Ladder-type polymers, obtained by small modifications of the atomic structure of ladder-type polythiophene, are studied using density-functional theory calculations. Within the local-density and GW approximations, it is found that upon a simple substitution of the sulfur atoms by nitrogen and boron atoms, the band structure of the resulting polymer exhibits band overlap between the occupied and the unoccupied states. However, the three-parameter Becke hybrid functional predicts these polymers to be small band gap semiconductors. Finally, results of time-dependent density-functional theory are reported on increasing length oligomers, indicating that the polymers would have very low excitation energies.

1.
J. L.
Bréadas
and
R. H.
Baughman
,
J. Polym. Sci., Polym. Lett. Ed.
21
,
475
(
1983
).
2.
U.
Scherf
and
K.
Mullen
,
Makromol. Chem., Rapid. Commun.
12
,
489
(
1991
).
3.
K.
Oyaizu
,
T.
Iwasaki
,
Y.
Tsukahara
, and
E.
Tsuchida
,
Macromolecules
37
,
1257
(
2004
).
4.
X.
Zhang
,
A.
Côté
, and
A.
Matzger
,
J. Am. Chem. Soc.
127
,
10502
(
2005
).
5.
H.
Kawabata
,
K.
Tokunaga
,
S.
Ohmori
,
K.
Matsushige
, and
H.
Tachikawa
,
Jpn. J. Appl. Phys., Part 1
47
,
420
(
2008
).
6.
K.
Xiao
,
Y.
Liu
,
T.
Qi
,
W.
Zhang
,
F.
Wang
,
J.
Gao
,
W.
Qui
,
Y.
Ma
,
G.
Cui
,
S.
Chen
,
X.
Zhan
,
G.
Yu
,
J.
Qin
,
W.
Hu
, and
D.
Zhu
,
J. Am. Chem. Soc.
127
,
13281
(
2005
).
7.
T.
Baumgartner
,
J. Inorg. Organomet. Polym.
15
,
389
(
2005
).
8.
J.
Gao
,
R.
Li
,
L.
Li
,
Q.
Meng
,
H.
Jiang
,
H.
Li
, and
W.
Hu
,
Adv. Mater. (Weinheim, Ger.)
19
,
3008
(
2007
).
9.
Y.
Zhang
,
X.
Cai
,
Y.
Bian
,
X.
Li
, and
J.
Jiang
,
J. Phys. Chem. C
112
,
5148
(
2008
).
10.
E.
Moore
and
D.
Yaron
,
J. Phys. Chem. A
106
,
5339
(
2002
).
11.
S.
Gunatunga
,
G.
Jones
,
M.
Kalaji
,
P.
Murphy
,
D.
Taylor
, and
G.
Williams
,
Synth. Met.
84
,
973
(
1997
).
12.
D.
Baigent
,
P.
Hamer
,
R.
Friend
,
S.
Moratti
, and
A.
Holmes
,
Synth. Met.
71
,
2175
(
1995
).
13.
See EPAPS Document No. E-JCPSA6-130-006909 for Supplementary materials: geometries, Bader analysis, work functions and GW details. For more information on EPAPS, see http://www.aip.org/pubservs/epaps.html.
14.
X.
Gonze
,
J. -M.
Beuken
,
R.
Caracas
,
F.
Detraux
,
M.
Fuchs
,
G. -M.
Rignanese
,
L.
Sindic
,
M.
Verstraete
,
G.
Zerah
,
F.
Jollet
,
M.
Torrent
,
A.
Roy
,
M.
Mikami
,
Ph.
Ghosez
,
J.-Y.
Raty
, and
D. C.
Allan
,
Comput. Mater. Sci.
25
,
478
(
2002
).
15.
D.
Ceperley
and
B.
Alder
,
Phys. Rev. Lett.
45
,
566
(
1980
).
16.
We used the Teter–Pade parametrization of the LDA functional, which reproduces the Ceperley–Alder data. The pseudopotentials were generated with the Trouiller–Martins scheme. Numerical convergence tests on the total energy with a requirement of a precision of 1 mhartree/atom was reached for a number of plane waves in the basis set corresponding to an energy cutoff of 35 hartree and a sampling of the Brillouin zone using 8 k-points in the case of semiconducting polymers and up to 20 k-points in the case of metallic polymers.
17.
A.
Becke
,
J. Chem. Phys.
98
,
5648
(
1993
).
18.
M. J.
Frisch
,
G. W.
Trucks
,
H. B.
Schlegel
 et al, GAUSSIAN 03, Revision C.02, Gaussian, Inc., Wallingford, CT,
2004
.
19.
We used the 6-311G basis set for all calculations if not otherwise stated. A difference of 0.1 eV on the singlet and triplet states of tetrathiophene (n=2 in Fig. 4) is calculated using the 6-311+G compared to 6-311G. Polymer Brillouin zones were sampled with over 100 k-points.
20.
L.
Hedin
and
S.
Lundqvist
,
Solid State Phys.
23
,
1
(
1970
).
21.
F.
Aryasetiawan
and
O.
Gunnarsson
,
Rep. Prog. Phys.
61
,
237
(
1998
).
22.
The distance of the periodic images that are inherent to the implementation used has also been optimized to ensure that the interactions between these images do not affect the properties studied.
23.
S.
Pesant
,
P.
Boulanger
,
M.
Cote
, and
M.
Ernzerhof
,
Chem. Phys. Lett.
450
,
329
(
2008
).
24.
E. R.
Margine
and
V. H.
Crespi
,
Phys. Rev. Lett.
96
,
196803
(
2006
).
25.
S. S.
Zade
and
M.
Bendikov
,
Org. Lett.
8
,
5243
(
2006
).
26.
J.
Muscat
,
A.
Wander
, and
N. M.
Harrison
,
Chem. Phys. Lett.
342
,
397
(
2001
).
27.
For the LLPyB-based oligomers, we used the 6-311G basis set since no significant change in the excitation energies was observed with the 6-311G for n=1,2,3,5.
28.
The number of rings is 2n.
29.
J.
Gierschner
,
H. -G.
Mack
,
H. -J.
Egelhaaf
,
S.
Schweizer
,
B.
Doser
, and
D.
Oelkrug
,
Synth. Met.
138
,
311
(
2003
).
30.
D.
Delaere
,
M.
Nguyen
, and
L. G.
Vanquickenborne
,
Phys. Chem. Chem. Phys.
4
,
1522
(
2002
).
31.
J.
Reimers
,
Z.
Cai
,
A.
Bilic
, and
N.
Hush
,
Ann. N. Y. Acad. Sci.
1006
,
235
(
2003
).
32.
M.
Bendikov
,
H. M.
Duong
,
K.
Starkey
,
K. N.
Houk
,
E. A.
Carter
, and
F.
Wudl
,
J. Am. Chem. Soc.
126
,
10493
(
2004
).
33.
D. -e.
Jiang
and
S.
Dai
,
J. Phys. Chem. A
112
,
332
(
2008
).
34.
J.
Gierschner
,
J.
Cornil
, and
H. -J.
Egelhaaf
,
Adv. Mater. (Weinheim, Ger.)
19
,
173
(
2007
).
35.
E. S.
Kadantsev
,
M. J.
Stott
, and
A.
Rubio
,
J. Chem. Phys.
124
,
134901
(
2006
).

Supplementary Material

You do not currently have access to this content.