Marcus' Electron Transfer Rate Revisited via a Rice-Ramsperger-Kassel-Marcus Analogue: A Unified Formalism for Linear and Nonlinear Solvation Scenarios

Yao Wang; Yu Su; Rui-Xue Xu; Xiao Zheng; YiJing Yan

doi:10.1063/1674-0068/cjcp2101004

Volume 34 Issue 4

Aug. 2021

Turn off MathJax

Article Contents

Article Navigation > Chinese Journal of Chemical Physics > 2021 > 34(4): 462-470

Yao Wang, Yu Su, Rui-Xue Xu, Xiao Zheng, YiJing Yan. Marcus' Electron Transfer Rate Revisited via a Rice-Ramsperger-Kassel-Marcus Analogue: A Unified Formalism for Linear and Nonlinear Solvation Scenarios[J]. Chinese Journal of Chemical Physics , 2021, 34(4): 462-470. doi: 10.1063/1674-0068/cjcp2101004

Citation:

Yao Wang, Yu Su, Rui-Xue Xu, Xiao Zheng, YiJing Yan. Marcus' Electron Transfer Rate Revisited via a Rice-Ramsperger-Kassel-Marcus Analogue: A Unified Formalism for Linear and Nonlinear Solvation Scenarios[J]. Chinese Journal of Chemical Physics , 2021, 34(4): 462-470. doi: 10.1063/1674-0068/cjcp2101004

Citation:

Yao Wang, Yu Su, Rui-Xue Xu, Xiao Zheng, YiJing Yan. Marcus' Electron Transfer Rate Revisited via a Rice-Ramsperger-Kassel-Marcus Analogue: A Unified Formalism for Linear and Nonlinear Solvation Scenarios[J]. Chinese Journal of Chemical Physics , 2021, 34(4): 462-470. doi: 10.1063/1674-0068/cjcp2101004

PDF( 327 KB)

Marcus' Electron Transfer Rate Revisited via a Rice-Ramsperger-Kassel-Marcus Analogue: A Unified Formalism for Linear and Nonlinear Solvation Scenarios

doi: 10.1063/1674-0068/cjcp2101004

Hefei National Laboratory for Physical Sciences at the Microscale and Department of Chemical Physics and Synergetic Innovation Center of Quantum Information and Quantum Physics and Collaborative Innovation Center of Chemistry for Energy Materials (iChEM), University of Science and Technology of China, Hefei 230026, China

More Information

Corresponding author: Wang Yao, E-mail: wy2010@ustc.edu.cn
Received Date: 2021-01-05
Accepted Date: 2021-01-26
Publish Date: 2021-08-27

Abstract

Abstract

In the pioneering work by R. A. Marcus, the solvation effect on electron transfer (ET) processes was investigated, giving rise to the celebrated nonadiabatic ET rate formula. In this work, on the basis of the thermodynamic solvation potentials analysis, we reexamine Marcus' formula with respect to the Rice-Ramsperger-Kassel-Marcus (RRKM) theory. Interestingly, the obtained RRKM analogue, which recovers the original Marcus' rate that is in a linear solvation scenario, is also applicable to the nonlinear solvation scenarios, where the multiple curve-crossing of solvation potentials exists. Parallelly, we revisit the corresponding Fermi's golden rule results, with some critical comments against the RRKM analogue proposed in this work. For illustration, we consider the quadratic solvation scenarios, on the basis of physically well-supported descriptors.
- Electron transfer,
- Marcus' rate formula,
- Rice-Ramsperger-Kassel-Marcus theory,
- Nonlinear solvation,
- Fermi's golden rule

FullText(HTML)

References(38)

References

[1]	R. A. Marcus, J. Chem. Phys. 24, 966 (1956). doi: 10.1063/1.1742723
[2]	R. A. Marcus, Annu. Rev. Phys. Chem. 15, 155 (1964). doi: 10.1146/annurev.pc.15.100164.001103
[3]	H. Sumi and R. A. Marcus, J. Phys. Chem. 84, 4894 (1986). doi: 10.1063/1.449978
[4]	R. A. Marcus, Rev. Mod. Phys. 65, 599 (1993). doi: 10.1103/RevModPhys.65.599
[5]	Q. Peng, Y. P. Yi, Z. G. Shuai, and J. S. Shao, J. Am. Chem. Soc. 129, 9333 (2007). doi: 10.1021/ja067946e
[6]	H. Wang and M. Thoss, J. Phys. Chem. A 111, 10369 (2007). doi: 10.1021/jp072367x
[7]	Y. Zhao and W. Z. Liang, Chem. Soc. Rev 41, 1075 (2012). doi: 10.1039/C1CS15207F
[8]	H. Zang, Y. L. Ke, Y. Zhao, and W. Z. Liang, J. Phys. Chem. C 120, 13351 (2016). doi: 10.1021/acs.jpcc.6b02943
[9]	Y. A. Yan, J. Chem. Phys. 150, 074106 (2019). doi: 10.1063/1.5052527
[10]	C. Hsieh and J. Cao, J. Chem. Phys. 148, 014104 (2018). doi: 10.1063/1.5018726
[11]	J. T. Hsiang and B. L. Hu, Phys. Rev. D 101, 125002 (2020). doi: 10.1103/PhysRevD.101.125002
[12]	J. T. Hsiang and B. L. Hu, Phys. Rev. D 101, 125003 (2020). doi: 10.1103/PhysRevD.101.125003
[13]	O. K. Rice and H. C. Ramsperger, J. Am. Chem. Soc. 49, 1617 (1927). doi: 10.1021/ja01406a001
[14]	O. K. Rice and H. C. Ramsperger, J. Am. Chem. Soc. 50, 617 (1928). doi: 10.1021/ja01390a002
[15]	L. S. Kassel, J. Phys. Chem. 32, 225 (1928). doi: 10.1021/j150284a007
[16]	L. S. Kassel, J. Phys. Chem. 32, 1065 (1928). doi: 10.1021/j150289a011
[17]	R. A. Marcus and O. K. Rice, J. Phys. Colloid. Chem. 55, 894 (1951). doi: 10.1021/j150489a013
[18]	R. A. Marcus, J. Chem. Phys. 20, 359 (1952). doi: 10.1063/1.1700424
[19]	K. A. Holbrook, M. Pilling, and S. Robertson, Unimolecular Reactions, 2nd Edn. Chichester, UK: Wiley, (1996).
[20]	M. G. Evans and M. Polanyi, Trans. Faraday Soc. 31, 875 (1935). doi: 10.1039/tf9353100875
[21]	H. Eyring, J. Chem. Phys. 3, 107 (1935). doi: 10.1063/1.1749604
[22]	H. Eyring, Chem. Rev. 17, 65 (1935). doi: 10.1021/cr60056a006
[23]	C. N. Hinshelwood, The Kinetics of Chemical Change in Gaseous Systems, London: Clarendon Press, (1926).
[24]	Y. J. Yan, J. Chem. Phys. 140, 054105 (2014). doi: 10.1063/1.4863379
[25]	Y. J. Yan, J. S. Jin, R. X. Xu, and X. Zheng, Frontiers Phys. 11, 110306 (2016). doi: 10.1007/s11467-016-0513-5
[26]	H. D. Zhang, R. X. Xu, X. Zheng, and Y. J. Yan, Mol. Phys. 116, 780 (2018). doi: 10.1080/00268976.2018.1431407
[27]	Y. Wang, R. X. Xu, and Y. J. Yan, J. Chem. Phys. 152, 041102 (2020). doi: 10.1063/1.5135776
[28]	R. X. Xu, Y. Liu, H. D. Zhang, and Y. J. Yan, Chin. J. Chem. Phys. 30, 395 (2017). doi: 10.1063/1674-0068/30/cjcp1706123
[29]	R. X. Xu, Y. Liu, H. D. Zhang, and Y. J. Yan, J. Chem. Phys. 148, 114103 (2018). doi: 10.1063/1.4991779
[30]	Y. Liu, R. X. Xu, H. D. Zhang, and Y. J. Yan, Chin. J. Chem. Phys. 31, 245 (2018). doi: 10.1063/1674-0068/31/cjcp1804083
[31]	U. Weiss, Quantum Dissipative Systems, 4rd edn., Singapore: World Scientific, (2012).
[32]	Y. J. Yan and R. X. Xu, Annu. Rev. Phys. Chem. 56, 187 (2005). doi: 10.1146/annurev.physchem.55.091602.094425
[33]	G. F. Bertsch, Online note: "Derivations of Marcus's formula". https://www.int.washington.edu/users/bertsch/marcus.1.pdf
[34]	L. Landau, Phys. Z. Sowjetunion 2, 46 (1932).
[35]	C. Zener, Proc. Roy. Soc. London A 137, 696 (1932). doi: 10.1098/rspa.1932.0165
[36]	C. Wittig, J. Phys. Chem. B 109, 8428 (2005). doi: 10.1021/jp040627u
[37]	A. O. Caldeira and A. J. Leggett, Physica A 121, 587 (1983). doi: 10.1016/0378-4371(83)90013-4
[38]	C. Zhu, J. Chem. Phys. 105, 4159 (1996). doi: 10.1063/1.472261