A model for taking into account surface temperature effects in molecule-surface reactions is reported and applied to the dissociation of H2 and D2 on Cu(111). In contrast to many models developed before, the model constructed here takes into account the effects of static corrugation of the potential energy surface rather than energy exchange between the impinging hydrogen molecule and the surface. Such an approximation is a vibrational sudden approximation. The quality of the model is assessed by comparison to a recent density functional theory study. It is shown that the model gives a reasonable agreement with recently performed ab initio molecular dynamics calculations, in which the surface atoms were allowed to move. The observed broadening of the reaction probability curve with increasing surface temperature is attributed to the displacement of surface atoms, whereas the effect of thermal expansion is found to be primarily a shift of the curve to lower energies. It is also found that the rotational quadrupole alignment parameter is generally lowered at low energies, whereas it remains approximately constant at high energies. Finally, it is shown that the approximation of an ideal static surface works well for low surface temperatures, in particular for the molecular beams for this system (Ts = 120 K). Nonetheless, for the state-resolved reaction probability at this surface temperature, some broadening is found.

1.
C.
Díaz
,
R. A.
Olsen
,
D. J.
Auerbach
, and
G. J.
Kroes
,
Phys. Chem. Chem. Phys.
12
,
6499
(
2010
).
2.
C.
Díaz
,
E.
Pijper
,
R. A.
Olsen
,
H. F.
Busnengo
,
D. J.
Auerbach
, and
G. J.
Kroes
,
Science
326
,
832
(
2009
).
3.
J.
Dai
and
J. C.
Light
,
J. Chem. Phys.
108
,
7816
(
1998
).
4.
J.
Dai
and
J. C.
Light
,
J. Chem. Phys.
107
,
1676
(
1997
).
5.
J.
Dai
,
J.
Sheng
, and
J. Z. H.
Zhang
,
J. Chem. Phys.
101
,
1555
(
1994
).
6.
J.
Dai
and
J. Z. H.
Zhang
,
J. Chem. Phys.
102
,
6280
(
1995
).
7.
J.
Dai
and
J. Z. H.
Zhang
,
Surf. Sci.
319
,
193
(
1994
).
8.
G. R.
Darling
and
S.
Holloway
,
Surf. Sci.
321
,
L189
(
1994
).
9.
G. R.
Darling
and
S.
Holloway
,
J. Chem. Phys.
101
,
3268
(
1994
).
10.
G. R.
Darling
and
S.
Holloway
,
Surf. Sci.
307–309
,
153
(
1994
).
11.
G. R.
Darling
and
S.
Holloway
,
J. Chem. Phys.
97
,
734
(
1992
).
12.
A.
Forni
,
G.
Wiesenekker
,
E. J.
Baerends
, and
G. F.
Tantardini
,
J. Phys.: Condens. Matter
7
,
7195
(
1995
).
13.
A.
Forni
,
G.
Wiesenekker
,
E. J.
Baerends
, and
G. F.
Tantardini
,
Int. J. Quantum Chem.
52
,
1067
(
1994
).
14.
A.
Gross
,
B.
Hammer
,
M.
Scheffler
, and
W.
Brenig
,
Phys. Rev. Lett.
73
,
3121
(
1994
).
15.
B.
Hammer
,
M.
Scheffler
,
K. W.
Jacobsen
, and
J. K.
Nørskov
,
Phys. Rev. Lett.
73
,
1400
(
1994
).
16.
S.
Nave
,
D.
Lemoine
,
M. F.
Somers
,
S. M.
Kingma
, and
G. J.
Kroes
,
J. Chem. Phys.
122
,
214709
(
2005
).
17.
U.
Nielsen
,
D.
Halstead
,
S.
Holloway
, and
J. K.
Nørskov
,
J. Chem. Phys.
93
,
2879
(
1990
).
18.
J.
Sheng
and
J. Z. H.
Zhang
,
J. Chem. Phys.
99
,
1373
(
1993
).
19.
M. F.
Somers
,
S. M.
Kingma
,
E.
Pijper
,
G. J.
Kroes
, and
D.
Lemoine
,
Chem. Phys. Lett.
360
,
390
(
2002
).
20.
G.
Anger
,
A.
Winkler
, and
K. D.
Rendulic
,
Surf. Sci.
220
,
1
(
1989
).
21.
H. F.
Berger
,
M.
Leisch
,
A.
Winkler
, and
K. D.
Rendulic
,
Chem. Phys. Lett.
175
,
425
(
1990
).
22.
S. J.
Gulding
,
A. M.
Wodtke
,
H.
Hou
,
C. T.
Rettner
,
H. A.
Michelsen
, and
D. J.
Auerbach
,
J. Chem. Phys.
105
,
9702
(
1996
).
23.
H.
Hou
,
S. J.
Gulding
,
C. T.
Rettner
,
A. M.
Wodtke
, and
D. J.
Auerbach
,
Science
277
,
80
(
1997
).
24.
H. A.
Michelsen
and
D. J.
Auerbach
,
J. Chem. Phys.
94
,
7502
(
1991
).
25.
H. A.
Michelsen
,
C. T.
Rettner
, and
D. J.
Auerbach
,
Surf. Sci.
272
,
65
(
1992
).
26.
H. A.
Michelsen
,
C. T.
Rettner
, and
D. J.
Auerbach
,
Phys. Rev. Lett.
69
,
2678
(
1992
).
27.
H. A.
Michelsen
,
C. T.
Rettner
,
D. J.
Auerbach
, and
R. N.
Zare
,
J. Chem. Phys.
98
,
8294
(
1993
).
28.
M. J.
Murphy
and
A.
Hodgson
,
J. Chem. Phys.
108
,
4199
(
1998
).
29.
C. T.
Rettner
,
D. J.
Auerbach
, and
H. A.
Michelsen
,
Phys. Rev. Lett.
68
,
1164
(
1992
).
30.
C. T.
Rettner
,
H. A.
Michelsen
, and
D. J.
Auerbach
,
J. Chem. Phys.
102
,
4625
(
1995
).
31.
C. T.
Rettner
,
H. A.
Michelsen
, and
D. J.
Auerbach
,
Chem. Phys.
175
,
157
(
1993
).
32.
D.
Wetzig
,
M.
Rutkowski
,
R.
David
, and
H.
Zacharias
,
Europhys. Lett.
36
,
31
(
1996
).
33.
P.
Nieto
,
E.
Pijper
,
D.
Barredo
,
G.
Laurent
,
R. A.
Olsen
,
E. J.
Baerends
,
G. J.
Kroes
, and
D.
Farías
,
Science
312
,
86
(
2006
).
34.
A.
Gross
and
A.
Dianat
,
Phys. Rev. Lett.
98
,
206107
(
2007
).
35.
F.
Nattino
,
C.
Díaz
,
B.
Jackson
, and
G. J.
Kroes
,
Phys. Rev. Lett.
108
,
236104
(
2012
).
36.
F. R.
Kroeger
and
C. A.
Swenson
,
J. Appl. Phys.
48
,
853
(
1977
).
37.
I. E.
Leksina
and
S. I.
Novikova
,
Soviet Phys. Solid State
5
,
798
(
1963
).
38.
K. H.
Chae
,
H. C.
Lu
, and
T.
Gustafsson
,
Phys. Rev. B
54
,
14082
(
1996
).
39.
V. F.
Sears
and
S. A.
Shelley
,
Acta Crystallographica
A47
,
441
(
1991
).
40.
E. C.
Svensson
,
B. N.
Brockhouse
, and
J. M.
Rowe
,
Phys. Rev.
155
,
619
(
1967
).
41.
M.
Dohle
and
P.
Saalfrank
,
Surf. Sci.
373
,
95
(
1997
).
42.
M.
Dohle
,
P.
Saalfrank
, and
T.
Uzer
,
J. Chem. Phys.
108
,
4226
(
1998
).
43.
M.
Dohle
,
P.
Saalfrank
, and
T.
Uzer
,
Surf. Sci.
409
,
37
(
1998
).
44.
M.
Hand
and
J.
Harris
,
J. Chem. Phys.
92
,
7610
(
1990
).
45.
A. C.
Luntz
and
J.
Harris
,
Surf. Sci.
258
,
397
(
1991
).
46.
P.
Saalfrank
and
W. H.
Miller
,
Surf. Sci.
303
,
206
(
1994
).
47.
H. F.
Busnengo
,
W.
Dong
,
P.
Sautet
, and
A.
Salin
,
Phys. Rev. Lett.
87
,
127601
(
2001
).
48.
S.
Nave
and
B.
Jackson
,
Phys. Rev. Lett.
98
,
173003
(
2007
).
49.
S.
Nave
and
B.
Jackson
,
J. Chem. Phys.
127
,
224702
(
2007
).
50.
N.
Pineau
,
H. F.
Busnengo
,
J. C.
Rayez
, and
A.
Salin
,
J. Chem. Phys.
122
,
214705
(
2005
).
51.
M.
Bonfanti
,
C.
Díaz
,
M. F.
Somers
, and
G. J.
Kroes
,
Phys. Chem. Chem. Phys.
13
,
4552
(
2011
).
52.
A. K.
Tiwari
,
S.
Nave
, and
B.
Jackson
,
J. Chem. Phys.
132
,
134702
(
2010
).
53.
A. K.
Tiwari
,
S.
Nave
, and
B.
Jackson
,
Phys. Rev. Lett.
103
,
253201
(
2009
).
54.
H. F.
Busnengo
,
A.
Salin
, and
W.
Dong
,
J. Chem. Phys.
112
,
7641
(
2000
).
55.
R.
Drautz
,
M.
Fänhle
, and
J. M.
Sanchez
,
J. Phys.: Condens. Matter
16
,
3843
(
2004
).
56.
J.
Ludwig
,
D. G.
Vlachos
,
A. C. T.
van Duin
, and
W. A.
Goddard
,
J. Phys. Chem. B
110
,
4274
(
2006
).
57.
P.
Valentini
,
T. E.
Schwartzentruber
, and
I.
Cozmuta
,
J. Chem. Phys.
133
,
084703
(
2010
).
58.
Y.
Xiao
,
W.
Dong
, and
H. F.
Busnengo
,
J. Chem. Phys.
132
,
014704
(
2010
).
59.
J. P.
Perdew
,
J. A.
Chevary
,
S. H.
Vosko
,
K. A.
Jackson
,
M. R.
Pederson
,
D. J.
Singh
, and
C.
Fiolhais
,
Phys. Rev. B
46
,
6671
(
1992
).
60.
B.
Hammer
,
L. B.
Hansen
, and
J. K.
Nørskov
,
Phys. Rev. B
59
,
7413
(
1999
).
61.
C. C.
Marston
and
G. G.
Balint-Kurti
,
J. Chem. Phys.
91
,
3571
(
1989
).
62.
J.
Stoer
and
R.
Burlisch
,
Introduction to Numerical Analysis
(
Springer
,
New York
,
1980
).
63.
M.
Bonfanti
, personal communication (
2011
).
64.
R. N.
Zare
,
Angular Momentum
(
Wiley
,
New York
,
1988
).
65.
D. P.
Anderson
, in
Proceedings of the 5th IEEE/ACM International Workshop on Grid Computing
,
Pittsburgh, PA
,
2004
.
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