The generator coordinate (GC) method is a variational approach to the quantum many-body problem in which interacting many-body wave functions are constructed as superpositions of (generally nonorthogonal) eigenstates of auxiliary Hamiltonians containing a deformation parameter. This paper presents a time-dependent extension of the GC method as a new approach to improve existing approximations of the exchange-correlation (XC) potential in time-dependent density-functional theory (TDDFT). The time-dependent GC method is shown to be a conceptually and computationally simple tool to build memory effects into any existing adiabatic XC potential. As an illustration, the method is applied to driven parametric oscillations of two interacting electrons in a harmonic potential (Hooke’s atom). It is demonstrated that a proper choice of time-dependent generator coordinates in conjunction with the adiabatic local-density approximation reproduces the exact linear and nonlinear two-electron dynamics quite accurately, including features associated with double excitations that cannot be captured by TDDFT in the adiabatic approximation.

1.
E.
Runge
and
E. K. U.
Gross
,
Phys. Rev. Lett.
52
,
997
(
1984
).
2.
M. A. L.
Marques
and
E. K. U.
Gross
,
Annu. Rev. Phys. Chem.
55
,
427
(
2004
).
3.
F.
Furche
and
K.
Burke
, in
Annual Reports in Computational Chemistry
, edited by
D.
Spellmeyer
(
Elsevier
,
Amsterdam
,
2005
), Vol.
1
, p.
19
.
4.
Time-Dependent Density Functional Theory
,
Lecture Notes in Physics
Vol.
706
, edited by
M. A. L.
Marques
,
C. A.
Ullrich
,
F.
Nogueira
,
A.
Rubio
,
K.
Burke
, and
E. K. U.
Gross
(
Springer
,
Berlin
,
2006
).
5.
E. K. U.
Gross
and
W.
Kohn
,
Phys. Rev. Lett.
55
,
2850
(
1985
);
E. K. U.
Gross
and
W.
Kohn
,
Phys. Rev. Lett.
57
,
923
(E) (
1986
).
6.
M.
Petersilka
,
U. J.
Gossmann
, and
E. K. U.
Gross
,
Phys. Rev. Lett.
76
,
1212
(
1996
).
7.
A.
Dreuw
,
J.
Weisman
, and
M.
Head-Gordon
,
J. Chem. Phys.
119
,
2943
(
2003
).
8.
N. T.
Maitra
,
F.
Zhang
,
R. J.
Cave
, and
K.
Burke
,
J. Chem. Phys.
120
,
5932
(
2004
).
9.
N. T.
Maitra
,
J. Chem. Phys.
122
,
234104
(
2005
).
10.
S.
Botti
,
A.
Schindlmayr
,
R.
Del Sole
, and
L.
Reining
,
Rep. Prog. Phys.
70
,
357
(
2007
).
11.
C. A.
Ullrich
and
A. D.
Bandrauk
, in
Time-Dependent Functional Theory
,
Lecture Notes in Physics
Vol.
706
, edited by
M. A. L.
Marques
,
C. A.
Ullrich
,
F.
Nogueira
,
A.
Rubio
,
K.
Burke
, and
E. K. U.
Gross
(
Springer
,
Berlin
,
2000
), p.
357
.
12.
D. N.
Fittinghoff
,
P. R.
Bolton
,
B.
Chang
, and
K. C.
Kulander
,
Phys. Rev. Lett.
69
,
2642
(
1992
).
13.
D.
Lappas
and
R.
van Leeuwen
,
J. Phys. B
31
,
L249
(
1998
).
14.
M.
Lein
and
S.
Kümmel
,
Phys. Rev. Lett.
94
,
143003
(
2005
).
15.
M.
Mundt
and
S.
Kümmel
,
Phys. Rev. Lett.
95
,
203004
(
2005
).
16.
H. O.
Wijewardane
and
C. A.
Ullrich
,
Phys. Rev. Lett.
95
,
086401
(
2005
).
17.
R.
D’Agosta
and
G.
Vignale
,
Phys. Rev. Lett.
96
,
016405
(
2006
).
18.
C. A.
Ullrich
and
I. V.
Tokatly
,
Phys. Rev. B
73
,
235102
(
2006
).
19.
C. A.
Ullrich
,
J. Chem. Phys.
125
,
234108
(
2006
).
20.
G.
Vignale
and
W.
Kohn
,
Phys. Rev. Lett.
77
,
2037
(
1996
).
21.
J. F.
Dobson
,
M. J.
Bünner
, and
E. K. U.
Gross
,
Phys. Rev. Lett.
79
,
1905
(
1997
).
22.
G.
Vignale
,
C. A.
Ullrich
, and
S.
Conti
,
Phys. Rev. Lett.
79
,
4878
(
1997
).
23.
C. A.
Ullrich
and
G.
Vignale
,
Phys. Rev. B
65
,
245102
(
2002
);
C. A.
Ullrich
and
G.
Vignale
,
Phys. Rev. B
70
,
239903
(E) (
2004
).
24.
Y.
Kurzweil
and
R.
Baer
,
J. Chem. Phys.
121
,
8731
(
2004
).
25.
I. V.
Tokatly
,
Phys. Rev. B
71
,
165104
(
2005
);
I. V.
Tokatly
,
Phys. Rev. B
71
,
165105
(
2005
).
26.
M.
van Faassen
,
P. L.
de Boeij
,
R.
van Leeuwen
,
J. A.
Berger
, and
J. G.
Snijders
,
Phys. Rev. Lett.
88
,
186401
(
2002
);
M.
van Faassen
,
P. L.
de Boeij
,
R.
van Leeuwen
,
J. A.
Berger
, and
J. G.
Snijders
,
J. Chem. Phys.
118
,
1044
(
2003
).
27.
M.
van Faassen
,
Int. J. Mod. Phys. B
20
,
3419
(
2006
).
28.
C. A.
Ullrich
and
G.
Vignale
,
Phys. Rev. Lett.
87
,
037402
(
2001
).
29.
C. A.
Ullrich
and
K.
Burke
,
J. Chem. Phys.
121
,
28
(
2004
).
30.
D. L.
Hill
and
J. A.
Wheeler
,
Phys. Rev.
89
,
1106
(
1953
).
31.
J. J.
Griffin
and
J. A.
Wheeler
,
Phys. Rev.
108
,
311
(
1957
).
32.
C. W.
Wong
,
Phys. Rep.
15
,
283
(
1975
).
33.
P.
Chattopadhyay
,
R. M.
Dreizler
,
M.
Trsic
, and
M.
Fink
,
Z. Phys. A
285
,
7
(
1978
).
34.
B.
Johansson
and
J.
da Providencia
,
Physica B
94
,
152
(
1978
).
35.
J. R.
Mohallem
,
R. M.
Dreizler
, and
M.
Trsic
,
Int. J. Quantum Chem.
20
,
45
(
1986
).
36.
A. B. F.
da Silva
,
H. M. F.
da Costa
, and
M.
Trsic
,
Mol. Phys.
68
,
433
(
1989
).
37.
F. E.
Jorge
and
A. B. F.
da Silva
,
J. Chem. Phys.
104
,
6278
(
1996
).
38.
F. E.
Jorge
and
A. B. F.
da Silva
,
J. Chem. Phys.
105
,
5503
(
1996
).
39.
O. E.
Alon
,
A. I.
Streltsov
, and
L. S.
Cederbaum
,
Phys. Rev. B
71
,
125113
(
2005
).
40.
X.-Y.
Pan
,
V.
Sahni
, and
L.
Massa
,
Phys. Rev. Lett.
93
,
130401
(
2004
).
41.
K.
Capelle
,
J. Chem. Phys.
119
,
1285
(
2003
).
42.
E.
Orestes
,
A. B. F.
da Silva
, and
K.
Capelle
(unpublished).
43.
N. R.
Keisner
and
O.
Sinanoglu
,
Phys. Rev.
128
,
2687
(
1962
).
44.
P. M.
Laufer
and
J. B.
Krieger
,
Phys. Rev. A
33
,
1480
(
1986
).
45.
S.
Kais
,
D. R.
Herschbach
,
N. C.
Handy
,
C. W.
Murray
, and
G. J.
Laming
,
J. Chem. Phys.
99
,
417
(
1993
).
46.
M.
Taut
,
J. Phys. A
27
,
1045
(
1994
).
47.
C.
Filippi
,
C. J.
Umrigar
, and
M.
Taut
,
J. Chem. Phys.
100
,
1290
(
1994
).
48.
I.
D’Amico
and
G.
Vignale
,
Phys. Rev. B
59
,
7876
(
1999
).
49.
P.
Hessler
,
J.
Park
, and
K.
Burke
,
Phys. Rev. Lett.
82
,
378
(
1999
);
P.
Hessler
,
J.
Park
, and
K.
Burke
,
Phys. Rev. Lett.
83
,
5184
(E) (
1999
).
50.
P.
Hessler
,
N. T.
Maitra
, and
K.
Burke
,
J. Chem. Phys.
117
,
72
(
2002
).
51.
M.
Petersilka
and
E. K. U.
Gross
,
Laser Phys.
9
,
105
(
1999
).
52.
C. A.
Ullrich
,
J. Mol. Struct.: THEOCHEM
501–502
,
315
(
2000
).
53.
W. H.
Press
,
S. A.
Teukolsky
,
W. T.
Vetterling
, and
B. P.
Flannery
,
Numerical Recipes
, 2nd ed. (
Cambridge University Press
,
Cambridge
,
1992
).
You do not currently have access to this content.