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Title: Free energy functionals for polarization fluctuations: Pekar factor revisited

Abstract

The separation of slow nuclear and fast electronic polarization in problems related to electron mobility in polarizable media was considered by Pekar 70 years ago. This separation leads to the Pekar factor in the free energy of solvation by the nuclear degrees of freedom, within dielectric continuum models. The main qualitative prediction of Pekar’s perspective is a significant, by about a factor of two, drop of the nuclear solvation free energy compared to the total (electronic plus nuclear) free energy of solvation. The Pekar factor enters the solvent reorganization energy of electron transfer reactions and is a significant mechanistic parameter accounting for the solvent effect on electron transfer. We study the separation of the fast and slow polarization modes in polar molecular liquids (polarizable dipolar liquids and polarizable water force fields) without relying on the continuum approximation. We derive the nonlocal free energy functional and use atomistic numerical simulations to obtain nonlocal, reciprocal space electronic and nuclear susceptibilities. A consistent transition to the continuum limit is introduced by extrapolating the results of finite-size numerical simulation to zero wavevector. The continuum nuclear susceptibility extracted from the simulations is numerically close to the Pekar factor. But, we derive a new functionality involvingmore » the static and high-frequency dielectric constants. The main distinction of our approach from the traditional theories is found in the solvation free energy due to the nuclear polarization: the anticipated significant drop of its magnitude with increasing liquid polarizability does not occur. The reorganization energy of electron transfer is either nearly constant with increasing the solvent polarizability and the corresponding high-frequency dielectric constant (polarizable dipolar liquids) or actually noticeably increases (polarizable force fields of water).« less

Authors:
ORCiD logo [1];  [2]; ORCiD logo [3]
  1. Arizona State Univ., Tempe, AZ (United States). School of Molecular Sciences
  2. Brookhaven National Lab. (BNL), Upton, NY (United States). Chemistry Dept.
  3. Arizona State Univ., Tempe, AZ (United States). Dept. of Physics and School of Molecular Sciences
Publication Date:
Research Org.:
Brookhaven National Lab. (BNL), Upton, NY (United States); Arizona State Univ., Tempe, AZ (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22); National Science Foundation (NSF)
OSTI Identifier:
1349561
Alternate Identifier(s):
OSTI ID: 1340505; OSTI ID: 1361771
Report Number(s):
BNL-113669-2017-JA
Journal ID: ISSN 0021-9606; R&D Project: CO004; KC0304030; TRN: US1700861
Grant/Contract Number:  
SC00112704; SC0015641
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 146; Journal Issue: 6; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; 14 SOLAR ENERGY

Citation Formats

Dinpajooh, Mohammadhasan, Newton, Marshall D., and Matyushov, Dmitry V. Free energy functionals for polarization fluctuations: Pekar factor revisited. United States: N. p., 2017. Web. doi:10.1063/1.4975625.
Dinpajooh, Mohammadhasan, Newton, Marshall D., & Matyushov, Dmitry V. Free energy functionals for polarization fluctuations: Pekar factor revisited. United States. doi:10.1063/1.4975625.
Dinpajooh, Mohammadhasan, Newton, Marshall D., and Matyushov, Dmitry V. Mon . "Free energy functionals for polarization fluctuations: Pekar factor revisited". United States. doi:10.1063/1.4975625. https://www.osti.gov/servlets/purl/1349561.
@article{osti_1349561,
title = {Free energy functionals for polarization fluctuations: Pekar factor revisited},
author = {Dinpajooh, Mohammadhasan and Newton, Marshall D. and Matyushov, Dmitry V.},
abstractNote = {The separation of slow nuclear and fast electronic polarization in problems related to electron mobility in polarizable media was considered by Pekar 70 years ago. This separation leads to the Pekar factor in the free energy of solvation by the nuclear degrees of freedom, within dielectric continuum models. The main qualitative prediction of Pekar’s perspective is a significant, by about a factor of two, drop of the nuclear solvation free energy compared to the total (electronic plus nuclear) free energy of solvation. The Pekar factor enters the solvent reorganization energy of electron transfer reactions and is a significant mechanistic parameter accounting for the solvent effect on electron transfer. We study the separation of the fast and slow polarization modes in polar molecular liquids (polarizable dipolar liquids and polarizable water force fields) without relying on the continuum approximation. We derive the nonlocal free energy functional and use atomistic numerical simulations to obtain nonlocal, reciprocal space electronic and nuclear susceptibilities. A consistent transition to the continuum limit is introduced by extrapolating the results of finite-size numerical simulation to zero wavevector. The continuum nuclear susceptibility extracted from the simulations is numerically close to the Pekar factor. But, we derive a new functionality involving the static and high-frequency dielectric constants. The main distinction of our approach from the traditional theories is found in the solvation free energy due to the nuclear polarization: the anticipated significant drop of its magnitude with increasing liquid polarizability does not occur. The reorganization energy of electron transfer is either nearly constant with increasing the solvent polarizability and the corresponding high-frequency dielectric constant (polarizable dipolar liquids) or actually noticeably increases (polarizable force fields of water).},
doi = {10.1063/1.4975625},
journal = {Journal of Chemical Physics},
number = 6,
volume = 146,
place = {United States},
year = {2017},
month = {2}
}

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Works referenced in this record:

Electronic States of a Topologically Disordered System: Exact Solution of the Mean Spherical Model for Liquids
journal, October 1982

  • Chandler, David; Schweizer, Kenneth S.; Wolynes, Peter G.
  • Physical Review Letters, Vol. 49, Issue 15
  • DOI: 10.1103/PhysRevLett.49.1100

Wave vector dependent static dielectric properties of associated liquids: Methanol
journal, December 1990

  • Fonseca, Teresa; Ladanyi, Branka M.
  • The Journal of Chemical Physics, Vol. 93, Issue 11
  • DOI: 10.1063/1.459345

On the Theory of Oxidation‐Reduction Reactions Involving Electron Transfer. I
journal, May 1956

  • Marcus, R. A.
  • The Journal of Chemical Physics, Vol. 24, Issue 5
  • DOI: 10.1063/1.1742723

Equilibrium and nonequilibrium solvation and solute electronic structure. III. Quantum theory
journal, April 1992

  • Kim, Hyung J.; Hynes, James T.
  • The Journal of Chemical Physics, Vol. 96, Issue 7
  • DOI: 10.1063/1.462752

Electrostatic Free Energy and Other Properties of States Having Nonequilibrium Polarization. I
journal, May 1956

  • Marcus, R. A.
  • The Journal of Chemical Physics, Vol. 24, Issue 5
  • DOI: 10.1063/1.1742724

Electron transfers in chemistry and biology
journal, August 1985

  • Marcus, R. A.; Sutin, Norman
  • Biochimica et Biophysica Acta (BBA) - Reviews on Bioenergetics, Vol. 811, Issue 3
  • DOI: 10.1016/0304-4173(85)90014-X

Quantum theory of polarization in liquids: Exact solution of the mean spherical and related approximations
journal, January 1982

  • Thompson, Mark J.; Schweizer, Kenneth S.; Chandler, David
  • The Journal of Chemical Physics, Vol. 76, Issue 2
  • DOI: 10.1063/1.443081

Molecular density functional theory of water including density–polarization coupling
journal, April 2016

  • Jeanmairet, Guillaume; Levy, Nicolas; Levesque, Maximilien
  • Journal of Physics: Condensed Matter, Vol. 28, Issue 24
  • DOI: 10.1088/0953-8984/28/24/244005

Wave vector dependent dielectric relaxation in hydrogen‐bonding liquids: A molecular dynamics study of methanol
journal, June 1993

  • Skaf, Munir S.; Fonseca, Teresa; Ladanyi, Branka M.
  • The Journal of Chemical Physics, Vol. 98, Issue 11
  • DOI: 10.1063/1.464452

Static transverse dielectric function of model molecular fluids
journal, June 1993

  • Raineri, Fernando O.; Friedman, Harold L.
  • The Journal of Chemical Physics, Vol. 98, Issue 11
  • DOI: 10.1063/1.464450

Scalable molecular dynamics with NAMD
journal, January 2005

  • Phillips, James C.; Braun, Rosemary; Wang, Wei
  • Journal of Computational Chemistry, Vol. 26, Issue 16, p. 1781-1802
  • DOI: 10.1002/jcc.20289

Green function theory of charge transfer processes in solution
journal, April 1988

  • Newton, Marshall D.; Friedman, Harold L.
  • The Journal of Chemical Physics, Vol. 88, Issue 7
  • DOI: 10.1063/1.453804

Role of Repulsive Forces in Determining the Equilibrium Structure of Simple Liquids
journal, June 1971

  • Weeks, John D.; Chandler, David; Andersen, Hans C.
  • The Journal of Chemical Physics, Vol. 54, Issue 12
  • DOI: 10.1063/1.1674820

Simulating Nanoscale Dielectric Response
journal, June 2006


Effects of Solvent and Solute Polarizability on the Reorganization Energy of Electron Transfer
journal, March 2004

  • Gupta, Shikha; Matyushov, Dmitry V.
  • The Journal of Physical Chemistry A, Vol. 108, Issue 11
  • DOI: 10.1021/jp036388c

Dipolar Correlations and the Dielectric Permittivity of Water
journal, June 2007


Gaussian field model of fluids with an application to polymeric fluids
journal, October 1993


Practical computation of electronic excitation in solution: vertical excitation model
journal, January 2011

  • Marenich, Aleksandr V.; Cramer, Christopher J.; Truhlar, Donald G.
  • Chemical Science, Vol. 2, Issue 11
  • DOI: 10.1039/c1sc00313e

Understanding the Optical Band Shape:  Coumarin-153 Steady-State Spectroscopy
journal, September 2001

  • Matyushov, Dmitry V.; Newton, Marshall D.
  • The Journal of Physical Chemistry A, Vol. 105, Issue 37
  • DOI: 10.1021/jp011074f

Electric Moments of Molecules in Liquids
journal, August 1936

  • Onsager, Lars
  • Journal of the American Chemical Society, Vol. 58, Issue 8
  • DOI: 10.1021/ja01299a050

Longitudinal dielectric relaxation
journal, September 1989

  • Kivelson, Daniel; Friedman, Harold
  • The Journal of Physical Chemistry, Vol. 93, Issue 19
  • DOI: 10.1021/j100356a029

Theory of Solvent Effects on Molecular Electronic Spectra. Frequency Shifts
journal, May 1957


Activation entropy of electron transfer reactions
journal, May 2006


Dispersion solute-solvent coupling in electron transfer reactions. I. Effective potential
journal, April 1998

  • Matyushov, Dmitry V.; Ladanyi, Branka M.
  • The Journal of Chemical Physics, Vol. 108, Issue 15
  • DOI: 10.1063/1.476043

Dipole Solvation in Nondipolar Solvents:  Experimental Studies of Reorganization Energies and Solvation Dynamics
journal, January 1996

  • Reynolds, L.; Gardecki, J. A.; Frankland, S. J. V.
  • The Journal of Physical Chemistry, Vol. 100, Issue 24
  • DOI: 10.1021/jp953110e

Static longitudinal dielectric function of model molecular fluids
journal, February 1992

  • Raineri, Fernando O.; Resat, Haluk; Friedman, Harold L.
  • The Journal of Chemical Physics, Vol. 96, Issue 4
  • DOI: 10.1063/1.461952

N-particle dynamics of polarizable Stockmayer-type molecules
journal, August 1977


Invited review solvatochromic shifts: The influence of the medium on the energy of electronic states
journal, January 1990


Statistical mechanics of polar systems. II
journal, March 1976

  • Ho/ye, J. S.; Stell, G.
  • The Journal of Chemical Physics, Vol. 64, Issue 5
  • DOI: 10.1063/1.432458

Dynamics of charge transfer chemical reactions in a polar medium within the scope of the Born-Kirkwood-Onsager model
journal, November 1991


An analysis of dielectric models of solvatochromism
journal, December 1985

  • Brady, James E.; Carr, Peter W.
  • The Journal of Physical Chemistry, Vol. 89, Issue 26
  • DOI: 10.1021/j100272a037

The fluctuation-dissipation theorem
journal, January 1966


Modeling induced polarization with classical Drude oscillators: Theory and molecular dynamics simulation algorithm
journal, August 2003

  • Lamoureux, Guillaume; Roux, Benoı̂t
  • The Journal of Chemical Physics, Vol. 119, Issue 6
  • DOI: 10.1063/1.1589749

Contemporary Issues in Electron Transfer Research
journal, January 1996

  • Barbara, Paul F.; Meyer, Thomas J.; Ratner, Mark A.
  • The Journal of Physical Chemistry, Vol. 100, Issue 31
  • DOI: 10.1021/jp9605663

Electrostatic models in the theory of solutions
journal, January 1976

  • Kharkats, Yu. I.; Kornyshev, A. A.; Vorotyntsev, M. A.
  • Journal of the Chemical Society, Faraday Transactions 2, Vol. 72
  • DOI: 10.1039/f29767200361

Solution reaction path Hamiltonian for reactions in polar solvents. I. Formulation
journal, June 1988

  • Lee, Sangyoub; Hynes, James T.
  • The Journal of Chemical Physics, Vol. 88, Issue 11
  • DOI: 10.1063/1.454383

Chemical and Electrochemical Electron-Transfer Theory
journal, October 1964


Electrostatics of liquid interfaces
journal, June 2014

  • Matyushov, Dmitry V.
  • The Journal of Chemical Physics, Vol. 140, Issue 22
  • DOI: 10.1063/1.4882284

Entropy of Attractive Forces and Molecular Nonsphericity in Real Liquids: A Measure of Structural Ordering
journal, February 1995

  • Schmid, Roland; Matyushov, Dmitry V.
  • The Journal of Physical Chemistry, Vol. 99, Issue 8
  • DOI: 10.1021/j100008a023

Calculation of UV/Vis Spectra in Solution
journal, January 1996

  • Klamt, Andreas
  • The Journal of Physical Chemistry, Vol. 100, Issue 9
  • DOI: 10.1021/jp950607f

Dielectric dispersion and dielectric friction in electrolyte solutions. I.
journal, December 1977

  • Hubbard, J.; Onsager, L.
  • The Journal of Chemical Physics, Vol. 67, Issue 11
  • DOI: 10.1063/1.434664

Statistical mechanics of polar fluids in electric fields
journal, February 1980

  • Ho/ye, J. S.; Stell, G.
  • The Journal of Chemical Physics, Vol. 72, Issue 3
  • DOI: 10.1063/1.439359

Classical solvent dynamics and electron transfer. II. Molecular aspects
journal, January 1983

  • Calef, Daniel F.; Wolynes, Peter G.
  • The Journal of Chemical Physics, Vol. 78, Issue 1
  • DOI: 10.1063/1.444472

Slow Electrons in a Polar Crystal
journal, February 1955


Computer simulation and the dielectric constant at finite wavelength
journal, January 1986


A thermodynamic analysis of solvation
journal, August 1988

  • Yu, Hsiang‐Ai; Karplus, Martin
  • The Journal of Chemical Physics, Vol. 89, Issue 4
  • DOI: 10.1063/1.455080

Fluctuations of partial polarisations in dielectrics
journal, June 1979


Activation Free Energy of the Nonadiabatic Processes of Electron Transfer and the Reorganization Energy of the Inhomogeneous Nonlocal Medium
journal, January 1996

  • Kuznetsov, A. M.; Medvedev, I. G.
  • The Journal of Physical Chemistry, Vol. 100, Issue 14
  • DOI: 10.1021/jp950918q

Solvation and reorganization energies in polarizable molecular and continuum solvents
journal, February 1997

  • Bader, Joel S.; Cortis, Christian M.; Berne, B. J.
  • The Journal of Chemical Physics, Vol. 106, Issue 6
  • DOI: 10.1063/1.473790

Nonequilibrium solvation: An ab initio quantum‐mechanical method in the continuum cavity model approximation
journal, May 1993

  • Aguilar, M. A.; Olivares del Valle, F. J.; Tomasi, J.
  • The Journal of Chemical Physics, Vol. 98, Issue 9
  • DOI: 10.1063/1.464728

Dielectric Friction on a Moving Ion
journal, April 1963

  • Zwanzig, Robert
  • The Journal of Chemical Physics, Vol. 38, Issue 7
  • DOI: 10.1063/1.1776929

Polarizable molecular interactions in condensed phase and their equivalent nonpolarizable models
journal, July 2014

  • Leontyev, Igor V.; Stuchebrukhov, Alexei A.
  • The Journal of Chemical Physics, Vol. 141, Issue 1
  • DOI: 10.1063/1.4884276

Separation of the Electric Polarization into Fast and Slow Components:  A Comparison of Two Partition Schemes
journal, November 2001

  • Aguilar, M. A.
  • The Journal of Physical Chemistry A, Vol. 105, Issue 45
  • DOI: 10.1021/jp011598f

Free Energy of Nonequilibrium Polarization Systems. 4. A Formalism Based on the Nonequilibrium Dielectric Displacement
journal, July 1994


Computational electrochemistry: prediction of liquid-phase reduction potentials
journal, January 2014

  • Marenich, Aleksandr V.; Ho, Junming; Coote, Michelle L.
  • Phys. Chem. Chem. Phys., Vol. 16, Issue 29
  • DOI: 10.1039/c4cp01572j

Microscopic free energy functional for polarization fluctuations: Generalization of Marcus–Felderhof expression
journal, February 1991

  • Chandra, Amalendu; Bagchi, Biman
  • The Journal of Chemical Physics, Vol. 94, Issue 3
  • DOI: 10.1063/1.459896

Fluctuations of polarization and magnetization in dielectric and magnetic media
journal, July 1977

  • Felderhof, B. U.
  • The Journal of Chemical Physics, Vol. 67, Issue 2
  • DOI: 10.1063/1.434895

Reorganization Energy for Electron Transfer at Film-Modified Electrode Surfaces: A Dielectric Continuum Model
journal, July 1994

  • Liu, Yi-Ping; Newton, Marshall D.
  • The Journal of Physical Chemistry, Vol. 98, Issue 29
  • DOI: 10.1021/j100080a011

Solvent reorganization energy of electron-transfer reactions in polar solvents
journal, April 2004

  • Matyushov, Dmitry V.
  • The Journal of Chemical Physics, Vol. 120, Issue 16
  • DOI: 10.1063/1.1676122

Molecular dynamics simulation of the wave vector‐dependent static dielectric properties of methanol–water mixtures
journal, April 1995

  • Skaf, Munir S.; Ladanyi, Branka M.
  • The Journal of Chemical Physics, Vol. 102, Issue 16
  • DOI: 10.1063/1.469368

Exact Solution of the Mean Spherical Model for Fluids of Hard Spheres with Permanent Electric Dipole Moments
journal, November 1971

  • Wertheim, M. S.
  • The Journal of Chemical Physics, Vol. 55, Issue 9
  • DOI: 10.1063/1.1676751

A polarizable model of water for molecular dynamics simulations of biomolecules
journal, January 2006


Theory and simulation of polar and nonpolar polarizable fluids
journal, November 1993

  • Cao, Jianshu; Berne, B. J.
  • The Journal of Chemical Physics, Vol. 99, Issue 9
  • DOI: 10.1063/1.465446

Separation between Fast and Slow Polarizations in Continuum Solvation Models
journal, November 2000

  • Cossi, Maurizio; Barone, Vincenzo
  • The Journal of Physical Chemistry A, Vol. 104, Issue 46
  • DOI: 10.1021/jp000997s

A molecular theory of electron transfer reactions in polar liquids
journal, July 1993


Dipole solvation in dielectrics
journal, January 2004

  • Matyushov, Dmitry V.
  • The Journal of Chemical Physics, Vol. 120, Issue 3
  • DOI: 10.1063/1.1633545

Theory of polar fluids: V. Thermodynamics and thermodynamic perturbation theory
journal, January 1979