We propose a non-perturbative method to simulate heterogeneous electron transfer dynamics in systems described by a Newns-Anderson type of model. The coupling between the molecule and the continuum electronic states at the metal or semiconductor surface is represented using a set of effective modes, by employing an exponential expansion of the bath correlation functions. Depending on the nature of the problems, the nuclear degrees of freedom are either treated explicitly using wave functions and density operators or as dissipative modes using the techniques from the hierarchical equations of the motion method. Numerical examples are also presented for applications in problems including (1) photo-induced charge transfer at the molecule-semiconductor interfaces, (2) heterogeneous electron transfer at the molecule-metal interface, and (3) vibrational relaxation on a metal surface.
REFERENCES
1.
D. M.
Newns
, Phys. Rev.
178
, 1123
(1969
).2.
J. K.
Norskov
, Rep. Prog. Phys.
53
, 1253
(1990
).3.
N.
Shenvi
, S.
Roy
, and J. C.
Tully
, Science
326
, 829
(2009
).4.
R. A.
Marcus
, Annu. Rev. Phys. Chem.
15
, 155
(1964
).5.
A. M.
Kuznetsov
, Charge Transfer in Physics, Chemistry and Biology: Physical Mechanisms of Elementary Processes and an Introduction to the Theory
(Gordon and Breach
, Amsterdam
, 1995
).6.
W.
Schmickler
and E.
Santos
, Interfacial Electrochemistry
, 2nd ed. (Springer
, Heidelberg
, 2010
).7.
M.
Gratzel
, Nature
414
, 338
(2001
).8.
N. A.
Anderson
and T.
Lian
, Annu. Rev. Phys. Chem.
56
, 491
(2005
).9.
W. R.
Duncan
and O. V.
Prezhdo
, Annu. Rev. Phys. Chem.
58
, 143
(2007
).10.
C. S.
Ponseca
, P.
Chabera
, J.
Uhlig
, P.
Persson
, and V.
Sundstrom
, Chem. Rev.
117
, 10940
(2017
).11.
M.
Head-Gordon
and J. C.
Tully
, J. Chem. Phys.
103
, 10137
(1995
).12.
W.
Dou
, A.
Nitzan
, and J. E.
Subotnik
, J. Chem. Phys.
142
, 084110
(2015
).13.
A.
Nitzan
, Annu. Rev. Phys. Chem.
52
, 681
(2001
).14.
Molecular Nanoelectronics
, edited by M. A.
Reed
and T.
Lee
(American Scientific
, Stevenson Ranch, CA
, 2003
).15.
M.
Galperin
, M. A.
Ratner
, and A.
Nitzan
, J. Phys.: Condens. Matter
19
, 103201
(2007
).16.
H.
Ueba
, Prog. Surf. Sci.
55
, 115
(1997
).17.
N.
Shenvi
, S.
Roy
, P.
Parandekar
, and J.
Tully
, J. Chem. Phys.
125
, 154703
(2006
).18.
V.
Krishna
and J. C.
Tully
, J. Chem. Phys.
125
, 054706
(2006
).19.
W.
Dou
and J. E.
Subotnik
, Phys. Rev. B
97
, 064303
(2018
).20.
P. W.
Anderson
, Phys. Rev.
124
, 41
(1961
).21.
W.
Schmickler
, J. Electroanal. Chem. Interfacial Electrochem.
204
, 31
(1986
).22.
A.
Yoshimori
and K.
Makoshi
, Prog. Surf. Sci.
21
, 251
(1986
).23.
J.
Mohr
and W.
Schmickler
, Phys. Rev. Lett.
84
, 1051
(2000
).24.
Y. G.
Boroda
and G. A.
Voth
, J. Chem. Phys.
104
, 6168
(1996
).25.
W.
Schmickler
and J.
Mohr
, J. Chem. Phys.
117
, 2867
(2002
).26.
I.
Navrotskaya
and S.
Hammes-Schiffer
, J. Chem. Phys.
131
, 024112
(2009
).27.
A. K.
Mishra
and D. H.
Waldeck
, J. Phys. Chem. C
113
, 17904
(2009
).28.
M.
Askerka
, R. J.
Maurer
, V. S.
Batista
, and J. C.
Tully
, Phys. Rev. Lett.
116
, 217601
(2016
).29.
W.
Dou
and J. E.
Subotnik
, J. Chem. Phys.
144
, 024116
(2016
).30.
W.
Ouyang
, W.
Dou
, A.
Jain
, and J. E.
Subotnik
, J. Chem. Theory Comput.
12
, 4178
(2016
).31.
W.
Dou
and J. E.
Subotnik
, J. Chem. Phys.
146
, 092304
(2017
).32.
D.
Segal
, A. J.
Millis
, and D. R.
Reichman
, Phys. Rev. B
82
, 205323
(2010
).33.
D.
Segal
, A. J.
Millis
, and D. R.
Reichman
, Phys. Chem. Chem. Phys.
13
, 14378
(2011
).34.
L.
Simine
and D.
Segal
, J. Chem. Phys.
141
, 014704
(2014
).35.
H.
Wang
and M.
Thoss
, J. Chem. Phys.
131
, 024114
(2009
).36.
K. F.
Albrecht
, H.
Wang
, L.
Mühlbacher
, M.
Thoss
, and A.
Komnik
, Phys. Rev. B
86
, 081412
(2012
).37.
H.
Wang
and M.
Thoss
, J. Phys. Chem. A
117
, 7431
(2013
).38.
E. Y.
Wilner
, H.
Wang
, G.
Cohen
, M.
Thoss
, and E.
Rabani
, Phys. Rev. B
88
, 045137
(2013
).39.
E. Y.
Wilner
, H.
Wang
, M.
Thoss
, and E.
Rabani
, Phys. Rev. B
92
, 195143
(2015
).40.
A.
Nitzan
, Chemical Dynamics in Condensed Phases
(Oxford University Press
, New York
, 2006
).41.
A.
Garg
, J. N.
Onuchic
, and V.
Ambegaokar
, J. Chem. Phys.
83
, 4491
(1985
).42.
S.
Ramakrishna
, F.
Willig
, and V.
May
, J. Chem. Phys.
115
, 2743
(2001
).43.
M.
Thoss
and H. B.
Wang
, Annu. Rev. Phys. Chem.
55
, 299
(2004
).44.
J.
Li
, I.
Kondov
, H.
Wang
, and M.
Thoss
, J. Phys.: Condens. Matter
27
, 134202
(2015
).45.
E.
Frishman
and M.
Shapiro
, Phys. Rev. A
54
, 3310
(1996
).46.
I.
Thanopulos
, P.
Brumer
, and M.
Shapiro
, J. Chem. Phys.
129
, 194104
(2008
).47.
C.
Meier
and D.
Tannor
, J. Chem. Phys.
111
, 3365
(1999
).48.
Y.
Tanimura
and R.
Kubo
, J. Phys. Soc. Jpn.
58
, 101
(1989
).49.
Y.
Tanimura
, J. Phys. Soc. Jpn.
75
, 082001
(2006
).50.
J.-S.
Jin
, X.
Zheng
, and Y.-J.
Yan
, J. Chem. Phys.
128
, 234703
(2008
).51.
M. W. Y.
Tu
and W.-M.
Zhang
, Phys. Rev. B
78
, 235311
(2008
).52.
X.
Zheng
, J.-S.
Jin
, S.
Welack
, M.
Luo
, and Y.-J.
Yan
, J. Chem. Phys.
130
, 164708
(2009
).53.
Z.-H.
Li
, N.-H.
Tong
, X.
Zheng
, D.
Hou
, J.-H.
Wei
, J.
Hu
, and Y.-J.
Yan
, Phys. Rev. Lett.
109
, 266403
(2012
).54.
R.
Härtle
, G.
Cohen
, D. R.
Reichman
, and A. J.
Millis
, Phys. Rev. B
88
, 235426
(2013
).55.
R.
Härtle
and A. J.
Millis
, Phys. Rev. B
90
, 245426
(2015
).56.
C.
Schinabeck
, A.
Erpenbeck
, R.
Härtle
, and M.
Thoss
, Phys. Rev. B
94
, 201407
(2016
).57.
U.
Weiss
, Quantum Dissipative Systems
, 4th ed. (World Scientific
, New Jersey
, 2012
).58.
Y.
Tanimura
, J. Chem. Phys.
141
, 044114
(2014
).59.
L.
Song
and Q.
Shi
, J. Chem. Phys.
143
, 194106
(2015
).60.
A.
Croy
and U.
Saalmann
, Phys. Rev. B
80
, 245311
(2009
).61.
S.
Ramakrishna
and F.
Willig
, J. Phys. Chem. B
104
, 68
(2000
).62.
A.
Ishizaki
and Y.
Tanimura
, J. Phys. Soc. Jpn.
74
, 3131
(2005
).63.
Q.
Shi
, L.-P.
Chen
, G.-J.
Nan
, R.-X.
Xu
, and Y.-J.
Yan
, J. Chem. Phys.
130
, 084105
(2009
).64.
X.
Zheng
, G.
Chen
, Y.
Mo
, S.
Koo
, H.
Tian
, C.
Yam
, and Y.
Yan
, J. Chem. Phys.
133
, 114101
(2010
).65.
H.
Liu
, L.
Zhu
, S.
Bai
, and Q.
Shi
, J. Chem. Phys.
140
, 134106
(2014
).66.
R.
Wang
, X.
Zheng
, Y.
Kwok
, H.
Xie
, G.
Chen
, and C.
Yam
, J. Chem. Phys.
142
, 144112
(2015
).67.
J.
Hu
, R.-X.
Xu
, and Y.-J.
Yan
, J. Chem. Phys.
133
, 101106
(2010
).68.
M.
Thoss
, I.
Kondov
, and H.
Wang
, Chem. Phys.
304
, 169
(2004
).69.
L.
Wang
, F.
Willig
, and V.
May
, J. Chem. Phys.
124
, 014712
(2006
).70.
I.
Kondov
, M.
Thoss
, and H.
Wang
, J. Phys. Chem. A
110
, 1364
(2006
).71.
C.
Zimmermann
, F.
Willig
, S.
Ramakrishna
, B.
Burfeindt
, B.
Pettinger
, R.
Eichberger
, and W.
Storck
, J. Phys. Chem. B
105
, 9245
(2001
).72.
Q.
Shi
, L.-P.
Chen
, G.-J.
Nan
, R.-X.
Xu
, and Y.-J.
Yan
, J. Chem. Phys.
130
, 164518
(2009
).73.
L.
Zhu
, H.
Liu
, W.
Xie
, and Q.
Shi
, J. Chem. Phys.
137
, 194106
(2012
).74.
L.-Z.
Song
and Q.
Shi
, Phys. Rev. B
95
, 064308
(2017
).© 2019 Author(s).
2019
Author(s)
You do not currently have access to this content.
