The electron-hole explicitly correlated Hartree-Fock method (eh-XCHF) is presented as a general strategy for investigation of electron-hole correlation and computation of electron-hole recombination probability. The eh-XCHF method is a variational method which uses explicitly correlated wavefunction that depends on the electron-hole inter-particle distances. It is shown that the explicitly correlated ansatz provides a systematic route to variationally minimize the total energy. The parabolic quantum dot is used as the benchmark system and the eh-XCHF method is used for computation of the ground state energy and electron-hole recombination probability. The results are compared to Hartree-Fock and explicitly correlated full configuration interaction (R12-FCI) calculations. The results indicate that an accurate description of the electron-hole wavefunction at short electron-hole inter-particle distances is crucial for qualitative description of the electron-hole recombination probability. The eh-XCHF method successfully addresses this issue and comparison of eh-XCHF calculations with R12-FCI shows good agreement. The quality of the mean field approximation for electron-hole system is also investigated by comparing HF and R12-FCI energies for electron-electron and electron-hole systems. It was found that performance of the mean field approximation is worse for the electron-hole system as compared to the corresponding electron-electron system.
REFERENCES
1.
M. G.
Bawendi
, M. L.
Steigerwald
, and L. E.
Brus
, Annu. Rev. Phys. Chem.
41
, 477
(1990
).2.
G. W.
Bryant
, Phys. Rev. B
37
, 8763
(1988
).3.
H.
Haug
and S. W.
Koch
, Quantum Theory of the Optical and Electronic Properties of Semiconductors
(World Scientific
, 2009
), p. 470
.4.
S.
Glutsch
, Excitons in Low-Dimensional Semiconductors
(Springer
, 2004
).5.
K.
Barnham
and D.
Vvedensky
, Low-Dimensional Semiconductor Structures: Fundamentals and Device Applications
(Cambridge University Press
, 2001
).6.
L.
He
, G.
Bester
, and A.
Zunger
, Phys. Rev. Lett.
94
, 016801
(2005
).7.
F.
Tassone
and C.
Piermarocchi
, Phys. Rev. Lett.
82
, 843
(1999
).8.
F.
Rossi
and E.
Molinari
, Phys. Rev. Lett.
76
, 3642
(1996
).9.
G.
Pal
, G.
Lefkidis
, H. C.
Schneider
, and W.
Hübner
, J. Chem. Phys.
133
, 154309
(2010
).10.
D. H.
Chae
, T.
Utikal
, S.
Weisenburger
, H.
Giessen
, K. V.
Klitzing
, M.
Lippitz
, and J.
Smet
, Nano Lett.
11
, 1379
(2011
).11.
V.
Perebeinos
, J.
Tersoff
, and P.
Avouris
, Nano Lett.
5
, 2495
(2005
).12.
P.
Puschnig
and C.
Ambrosch-Draxl
, Phys. Rev. Lett.
89
, 056405
–1
(2002
).13.
N.
Baer
, C.
Gies
, J.
Wiersig
, and F.
Jahnke
, Eur. Phys. J. B
50
, 411
(2006
).14.
J.
Krüger
, R.
Plass
, M.
Grätzel
, P. J.
Cameron
, and L. M.
Peter
, J. Phys. Chem. B
107
, 7536
(2003
).15.
M.
Achermann
, M. A.
Petruska
, S.
Kos
, D. L.
Smith
, D. D.
Koleske
, and V. I.
Klimov
, Nature (London)
429
, 642
(2004
).16.
M. J.
Hetzer
, Y. M.
Strzhemechny
, M.
Gao
, M. A.
Contreras
, A.
Zunger
, and L. J.
Brillson
, Appl. Phys. Lett.
86
, 162105
(2005
).17.
S.
Lacic
and O.
Inganäs
, J. Appl. Phys.
97
, 124901
(2005
).18.
C.
Chen
, S.
Wu
, J.
Li
, C.
Wu
, J.
Chen
, and K.
Ho
, Adv. Mater.
19
, 3888
(2007
).19.
R. R.
King
, D. C.
Law
, K. M.
Edmondson
, C. M.
Fetzer
, G. S.
Kinsey
, H.
Yoon
, R. A.
Sherif
, and N. H.
Karam
, Appl. Phys. Lett.
90
, 183516
(2007
).20.
C.
Wang
, A.
Heller
, and H.
Gerischer
, J. Am. Chem. Soc.
114
, 5230
(1992
).21.
J.
Tang
, J. R.
Durrant
, and D. R.
Klug
, J. Am. Chem. Soc.
130
, 13885
(2008
).22.
N. O.
Gopal
, H.
Lo
, S.
Sheu
, and S.
Ke
, J. Am. Chem. Soc.
132
, 10982
(2010
).23.
N.
Wu
, J.
Wang
, D. N.
Tafen
, H.
Wang
, J.
Zheng
, J. P.
Lewis
, X.
Liu
, S. S.
Leonard
, and A.
Manivannan
, J. Am. Chem. Soc.
132
, 6679
(2010
).24.
C. W.
Tang
and S. A.
Vanslyke
, Appl. Phys. Lett.
51
, 913
(1987
).25.
C. W.
Tang
, S. A.
Vanslyke
, and C. H.
Chen
, J. Appl. Phys.
65
, 3610
(1989
).26.
J. E.
Kroeze
, N.
Hirata
, S.
Koops
, M. K.
Nazeeruddin
, L.
Schmidt-Mende
, M.
Grätzel
, and J. R.
Durrant
, J. Am. Chem. Soc.
128
, 16376
(2006
).27.
L. V.
Butov
, C. W.
Lai
, A. L.
Ivanov
, A. C.
Gossard
, and D. S.
Chemla
, Nature (London)
417
, 47
(2002
).28.
S.
Kim
, B.
Fisher
, H.-J.
Eisler
, and M.
Bawendi
, J. Am. Chem. Soc.
125
, 11466
(2003
).29.
S. A.
Ivanov
, A.
Piryatinski
, J.
Nanda
, S.
Tretiak
, K. R.
Zavadil
, W. O.
Wallace
, D.
Werder
, and V. I.
Klimov
, J. Am. Chem. Soc.
129
, 11708
(2007
).30.
P.
Reiss
, M.
Protière
, and L.
Li
, Small
5
, 154
(2009
).31.
V. I.
Klimov
, J. Phys. Chem. B
110
, 16827
(2006
).32.
V. I.
Klimov
, S. A.
Ivanov
, J.
Nanda
, M.
Achermann
, I.
Bezel
, J. A.
McGuire
, and A.
Piryatinski
, Nature (London)
447
, 441
(2007
).33.
G.
Onida
, L.
Reining
, and A.
Rubio
, Rev. Mod. Phys.
74
, 601
(2002
).34.
M.
Rohlfing
and S. G.
Louie
, Phys. Rev. B: Condens. Matter Mater. Phys.
62
, 4927
(2000
).35.
L. S.
Cederbaum
, J. Phys. B
8
, 290
(1975
).36.
L. E.
Brus
, J. Chem. Phys.
80
, 4403
(1984
).37.
M.
Braskén
, M.
Lindberg
, D.
Sundholm
, and J.
Olsen
, Phys. Rev. B
61
, 7652
(2000
).38.
Y. Z.
Hu
, M.
Lindberg
, and S. W.
Koch
, Phys. Rev. B
42
, 1713
(1990
).39.
T.
Vänskä
, M.
Lindberg
, J.
Olsen
, and D.
Sundholm
, Phys. Status Solidi B
243
, 4035
(2006
).40.
J.
Shumway
, Phys. E
32
, 273
(2006
).41.
X.
Zhu
, M. S.
Hybertsen
, and P. B.
Littlewood
, Phys. Rev. B
54
, 13575
(1996
).42.
O.
Lehtonen
, D.
Sundholm
, and T.
Vanska
, Phys. Chem. Chem. Phys.
10
, 4535
(2008
).43.
A.
Franceschetti
and A.
Zunger
, Phys. Rev. Lett.
78
, 915
(1997
).44.
A.
Franceschetti
, H.
Fu
, L.
Wang
, and A.
Zunger
, Phys. Rev. B
60
, 1819
(1999
).45.
A.
Franceschetti
and A.
Zunger
, Phys. Rev. B
62
, 2614
(2000
).46.
L. W.
Wang
, M.
Califano
, A.
Zunger
, and A.
Franceschetti
, Phys. Rev. Lett.
91
, 056404
(2003
).47.
J. W.
Luo
, A.
Franceschetti
, and A.
Zunger
, Nano Lett.
8
, 3174
(2008
).48.
M.
Califano
, A.
Franceschetti
, and A.
Zunger
, Phys. Rev. B
75
, 115401
(2007
).49.
G.
Narvaez
, G.
Bester
, and A.
Zunger
, Phys. Rev. B
72
, 245318
(2005
).50.
M.
Califano
, A.
Zunger
, and A.
Franceschetti
, Nano Lett.
4
, 525
(2004
).51.
M.
Califano
, A.
Zunger
, and A.
Franceschetti
, Appl. Phys. Lett.
84
, 2409
(2004
).52.
S.
Corni
, M.
Brasken
, M.
Lindberg
, J.
Olsen
, and D.
Sundholm
, Phys. Rev. B
67
, 085314
(2003
).53.
S.
Corni
, M.
Brasken
, M.
Lindberg
, J.
Olsen
, and D.
Sundholm
, Phys. E
18
, 436
(2003
).54.
W.
Lester
and B.
Hammond
, Annu. Rev. Phys. Chem.
41
, 283
(1990
).55.
W.
Foulkes
, L.
Mitas
, R.
Needs
, and G.
Rajagopal
, Rev. Mod. Phys.
73
, 33
(2001
).56.
W.
Klopper
, F. R.
Manby
, S.
Ten-No
, and E. F.
Valeev
, Int. Rev. Phys. Chem.
25
, 427
(2006
).57.
58.
S.
Corni
, M.
Brasken
, M.
Lindberg
, J.
Olsen
, and D.
Sundholm
, Phys. Rev. B
67
, 045313
(2003
).59.
J.
Shumway
and D. M.
Ceperley
, Phys. Rev. B
63
, 165209
(2001
).60.
B. J.
Persson
and P. R.
Taylor
, J. Chem. Phys.
105
, 5915
(1996
).61.
S. F.
Boys
, Proc. R. Soc. London, Ser. A
258
, 402
(1960
).62.
S. A.
Varganov
and T. J.
Martínez
, J. Chem. Phys.
132
(2010
).63.
C.
Swalina
, M. V.
Pak
, A.
Chakraborty
, and S.
Hammes-Schiffer
, J. Phys. Chem. A
110
, 9983
(2006
).64.
A.
Chakraborty
, M. V.
Pak
, and S.
Hammes-Schiffer
, J. Chem. Phys.
129
, 014101
(2008
).65.
A.
Chakraborty
and S.
Hammes-Schiffer
, J. Chem. Phys.
129
, 204101
(2008
).66.
M. V.
Pak
, A.
Chakraborty
, and S.
Hammes-Schiffer
, J. Phys. Chem. A
113
, 4004
(2009
).67.
M.
Chamarro
, C.
Gourdon
, P.
Lavallard
, O.
Lublinskaya
, and A.
Ekimov
, Phys. Rev. B
53
, 1336
(1996
).68.
A. L.
Efros
and M.
Rosen
, Annu. Rev. Mater. Sci.
30
, 475
(2000
).69.
T.
Takagahara
, Phys. Rev. B
47
, 4569
(1993
).70.
G. W.
Bryant
, Phys. Rev. B
37
, 8763
(1988
).71.
T.
Takagahara
and K.
Takeda
, Phys. Rev. B
46
, 15578
(1992
).72.
B.
Delley
and E. F.
Steigmeier
, Phys. Rev. B
47
, 1397
(1993
).73.
S. H.
Tolbert
, A. B.
Herhold
, C. S.
Johnson
, and A. P.
Alivisatos
, Phys. Rev. Lett.
73
, 3266
(1994
).74.
G.
Ledoux
, J.
Gong
, F.
Huisken
, O.
Guillois
, and C.
Reynaud
, Appl. Phys. Lett.
80
, 4834
(2002
).75.
A.
Franceschetti
, L.
Wang
, H.
Fu
, and A.
Zunger
, Phys. Rev. B
58
, 13367
(1998
).76.
J.
Luo
, A.
Franceschetti
, and A.
Zunger
, Nano Lett.
9
, 2648
(2009
).77.
F.
Reboredo
, A.
Franceschetti
, and A.
Zunger
, Phys. Rev. B
61
, 13073
(2000
).78.
A.
Efros
and M.
Rosen
, Annu. Rev. Mater. Sci.
30
, 475
(2000
).79.
S.
Brovelli
, R. D.
Schaller
, S. A.
Crooker
, F.
Garcia-Santamaria
, Y.
Chen
, R.
Viswanatha
, J. A.
Hollingsworth
, H.
Htoon
, and V. I.
Klimov
, Nat. Commun.
2
, 280
(2011
).80.
G.
Bester
, S.
Nair
, and A.
Zunger
, Phys. Rev. B
67
, 161306
(2003
).81.
I. A.
Akimov
, K. V.
Kavokin
, A.
Hundt
, and F.
Henneberger
, Phys. Rev. B: Condens. Matter Mater. Phys.
71
, 1
(2005
).82.
G. V.
Astakhov
, A. V.
Koudinov
, K. V.
Kavokin
, I. S.
Gagis
, Y. G.
Kusrayev
, W.
Ossau
, and L. W.
Molenkamp
, Phys. Rev. Lett.
99
, 016601
(2007
).83.
J.
He
, H.
Zhong
, and G. D.
Scholes
, Phys. Rev. Lett.
105
, 046601
(2010
).84.
S. M.
Santos
, B.
Yuma
, S.
Berciaud
, J.
Shaver
, M.
Gallart
, P.
Gilliot
, L.
Cognet
, and B.
Lounis
, Phys. Rev. Lett.
107
, 187401
(2011
).85.
R.
Matsunaga
, K.
Matsuda
, and Y.
Kanemitsu
, Phys. Rev. Lett.
106
, 037404
(2011
).86.
W. F.
Xie
, Physica B
358
, 109
(2005
).87.
G.
Lamouche
and G.
Fishman
, J. Phys.: Condens. Matter
10
, 7857
(1998
).88.
M.
Elsaid
, Semicond. Sci. Technol.
9
, 272
(1994
).89.
S.
Chen
, Physica B
406
, 2033
(2011
).90.
C. M.
Duque
, M. E.
Mora-Ramos
, and C. A.
Duque
, J. Nanopart. Res.
13
, 6103
(2011
).91.
E.
Sadeghi
and A.
Avazpour
, Physica B
406
, 241
(2011
).92.
W.
Xie
, Opt. Commun.
282
, 2604
(2009
).93.
M.
Ikezawa
, S. V.
Nair
, H. W.
Ren
, Y.
Masumoto
, and H.
Ruda
, Phys. Rev. B
73
, 125321
(2006
).94.
T.
Chakraborty
and P.
Pietiläinen
, Phys. Rev. Lett.
95
, 136603
(2005
).95.
E.
Matito
, J.
Cioslowski
, and S. F.
Vyboishchikov
, Phys. Chem. Chem. Phys.
12
, 6712
(2010
).96.
J. P.
Coe
, A.
Sudbery
, and I.
D’Amico
, Phys. Rev. B
77
(2008
).97.
N. H.
March
and A.
Rubio
, Chem. Phys. Lett.
398
, 445
(2004
).98.
D.
Hestenes
, Am. J. Phys.
39
, 1013
(1971
).99.
P.
Cassam-Chenai
, J. Math. Chem.
15
, 303
(1994
).100.
K. C.
Mundim
, M.
Giambiagi
, and M. S.
De Giambiagi
, J. Phys. Chem.
98
, 6118
(1994
).101.
P.
Cassam-Chenai
and F.
Patras
, J. Math. Phys.
44
, 4884
(2003
).102.
103.
E.
Burovski
, A.
Mishchenko
, N.
Prokof'ev
, and B.
Svistunov
, Phys. Rev. Lett.
87
, 186402
(2001
).104.
M.
Wimmer
, S. V.
Nair
, and J.
Shumway
, Phys. Rev. B
73
, 165305
(2006
).105.
106.
107.
T.
Helgaker
, P.
Jorgensen
, and J.
Olsen
, Molecular Electronic-Structure Theory
(Wiley
, 2000
), p. 938
.108.
B. J.
Persson
and P. R.
Taylor
, Theor. Chem. Acc.
97
, 240
(1997
).109.
J.
Karwowski
and L.
Cyrnek
, Collect. Czech. Chem. Commun.
70
, 864
(2005
).110.
J.
Karwowski
, Int. J. Quantum Chem.
109
, 2456
(2009
).111.
R. T.
Pack
and W.
Byers Brown
, J. Chem. Phys.
45
, 625
(1966
).112.
C. R.
Myers
, C. J.
Umrigar
, J. P.
Sethna
, and J. D.
Morgan
III, Phys. Rev. A
44
, 5537
(1991
).113.
D.
Prendergast
, M.
Nolan
, C.
Filippi
, S.
Fahy
, and J. C.
Greer
, J. Chem. Phys.
115
, 1626
(2001
).114.
W. J.
Hehre
, R. F.
Stewart
, and J. A.
Pople
, J. Chem. Phys.
51
, 2657
(1969
).115.
R. F.
Stewart
, J. Chem. Phys.
52
, 425
(1970
).116.
S.
Ten-no
, Chem. Phys. Lett.
398
, 56
(2004
).117.
J.-.
Van Der Horst
, P. A.
Bobbert
, M. A. J.
Michels
, and H.
Bässler
, J. Chem. Phys.
114
, 6950
(2001
).118.
J.
Elward
, J.
Hoffman
, and A.
Chakraborty
, “Investigation of electron-hole correlation using explicitly correlated configuration interaction method
,” Chem. Phys. Lett. (in press).119.
R. A.
Kendall
and H. A.
Früchtl
, Theor. Chem. Acc.
97
, 158
(1997
).120.
F.
Neese
, J. Comput. Chem.
24
, 1740
(2003
).121.
E. F.
Valeev
, Chem. Phys. Lett.
395
, 190
(2004
).122.
D. P.
Tew
, W.
Klopper
, and F. R.
Manby
, J. Chem. Phys.
127
, 174105
(2007
).123.
H.-J.
Werner
, T. B.
Adler
, and F. R.
Manby
, J. Chem. Phys.
126
, 164102
(2007
).124.
E. F.
Valeev
, J. Chem. Phys.
125
, 244106
(2006
).125.
J.
Elward
, J.
Hoja
, and A.
Chakraborty
, “Application of XCCI method for many-electron systems
” (unpublished).© 2012 American Institute of Physics.
2012
American Institute of Physics
You do not currently have access to this content.
