Atomic clusters of TiO2 are modeled by means of state-of-the-art techniques to characterize their structural, electronic and optical properties. We combine ab initio molecular dynamics, static density functional theory, time-dependent density functional theory, and many body techniques, to provide a deep and comprehensive characterization of these systems. TiO2 clusters can be considered as the starting seeds for the synthesis of larger nanostructures, which are of technological interest in photocatalysis and photovoltaics. In this work, we prove that clusters with anatase symmetry are energetically stable and can be considered as the starting seeds to growth much larger and complex nanostructures. The electronic gap of these inorganic molecules is investigated, and shown to be larger than the optical gap by almost 4 eV. Therefore, strong excitonic effects appear in these systems, much more than in the corresponding bulk phase. Moreover, the use of various levels of theory demonstrates that charge transfer effects play an important role under photon absorption, and therefore the use of adiabatic functionals in time dependent density functional theory has to be carefully evaluated.

3.
M.
Grätzel
,
J. Photochem. Photobiol. C
4
,
145
(
2003
).
4.
D. V.
Bavykin
,
J. M.
Friedrich
, and
F. C.
Walsh
,
Adv. Mater.
18
,
2807
(
2006
).
5.
K. M.
Glassford
and
J. R.
Chelikovsy
,
Phys. Rev. B
45
,
3874
(
1992
).
6.
K. M.
Glassford
and
J. R.
Chelikovsy
,
Phys. Rev. B
46
,
1284
(
1992
).
7.
R.
Asahi
,
Y.
Taga
,
W.
Mannstadt
, and
A. J.
Freeman
,
Phys. Rev. B
61
,
7459
(
2000
).
8.
M.
Mikami
,
S.
Nakamura
,
O.
Kitao
,
H.
Arakawa
, and
X.
Gonze
,
Jpn. J. Appl. Phys.
39
,
L847
(
2000
).
9.
N.
Hosaka
,
T.
Sekiya
,
C.
Satoko
, and
S.
Kurita
,
J. Phys. Soc. Jpn
66
,
877
(
1997
).
10.
L. K.
Dash
,
F.
Bruneval
,
V.
Trinité
,
N.
Vast
, and
L.
Reining
,
Comput. Mater. Sci.
38
,
482
(
2007
).
11.
S.-D.
Mo
and
W. Y.
Ching
,
Phys. Rev. B
51
,
13023
(
1995
).
12.
H.
Tang
,
F.
Levy
,
H.
Berger
, and
P. E.
Schmid
,
Phys. Rev. B.
52
,
7771
(
1995
).
13.
N.
Hosaka
,
T.
Sekiya
, and
S.
Kurita
,
J. Lumin.
72
,
874
(
1997
).
14.
L.
Chiodo
,
J. M.
García-Lastra
,
A.
Iacomino
,
S.
Ossicini
,
J.
Zhao
,
H.
Petek
, and
A.
Rubio
,
Phys. Rev. B
82
,
045207
(
2010
).
15.
16.
R. A.
Evarestov
and
A. V.
Bandura
,
Int. J. Quantum Chem.
96
,
282
(
2004
).
17.
M.
Ramamoorthy
,
D.
Vanderbilt
, and
R. D.
King-Smith
,
Phys. Rev. B
49
,
16721
(
1994
).
18.
R. A.
Evarestov
and
A. V.
Bandura
,
Surf. Sci.
603
,
L117
(
2009
).
19.
H.
Perron
,
C.
Domain
,
J.
Roques
,
R.
Drot
,
E.
Simoni
, and
H.
Catalette
,
Theor. Chem. Acc.
117
,
565
(
2007
).
20.
G. S.
Herman
,
Z.
Dohnàlek
,
N.
Ruzycki
, and
U.
Diebold
,
J. Phys. Chem. B
107
,
2788
(
2003
).
21.
D.
Vogtenhuber
,
R.
Podloucky
,
A.
Neckel
,
S. G.
Steinemann
, and
A. J.
Freeman
,
Phys. Rev. B
49
,
2099
(
1994
).
22.
M.
Lazzeri
,
A.
Vittadini
, and
A.
Selloni
,
Phys. Rev. B
63
,
155409
(
2001
).
23.
Y.
Liang
,
S.
Gan
,
S. A.
Chambers
, and
E. I.
Altman
,
Phys. Rev. B
63
,
235402
(
2001
).
24.
A. S.
Barnard
,
S.
Erdin
,
Y.
Lin
,
P.
Zapol
, and
J. W.
Halley
,
Phys. Rev. B
73
,
205405
(
2006
).
25.
A. S.
Barnard
and
P.
Zapol
,
J. Phys. Chem. B
108
,
18435
(
2004
).
26.
L.
Chiodo
,
J. M.
García-Lastra
,
D. J.
Mowbray
,
A.
Iacomino
, and
A.
Rubio
, “
Tailoring electronic and optical properties of TiO2: nanostructuring, doping and molecular-oxide interactions
,” in
Computational Studies of New Materials: From Nanostructures to Bulk Energy Conversion Materials
, edited by
T. F.
George
,
D.
Jelski
,
R. R.
Letfullin
, and
G.
Zhang
(
World Scientific
,
Singapore
,
2011
).
27.
M. R.
Ranade
,
A.
Navrotsky
,
H. Z.
Zhang
,
J. F.
Banfield
,
S. H.
Elder
,
A.
Zaban
,
P. H.
Borse
,
S. K.
Kulkarni
,
G. S.
Doran
, and
H. J.
Whitfield
,
Proc. Natl. Acd. Sci. U.S.A.
99
,
6476
(
2002
).
28.
D. J.
Mowbray
,
J. I.
Martinez
,
J. M.
García-Lastra
,
K. S.
Thygesen
, and
K. W.
Jacobsen
,
J. Phys. Chem. C
113
,
12301
(
2009
).
29.
S. A.
Shevlin
and
S. M.
Woodley
,
J. Phys. Chem. C
114
,
17333
(
2010
).
30.
A. A.
Gribb
and
J. F.
Banfield
,
Am. Mineral.
82
,
717
(
1997
).
31.
H.
Zhang
and
J. F.
Banfield
,
J. Mater. Chem.
8
,
2073
(
1998
).
32.
J.
Muscat
,
V.
Swamy
, and
N.
Harrison
,
Phys. Rev. B
65
,
224112
(
2002
).
33.
G.
Giorgi
,
M.
Palummo
,
L.
Chiodo
, and
K.
Yamashita
,
Phys. Rev. B
84
,
073404
(
2011
).
34.
P.
Hohenberg
and
W.
Kohn
,
Phys. Rev.
136
,
B864
(
1964
).
35.
W.
Kohn
and
L. J.
Sham
,
Phys. Rev.
140
,
A1133
, (
1965
).
36.
A.
Selloni
,
Nature Mater.
7
,
613
(
2008
).
37.
T.
Helgaker
,
P.
Jørgensen
, and
J.
Olsen
,
Molecular Electronic-Structure Theory
(
Wiley
,
England
,
2000
).
38.
S.
Li
and
D. A.
Dixon
,
J. Phys. Chem. A
112
,
6646
(
2008
).
40.
M. S.
Hybertsen
and
S. G.
Louie
,
Phys. Rev. B
34
,
5390
(
1986
).
41.
R. W.
Godby
,
M.
Schlüter
, and
L. J.
Sham
,
Phys. Rev. B
37
,
10159
(
1988
).
42.
F.
Aryasetiawan
and
O.
Gunnarsson
,
Rep. Prog. Phys.
61
,
237
(
1998
).
43.
G.
Onida
,
L.
Reining
, and
A.
Rubio
,
Rev. Mod. Phys.
74
,
601
(
2002
).
44.
Time-Dependent Density Functional Theory
, edited by
M. A. L.
Marques
,
C.
Ullrich
,
F.
Nogueira
,
A.
Rubio
,
K.
Burke
, and
E. K. U.
Gross
(
Springer
,
Berlin
,
2006
), Vol.
706
.
45.
A.
Iacomino
,
G.
Cantele
,
D.
Ninno
,
I.
Marri
, and
S.
Ossicini
,
Phys. Rev. B
78
,
075405
(
2008
).
46.
F.
De Angelis
,
A.
Tilocca
, and
A.
Selloni
,
J. Am. Chem. Soc.
126
,
15024
(
2004
).
47.
F.
De Angelis
,
S.
Fantacci
, and
A.
Selloni
,
Nanotechnology
19
,
424002
(
2008
).
48.
W. R.
Duncan
and
O. V.
Prezhdo
,
Annu. Rev. Phys. Chem.
58
,
143
(
2007
).
49.
W. R.
Duncan
,
C. F.
Craig
, and
O. V.
Prezhdo
,
J. Am. Chem. Soc.
129
,
8528
(
2007
).
50.
O. V.
Prezhdo
,
W. R.
Duncan
, and
V. V.
Prezhdo
,
Acc. Chem. Res.
41
,
339
(
2008
).
51.
W. R.
Duncan
and
O. V.
Prezhdo
,
J. Am. Chem. Soc.
130
,
9756
(
2008
).
52.
F.
Balletto
and
R.
Ferrando
,
Rev. Mod. Phys.
77
,
371
(
2005
).
53.
Z.-W.
Qu
and
G.-J.
Kroes
,
J. Phys. Chem. B
110
,
8998
(
2006
).
54.
D. J.
Taylor
and
M. J.
Paterson
,
J. Chem. Phys.
133
,
204302
(
2010
).
55.
F.
Grein
,
J. Chem. Phys.
126
,
034313
(
2007
).
56.
A.
Hagfeldt
,
R.
Bergstriim
,
H. O. G.
Siegbahn
, and
S.
Lunell
,
J. Phys. Chem.
97
,
12725
(
1993
).
57.
A. C.
Tsipis
and
C. A.
Tsipis
,
Phys. Chem. Chem. Phys.
1
,
4453
(
1999
).
58.
S.
Lago
,
J. A.
Mejías
,
S.
Hamad
,
C. R. A.
Catlow
, and
S. M.
Woodley
,
J. Phys. Chem. B
109
,
15741
(
2005
).
59.
Z.-W.
Qu
and
G.-J.
Kroes
,
J. Phys. Chem. C
111
,
16808
(
2007
).
60.
T.
Albaret
,
F.
Finocchi
, and
C.
Noguera
,
 J. Chem. Phys.
113
,
2238
(
2000
).
61.
T.
Albaret
,
F.
Finocchi
, and
C.
Noguera
,
Faraday Discuss.
114
,
285
(
1999
).
62.
I.
Onal
,
S.
Soyer
, and
S.
Senkan
,
Surf. Sci.
600
2457
(
2006
).
63.
P. C.
Redfern
,
P.
Zapol
,
L. A.
Curtiss
,
T.
Rajh
, and
M. C.
Thurnauer
,
J. Phys. Chem. B
107
,
11419
(
2003
).
64.
Z.
Guo
,
W. Z.
Liang
,
Y.
Zhao
, and
G. H.
Chen
,
J. Phys. Chem. C
112
,
16655
(
2008
).
65.
R.
Sánchez-de-Armas
,
M. A.
San-Miguel
,
J.
Oviedo
,
A.
Márquez
, and
J. F.
Sanz
,
Phys. Chem. Chem. Phys.
13
,
1506
(
2011
).
66.
D.
Zhang
,
H.
Sun
,
J.
Liu
, and
C.
Liu
,
J. Phys. Chem. C
113
,
21
(
2009
).
67.
H.
Zhang
,
B.
Chen
,
J. F.
Banfield
, and
G. A.
Waychunas
,
Phys. Rev. B
78
,
214106
(
2008
).
68.
A.
Castro
,
H.
Appel
,
M.
Oliveira
,
C. A.
Rozzi
,
X.
Andrade
,
F.
Lorenzen
,
M. A. L.
Marques
,
E. K. U.
Gross
, and
A.
Rubio
,
Phys. Status Solildi B
243
,
2465
(
2006
).
69.
See http://www.turbomole.com for TURBOMOLE V6, 2009, a development of University of Karlsruhe and Forschungszentrum Karlsruhe GmbH, 1989-2007, TURBOMOLE GmbH, since 2007.
70.
B.
Delley
,
J. Chem. Phys.
92
,
508
(
1990
).
71.
B.
Delley
,
J. Chem. Phys.
94
,
7245
(
1991
).
72.
J. P.
Perdew
,
K.
Burke
, and
M.
Ernzerhof
,
Phys. Rev. Lett.
77
,
3865
(
1996
).
73.
D. D.
Koelling
and
B. N.
Harmon
,
J. Phys. C
10
,
3107
(
1977
).
74.
75.
P.
Giannozzi
,
S.
Baroni
,
N.
Bonini
,
M.
Calandra
,
R.
Car
,
C.
Cavazzoni
,
D.
Ceresoli
,
G. L.
Chiarotti
,
M.
Cococcioni
,
I.
Dabo
,
A.
Dal Corso
,
S.
Fabris
,
G.
Fratesi
,
S.
de Gironcoli
,
R.
Gebauer
,
U.
Gerstmann
,
C.
Gougoussis
,
A.
Kokalj
,
M.
Lazzeri
,
L.
Martin-Samos
,
N.
Marzari
,
F.
Mauri
,
R.
Mazzarello
,
S.
Paolini
,
A.
Pasquarello
,
L.
Paulatto
,
C.
Sbraccia
,
S.
Scandolo
,
G.
Sclauzero
,
A. P.
Seitsonen
,
A.
Smogunov
,
P.
Umari
, and
R. M.
Wentzcovitch
,
J. Phys. Condens. Matter
21
,
395502
(
2009
).
76.
G.
Makov
and
M. C.
Payne
,
Phys. Rev. B
51
,
4014
(
1995
).
77.
K.
Schonhammer
and
O.
Gunnarsson
,
J. Phys. C
20
,
3675
(
1987
).
78.
J.
Simons
and
K. D.
Jordan
,
Chem. Rev.
87
,
535
(
1987
).
79.
A.
Marini
,
C.
Hogan
,
M.
Grüning
, and
D.
Varsano
,
Comput. Phys. Commun.
180
,
1392
(
2009
).
80.
C. A.
Rozzi
,
D.
Varsano
,
A.
Marini
,
E. K. U.
Gross
, and
A.
Rubio
,
Phys. Rev. B
73
,
205119
(
2006
).
81.
B. I.
Lundqvist
,
Phys. Kondens. Mater.
6
,
193
(
1967
);
B. I.
Lundqvist
,
Phys. Kondens. Mater.
6
,
206
(
1967
);
A. W.
Overhauser
,
Phys. Rev. B
3
,
1888
(
1971
).
82.
M.
Palummo
,
C.
Hogan
,
F.
Sottile
,
P.
Bagala
, and
A.
Rubio
,
J. Chem. Phys.
131
,
084102
(
2009
).
83.
C.
Adamo
and
V.
Barone
,
J. Chem. Phys.
110
,
6158
(
1999
).
84.
F.
Weigend
and
R.
Ahlrichs
,
Phys. Chem. Chem. Phys.
7
,
3297
(
2005
).
85.
See supplementary material at http://dx.doi.org/10.1063/1.3668085 for structures of chain-like, ring-like, rutile-like and anatase-like clusters and for ground state electronic properties of anatase-like clusters.
86.
H.-J.
Zhai
and
L.-S.
Wang
,
J. Am. Chem. Soc.
129
,
3022
(
2007
).
87.
L.
Thulin
and
J.
Guerra
,
Phys. Rev. B
77
,
195112
(
2008
).
88.
W.
Kang
and
M. S.
Hybertsen
,
Phys. Rev. B
82
,
085203
(
2010
).
89.
M. E.
Casida
,
F.
Gutierrez
,
J.
Guan
,
F.-X.
Gadea
,
D.
Salahub
, and
J.-P.
Daudey
,
J. Chem. Phys.
113
,
7062
(
2000
).
90.
Z.-L.
Cai
,
K.
Sendt
, and
J. R.
Reimers
,
J. Chem. Phys.
117
,
5543
(
2002
).
91.
A.
Dreuw
,
J. L.
Weisman
, and
M.
Head-Gordon
,
J. Chem. Phys.
119
,
2943
(
2003
).
92.
D. J.
Tozer
,
J. Chem. Phys.
119
,
12697
(
2003
).
93.
S.
Grimme
and
M.
Parac
,
ChemPhysChem
4
,
292
(
2003
).
94.
A.
Dreuw
and
M.
Head-Gordon
,
J. Am. Chem. Soc.
126
,
4007
(
2004
).

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