Vertical Detachment Energy of Hydrated Electron Based on a Modified Form of Solvent Reorganization Energy

Wang, Xingjian; Zhu, Quan; Li, Yun-Kui; Cheng, Xue-Min; Li, Xiangyuan; Fu, Ke‐Xiang; He, Fucheng

doi:10.1021/jp908759s

Cited by 15 publications

(13 citation statements)

References 57 publications

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“…If we alternatively make the discussion with the constraining external field

{boldE}_{ex}

which is used to hold the equilibrium with the “residual” polarization

P^{'} = {boldP}_{2}^{non} - {boldP}_{2}^{eq}

, the solvent reorganization energy can be given in the parallel way, that is,

λ = \frac{1}{2} \int_{v} E_{ex} \cdot boldnormal P^{'} d V

…”

Section: Solvent Reorganization Energymentioning

confidence: 77%

“…Combining Eqs. and , the constraining field strength is given by

{boldE}_{ex} = \frac{χ_{op} - χ_{normals}}{χ_{normals}} Δ {boldE}^{dyn} = \frac{ε_{op} - ε_{normals}}{ε_{normals} - 1} Δ {boldE}^{dyn}

and Eq. becomes

λ = \frac{1}{2} \frac{ε_{normals} - ε_{op}}{ε_{normals} - 1} \int_{V} Δ E^{dyn} \cdot false(Δ P^{eq} - Δ P^{dyn} false) d V

…”

Section: Solvent Reorganization Energymentioning

confidence: 80%

“…The energy change of the system in the fast process is as follows

Δ U = U^{non} - U^{normalc} = - W = - \sum_{k} ξ_{k} \int_{x_{k}}^{0} d x_{k} - \sum_{l} {A_{l}}^{'} \int_{a_{l} + x_{l}}^{a_{l}} d {a_{l}}^{'} = \sum_{k} ξ_{k} x_{k} + \sum_{l} {A_{l}}^{'} x_{l}

where

\sum_{k} ξ_{k} x_{k}

and

\sum_{l} {A_{l}}^{'} x_{l}

are work done by getting rid of the second and the third kinds of additional external fields quickly.…”

Section: Nonequilibrium Solvation Theory Based On Constrained Equilibmentioning

confidence: 99%

“…

boldnormal P^{'}

denotes the polarization difference between

{boldP}_{2}^{non}

and

{boldP}_{2}^{eq}

which we call the “residual” polarization and it equilibrates with

{boldE}_{ex}

in the medium of

ε_{normals}

. With the similar treatment by the charge‐potential notation, starting from the constrained equilibrium “C,” we prepare the nonequilibrium state “N” by removing the

{boldE}_{ex}

suddenly without friction, thus free energy of the nonequilibrium state N is readily established as the polarization‐field form, that is,

F^{non} = F^{normalc} + \int false(P_{2}^{eq} + boldnormal P^{'} false) \cdot E_{ex} d V

…”

Section: Nonequilibrium Solvation Theory Based On Constrained Equilibmentioning

confidence: 99%

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An overview of continuum models for nonequilibrium solvation: Popular theories and new challenge

2015

Int J of Quantum Chemistry

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The effect of solvent on the electron transfer (ET) and spectral shifts has been the focus of experimental and theoretical studies and a key quantity in these studies is the solvent reorganization energy. There are a number of theoretical models toward the evaluation of nonequilibrium solvation free energy that were proposed decades ago and have been applied widely. In the past decade, however, we revisited the original theoretical derivations and identified a serious defect in the popular nonequilibrium solvation models which causes the significant overestimation of solvent reorganization energy and hence predicts a much lowed rate constant for ET in some cases. A rigorous derivation by means of contrained equilibrium principle of thermodynamics was subsequently conducted for the study of nonequilibrium solvation. In this review, the author outlined the intimate interplays among the representative models and analyzed what the possible problem could be. The key idea presented in our recent papers was highlighted. The constrained equilibrium principle in classical thermodynamics and its application to the nonequilibrium solvation were detailed, and a few argumentative examples in literature were taken for the validation of our theory.

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“…If we alternatively make the discussion with the constraining external field

{boldE}_{ex}

which is used to hold the equilibrium with the “residual” polarization

P^{'} = {boldP}_{2}^{non} - {boldP}_{2}^{eq}

, the solvent reorganization energy can be given in the parallel way, that is,

λ = \frac{1}{2} \int_{v} E_{ex} \cdot boldnormal P^{'} d V

…”

Section: Solvent Reorganization Energymentioning

confidence: 77%

“…Combining Eqs. and , the constraining field strength is given by

{boldE}_{ex} = \frac{χ_{op} - χ_{normals}}{χ_{normals}} Δ {boldE}^{dyn} = \frac{ε_{op} - ε_{normals}}{ε_{normals} - 1} Δ {boldE}^{dyn}

and Eq. becomes

λ = \frac{1}{2} \frac{ε_{normals} - ε_{op}}{ε_{normals} - 1} \int_{V} Δ E^{dyn} \cdot false(Δ P^{eq} - Δ P^{dyn} false) d V

…”

Section: Solvent Reorganization Energymentioning

confidence: 80%

“…The energy change of the system in the fast process is as follows

Δ U = U^{non} - U^{normalc} = - W = - \sum_{k} ξ_{k} \int_{x_{k}}^{0} d x_{k} - \sum_{l} {A_{l}}^{'} \int_{a_{l} + x_{l}}^{a_{l}} d {a_{l}}^{'} = \sum_{k} ξ_{k} x_{k} + \sum_{l} {A_{l}}^{'} x_{l}

where

\sum_{k} ξ_{k} x_{k}

and

\sum_{l} {A_{l}}^{'} x_{l}

are work done by getting rid of the second and the third kinds of additional external fields quickly.…”

Section: Nonequilibrium Solvation Theory Based On Constrained Equilibmentioning

confidence: 99%

“…

boldnormal P^{'}

denotes the polarization difference between

{boldP}_{2}^{non}

and

{boldP}_{2}^{eq}

which we call the “residual” polarization and it equilibrates with

{boldE}_{ex}

in the medium of

ε_{normals}

. With the similar treatment by the charge‐potential notation, starting from the constrained equilibrium “C,” we prepare the nonequilibrium state “N” by removing the

{boldE}_{ex}

suddenly without friction, thus free energy of the nonequilibrium state N is readily established as the polarization‐field form, that is,

F^{non} = F^{normalc} + \int false(P_{2}^{eq} + boldnormal P^{'} false) \cdot E_{ex} d V

…”

Section: Nonequilibrium Solvation Theory Based On Constrained Equilibmentioning

confidence: 99%

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An overview of continuum models for nonequilibrium solvation: Popular theories and new challenge

2015

Int J of Quantum Chemistry

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show abstract

“…Such a nonequilibrium solvation effect can make a non-negligible contribution to a bathochromic shift (for example, 0.2 eV in a charge transfer excitation of a merocyanine in solutions). Various approaches have been proposed to deal with this nonequilibrium effect in a quantum mechanical calculation combined with continuum models, − as well as in the QM/MM method using a polarizable force field. − ,− Although theoretical bases using QM/MM methodology have mostly been established, actual calculations are difficult to perform. The reason is the large computational cost for an extensive number of high-level QM calculations required for the statistical configuration sampling, in which explicit electronic polarization of the medium and nonequilibrium solvation have to be taken into account.…”

Section: Introductionmentioning

confidence: 99%

An Ab Initio QM/MM-Based Approach to Efficiently Evaluate Vertical Excitation Energies in Condensed Phases Including the Nonequilibrium Solvation Effect

Nakano

Sato

2015

J. Phys. Chem. B

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An efficient quantum mechanical/molecular mechanics-based approach is presented to calculate a vertical excitation energy of a chromophore in condensed phases including the nonequilibrium solvation effect. The electronic polarization of a medium and the related nonequilibrium solvation effect associated with the vertical excitation are described using a polarizable solvent model. By virtue of the mean-field approximation, the target energy can be completely separated into classical and quantum mechanical parts, which enables us to efficiently evaluate the vertical excitation energy with a high-level quantum mechanical method. The method is applied to N,N-dimethyl-4-nitroaniline in a variety of solutions at the MRMP2/CASSCF level, showing quantitative agreement with the experimental reports. The observed large bathochromic shifts are analyzed by focusing on the induction effects of the solvents.

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Numerical solution of solvent reorganization energy and its application in electron transfer reaction

Ming²,

Ren³

et al. 2014

Theor Chem Acc

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Vertical Detachment Energy of Hydrated Electron Based on a Modified Form of Solvent Reorganization Energy

Cited by 15 publications

References 57 publications

An overview of continuum models for nonequilibrium solvation: Popular theories and new challenge

An overview of continuum models for nonequilibrium solvation: Popular theories and new challenge

An Ab Initio QM/MM-Based Approach to Efficiently Evaluate Vertical Excitation Energies in Condensed Phases Including the Nonequilibrium Solvation Effect

Numerical solution of solvent reorganization energy and its application in electron transfer reaction

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