the electron acceptor site, and transferring proton, respectively. (e) The fraction of ring-polymer configurations at the dividing surface for concerted PCET that contain either a single kink-pair (black) or multiple kink-pairs (red) as a function of the temperature-reduced electronic coupling.

Image of FIG. 7.
FIG. 7.

(a) Concerted PCET reaction rates as a function of the temperature-reduced vibrational coupling, obtained using RPMD (red), the partially adiabatic rate expression (Eq. (16) , blue), and the fully adiabatic rate expression (Eq. (15) , green) for Systems 3a-3e. (b) The expectation value for the radius of gyration in the proton coordinate (Eq. (50) ) calculated either in the ensemble for the PCET reactant basin (blue) or the ensemble constrained to the PCET dividing surface (red). The insets schematically illustrate the potential that is experienced by the transferring proton and the lowest vibrational eigenstate for the proton at the concerted PCET dividing surface, as well as the ring-polymer configurations in the proton position coordinate for System 3a (log (βV PT) = −4.3, bottom-left) and System 3e (log (βV PT) = 0.95, top-right).

Tables

Generic image for table
Table I.

Values of the electronic coupling, V ET, vibrational coupling, V PT, and reorganization energy, λ, for the system-bath model systems for PCET. a

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Table II.

Values of the electronic coupling, V ET and reorganization energy, λ, for ET systems that vary between the adiabatic and non-adiabatic regimes. a

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Table III.

RPMD rates for the forward and reverse ET and PT reactions in the sequential mechanism.

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Table IV.

Reaction rates for the full ET-PT, PT-ET, and concerted PCET mechanisms calculated using RPMD and Eqs. (45) and (46) . a

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Table V.

Parameters for the donor coulombic well in the intrinsic electron potential energy function of Eq. (26) . a

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Table VI.

Parameters for the PCET and ET systems. a

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Table VII.

Potential energy function parameters for the PCET systems. a

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Table VIII.

Potential energy function parameters for the ET systems. a

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Table IX.

Parameters for the auxiliary restraining potential in Eqs. (C1)–(C3) . a

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Table X.

Parameters for the polynomial fit to the lowest adiabatic electronic state (Eq. (42) ). a

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/content/aip/journal/jcp/138/13/10.1063/1.4797462
2013-04-02
2014-04-23
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Direct simulation of proton-coupled electron transfer across multiple regimes
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/13/10.1063/1.4797462
10.1063/1.4797462
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