We study a moving adsorbate interacting with a metal electrode immersed in a solvent using the time-dependent Newns–Anderson–Schmickler model Hamiltonian. We have adopted a semiclassical trajectory treatment of the adsorbate to discuss the electron and energy transfers that occur between the adsorbate and the electrode. Using Keldysh Green’s function scheme, we found a non-adiabatically suppressed electron transfer caused by the motion of the adsorbate and coupling with bath phonons that model the solvent. The energy is thus dissipated into electron–hole pair excitations, which are hindered by interacting with the solvent modes and facilitated by the applied electrode potential. The average energy transfer rate is discussed in terms of the electron friction coefficient and given an analytical expression in the slow-motion limit.

1.
R. A.
Marcus
,
J. Chem. Phys.
43
,
679
(
1965
).
2.
N. S.
Hush
,
J. Chem. Phys.
28
,
962
(
1958
).
3.
V.
Levich
, in
Physical Chemistry. An Advanced Treatise
, edited by
H.
Eyring
,
D.
Henderson
, and
W.
Jost
(
Academic Press
,
1970
), Vol.
Xb
.
4.
W.
Schmickler
,
J. Electroanal. Chem. Interfacial Electrochem.
204
,
31
(
1986
).
5.
A. C.
Hewson
and
D. M.
Newns
,
Jpn. J. Appl. Phys.
13
,
121
(
1974
).
6.
P. H.
Citrin
and
D. R.
Hamann
,
Phys. Rev. B
15
,
2923
(
1977
).
7.
X.
Song
and
R. A.
Marcus
,
J. Chem. Phys.
99
,
7768
(
1993
).
8.
K. L.
Sebastian
,
J. Chem. Phys.
90
,
5056
(
1989
).
9.
B. B.
Smith
and
J. T.
Hynes
,
J. Chem. Phys.
99
,
6517
(
1993
).
10.
J.-H.
Mohr
and
W.
Schmickler
,
Phys. Rev. Lett.
84
,
1051
(
2000
).
11.
S.
Tanaka
and
C. P.
Hsu
,
J. Chem. Phys.
111
,
11117
(
1999
).
12.
A. M.
Wodtke
,
J. C.
Tully
, and
D. J.
Auerbach
,
Int. Rev. Phys. Chem.
23
,
513
(
2004
).
13.
E. J.
Piechota
and
G. J.
Meyer
,
J. Chem. Educ.
96
,
2450
(
2019
).
14.
R.
Brako
and
D. M.
Newns
,
Surf. Sci.
108
,
253
(
1981
).
15.
A.
Blandin
,
A.
Nourtier
, and
D.
Hone
,
J. Phys.
37
,
369
(
1976
).
16.
A.
Yoshimori
,
H.
Kawai
, and
K.
Makoshi
,
Prog. Theor. Phys. Suppl.
80
,
203
(
1984
).
17.
H.
Kasai
and
A.
Okiji
,
Surf. Sci.
183
,
147
(
1987
).
18.
A.
Yoshimori
and
K.
Makoshi
,
Prog. Surf. Sci.
21
,
251
(
1986
).
19.
M. S.
Mizielinski
,
D. M.
Bird
,
M.
Persson
, and
S.
Holloway
,
J. Chem. Phys.
122
,
084710
(
2005
).
20.
R.
Brako
and
D. M.
Newns
,
Solid State Commun.
33
,
713
(
1980
).
21.
M.
Plihal
and
D. C.
Langreth
,
Phys. Rev. B
58
,
2191
(
1998
).
23.
H.
Kasai
and
A.
Okiji
,
Surf. Sci.
242
,
394
(
1991
).
24.
A.
Gross
and
W.
Brenig
,
Chem. Phys.
177
,
497
(
1993
).
25.
Y. C.
Lam
,
A. V.
Soudackov
, and
S.
Hammes-Schiffer
,
J. Phys. Chem. Lett.
10
,
5312
(
2019
).
26.
W.
Dou
and
J.
Subotnik
,
J. Phys. Chem. A
124
,
757
(
2020
).
27.
A. C.
Hewson
and
D. M.
Newns
,
J. Phys. C: Solid State Phys.
13
,
4477
(
1980
).
28.
Z. Z.
Chen
,
R.
Lu
, and
B.
Zhu
,
Phys. Rev. B.
71
,
165324
(
2005
).
29.
A.-P.
Jauho
,
N. S.
Wingreen
, and
Y.
Meir
,
Phys. Rev. B
50
,
5528
(
1994
).
30.
D.
Langreth
, in
Linear and Non Linear Electron Transport in Solids
,
NATO Science Series B
, edited by
J. T.
Devreese
and
E.
van Doren
(
Plenum
,
1976
), Vol.
17
, p.
3
.
31.
M. M.
Odashima
and
C. H.
Lewenkopf
,
Phys. Rev. B
95
,
104301
(
2017
).
32.
J. X.
Zhu
and
A. V.
Balatsky
,
Phys. Rev. B
67
,
165326
(
2003
).
33.
Y.
Tanimura
and
R.
Kubo
,
J. Phys. Soc. Jpn.
58
,
101
(
1989
).
35.
Y.
Tanimura
,
J. Chem. Phys.
153
,
020901
(
2020
).
36.
N.
Lambert
,
T.
Raheja
,
S.
Cross
,
P.
Menczel
,
S.
Ahmed
,
A.
Pitchford
,
D.
Burgarth
, and
F.
Nori
,
Phys. Rev. Res.
5
,
013181
(
2023
).
37.
D. C.
Langreth
and
P.
Nordlander
,
Phys. Rev. B
43
,
2541
(
1991
).
38.
N. S.
Wingreen
,
K. W.
Jacobsen
, and
J. W.
Wilkins
,
Phys. Rev. B
40
,
11834
(
1989
).
39.
W.
Dou
and
J. E.
Subotnik
,
J. Chem. Phys.
148
,
230901
(
2018
).
40.
R.
Brako
and
D. M.
Newns
,
J. Phys. C: Solid State Phys.
14
,
3065
(
1981
).
41.
K.
Schönhammer
and
O.
Gunnarsson
,
Phys. Rev. B
22
,
1629
(
1980
).
42.
K.
Schönhammer
,
Z. Phys. B: Condens. Matter
45
,
23
(
1981
).
43.
A. M.
Kuznetsov
, in
Physical Chemistry: An Andvanced Treatise
, edited by
B. E.
Conway
,
R. J.
White
, and
J. O.
Bockris
(
Plenum
,
1989
), Vol.
20
.
44.
W.
Schmickler
,
Interfacial Electrochemistry
(
Oxford University
,
1996
).
45.
E.
Santos
,
M. T.
Koper
, and
W.
Schmickler
,
Chem. Phys. Lett.
419
,
421
(
2006
).
46.
E.
Santos
,
M. T.
Koper
, and
W.
Schmickler
,
Chem. Phys.
344
,
195
(
2008
).
47.
H.
Nakanishi
,
H.
Kasai
, and
A.
Okiji
,
Surf. Sci.
197
,
515
(
1988
).
48.
A.
Hamelin
and
M. J.
Weaver
,
J. Electroanal. Chem. Interfacial Electrochem.
223
,
171
(
1987
).
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