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Electronic structure of polysilanes: influence of substitution and conformation
Synthetic Metals, 55-57 (1993) 4419-4424
4419
ELECTRONIC STRUCTURE OF POLYSILANES: INFLUENCE OF SUBSTITUTION AND CONFORMATION
E. ORTI, R. CRESPO, M.C. PIQUERAS, F. TOMAS and J.L. BREDASt Departament de Quimica Fisica, Universitat de Valbncia Dr. Moliner 50, E-46100 Burjassot, Valencia (Spain) tService de Chimie des Mat6riaux Nouveaux et D6partament des Mat6riaux et Proc6d6s, Universit6 de Mons, Place du Parc 20, B-7000 Mons (Belgium)
ABSTRACT The valence effective Hamiltonian (VEH) quantum-chemical approach is used to investigate the electronic properties of polysilane. The valence band structure calculated for this fully saturated polymer is analyzed in terms of orbital contributions and compared to that of the closely related carbon polymer, polyethylene. The effects of alkyl substitution and silicon backbone conformation are studied by elucidating the modifications t h a t these structural changes induce on the electronic valence band structure of all-trans unsubstituted polysilane. The VEH results predict a decrease of the band gap upon alkyl substitution and on going from helical to all-trans conformations.
INTRODUCTION The reasons for the growing interest in inorganic-based polymers fall into two main groups. First, organic polymers differ from "ideal" materials. Most of them react with oxygen, burn releasing toxic smokes, degrade upon irradiation, dissolve on organic solvents, soften at low temperatures, etc... It is generally accepted that polymers that contain inorganic elements in the molecular structure may avoid some of these problems. Second, inorganic polymers provide different combinations of properties t h a n their totally organic counterparts. Inorganic elements often form longer, stronger, and more resistant to free radical reactions bonds than carbon atoms and they provide opportunities for tailoring the chemistry in ways that are not possible in totally organic macromolecules. The main difference between polysilanes and other important inorganic polymers such as polysiloxanes and polyphosphazenes is that polysilanes are constituted by an all-silicon saturated backbone, i.e., the polymer chain is homoatomic [1,2]. Therefore, they are structurally related to homoatomic organic polymers such as polyolefins. However, because the units along the chain are silicon atoms, polysflanes exhibit quite unusual electronic properties that were previously thought to arise exclusively from n-conjugated polymers such as polyacetylene. 0379-6779/93/$6.00
© 1993- Elsevier Sequoia. All rights reserved
4420
The concatenated silicon atoms allow extensive electron delocalization to take place along the chain. In a previous paper [3], we studied the evolution of the electronic properties of oligosilanes, H(SiH2)nH (n=2 to 8), with the length of the chain. We found t h a t both the first ionization potential and the first optical transition decrease in energy as the number of Si atoms in the chain increases. This behaviour agrees with experimental observations on short oligosilanes (n=2 to 5) [4,5] and permethylated oligosilanes, Me(SiMe2)nMe (n=2 to 12) [6], and is reminiscent of that found for conjugated polyenes, indicating that electrons in the silicon backbone of polysilanes might be delocalized. As a consequence, the electronic and photochemical behaviour of polysilanes is very different from t h a t of most other inorganic and organic polymers, in which electron delocalization is much less important. Many of the t e c h n i c a l uses (ultraviolet acting p h o t o r e s i s t s for microelectronics [7], photoconductors in electrophotography [8], etc...), as well as the remarkable p r o p e r t i e s ( i n t e n s e UV a b s o r p t i o n , t h e r m o c h r o m i s m , piezochromism, semiconductivity, nonlinear optical effects, etc...) [1,9] of polysilanes result from this unusual mobility of the sigma electrons. Other important applications of polysilanes are as precursors to silicon carbide ceramics [10] and as photoiniciators for free radical polymerization reactions [ 11]. The determination of the electronic structure of polysilanes therefore is of prime importance to rationalize the remarkable properties that they exhibit. Two main effects should be considered in studying this electronic structure: (i) the effect of substituents, t h a t determines a bathochromic shift of the absorption maximum as the size of the substituent increases, and (ii) the effect of backbone conformation, that is t h o u g h t to be responsible for the thermochromism and piezochromism that polysilanes show [2,9]. We have applied the valence effective Hamiltonian (VEH) technique [12,13] to calculate the electronic band structure of one-dimensional polysilane chains. The VEH method is completely non-empirical and compared to standard ab initio Hartree-Fock calculations gives good estimates of the lowestenergy optical transitions [13]. It has been recently used to study silicon containing compounds and has been shown to provide accurate estimates of essential electronic properties [3,14]. The electronic band structure of polysilanes has been investigated by a variety of theoretical methods [15-18].
THEORETICAL BAND STRUCTURE CALCULATIONS All-t~ans nolvsilane The VEH valence band structure obtained for all-trans polysilane is displayed in Fig. la. In order to facilitate the analysis, this band structure has been computed making use of the helical symmetry of the chain which reduces the traslational (Sill 2Sill2) unit cell to a simple Sill 2 unit. The geometric parameters used for the unit cell are also depicted in Fig. l a and are obtained from a 3-21G" ab initio optimization of trisilane. They are almost identical to those reported by Teramae et al. [15] using the more extended 6-31G'" basis set. These authors show that the parameters obtained for trisilane are almost equal to those obtained for longer oligosilanes. Bands in Fig. l a are classified as u-like or ~-like bands depending on whether oneelectron wave functions are either symmetric or antisymmetric with respect to the silicon backbone plane. Starting from the bottom of the valence band structure, the lowest band corresponds to a o band and mainly results from Si-3s atomic orbitals but
4421
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Fig.1. V E H c a l c u l a t e d b a n d s t r u c t u r e s for (a) a l l - t r a n s polysilane a n d Co) a l l - t r a n s polydimethylsilane, o-like b a n d s a r e denoted with solid lines, ~-like bands with d a s h e d lines. The 3-21G* optimized g e o m e t r i e s u s e d to build up the unit cells are d e p i c t e d on t h e left of the b a n d structures. Bonds lengths are in A and bond angles in degrees.
i m p o r t a n t contributions from H - l s a n d Si-3py orbitals are also present. At t h e c e n t e r of t h e Brillouin zone (k=0), Si-3s c o n t r i b u t i o n s d o m i n a t e and define strong b o n d i n g i n t e r a c t i o n s b e t w e e n a d j a c e n t a t o m s along t h e chain. At the edges of the B r i l l o u i n zone (k=_+~a), Si3p -His b o n d i n g i n t e r a c t i o n s a r e as i m p o r t a n t as Si-3s a n t i b o n d i n g i n t e r a c t i o n s [19]. ~ h e second occupied b a n d is a ~ b a n d r e s u l t i n g from t h e b o n d i n g interaction of t h e H - l s orbitals w i t h t h e Si-3p z orbitals. This b a n d decreases in e n e r g y from k=O to k=_+rv'a due to t h e a n t i b o n d i n g i n t e r a c t i o n s between a d j a c e n t S i l l 2 u n i t s at k=0. T h e h i g h e s t occupied or v a l e n c e b a n d is a a b a n d and, at k=0, shows a n a t o m i c c o m p o s i t i o n s i m i l a r to t h a t of t h e lowest o b a n d a t k=+~/a, i.e., Si3p -His b o n d i n g i n t e r a c t i o n s . T h e s i t u a t i o n is c o m p l e t e l y d i f f e r e n t at k=_+~/a, wheYre t h e H O C O (highest occupied c r y s t a l orbital) is located, since no contribution from Si-3py or H - l s orbitals is detected and only Si-3px orbitals are found. This is an i m p o r t a n t point, since t h e H O C O t h e r e f o r e c o r r e s p o n d s to a p u r e silicon level and only involves t o t a l l y b o n d i n g 3p x interactions along t h e chain. This situation is also found for p o l y e t h y l e n e [17], t h e carbon a n a l o g u e of p o l y s i l a n e , for which is generally s a i d t h a t t h e H O C O m a i n l y corresponds to C-H contributions. T h e lowest u n o c c u p i e d or c o n d u c t i o n b a n d is a a b a n d a n d shows a n a t o m i c c o m p o s i t i o n s i m i l a r to t h a t f o u n d for t h e valence band. At k=0, w h e r e t h e L U C O (lowest unoccupied c r y s t a l o r b i t a l ) is located, it r e s u l t s only form Si-3px a n t i b o n d i n g i n t e r a c t i o n s along t h e c h a i n . A t k=+_x/a, Si-3s a n d -3py a n d H - l s c o n t r i b u t i o n s c o n s t i t u t e t h i s b a n d . Since t h e t r a s l a t i o n a l u n i t cell is twice the helical u n i t cell we h a v e to fold b a c k t h e b a n d s t r u c t u r e of Fig. l a . We therefore found a direct b a n d g a p
4422
of 4.50 eV at k=0 that corresponds to a a(Si-3Px)-a*(Si-3p x) transition. If we take into account that the VEH method overestimates the HOMO-LUMO energy gap of oligosilanes by about 0.78 eV [3], the direct-absorption band gap calculated for alltrans polysilane (4.50 - 0.78 = 3.72 eV) is in excellent agreement with the solid-state UV absorption maximum measured for all-trans poly(di-n-alkylsilanes) which lies between 335 nm (3.70 eV for poly(diethylsilane) [20] and 374 nm (3.32 eV) for poly(din-hexylsilane) [21]. The shape of the valence band structure presented in Fig. l a for all-trans polysilane is almost identical to that calculated for polyethylene and a one-to-one correspondence can be established between the atomic composition of the bands of the two systems. However, there are relevant differences that should be pointed out. (i) Bands in polyethylene are broader that in polysilane. For example, the occupied u-band has a width of 5.68 eV for polyethylene and only 1.74 eV for polysilane. This can be explained as a result of the higher bond energies of the C-C (348 kJ/mol) and CH (412 kJ/mol) bonds with respect to Si-Si (176 kJ/mol) and Si-H (318 kJ/mol) bonds [22]. (ii) The average position of polysilane bands is higher in energy (less stable) than for polyethylene. For example band 2 is centered at an energy of -13.4 eV for polysilane and of -15.8 eV for polyethylene. This result is due to the lower electronegativity of Si compared to C. (iii) The Koopmans' ionization potential predicted by the VEH method for an isolated chain of polysilane (8.01 eV) is about 2 eV lower than that obtained for polyethylene (9.98 eV). (iv) A band gap of about 4 eV is expected for polysilane compared with the band gap of 8.8 eV experimentally reported for polyethylene [23]. Effects of Substitution The electronic valence band structure calculated for all-trans polydimethylsilane is depicted in Fig. lb to be compared with that of polysilane (Fig. la). The band structure has been obtained using the helical [Si(CH3)2] unit cell and the 3-21G* geometry optimized for 1,1',2,2',3,3'-hexamethyltrisilane depicted in Fig. 1. The band structure of polydimethylsilane shows the same trends discussed above for polysilane, the main difference being the appearance of the C-H bands. The first two C-H bands lie at energies of about -25 and -27 eV and mainly originate in C-2p and H-ls atomic orbital contributions, some participation from Si orbitals being also observed. The appearance of these bands leads to a shift to higher energies of the first band of polysilane which is more pronounced at the bottom of the band. The remaining four C-H bands are located about -15 eV and are almost degenerate. These bands are very flat because they correspond to C2p - His interactions. The shape of the highest two occupied bands of polysilane is preserved in polydimethylsilane but they are also shifted to higher energies. Table 1 summarizes the VEH values calculated for the main electronic properties (Koopmans' ionization potentials and electron a_ff~ties, band gaps, and bandwidths) of polysflane and polydimethylsilane. As can be seen from this table, the introduction of methyl groups drastically reduces the width of the valence and conduction bands. This narrowing has almost no effect on the position of the HOCO and the ionization potential r e m a i n s almost c o n s t a n t in passing from polysilane (8.01 eV) to polydimethylsilane (7.92 eV). This is an expected result, since the HOCO of polydimethylsilane is mainly composed of Si-3p x orbitals and the attachment of methyl groups only introduces weak contributions from C-2px orbitals and from the hydrogen atoms lying out of the CSiC planes. In a similar way, the LUCO
4423
TABLE 1 VEH b a n d w i d t h s of the valence (BW-VB) and conduction (BW-CB) bands, Koopmans' ionization p o t e n t i a l s (IP) a n d electron affinities (EA), and direct b a n d gaps (Eg) for different polysilane chains. All energy values are in eV. System Polysilane
Conformation
2/1 (180 °) 7/3 (148.80 °) 4/1 (62.60 °) Polydimethylsilane 2/1 (180 °)
BW-VB
BW-CB
IP a
4.10 3.50 2.45 2.93
3.45 2.69 1.99 1.79
8.01 8.27 9.95 7.92
EA a 3.58 3.77 3.67 4.58
Eg b 4.50 4.68 8.03 3.34
(k=0) (k=_+~a) (k=0) (k=0)
a I p a n d EA v a l u e s are those obtained for isolated chains and no factor is subtracted to take into account the polarization energy of the lattice. b M i n i m u m direct-absorption-type b a n d gaps using t r a s l a t i o n a l u n i t cells. The points of the Brillouin zone where they occur are indicated.
of p o l y s i l a n e t h a t r e s u l t s from Si-3Px a n t i b o n d i n g interactions, is n o t affected by m e t h y l a t i o n . However, this orbital is nomore the LUCO of p o l y d i m e t h y l s i l a n e since the b o n d i n g i n t e r a c t i o n t h a t t a k e s place between C-2s a n d Si-3s orbitals at k=_+r~/a stabilizes t h e c r y s t a l orbital at this point of the Brillouin zone, which becomes the LUCO. As a r e s u l t , a b a n d gap of 3.34 eV is obtained for p o l y d i m e t h y l s i l a n e . The i n t e r p r e t a t i o n t h a t our VEH r e s u l t s afford for the b a n d gap decrease on going from u n s u b s t i t u t e d polysilane to polydimethylsilane differs from t h a t reported by Mintmire [16] which suggests t h a t the decrease is mostly attributable to a n u p w a r d shift of the valence b a n d edge.
Effects of c o n f o r m a t i o n T a b l e 1 also collects the VEH electronic properties o b t a i n e d for t h e 7/3 a n d 4/1 helical c o n f o r m a t i o n s of a n u n s u b s t i t u t e d polysilane chain. T h e s e conformations c o r r e s p o n d to d i h e d r a l a n g l e s of 148.80 ° a n d 62.60 ° for t h e silicon backbone, respectively. As c a n be seen from Table 1, the width of the valence a n d conduction b a n d s is drastically reduced as the dihedral angle decreases from 180 ° (all-trans). This r e s u l t s from t h e fact t h a t the interaction between Si-3px orbitals, which lie parallel to the chain, decreases as the dihedral angle is reduced. As a consequence, the m i n i m u m d i r e c t - a b s o r p t i o n - t y p e b a n d gap increases on going from a l l - t r a n s to 4/1 polysilane. For the 7/3 conformation, this b a n d gap corresponds to a n energy of 4.68 eV at k=_+~/a after folding b a c k the Brillouin zone to recover the t r a s l a t i o n a l u n i t cell consisting of seven S i l l 2 u n i t s . For 4/1 polysilane, the m i n i m u m b a n d gap is found at k=0 a n d has a value of 8.03 eV, i.e., 3.52 eV larger t h a n for all-trans polysilane. T h e V E H r e s u l t s therefore support the c u r r e n t i n t e r p r e t a t i o n of e x p e r i m e n t a l t h e r m o c h r o m i s m a n d piezochromism as r e s u l t s of the e n h a n c e d o - c o n j u g a t i o n achieved w h e n a l l - t r a n s silicon chains are adopted. U n d e r pressure, a conformation t r a n s f o r m a t i o n from a 7/3 helical crystalline phase to an all-trans crystalline form are r e p o r t e d for poly(di-n-pentylsilane) a n d poly(di-n-butylsilane) accompanied by a red shift of the UV a b s o r p t i o n m a x i m a of 0.52 and 0.42 eV, r e s p e c t i v e l y [24]. These v a l u e s s e e m s to converge to the VEH bathochromic shift of 0.18 eV calculated for u n s u b s t i t u t e d polysilane on going from the 7/3 to the all-trans conformation.
4424
ACKNOWLEDGEMENTS We t h a n k the Servei d'Inform~tica de la Universitat de Valencia for the use of their computing facilities. M.C.P. and R.C. are grateful to the Ministerio de Educacidn y Ciencia of Spain for a Doctoral Grant. This work has been supported by the Generalitat Valenciana and the DGYCIT Projects PS88-0112 and OP90-0042.
REFERENCES 1 For a comprehensive review on polysilanes see, R.D. Miller and J. Michl, Qhem.. Rev.. 89 (1989) 1359. 2 See also, J.M. Zeigler and F.G. Fearon (eds.), Silicon-Based Polymer Science. A Comurehensive Rc@Qurce. American Chemical Society, Washington, 1990; J.E. Mark, H.R. Allcock and R. West, Inorganic Polymers. Prentice Hall, Englewood Cliffs, 1990, Ch. 5, p. 186. 3 R. Crespo, M.C. Piqueras, E. Orti and J.L. Br4das, Svnth. Met.. 43 (1991) 3457. 4 H. Bock, W. Ensslin, F. Feh4r and R. Freund, J. Am. Chem. Soc.. 98 (1976) 668. 5 U. Itoh, Y. Toyoshima, H. Onuki, N. Washida and T. Ibuki, J. Chem. Phvs.. 85 (1986) 4867. 6 M. Kumada and K. Tamao, Adv. Or~anometal. Chem.. 6 (1968) 19. 7 S. Gauthier and D.J. Worsfold, Macromolecules. 22 (1989) 2213. 8 M. Abkowitz, F.R. Knier, H.~I. Yuh, R.J. Weagley and M. Stolka, (1987) 547. 9 J.M. Zeigler, Mol. Crvst. Lio. Crvst.. 190 (1990) 265. 10 S. Yajima, Am. Ceram. Soc. Bull.. 62 (1983) 893. 11 A.R. Wolf and R. West, ~Dul. Or~anomct. Chem.. 1 (1987) 7. 12 G. Nicolas and Ph. Durand, ~ (1979); 72 (1980) 453. 13 J.M. Andr4, L.A. Burke, J. Delhalle, G. Nicolas and Ph. Durand, Chem. Svmu.. 13 (1979) 283; J.L. Bredas, R.R. Chance, R. Silbey, G. Nicolas and Ph. Durand, J. Chem. Phys.. 75 (1981) 255. 14 R. Orti, R. Crespo and M.C. Piqueras, ~ (1991) 1575. 15 H. T e r a m a e and K. Takeda, J. Am. Chem. Soc.. 111 (1989) 1281; K. Takeda, K. Shiraishi and N. Matsumoto, J. Am. Chem. Soc.. 112 (1990) 5043; N. Matsumoto and H. Teramae, ~l. Am. Chem. Soc.. 113 (1991) 4481. 16 J.W. Mintmire, ~ 9 (1989) 13350. 17 J.-M. Andre, Int. J. Ouantum Chem. Svmn.. 24 (1990) 65. 18 C,X. Cui, A. Karpfen and M. Kertesz, ~_acromolecules. 23 (1990) 3302. 19 See ref. 19 for a very detailed discussion of the atomic composition of the occupied electronic bands. 20 A.J. Lovinger, D.D. Davis, F.C. Schilling, F.A. Bovey and J.M. Zeigler, Polvm. Commun.. 30 (1989) 356. 21 H. Kuzmany, J.F. Rabolt, B.L. Farmer and R.D. Miller, J. Chem. Phvs,. 85 (1986) 7413. 22 See for example, P.W. Atkins, Physical Chemistry, Oxford University Press, Oxford, 3rd edn., 1986, Table 4.5, p. 822. 23 K J . Less and E.G. Wilson, ~ (1973) 3110. 24 K. Song, R.D. Miller, G.M. Wallraff and J.F. Rabolt, MacrQmolecule~, 24 (1986) 7413.
4419
ELECTRONIC STRUCTURE OF POLYSILANES: INFLUENCE OF SUBSTITUTION AND CONFORMATION
E. ORTI, R. CRESPO, M.C. PIQUERAS, F. TOMAS and J.L. BREDASt Departament de Quimica Fisica, Universitat de Valbncia Dr. Moliner 50, E-46100 Burjassot, Valencia (Spain) tService de Chimie des Mat6riaux Nouveaux et D6partament des Mat6riaux et Proc6d6s, Universit6 de Mons, Place du Parc 20, B-7000 Mons (Belgium)
ABSTRACT The valence effective Hamiltonian (VEH) quantum-chemical approach is used to investigate the electronic properties of polysilane. The valence band structure calculated for this fully saturated polymer is analyzed in terms of orbital contributions and compared to that of the closely related carbon polymer, polyethylene. The effects of alkyl substitution and silicon backbone conformation are studied by elucidating the modifications t h a t these structural changes induce on the electronic valence band structure of all-trans unsubstituted polysilane. The VEH results predict a decrease of the band gap upon alkyl substitution and on going from helical to all-trans conformations.
INTRODUCTION The reasons for the growing interest in inorganic-based polymers fall into two main groups. First, organic polymers differ from "ideal" materials. Most of them react with oxygen, burn releasing toxic smokes, degrade upon irradiation, dissolve on organic solvents, soften at low temperatures, etc... It is generally accepted that polymers that contain inorganic elements in the molecular structure may avoid some of these problems. Second, inorganic polymers provide different combinations of properties t h a n their totally organic counterparts. Inorganic elements often form longer, stronger, and more resistant to free radical reactions bonds than carbon atoms and they provide opportunities for tailoring the chemistry in ways that are not possible in totally organic macromolecules. The main difference between polysilanes and other important inorganic polymers such as polysiloxanes and polyphosphazenes is that polysilanes are constituted by an all-silicon saturated backbone, i.e., the polymer chain is homoatomic [1,2]. Therefore, they are structurally related to homoatomic organic polymers such as polyolefins. However, because the units along the chain are silicon atoms, polysflanes exhibit quite unusual electronic properties that were previously thought to arise exclusively from n-conjugated polymers such as polyacetylene. 0379-6779/93/$6.00
© 1993- Elsevier Sequoia. All rights reserved
4420
The concatenated silicon atoms allow extensive electron delocalization to take place along the chain. In a previous paper [3], we studied the evolution of the electronic properties of oligosilanes, H(SiH2)nH (n=2 to 8), with the length of the chain. We found t h a t both the first ionization potential and the first optical transition decrease in energy as the number of Si atoms in the chain increases. This behaviour agrees with experimental observations on short oligosilanes (n=2 to 5) [4,5] and permethylated oligosilanes, Me(SiMe2)nMe (n=2 to 12) [6], and is reminiscent of that found for conjugated polyenes, indicating that electrons in the silicon backbone of polysilanes might be delocalized. As a consequence, the electronic and photochemical behaviour of polysilanes is very different from t h a t of most other inorganic and organic polymers, in which electron delocalization is much less important. Many of the t e c h n i c a l uses (ultraviolet acting p h o t o r e s i s t s for microelectronics [7], photoconductors in electrophotography [8], etc...), as well as the remarkable p r o p e r t i e s ( i n t e n s e UV a b s o r p t i o n , t h e r m o c h r o m i s m , piezochromism, semiconductivity, nonlinear optical effects, etc...) [1,9] of polysilanes result from this unusual mobility of the sigma electrons. Other important applications of polysilanes are as precursors to silicon carbide ceramics [10] and as photoiniciators for free radical polymerization reactions [ 11]. The determination of the electronic structure of polysilanes therefore is of prime importance to rationalize the remarkable properties that they exhibit. Two main effects should be considered in studying this electronic structure: (i) the effect of substituents, t h a t determines a bathochromic shift of the absorption maximum as the size of the substituent increases, and (ii) the effect of backbone conformation, that is t h o u g h t to be responsible for the thermochromism and piezochromism that polysilanes show [2,9]. We have applied the valence effective Hamiltonian (VEH) technique [12,13] to calculate the electronic band structure of one-dimensional polysilane chains. The VEH method is completely non-empirical and compared to standard ab initio Hartree-Fock calculations gives good estimates of the lowestenergy optical transitions [13]. It has been recently used to study silicon containing compounds and has been shown to provide accurate estimates of essential electronic properties [3,14]. The electronic band structure of polysilanes has been investigated by a variety of theoretical methods [15-18].
THEORETICAL BAND STRUCTURE CALCULATIONS All-t~ans nolvsilane The VEH valence band structure obtained for all-trans polysilane is displayed in Fig. la. In order to facilitate the analysis, this band structure has been computed making use of the helical symmetry of the chain which reduces the traslational (Sill 2Sill2) unit cell to a simple Sill 2 unit. The geometric parameters used for the unit cell are also depicted in Fig. l a and are obtained from a 3-21G" ab initio optimization of trisilane. They are almost identical to those reported by Teramae et al. [15] using the more extended 6-31G'" basis set. These authors show that the parameters obtained for trisilane are almost equal to those obtained for longer oligosilanes. Bands in Fig. l a are classified as u-like or ~-like bands depending on whether oneelectron wave functions are either symmetric or antisymmetric with respect to the silicon backbone plane. Starting from the bottom of the valence band structure, the lowest band corresponds to a o band and mainly results from Si-3s atomic orbitals but
4421
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".
/ H
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~c~ 4~)si- 19o~ Si
(b)
2/ . . CH:l CH3
O0 0.0
I
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0.5
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1 .0
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(b)
Fig.1. V E H c a l c u l a t e d b a n d s t r u c t u r e s for (a) a l l - t r a n s polysilane a n d Co) a l l - t r a n s polydimethylsilane, o-like b a n d s a r e denoted with solid lines, ~-like bands with d a s h e d lines. The 3-21G* optimized g e o m e t r i e s u s e d to build up the unit cells are d e p i c t e d on t h e left of the b a n d structures. Bonds lengths are in A and bond angles in degrees.
i m p o r t a n t contributions from H - l s a n d Si-3py orbitals are also present. At t h e c e n t e r of t h e Brillouin zone (k=0), Si-3s c o n t r i b u t i o n s d o m i n a t e and define strong b o n d i n g i n t e r a c t i o n s b e t w e e n a d j a c e n t a t o m s along t h e chain. At the edges of the B r i l l o u i n zone (k=_+~a), Si3p -His b o n d i n g i n t e r a c t i o n s a r e as i m p o r t a n t as Si-3s a n t i b o n d i n g i n t e r a c t i o n s [19]. ~ h e second occupied b a n d is a ~ b a n d r e s u l t i n g from t h e b o n d i n g interaction of t h e H - l s orbitals w i t h t h e Si-3p z orbitals. This b a n d decreases in e n e r g y from k=O to k=_+rv'a due to t h e a n t i b o n d i n g i n t e r a c t i o n s between a d j a c e n t S i l l 2 u n i t s at k=0. T h e h i g h e s t occupied or v a l e n c e b a n d is a a b a n d and, at k=0, shows a n a t o m i c c o m p o s i t i o n s i m i l a r to t h a t of t h e lowest o b a n d a t k=+~/a, i.e., Si3p -His b o n d i n g i n t e r a c t i o n s . T h e s i t u a t i o n is c o m p l e t e l y d i f f e r e n t at k=_+~/a, wheYre t h e H O C O (highest occupied c r y s t a l orbital) is located, since no contribution from Si-3py or H - l s orbitals is detected and only Si-3px orbitals are found. This is an i m p o r t a n t point, since t h e H O C O t h e r e f o r e c o r r e s p o n d s to a p u r e silicon level and only involves t o t a l l y b o n d i n g 3p x interactions along t h e chain. This situation is also found for p o l y e t h y l e n e [17], t h e carbon a n a l o g u e of p o l y s i l a n e , for which is generally s a i d t h a t t h e H O C O m a i n l y corresponds to C-H contributions. T h e lowest u n o c c u p i e d or c o n d u c t i o n b a n d is a a b a n d a n d shows a n a t o m i c c o m p o s i t i o n s i m i l a r to t h a t f o u n d for t h e valence band. At k=0, w h e r e t h e L U C O (lowest unoccupied c r y s t a l o r b i t a l ) is located, it r e s u l t s only form Si-3px a n t i b o n d i n g i n t e r a c t i o n s along t h e c h a i n . A t k=+_x/a, Si-3s a n d -3py a n d H - l s c o n t r i b u t i o n s c o n s t i t u t e t h i s b a n d . Since t h e t r a s l a t i o n a l u n i t cell is twice the helical u n i t cell we h a v e to fold b a c k t h e b a n d s t r u c t u r e of Fig. l a . We therefore found a direct b a n d g a p
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of 4.50 eV at k=0 that corresponds to a a(Si-3Px)-a*(Si-3p x) transition. If we take into account that the VEH method overestimates the HOMO-LUMO energy gap of oligosilanes by about 0.78 eV [3], the direct-absorption band gap calculated for alltrans polysilane (4.50 - 0.78 = 3.72 eV) is in excellent agreement with the solid-state UV absorption maximum measured for all-trans poly(di-n-alkylsilanes) which lies between 335 nm (3.70 eV for poly(diethylsilane) [20] and 374 nm (3.32 eV) for poly(din-hexylsilane) [21]. The shape of the valence band structure presented in Fig. l a for all-trans polysilane is almost identical to that calculated for polyethylene and a one-to-one correspondence can be established between the atomic composition of the bands of the two systems. However, there are relevant differences that should be pointed out. (i) Bands in polyethylene are broader that in polysilane. For example, the occupied u-band has a width of 5.68 eV for polyethylene and only 1.74 eV for polysilane. This can be explained as a result of the higher bond energies of the C-C (348 kJ/mol) and CH (412 kJ/mol) bonds with respect to Si-Si (176 kJ/mol) and Si-H (318 kJ/mol) bonds [22]. (ii) The average position of polysilane bands is higher in energy (less stable) than for polyethylene. For example band 2 is centered at an energy of -13.4 eV for polysilane and of -15.8 eV for polyethylene. This result is due to the lower electronegativity of Si compared to C. (iii) The Koopmans' ionization potential predicted by the VEH method for an isolated chain of polysilane (8.01 eV) is about 2 eV lower than that obtained for polyethylene (9.98 eV). (iv) A band gap of about 4 eV is expected for polysilane compared with the band gap of 8.8 eV experimentally reported for polyethylene [23]. Effects of Substitution The electronic valence band structure calculated for all-trans polydimethylsilane is depicted in Fig. lb to be compared with that of polysilane (Fig. la). The band structure has been obtained using the helical [Si(CH3)2] unit cell and the 3-21G* geometry optimized for 1,1',2,2',3,3'-hexamethyltrisilane depicted in Fig. 1. The band structure of polydimethylsilane shows the same trends discussed above for polysilane, the main difference being the appearance of the C-H bands. The first two C-H bands lie at energies of about -25 and -27 eV and mainly originate in C-2p and H-ls atomic orbital contributions, some participation from Si orbitals being also observed. The appearance of these bands leads to a shift to higher energies of the first band of polysilane which is more pronounced at the bottom of the band. The remaining four C-H bands are located about -15 eV and are almost degenerate. These bands are very flat because they correspond to C2p - His interactions. The shape of the highest two occupied bands of polysilane is preserved in polydimethylsilane but they are also shifted to higher energies. Table 1 summarizes the VEH values calculated for the main electronic properties (Koopmans' ionization potentials and electron a_ff~ties, band gaps, and bandwidths) of polysflane and polydimethylsilane. As can be seen from this table, the introduction of methyl groups drastically reduces the width of the valence and conduction bands. This narrowing has almost no effect on the position of the HOCO and the ionization potential r e m a i n s almost c o n s t a n t in passing from polysilane (8.01 eV) to polydimethylsilane (7.92 eV). This is an expected result, since the HOCO of polydimethylsilane is mainly composed of Si-3p x orbitals and the attachment of methyl groups only introduces weak contributions from C-2px orbitals and from the hydrogen atoms lying out of the CSiC planes. In a similar way, the LUCO
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TABLE 1 VEH b a n d w i d t h s of the valence (BW-VB) and conduction (BW-CB) bands, Koopmans' ionization p o t e n t i a l s (IP) a n d electron affinities (EA), and direct b a n d gaps (Eg) for different polysilane chains. All energy values are in eV. System Polysilane
Conformation
2/1 (180 °) 7/3 (148.80 °) 4/1 (62.60 °) Polydimethylsilane 2/1 (180 °)
BW-VB
BW-CB
IP a
4.10 3.50 2.45 2.93
3.45 2.69 1.99 1.79
8.01 8.27 9.95 7.92
EA a 3.58 3.77 3.67 4.58
Eg b 4.50 4.68 8.03 3.34
(k=0) (k=_+~a) (k=0) (k=0)
a I p a n d EA v a l u e s are those obtained for isolated chains and no factor is subtracted to take into account the polarization energy of the lattice. b M i n i m u m direct-absorption-type b a n d gaps using t r a s l a t i o n a l u n i t cells. The points of the Brillouin zone where they occur are indicated.
of p o l y s i l a n e t h a t r e s u l t s from Si-3Px a n t i b o n d i n g interactions, is n o t affected by m e t h y l a t i o n . However, this orbital is nomore the LUCO of p o l y d i m e t h y l s i l a n e since the b o n d i n g i n t e r a c t i o n t h a t t a k e s place between C-2s a n d Si-3s orbitals at k=_+r~/a stabilizes t h e c r y s t a l orbital at this point of the Brillouin zone, which becomes the LUCO. As a r e s u l t , a b a n d gap of 3.34 eV is obtained for p o l y d i m e t h y l s i l a n e . The i n t e r p r e t a t i o n t h a t our VEH r e s u l t s afford for the b a n d gap decrease on going from u n s u b s t i t u t e d polysilane to polydimethylsilane differs from t h a t reported by Mintmire [16] which suggests t h a t the decrease is mostly attributable to a n u p w a r d shift of the valence b a n d edge.
Effects of c o n f o r m a t i o n T a b l e 1 also collects the VEH electronic properties o b t a i n e d for t h e 7/3 a n d 4/1 helical c o n f o r m a t i o n s of a n u n s u b s t i t u t e d polysilane chain. T h e s e conformations c o r r e s p o n d to d i h e d r a l a n g l e s of 148.80 ° a n d 62.60 ° for t h e silicon backbone, respectively. As c a n be seen from Table 1, the width of the valence a n d conduction b a n d s is drastically reduced as the dihedral angle decreases from 180 ° (all-trans). This r e s u l t s from t h e fact t h a t the interaction between Si-3px orbitals, which lie parallel to the chain, decreases as the dihedral angle is reduced. As a consequence, the m i n i m u m d i r e c t - a b s o r p t i o n - t y p e b a n d gap increases on going from a l l - t r a n s to 4/1 polysilane. For the 7/3 conformation, this b a n d gap corresponds to a n energy of 4.68 eV at k=_+~/a after folding b a c k the Brillouin zone to recover the t r a s l a t i o n a l u n i t cell consisting of seven S i l l 2 u n i t s . For 4/1 polysilane, the m i n i m u m b a n d gap is found at k=0 a n d has a value of 8.03 eV, i.e., 3.52 eV larger t h a n for all-trans polysilane. T h e V E H r e s u l t s therefore support the c u r r e n t i n t e r p r e t a t i o n of e x p e r i m e n t a l t h e r m o c h r o m i s m a n d piezochromism as r e s u l t s of the e n h a n c e d o - c o n j u g a t i o n achieved w h e n a l l - t r a n s silicon chains are adopted. U n d e r pressure, a conformation t r a n s f o r m a t i o n from a 7/3 helical crystalline phase to an all-trans crystalline form are r e p o r t e d for poly(di-n-pentylsilane) a n d poly(di-n-butylsilane) accompanied by a red shift of the UV a b s o r p t i o n m a x i m a of 0.52 and 0.42 eV, r e s p e c t i v e l y [24]. These v a l u e s s e e m s to converge to the VEH bathochromic shift of 0.18 eV calculated for u n s u b s t i t u t e d polysilane on going from the 7/3 to the all-trans conformation.
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ACKNOWLEDGEMENTS We t h a n k the Servei d'Inform~tica de la Universitat de Valencia for the use of their computing facilities. M.C.P. and R.C. are grateful to the Ministerio de Educacidn y Ciencia of Spain for a Doctoral Grant. This work has been supported by the Generalitat Valenciana and the DGYCIT Projects PS88-0112 and OP90-0042.
REFERENCES 1 For a comprehensive review on polysilanes see, R.D. Miller and J. Michl, Qhem.. Rev.. 89 (1989) 1359. 2 See also, J.M. Zeigler and F.G. Fearon (eds.), Silicon-Based Polymer Science. A Comurehensive Rc@Qurce. American Chemical Society, Washington, 1990; J.E. Mark, H.R. Allcock and R. West, Inorganic Polymers. Prentice Hall, Englewood Cliffs, 1990, Ch. 5, p. 186. 3 R. Crespo, M.C. Piqueras, E. Orti and J.L. Br4das, Svnth. Met.. 43 (1991) 3457. 4 H. Bock, W. Ensslin, F. Feh4r and R. Freund, J. Am. Chem. Soc.. 98 (1976) 668. 5 U. Itoh, Y. Toyoshima, H. Onuki, N. Washida and T. Ibuki, J. Chem. Phvs.. 85 (1986) 4867. 6 M. Kumada and K. Tamao, Adv. Or~anometal. Chem.. 6 (1968) 19. 7 S. Gauthier and D.J. Worsfold, Macromolecules. 22 (1989) 2213. 8 M. Abkowitz, F.R. Knier, H.~I. Yuh, R.J. Weagley and M. Stolka, (1987) 547. 9 J.M. Zeigler, Mol. Crvst. Lio. Crvst.. 190 (1990) 265. 10 S. Yajima, Am. Ceram. Soc. Bull.. 62 (1983) 893. 11 A.R. Wolf and R. West, ~Dul. Or~anomct. Chem.. 1 (1987) 7. 12 G. Nicolas and Ph. Durand, ~ (1979); 72 (1980) 453. 13 J.M. Andr4, L.A. Burke, J. Delhalle, G. Nicolas and Ph. Durand, Chem. Svmu.. 13 (1979) 283; J.L. Bredas, R.R. Chance, R. Silbey, G. Nicolas and Ph. Durand, J. Chem. Phys.. 75 (1981) 255. 14 R. Orti, R. Crespo and M.C. Piqueras, ~ (1991) 1575. 15 H. T e r a m a e and K. Takeda, J. Am. Chem. Soc.. 111 (1989) 1281; K. Takeda, K. Shiraishi and N. Matsumoto, J. Am. Chem. Soc.. 112 (1990) 5043; N. Matsumoto and H. Teramae, ~l. Am. Chem. Soc.. 113 (1991) 4481. 16 J.W. Mintmire, ~ 9 (1989) 13350. 17 J.-M. Andre, Int. J. Ouantum Chem. Svmn.. 24 (1990) 65. 18 C,X. Cui, A. Karpfen and M. Kertesz, ~_acromolecules. 23 (1990) 3302. 19 See ref. 19 for a very detailed discussion of the atomic composition of the occupied electronic bands. 20 A.J. Lovinger, D.D. Davis, F.C. Schilling, F.A. Bovey and J.M. Zeigler, Polvm. Commun.. 30 (1989) 356. 21 H. Kuzmany, J.F. Rabolt, B.L. Farmer and R.D. Miller, J. Chem. Phvs,. 85 (1986) 7413. 22 See for example, P.W. Atkins, Physical Chemistry, Oxford University Press, Oxford, 3rd edn., 1986, Table 4.5, p. 822. 23 K J . Less and E.G. Wilson, ~ (1973) 3110. 24 K. Song, R.D. Miller, G.M. Wallraff and J.F. Rabolt, MacrQmolecule~, 24 (1986) 7413.