13334
J. Phys. Chem. 1994, 98, 13334-13338
Conformational Analysis of Tetrathiafulvalene Isomers and the Band Structure of Their One-Dimensional Polymers Seeyearl Seong and Dennis S. Marynick” Center for Advanced Research in Polymers and Department of Chemistry and Biochemistry, The University of Texas at Arlington, Arlington, Texas 76019-0065 Received: May 12, 1994; In Final Form: August 22, I994@
The electronic structure of tetrathiafulvalene (TTF)and its three conformational isomers, 2,5-dimethylene1,3-dithiol0[4,5-6]- 1,3-dithiol (DDD), 1,4,5&tetrathianaphthalene (TTN), and bis(6methylene- 1,3-dithietan2-ylidene) (BMDY), are studied using ab initio and PRDDO molecular orbital calculations and extended Hiickel band calculations. The one-dimensional expansion of DDD is identical to that of TTF. TTN has two conformations, corresponding to a boat and chair form. Our calculations show that TTF is the most stable structure among the monomers studied. The stability of the polymers arising from these monomers is estimated by oligomer calculations extrapolated to infinite chain length. The bandwidths of their highest occupied band are rather narrow (0.54-1.03 eV); however, the three highest valence bands of each isomer are separated from each other by 0.1-0.4 eV. The calculated band gaps (2.7-2.9 eV) of all the isomers are larger than that of polythiophene (1.75 eV), whereas the ionization potentials (9.7- 10.1 eV) are smaller than that of polythiophene (1 1.0 eV). Thus, it should be easier to make a p-type conductor by doping the systems with an electron-accepting molecule.
Introduction
3
Electrically conducting polymers or “organic metals” are an active area of research in the fields of polymer chemistry and materials science. Such materials can, in principle, combine the mechanical properties of polymers, namely, flexibility and ease of fabrication as thin films, with the high electrical conductivity normally reserved for metals. 1-3 There has been much interest for several years in twocomponent organic systems in which one component is a x-electron donor and the other an electron acceptor. Some of these behave as highly conducting synthetic metals, and a few are superconducting at very low temperature. The discovery4 of the first organic superconductor, TMTSF (tetramethyltetraselenafulvalene)-PF6, engendered a tremendous amount of research in this area. Subsequently, superconducting P-(BEDTTTF)2 (bis-(ethylenedithiolo)tetrathiafulvalene)I3 was synthesized by several group^.^ Additionally, (BEDT-TTF)2-Cu(NCS)z6and K-(ET)~CU[N(CN)~]B~~ have since been prepared. Aside from the TMTSF systems, many organic superconductors have been prepared from a variety of organic electron donor molecules including TTF, BEDT-TTF,8 DMET (dimethyl(ethy1enedithio)diselenadithiafulvalene): MDT (methy1enedithio)TTF,l0 and BED0 (bis-(ethy1enedioxo))-TTF,’ as well as some organic acceptor complexes such as [M(dmit)2I2- l 2 and the fullerenes.l 3 It is well-known that many of the organic superconducting materials mentioned above have short S--S intermolecular contacts between adjacent stack^.^^^^^^^ These intermolecular S--S contacts provide the dimensionality needed for superconducting coherence. All of the compounds above contain TTF, a sulfur abundant moiety. Thus, it is meaningful to investigate the electronic structure of TTF and its conformational isomers (1-3). Both TTF (la)16and l T N (2a),17as well as their dimers, have been synthesized r e ~ e n t l y . New ~ ~ , ~TTF ~ derivatives, bis(2-methylene-1,3-dithio[4,5-6])-tetrathiafulvalenes(BDT-TTF) and their unsymmetrical derivatives, (2-methylidene-1,3-dithiolo‘Abstract published in Advance ACS Abstracts, November 1, 1994.
0022-365419412098- 13334$04.5010
1
2
Ib
la d
3 2
2
3
2a
2b
0:s
3
2
4
0:c 0
:H
3 [4,5-6])-tetrathiafulvalenes(MeDT-TTF), have been studied by means of cyclic voltametry.18 Most of the doped complexes showed metallic behavior. Additionally, the dimer of TTN, 1,4,5,6,9,1O-octathianaphthacene, and its derivatives were reported to have low oxidation potentials, and it is expected that they could act as donor components for organic metals.19 The measurement of oxidation potentials also suggested no extension of x conjugation by increasing the number of 1,4-dithiin units.19 We believe that the oligomers of these isomers and their onedimensional expansions are an interesting area of study because such structures could potentially exhibit enhanced electrical conductivities due to the high population of sulfur atoms on the periphery of the polymer chains. In this paper, we present (1) the optimized geometry of four isomers of TTF at the PRDDO, STO-3G, 4-31G, and 6-31G* levels; ( 2 ) the relative energies of the polymers derived from these isomers, as estimated by extrapolations from oligomer calculations; and (3) the band structure of the polymers calculated using the extended Hiickel method. We show that the ’ITF structure is the most stable of the conformations in the monomer; however, a different trend is seen in the polymers. 0 1994 American Chemical Society
J. Phys. Chem., Vol. 98,No. 50, 1994 13335
Conformational Analysis of Tetrathiafulvalene Isomers
TABLE 1: Relative Stabilities of TTF Isomers via Different Calculation Methods (AE= E m - E& (kcaYmo1)) EHT PRDDO STO-3G//STO-3G 4-31G//4-31G 6-3lG*//6-31G* MP2//6-31G* l a ('lTF) l b (DDD) 2a1"( 2b 1"(
3 (BMDY)
0.0
0.0
0.3 2.9
-6.0
8.8
8.2 35.4
18.0
8.8
0.0
0.0
0.0
0.0
1.5 14.3 15.6 35.8
6.3 2.6 5.2 27.1
7.3 4.3 8.6 26.4
8.3 1.7 5.4 31.6
Calculations For the initial calculations on these systems we employed the method of partial retention of diatomic differential overlap (PRDD0).20-22 Subsequently, ab initio MO calculations were performed with GAUSSIAN 9223on both CONVEX C-220 and CRAY Y-MP computers. STO-3G, 4-31G and 6-31G*24basis sets were used for the geometry optimizations. The effects of electron correlation on the relative energies of the monomers were taken into account by performing second-order MollerPlesset (MP2)25perturbation calculations. To obtain the oligomer geometries, we first optimized the trimers of all the isomers at the PRDDO level. Then, the central monomer unit was used to build up the geometries of the trimer, tetramer, pentamer, and hexamer. The 4-31GZ6basis set was used to evaluate the energetics of the oligomers, since it yielded results very close to those obtained from MP2 calculation on the monomers (see below). These optimized geometries were used for the band structure calculation using extended Hiickel t h e ~ r y . ~Extended ~ ~ ~ * Hiickel theory was employed since it is commonly known that Hartree-Fock based methods greatly overestimate band gaps.z9s30The atomic valence state ionization potentials (VSIP) of carbon 2s and 2p orbitals are -21.4 and - 11.4 eV, and sulfur 2s and 2p orbitals are -20.0 and - 11.0 eV, respectively. The corresponding valence shell exponents are 1.62527afor carbon 2s and 2p and 2.21728*30 for sulfur 2s and 2p orbitals.
Conformational Analysis of Tetrathiafulvalene As alluded to earlier, we have investigated the relative stability and the electronic structure of structural isomers derived from 'ITF (see 1-3). We fiist compare the calculated geometry of TTF and TTN with the experimentally determined structures. For TTF, the PRDDO method agrees well with experiment, with average errors in bond lengths and bond angles of 0.02 A and 0.70", respectively (see supplementary material). The ab initio calculations with various basis sets yield errors (bond lengths, bond angles) as follows: STO-3G (0.02 A, 0.24'), 4-31G (0.07 A, 0.74"), 6-31G* (0.02 A, 1.39'). Thus, calculations at all levels, except the 4-3 1G level, yield excellent geometries. The optimized structure of isomer lb, 2,5dimethylene- 1,3-dithiolo[4,5-6]-1,3-dithiol (DDD) (see supplementary material), has S-C and C-C bond lengths which differ only slightly from those of TTF. The hexacyclic isomer 1,4,5,8-tetrathianaphthalene(TTN) exhibits two different isomers, corresponding to a chair (2a) and a boat (2b) form; however, the only experimentally characterized structure has the chair form.28 The average error in bond lengths is 0.01 A, and that for angles is 0.84" at the PRDDO level. The ab initio calculations with various basis sets yield errors (bond lengths, bond angles) as follows: STO3G (0.02 W, 4.00°), 4-31G (0.06 W, 0.94"), 6-31G* (0.01 A, 1.82") (see supplementary material). The calculated angle between C-S-S-C planes at the PRDDO level is 129.5" in the chair form and 132.5" in the boat form. The calculated value for the chair form is very close to that of experiment (129.1'). The last isomer, bis(4-methylene-l,3-dithiatane-2ylidene) (BMDY) (3), consists of two tetracyclic rings; however,
s4
%H4
Figure 1. Important orbital interactions in l T F (la).
it has not been characterized experimentally. It was also optimized at the same computational levels as isomers 1 and 2, as shown in the supplementary material. The calculated energy of those isomers are listed in Table 1. At the 6-3 1G*-MP2 level, the stabilities of representative isomers have the following order: BMDY (3) < DDD (lb) < TTN (2b) < TTN (2a) < TTF (la). Thus, our calculations are completely consistent with experiment. The most stable isomer is the well-known TTF structure, while the chair form of the hexacyclic system, which has also been experimentally characterized, is calculated to be the second most stable isomer. We have chosen to discuss the relative stabilities of the various isomers at the extended Huckel level because it yields energetics that are qualitatively similar to higher level methods (see Table 1) and because of the ease with which it can be analyzed. The electronic effects of the ethylene moiety, which is interacting with four sulfur atoms, can be understood from the schematic molecular orbital correlation diagrams in Figures 1-3. The structural difference in these compounds depends on the relative orientations of the ethylene moieties in the three isomers. They are lying along the same direction in BMDY, perpendicular to each other in TTF and parallel in TI". Although the HOMO in TTF has highest energy among the three isomers, 'ITF is the most stable isomer because three high-lying orbitals of the C& fragment of 2bzg, lblg, and la,, symmetry form bonding combinations with corresponding S4 orbitals of the same symmetry (Figure 1). Its HOMO is an antibonding combination of 3b3, and lbsu orbitals, while the second HOMO, of bZg symmetry, is stabilized by mixing with unoccupied 2bzg orbital. The HOMO of TTN is stabilized (Figure 2) via significant mixing with a 4b, orbital while the second HOMO is not. Overlap between important orbitals and overlap populations are listed in Table 2. There is a large overlap population between the 4b, and 2b,, orbitals (Figure 2). BMDY (Figure 3) has largest HOMO-LUMO gap. This is due to second-order mixing of the empty 2bzg orbital in a bonding fashion, which stabilizes the HOMO. The LUMO is a carbon-centered b3g nonbonding orbital. However, this conformation is the most unstable because of its three nearly degenerate nonbonding MOs and angle strain (Figure 3).
Seong and Marynick
13336 J. Phys. Chem., Vol. 98, No. 50, 1994 TABLE 2: Interaction Parameters for TTF and Its Isomers l a (m) 2a SZI
PZI
3 (BMDY)
SZ, 0.09
PL,
0.08
-0.03 0.09 0.36
0.05
0.13 0.29
P C I
st1
(3b~g12b~g) (3b~,l%) (3bi,12biU) (3hul 1blu)
0.20 0.12 0.11 0.19
0.21 -0.03
0.10 -0.12
0.08
mbl.
0.16
0.22 1.27
nZbZ*
0.28
from the monomers to the oligomers. As discussed in the previous section, high-lying p-u orbital mixing stabilizes the HOMO of TTN. Accumulation of this effect in the oligomers results in the stability order switching to BMDY < TTF TTN in the oligomer form as well as in the polymer. These results strongly suggest that the highly fused derivative of TTF would prefer the hexacyclic ring to their penta- or tetracyclic isomers.
Electronic Band Structure
C6H4
s4
Figure 2. Important orbital interactions in TTN (2a).
C6H4
s4
Figure 3. Important orbital interactions in BMDY (3).
Oligomers Since calculations on monomers have no direct bearing on the question of relative stability of the corresponding polymers, we have performed calculations on the oligomers of those isomers. We used TTF as the reference structure to compare the stabilities of the other isomers. Such a series of calculations at the ab initio level with a 4-31G basis set was performed for the structures TTF (la), DDD (lb), TTN (2a), TTN (2b), and BMDY (3). We employed the 4-31G basis set because it nearly quantitatively reproduces the relative energies of the monomers calculated at the 6-31G*-MP2 level, the highest level of theory used (Table 1). AE is defined as the difference between the energy of an oligomer of TTF and one of its isomers ( A E = E m - E,,,,& AEIN (N = chain length) falls off smoothly with N, which suggests that extrapolation to the infinite system may be possible. Such extrapolations have been found to be remarkably accurate in related systems.31 Indeed, excellent least-squares fits (average absolute deviation = 0.42 kcaymol) of AEIN vs N are obtained from the simple three-parameter function:31 AEIN = a.
+ a,lN -I- a21N2
The infinite chain length limits of AEIN are clearly equal to a0 and were found to be 1.7, -4.4, -1.3, and 25.8 kcal/mol per repeat unit for DDD (lb), TTN (Za), TTN (2b), and BMDY (3), respectively. The order of stability switches upon going
Recently, ladder polymers constructed by linking two polyacetylene (PA) chains have attracted interest with regard to developing new conducting materials with good stability. Much theoretical work32has been done concerning the geometrical and electronic structures of a prototypical ladder polymer, polyacene. Heterocyclic ladder polymers such as polyphenoq~inoxaline,~~ polyphenothiazine," and polypheno~azine~~ have been synthesized and also reviewed the~retically.~~ There are several competing factors controlling the band gap of conjugated polymer^.^^,^^-^^ Rice and Mele have pointed out the perturbation of heteroatoms as one of the important factors.39 The effect of heteroatoms on the band gaps of conjugated polymers has been intensively studied by Kafafi and L ~ w e We . ~ find ~ poly'ITN can be viewed as polyacene which is substituted with sulfur atoms at the para positions. The three conformational isomers of the polymerized forms are illustrated in 4 (PDTDY: poly(1,3-dithietane-2,4-diylidene)),5 (PDTDT: poly( 1,3-dithiolo[4,5-4-1,3-dithiole)), and 6 (PDTA: poly( 1,Cdithiacene)).EHT band calculations were performed on those three representative structures. The band features are shown in Figure 4. The [C4S4] unit was chosen as the unit cell to compare the electronic structure of PDTDY (4: Figure 4a) and PDTA (6: Figure 4c) with that of PDTDT (5: Figure 4b). 0 : s
4
0 : c
5
6
Generally, the rc bands (solid lines) fall in the energy range between -6.00 and -14.00 eV, whereas the u and u* bands are dispersed below -14.00 and above -5.00 eV. Many bands are degenerate at the zone edge due to band back-folding4I since we use two formula units for PDTDY (4) and PDTA (6)(Figure 4a,c). Eight pz-n bands are found in the band structure, and six of those are occupied. They are labeled in alphabetical order, a-h, with the highest occupied band being "f" and the lowest unoccupied band being "g" in all three band plots. The bandwidths around the Fermi level, which are relevant to electrical transport phenomena via mobilities of electrons and holes, are rather nmow in all three isomers. They are 1.02 eV for PDTDY (4), 0.54 eV for PDTDT (9,and 0.38 eV for PDTA (6). The highest occupied band is stabilized by interactions with a conduction band in both PDTDY (4) and PDTA (6). In PDTDY (Figure 4a), the highest occupied band (f) mixes with
. I F 1
Conformational Analysis of Tetrathiafulvalene Isomers
J. Phys. Chem., Vol. 98, No. 50, 1994 13337
-3
.......................
............-... ......... ........................ ..................
-7
-9
1
I
- - - f - - f -1 e1
-91
-1 1
.............. .................. ............................. ....... .......::::::::: ........................................... ....,:.-.. ;.: .................... ..... ................... 1 3 ................ b :..::;::#uoV-*
###,#,:
-
0
0.1
0.2 0.3 0.4 wave vector (k)
1 - 51 0.5
-15
0
0.1
0.2 0.3 0.4 wave vector (k)
0.5
........................
I., 0
,
. 0.1
l
............
I
0.2
,
.
,
,.
, , ,
, ,...., : I
0.3 0.4 wave vector (k)
I.. I
0.5
Figure 4. Band structure of polymer 4 (PDTDT) (a), 5 (PDTDT) (b), and 6 (PDTA) (c). Crystal orbital of the i band in (c) consists of Px and PY
orbitals.
the lowest unoccupied band (g) and is stabilized at k = 0, whereas the d and e bands are degenerate along the Brillouin zone. The f band of PDTA (Figure 4c) is also stabilized through interaction with the high-lying i band which consists of p-o orbitals (the p orbitals involved in the framework bonding of monomer). The g band is pushed up by mixing with d bands. In PDTDT (3,the f band is destabilized at the zone edge by mixing with low-lying d band. This interaction yields very narrow bandwidth as shown in Figure 4b. The band g and h are degenerate along the k = 0-0.5 line as they have nodes on carbon atoms. The interactions near the Fermi level of each compound are presented in 7, 8, and 9. The Fermi energy levels of PDTDY
Calculations on the monomeric forms of TTF and its isomers predict that the two forms which have been characterized experimentally, l a and 2a, are the most stable, with l a being about 3 kcdmol more stable than 2a. The relative instability of 3 is attributed to a lack of stabilization of several neardegenerate orbitals in the n system, as well as to the angle strain associated with the tetracyclic rings. The accumulation of p-o orbital mixing effects, which stabilizes the HOMO in TTN, makes poly(l,4-dithiacene) (6) -4 kcal/mol more stable than poly( 1,3-dithiolo[4,5-d]-1,3-dithiole-2,5-diylidene)(5). All of the poly-TTF isomers are expected to have semiconducting properties, with band gaps in the range 2.7-2.9 eV. The bandwidths of the highest-occupied band are rather narrow. The electrical properties of these compounds may be modulated through doping with electron-accepting ions or molecules.
Acknowledgment. We thank Dr. R. L. Elsenbaumer for helpful discussions. We acknowledge support from the US. Air Force Office of Scientific Research, the Robert A. Welch Foundation (Grant Y-743), and the University of Texas Center for High Performance Computing for their generous allocation of computer time.
-7 08
-9.73 .9 86
Conclusions
U
Supplementary Material Available: Tables of optimized structural parameters for TTF (la), TTF (lb), 2, and 3 (4 pages). Ordering information is given on any current masthead page. 7
8
9
(4) and PDTA (6) are lower than that of PDTDT (5), as explained earlier. Specifically, the bent geometry around the sulfur atom weakens n* interaction with the adjacent carbon atom in PDTA (6),which has the lowest Fermi level. Property calculations yield Fermi levels of -9.86, -9.73, and -10.11 eV and band gaps of 2.78, 2.82, and 2.74 eV for PDTDY (4), PDTDT (5), and PDTA (6), respectively. The highest-occupied crystal orbital (HOCO) is centered on sulfur atoms whereas the lowest-unoccupied crystal orbital (LUCO) is centered on carbon atoms. Therefore, a reductive doping is expected to cause a significant geometrical deformation which would lengthen the C-C bonds of the system.
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