7680
J . Phys. Chem. 1991, 95, 7680-7681
Energetlcs and Geometry of Conductlng Polymers from Oligomers Alfred Karpfen* Institute of Theoretical Chemistry, University of Vienna, A- 1090, Vienna, Austria
and Miklos Kertesz* Department of Chemistry, Georgetown University, Washington, D.C. 20057 (Received: March 4, 1991)
Reliable estimates concerning the energy difference of the aromatic-benzenoid and quinonoid forms of conducting polymers can be obtained from small cluster calculations if the oligomers are terminated properly, and the energy per repeating unit of the polymer is estimated by the finite difference method. Accordingly, polythiophene and polypyrrole should have an aromatic ground state in agreement with other theoretical and experimental results. Poly(is0thianaphthene) and poly(thiathiophene), on the other hand, should have quinonoid ground states.
The structures of many conducting polymers'2 can be described as having one of two form^,^-^ an aromatic-benzenoid (A) and a quinonoid (Q)form; a few examples are listed in Figure 1. Due to the flexibility of their *-electrons, these two forms are often not extremely far in energy?.' and many of their properties depend on the issue of (i) which of the two (or perhaps more) forms is more stable and (ii) by how much. The answer to these questions will determine the energy gap, the energetics of highly mobile defect states,* such as polarons and bipolarons, and also the properties of the highly doped and well-conducting phases of these materials. A consensus exists in the case of several polymers among experimentalists and theorists as to which of the two forms is more stable. For others, such as PITN? the issue is open. The magnitude of the energy difference is more subtle of course, and the data in the literature differ widely depending on the methods used. The aim of this work is 2-fold. We are showing that small oligomer calculations with trivially available molecular orbital packagesl"Ji can be directly used to address the energetics and geometry of these materials, provided the oligomers are terminated properly. Then we show that all theoretical evidence supports the notion that the Q form is the more stable form for both PITN and FTT,even if out-of-plane rotations of the repeating units (Tu) are taken into account. Of course, full geometry optimization is essential to obtain any meaningful results for the issues in question. Two basically different approaches can be used to calculate the energy per repeating unit (E,) of a polymer or solid. One is based on the traditional energy band theory of solid-state physics using k space and periodic boundary conditions. This approach has been used on several occasions for the purpose to resolve questions of stability of various conformations of polymers at the semiempirical and ab initio level^.^^*^* The other is based on oligomers (N-mers), where the desired quantity is extracted in an extrapolation process ( I ) Handbook of Conducting Polymers; Skotheim, T. A., Ed.; Marcel Dekker: New York. 1986. (2) Int. ConJ Synrh. Met., 1990, Tubingen, Synrh, Met., in press. (3) Bredas, J. L.; Themans, B.; Fripiat, J. P.; Andre, J. M.; Chance, R. R. Phys. Rev. 1984,829, 6761. (4) Brazovskii, S . A.; Kirova, N. Pisma Zh. Eskp. Teor. Fiz. 1981,33,
6( 1981 ). ( 5 ) Mintmire, J. W.; White, C. T.; Elert, M. L. Synth. Met. 1988, 25, 109. ( 6 ) Lee, Y.S.; Kertesz, M. J . Chem. Phys. 1988,88, 2609. (7) Lee, Y. S.; Kertesz, M. Int. J. Quanrum. Chem. Symp. 1987,ZI.163. (8) Bredas, J. L.; Chance, R. R.; Silbey, R. Phys. Rev. 1982,B26.5843. (9) Wallnofer, W.; Faulques, E.; Kuzmany, H. K. J . Chem. Phys. 1989, 90. 7585. (IO) Frisch, M. J.; Head-Gordon, M.; Schlegel, H. B.; Raghavachari, K.; Binkley, J. S.; Gonzalez. C.; Defrees, D. J.; Fox, D. J.; Whiteside, R. A.; Seeger, R.; Melius, C. F.; Baker, J.; Martin, R. L.; Kahn, L. R.; Stewart, J . J. P.; Fluder, E. M.; Topiol, S.; Pople, J. A. Gaussian 88; Gaussian, Inc.:
Pittsburgh, PA.
( I I ) Stewart, J. J. P. J . Comput.-Aided Des. 1990,4,I: QCPE No. 455. (12) Karpfen, A. Phys. Scr. 1982,T I , 79.
0022-3654191/2095-7680SO2.50/0
of Polythiopbene (kcal/mol)o STO 3G2' 3-21G*22 MNDObJ3
TABLE I:
N 2 3 4
-9.62 -9.57
-7.90 -8.01
-4.48 -4.51 -4.53
PM3M LHS" -5.84 -5.71 -5.76
-7.65
'Geometry fully optimized in the plane; negative value indicates a more stable aromatic structure. For the infinite chain, -3.52 was obtained.6 TABLE II: E" of Polypyrrole (kcrl/mol)' N STO 3G" 3-21GZ2 M N D O ~ S ~ PM32' ~ 2 -18.78 -16.09 -12.30 -15.29 3 -18.58 -15.97 -I 1.84 -14.65 4 -1 1.a0 -14.49
'Geometry fully optimized in the plane; negative value indicates a more stable aromatic structure. For the infinite chain, -8.62 was obtained.6 TABLE III: E" of Poly(isotbianspMhene)(kcrl/mol)a N STO 3G" 3-21G**' M N D O ~ S ~ ~PM32' LHS25 2 11.19 9.20 6.82 (0.77)b 7.48 (4.73)* 3.04 3 7.11 (0.36)b 7.85 (5.14)b
'Geometry fully optimized in the plane. bGeometryfully optimized, nonplanar structure.
. ,.
TABLE IV: E" of Polv(isothintbionhene) (kcal/moW .. . , N MNDOZ3 PM324 2 18.71 20.87 3 16.95 19.29
to the N
-.
Iimki3-l7 The latter approach has been considered impractical, because of the slow convergence of E(N)/Nto EPW. However, it has been recognized recently that in many casesalbeit certain exceptions e ~ i s t ' ~ ~ ' ~ - tconvergence he of EpruN E ( N ) - E ( N - 1)
to Epp is fast, both at the semiempirical and ab initio l e ~ e l s . l ~ * ~ ~ - ' ~ Specifically for the case of a polymer with two alternative structures, this observation provides a straightforward scheme in ( I 3) Karpfen, A.; Ladik, J.; Russegger, R.; Schuster, P.; Suhai, S . Theor. Chim. Acta 1974,34, 1 1 5. (14) Kirtman, B.; Nilsson, W. B.; Palke, W. E. Solid State Commun. 1983,46, 791. ( 1 5 ) Wheeler, R. A.; Piela, L.; Hoffmann, R. J . Am. Chem. Soc. 1988, 110. 7302.
(16) Cioslowski, J. Chem. Phys. Letr. 1988,153. 446. (17) Cui, C . X.; Kertesz, M.; Jiang, Y. J . Phys. Chem. 1990,94, 5172. (18) Kiirti, J.; S u r j h , P. R. J . Chem. Phys. 1990, 92, 3247.
0 199 I American Chemical Society
Energetics and Geometry of Conducting Polymers
and other properties of the more stable form only. In such cases, one can only suspect that the other form is very high in energy, and therefore, the quantum chemical method in question d m not converge. In order to test this approach, we present in Table I and Table I1 stabilization energy values per repeating unit of the polymer as calculated by
Q
A
The Journal of Physical Chemistry, Vol. 95, No. 20, 1991 7681
EN
Y
Y
0
Figure 1. Aromatic (A) and quinonoid (Q) structures of PT (polythiophene), PpY (polypyrrole), PITN (poly(isothianaphthene)), and PTT
(poly(isothiathi0phene)).
obtaining Ep(A) and E,(Q) and their difference, even though the terminal groups have to be different. The trick lies in properly choosing these end groups, which will ascertain that the structure will be in the A or in the Q form. Using end groups with a single bond (e.g., H-) will favor the A form, while a CH2= group will favor the other, i.e., the Q form. (These two terminal groups will be used in the present work throughout.) In our view, this feature has been overlooked in the literature on a few occasi0ns,'~J0leading to incorrect conclusions concerning the structure and consequently the band gaps of certain polymers, such as PITN'9*20and PTT." An added advantage of this scheme is that, in certain cases, the band theoretical approach provides information on the geometry (19) Bredas. J. L.: Heener. A. J.: Wudl. F. J . Chem. Phus. 1986.85.4673. (20) Bredas; J. L:;Thgmans, B:; Andre, J. M.; Heegir, A. J.i Wudl, F. Synth. Metals 1985, 11, 343. (21) Hehre, W. J.; Stewart, R. F.; Pople, J. A. J . Chem. Phys. 1969,51, 2657. (22) Brinkley, J. S.;Pople, J. A.; Hehre, W. J. J . Am. Chem. Soc. 1980, 102, 939. (23) Dewar, M. J. S.;Thiel, W. J . Am. Chem. Soc. 1977, 99, 4899. (24) Stewart, J. J. P. J . Compuf.Chem. 1989, IO, 209; J . Am. Chem. Soc. 1989, 10, 221. (25) Kurti, J. Private communication, 1990.
= E,,N(u
-
(2)
The values have been obtained from small oligomers up to N = 4 for PT and PPy using various semiempirical and a b initio methods. In agreement with previous experience, the convergence is f a ~ t ; ~the ~ ,signs ' ~ of the energy differences of the A vs Q form are the same with all methods considered. Most importantly, meaningful results can be extracted already from dimer calculations. For comparison, the values from band theory-where available-are also given. These correspond to slightly different parametrizations, and the agreement with the present oligomer data is not perfect. These tables demonstrate the usefulness of the oligomer approach, which produces results in agreement with previous theoretical and experimental data for two well-studied cases, For polymers with six *-electrons per repeating unit, the A form is found to be more stable in all cases. The results for the more controversial PITN and PTT are given in Tables I11 and IV. Here, due to larger size, only smaller oligomers could be included in the calculations. Still, a meaningful conclusion can be drawn, which is that in both cases the Q form is more stable than the A form. This is in agreement with the band theoretical calculations at the MNDO leve1.6~~ So far planarity of the polymers has been assumed. Nonplanarity may change the conclusions insofar as it might bring down the energy of the A form, which may be essential only if this is the higher lying form. Torsional potentials are difficult to determine accurately. The corresponding results are indicated in Table I11 in parentheses. In some cases,the energy of the A form is reduced significantly. Most remarkable is the case of MNDO, which is, however, known to produce too large equilibrium torsional angles for rings rotated around single bonds. (For example, biphenyl is predicted by MNDO to be twisted by 90°, as opposed to the actual 40' in the gas phase.26) Therefore, we conclude that both PITN and PTT favor the Q form in their ground states. Further experimental work is needed to test this prediction.26 Acknowledgment. We are indebted to Dr. J. Kurti for providing us with his LHS data. This work has been partially supported by N S F Grant INT-8912665 and by the Austrian "Fonds zur Forderung der wissenschaftlichen Forschung" Project No. P65OOC. The calculations were performed on the IBM 3090-400 VF of the Computer Center of the University of Vienna within the European Academic Supercomputing Initiative (EASI) sponsored by IBM and on the NAS 9160 computer of the "Interuniversitares Rechenzentrum", Vienna. We are grateful for the ample supply of computer time on these installations. Registry No. PT (homopolymer), 25233-34-5; PPy (homopolymer), 30604-8 1-0; PITN (homopolymer), 9 1201-85-3; PTT (homopolymer), 1 1 1740-85-3. (26) Almenningen, A.; Bastiansen, 0.;Fernholt, L.; Cyvin, B. N.; Cyvin,
S.J.; Sandal, S.J . Mol. Struct. 1985, 128, 59.
