Most of today's molecular-dynamics simulations of materials are based on the Born-Oppenheimer approximation. There are many cases, however, in which the coupling of the electrons and nuclei is important and it is necessary to go beyond the Born-Oppenheimer approximation. In these methods, the non-adiabatic coupling vectors are fundamental since they represent the link between the classical atomic motion of the nuclei and the time evolution of the quantum electronic state. In this paper we analyze the calculation of non-adiabatic coupling vectors in a basis set of local orbitals and derive an expression to calculate them in a practical and computationally efficient way. Some examples of the application of this expression using a local-orbital density functional theory approach are presented for a few simple molecules: H3, formaldimine, and azobenzene. These results show that the approach presented here, using the Slater transition-state density, is a very promising way for the practical calculation of non-adiabatic coupling vectors for large systems.

1.
P.
Hohenberg
and
W.
Kohn
,
Phys. Rev.
136
,
B864
(
1964
).
2.
W.
Kohn
and
L. J.
Sham
,
Phys. Rev.
140
,
A1133
(
1965
).
3.
N. L.
Doltsinis
and
D.
Marx
,
J. Theor. Comput. Chem.
1
,
319
(
2002
).
4.
A. P.
Horsfield
,
D. R.
Bowler
,
H.
Ness
,
C. G.
Sánchez
,
T. N.
Todorov
, and
A. J.
Fisher
,
Rep. Prog. Phys.
69
,
1195
(
2006
).
5.
E. J.
McEniry
,
Y.
Wang
,
D.
Dundas
,
T. N.
Todorov
,
L.
Stella
,
R. P.
Miranda
,
A. J.
Fisher
,
A. P.
Horsfield
,
C. P.
Race
,
D. R.
Mason
,
W. M. C.
Foulkes
, and
A. P.
Sutton
,
Eur. Phys. J. B
77
,
305
(
2010
).
6.
C. P.
Race
,
D. R.
Mason
,
M. W.
Finnis
,
W. M. C.
Foulkes
,
A. P.
Horsfield
, and
A. P.
Sutton
,
Rep. Prog. Phys.
73
,
116501
(
2010
).
7.
S. R.
Billeter
and
A.
Curioni
,
J. Chem. Phys.
122
,
034105
(
2005
).
8.
D. F.
Coker
and
L.
Xiao
,
J. Chem. Phys.
102
,
496
(
1995
).
9.
I.
Tavernelli
,
E.
Tapavicza
, and
U.
Rothlisberger
,
J. Chem. Phys.
130
,
124107
(
2009
).
10.
S. R.
Billeter
and
D.
Egli
,
J. Chem. Phys.
125
,
224103
(
2006
).
11.
V.
Chernyak
and
S.
Mukamel
,
J. Chem. Phys.
112
,
3572
(
2000
).
12.
C.
Hu
,
O.
Sugino
,
H.
Hirai
, and
Y.
Tateyama
,
Phys. Rev. A
82
,
062508
(
2010
).
13.
I.
Tavernelli
,
E.
Tapavicza
, and
U.
Rothlisberger
,
J. Mol. Struct.: THEOCHEM
914
,
22
(
2009
).
14.
M.
Tommasini
,
V.
Chernyak
, and
S.
Mukamel
,
Int. J. Quantum Chem.
85
,
225
(
2001
).
15.
M.
Wohlgemuth
,
V.
Bonai-Koutecký
, and
R.
Mitri
,
J. Chem. Phys.
135
,
054105
(
2011
).
16.
M.
Böckmann
,
N. L.
Doltsinis
, and
D.
Marx
,
J. Phys. Chem. A
114
(
2
),
745
(
2010
).
17.
M.
Böckmann
,
D.
Marx
,
C.
Peter
,
L.
Delle Site
,
K.
Kremer
, and
N. L.
Doltsinis
,
Phys. Chem. Chem. Phys.
13
,
7604
(
2011
).
18.
O. F.
Sankey
and
D. J.
Niklewski
,
Phys. Rev. B
40
,
3979
(
1989
).
19.
S.
Hammes-Schiffer
and
J. C.
Tully
,
J. Chem. Phys.
101
,
4657
(
1994
).
20.
C.
Craig
,
W.
Duncan
, and
O.
Prezhdo
,
Phys. Rev. Lett.
95
,
163001
(
2005
).
21.
T. W.
Keal
,
A.
Koslowski
, and
W.
Thiel
,
Theor. Chem. Acc.
118
,
837
(
2007
).
22.
M. J.
Bearpark
,
M. A.
Robb
, and
H. B.
Schlegel
,
Chem. Phys. Lett.
223
,
269
(
1994
).
23.
M. R.
Manaa
and
D. R.
Yarkony
,
J. Chem. Phys.
99
,
5251
(
1993
).
24.
D. R.
Yarkony
,
J. Phys. Chem. A
108
,
3200
(
2004
).
25.
M. F.
Herman
,
J. Chem. Phys.
81
,
754
(
1984
).
26.
J. C.
Tully
,
J. Chem. Phys.
93
,
1061
(
1990
).
27.
O. V.
Prezhdo
and
P. J.
Rossky
,
J. Chem. Phys.
107
,
825
(
1997
).
28.
J. P.
Lewis
,
P.
Jelínek
,
J.
Ortega
,
A. A.
Demkov
,
D. G.
Trabada
,
B.
Haycock
,
H.
Wang
,
G.
Adams
,
J. K.
Tomfohr
,
E.
Abad
,
H.
Wang
, and
D. A.
Drabold
,
Phys. Status Solidi B
248
,
1989
(
2011
);
P.
Jelínek
,
H.
Wang
,
J. P.
Lewis
,
O. F.
Sankey
, and
J.
Ortega
,
Phys. Rev. B
71
,
235101
(
2005
);
J. P.
Lewis
,
K. R.
Glaesemann
,
G. A.
Voth
,
J.
Fritsch
,
A. A.
Demkov
,
J.
Ortega
, and
O. F.
Sankey
,
Phys. Rev. B
64
,
195103
(
2001
);
A. A.
Demkov
,
J.
Ortega
,
O. F.
Sankey
, and
M. P.
Grumbach
,
Phys. Rev. B
52
,
1618
(
1995
).
29.
Time-Dependent Density Functional Theory
,
Lecture Notes in Physics
Vol.
706
, edited by
M. A. L.
Marques
 et al. (
Springer
,
Berlin Heidelberg
,
2006
).
30.
C. M.
Isborn
,
X.
Li
, and
J. C.
Tully
,
J. Chem. Phys.
126
,
134307
(
2007
).
31.
A.
Castro
,
M.
Isla
,
J. I.
Martínez
, and
J. A.
Alonso
,
Chem. Phys.
399
,
130
(
2012
).
32.
S.
Meng
and
E.
Kaxiras
,
J. Chem. Phys.
129
,
054110
(
2008
).
33.
N.
Doltsinis
and
D.
Marx
,
Phys. Rev. Lett.
88
,
166402
(
2002
).
34.
E.
Tapavicza
,
I.
Tavernelli
, and
U.
Rothlisberger
,
Phys. Rev. Lett.
98
,
023001
(
2007
).
35.
J. C.
Tully
and
R. K.
Preston
,
J. Chem. Phys.
55
,
562
(
1971
).
36.
C. E.
Crespo-Hernández
,
B.
Cohen
,
P. M.
Hare
, and
B.
Kohler
,
Chem. Rev.
104
,
1977
(
2004
).
37.
E.
Collini
,
C. Y.
Wong
,
K. E.
Wilk
,
P. M. G.
Curmi
,
P.
Brumer
, and
G. D.
Scholes
,
Nature (London)
463
,
644
(
2010
).
38.
I.
Goikoetxea
,
J.
Beltrn
,
J.
Meyer
,
J. I.
Juaristi
,
M.
Alducin
, and
K.
Reuter
,
New J. Phys.
14
,
013050
(
2012
).
39.
P. V.
Parandekar
and
J. C.
Tully
,
J. Chem. Phys.
122
,
094102
(
2005
).
40.
M.
Elstner
,
D.
Porezag
,
G.
Jungnickel
,
J.
Elsner
,
M.
Haugk
,
T.
Frauenheim
,
S.
Suhai
, and
G.
Seifert
,
Phys. Rev. B
58
,
7260
(
1998
).
41.
M. A.
Basanta
,
Y. J.
Dappe
,
P.
Jelínek
, and
J.
Ortega
,
Comput. Mater. Sci.
39
,
759
(
2007
).
42.
W. R.
Duncan
,
C. F.
Craig
, and
O. V.
Prezhdo
,
J. Am. Chem. Soc.
129
,
8528
(
2007
).
43.
B. F.
Habenicht
and
O. V.
Prezhdo
,
Phys. Rev. Lett.
100
,
197402
(
2008
).
44.
S. V.
Kilina
,
D. S.
Kilin
, and
O. V.
Prezhdo
,
ACS Nano
3
,
93
(
2009
).
45.
S. A.
Fischer
,
B. F.
Habenicht
,
A. B.
Madrid
,
W. R.
Duncan
, and
O. V.
Prezhdo
,
J. Chem. Phys.
134
,
024102
(
2011
).
46.
47.
A. J. C.
Varandas
,
F. B.
Brown
,
C. A.
Mead
,
D. G.
Truhlar
, and
N. C.
Blais
,
J. Chem. Phys.
86
,
6258
(
1987
).
48.
R.
Abrol
,
A.
Shaw
,
A.
Kuppermann
, and
D. R.
Yarkony
,
J. Chem. Phys.
115
,
4640
(
2001
).
49.
C. P.
Hu
,
H.
Hirai
, and
O.
Sugino
,
J. Chem. Phys.
127
,
064103
(
2007
).
50.
A.
Cembran
,
F.
Bernardi
,
M.
Garavelli
,
L.
Gagliardi
, and
G.
Orlandi
,
J. Am. Chem. Soc.
126
,
3234
(
2004
).
51.
C.-W.
Jiang
,
R.-H.
Xie
,
F.-L.
Li
, and
R. E.
Allen
,
J. Phys. Chem. A
115
,
244
(
2011
).
You do not currently have access to this content.