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VEH electronic band structure of poly(phenylsilane)
Synthetic Metals, 61 (1993) 107-111
107
VEH electronic band structure of poly(phenylsilane) R. Crespo, M.C. Piqueras, E. O r t f a n d F. T o m , i s Departament de Qulmica Flsica, Universitat de Valdncia, Dr. Moliner 50, E-46100 Burjassot, Valencia (Spare)
Abstract The electronic structure of all-trans syndiotactic and isotactic poly(phenylsilane) has been calculated using the valence effective Hamiltonian (VEH) method. The effects of attachment of the phenyl group on the electronic properties of polysilane are analysed in detail. The VEH results show a decrease of ionization potential and an increase of electron affinity which determine an important reduction of the bandgap. These features are correlated with tr-~- and tr*-~r* interactions between the silicon backbone and the phenyl group.
Introduction Conjugated polymers have been intensively investigated in recent years because of their interesting electronic properties and potential useful applications [1]. These polymers resemble both organic molecular solids with van der Waals contacts between chains and onedimensional semiconductors. Most of the studies on conjugated polymers have been focused on Tr-conjugated systems; polyacetylene, polythiophene and polyaniline are examples of the most investigated ones. Recently, similar electronic properties have been recognized in tr-conjugated polymers, particularly in polysilanes which are high-molecular-weight polymers the backbone of which consists entirely of silicon atoms [2]. These findings together with the development of soluble polysilanes have led to widespread interest in their application as precursors of silicon carbide, polymerization catalysts, photoresists and photoconductors [3]. One of the more interesting features of polysilanes is their unusual electronic spectra. In this context, the thermochromic behaviour of symmetrically substituted poly(di-n-alkylsilanes) in solution and in the solid state has been widely documented [2, 3]. Furthermore, although aryl substituents linked to the silicon backbone by saturated chains have very little effect on the electronic properties, significant spectral changes occur when the aromatic group is directly bonded to the silicon backbone. It has been reported that the oxidation and ionization potentials of poly(methylphenylsilane) films are lower than those presented by simple alkylsubstituted derivatives [4, 5]. Moreover, the electronic spectrum of diaryl-substituted polysilanes shows that the maximum of absorption is located at 390-400 nm [6] while that presented by
0379-6779/93/$6.00
dialkyl-substituted polysilanes in an all-tram conformation appears at 350-380 nm in the solid state [7]. This bathochromic shift has been attributed to the mixing of the tr and ~r* orbitals of the silicon backbone with the ~- and ~r* orbitals of the aromatic substituents. Furthermore, the presence of the two aromatic substituents favours the trans conformation of the polymer backbone, even in solution. In this context, molecular mechanics calculations including full geometry optimization on oligomers of poly(methylphenylsilane) and poly(silastyrene) suggest that the planar zigzag conformation of the backbone is preferred over transgauche or gauche-gauche conformations in both syndiotactic and isotactic isomers [8]. Theoretical calculations on the electronic structure of phenyl derivatives of polysilane have shown that the valence band displays interactions between or electrons of the silicon backbone and ~" electrons of the phenyl group [9, 10]. However, there is a little controversy about the composition of the conduction band. Takeda et al. [9] predict that this band mainly results from the ~-* states of phenyl groups, while Mintmire and Ortiz [10] obtain tr*-w* interactions similar to those observed in the valence band. In this paper, we investigate the effect of phenyl substitution on the electronic structure and optical properties of polysilane. We focus on two structural isomers of poly(phenylsilane), syndiotactic and isotactic. For this purpose, we have used the valence effective Hamiltonian (VEH) technique [11] to calculate the one-dimensional electronic band structure of these polymers in their all-trans conformation. The VEH approach has been successfully applied to silicon-containing polymers [12, 13] and has been shown to provide accurate predictions of essential electronic properties, including
© 1993- Elsevier Sequoia. All rights reserved
108
the energies of the lowest optical transitions [14]. This feature is a clear indication that the VEH technique includes part of the electron-hole correlation into virtual one-electron levels [15].
Results and discussion
The geometrical parameters used to build up the unit cells employed in the electronic band structure calculations have been obtained by optimizing the geometries of both isomers of the closely related molecule 1,2,3-triphenyltrisilane at the ab initio level. We have followed this methodological approach as previous studies on n-oligosilanes have demonstrated that the geometrical parameters calculated for trisilane are almost identical to those obtained for longer n-oligosilanes [16]. This same approach has been previously applied to methyl-substituted polysilanes [13] for which it was found that the calculated electronic properties were in excellent agreement with reported experimental data. All the optimization calculations have been performed using the 3-21G* basis set as implemented in the GAUSSIAN 88 program [17]. This basis has been shown to provide accurate geometrical parameters, particularly those directly related to the silicon atoms [16]. The geometries have been fully optimized maintaining the three HSiC planes parallel to each other (see Fig. 1) in order to reproduce the environment of the -SiHPhunits in the polymer. We have optimized both the up-down-up (R~=Ph, R 2 = H ) and the up-up-up (R~ = H, R2 = Ph) isomers of 1,2,3-triphenyltrisilane because they reproduce accurately the environment of syndiotactic and isotactic poly(phenylsilane), respectively. These isomers only differ in the position of the central phenyl group with respect to the plane of the
R,~ ...-R1
YT ,,...i--"z H
(a)
si
H~si/ / '-Ph H
xp
Ph
Ph
Ph
H
(b)
~Si
,/H / '-Ph H
H
Ph
H
Fig. 1. Geometric parameters used to build up the unit cells of syndiotactic poly(phenylsilane) (a) and isotactic poly(phenylsilane) (b). Distances are in .~ and angles in degrees. Parameters not directly related to silicon atoms are not indicated.
silicon backbone. The parameters chosen to build up the unit cell of the corresponding polymer are those calculated for the central silicon atom. Figure I displays the geometrical parameters obtained for the unit cells of syndiotactic and isotactic poly(phenylsilane). The attachment of phenyl groups induces minor changes on the Si-Si bond length with respect to that obtained for polysilane (2.3456/~) [13]. However, the changes produced in the SiSiSi bond angle are more acute (from 110.91 ° in trisilane to 113.88 ° and 113.26 ° in 1,2,3-triphenyltrisilane isomers) because of the steric hindrance that the phenyl groups in positions 1 and 3 produce. These features are similar to those observed in methyl-substituted oligosilanes [13]. As can be seen, the geometries calculated for both isomers of 1,2,3-triphenyltrisilane are almost identical, except for that which concerns the CSiSi and HSiSi bond angles. While in the up--down-up isomer both angles are very similar (109.29 ° and 108.39°), in the up-up-up isomer the interaction between the three phenyl groups produces an increase of the CSiSi angle (112.84 °) and, as a consequence, a decrease of the HSiSi angle (105.45°). The VEH band structure calculated for syndiotactic poly(phenylsilane) (s-PHPhS) is displayed in Fig. 2. In order to provide an easy comparison, we have also included the band structure previously reported for polysilane [13] and the one-electron energy levels diagram of benzene. All the band structure calculations have been carried out assuming an all-trans conformation of the silicon backbone and taking into account the helical symmetry these polymers present. The energy levels of benzene have been obtained from VEH calculations based on ab initio 3-21G geometry. The band structures calculated for isotactic poly(phenylsilane) (iPHPhS) and s-PHPhS display similar features when the translational unit cell is used. As can be seen in Fig. 2, the band structure of sPHPhS looks quite different from that calculated for polysilane because of the great number of bands that the phenyl group incorporates into the electronic structure. However, the four bands displayed by polysilane can be clearly differentiated in s-PHPhS. Going from the bottom to the top of the valence band structure of s-PHPhS, the first three bands are very narrow because they are localized in the phenyl group and correlate with the lals and lelu levels of benzene. The next four bands (from 4 to 7) come from the le2g and 2alg levels of benzene and the first band of polysilane (which is mainly composed of silicon 3s orbital and weak contributions from hydrogen ls orbitals). A strong interaction of the polysilane band with one of the le2s levels and with the 2alg level is observed. This interaction produces a drastic narrowing of the polysilane band and a shift of the le2g level to lower energies at k = 0, and of the 2a18 level to higher energies at k = + 7r/a.
109 _ _ LUMO
~UCO CO - 0 4J -r-I C'D
653
25
-
HOMO
-0 5O
-
-
_
_
(_1
75
W-I
O0
f
J
lelg
2e2g la2u 2e lblu lb2a 2~lu
J
-1 25 0.0 (a)
le2u '
LUCO - -
E ©-0 4-J co
2blu"
lg
le2g
I
I
I
0.5 k (~/a)
I
.0
0.0 (b)
I
- -
lelu
- -
lalg
I
0.5 k (~/a)
~.0 (c)
Fig. 2. VEH band structures calculated for polysitane (a) and syndiotactic poly(phenylsilane) (b), and V E I l molecular orbital distribution obtained for benzene (c). Energies are in atomic units. Unoccupied bands and molecular levels with energies larger than 0.0 a.u. are not shown. VB denotes valence band and CB denotes conduction band. H O C O (HOMO) and L U C O (LUMO) denote the highest occupied and lowest unoccupied crystal (molecular) orbital, respectively.
The upper band of this group (7) is the first that presents significant contributions from hydrogen ls orbitals of the phenyl group. Bands 8 to 12 correlate with the lblu, lb2u, 2elu and one of the 2e2g orbitals of benzene. The most important contributions to these bands come from C - H interactions. These bands are located at the same energies as their analogue C - H bands in poly(methylsilane) [13]. The next band (13) correlates with the la2u orbital of benzene, which is the first rr orbital. This band presents weak contributions from the silicon 3px orbital (see Fig. 1 for assignment of axes). The 14th band corresponds to the second band of polysilane and results from the bonding interaction of the silicon 3pz orbital with the hydrogen and carbon atoms attached to silicon. As discussed for the first band of polysilane, the width of this band (14) presents a drastic reduction (with respect to that displayed for polysilane), which is more accentuated because of the greater proximity of the adjacent bands. The next three bands (from 15 to 17) come from the lel, levels of benzene (Tr orbitals) and the third band of polysilane (valence band). The central band (16) correlates with the antisymmetric leag level and displays a narrow width as a consequence of the nonparticipation of the 2px orbital of the carbon attached to the silicon atom. The other two bands mainly result from the interaction between the symmetric le,g level of benzene and the 3px orbital of the silicon atom. Bands 15 and 17 correspond, respectively, to the bonding and antibonding interaction between silicon and carbon atoms. As a result, the valence band (17) suffers a shift to higher energies with respect to that of polysilane.
The next four bands (from 18 to 21) are the first unoccupied ones and lie at negative energies and mainly correspond to the antibonding picture of the last four occupied bands. Bands 18 and 19 correlate with bands 17 and 16, respectively, while bands 20 and 21 correspond to bands 14 and 15, respectively. The VEH values obtained for Koopmans' ionization potentials (IP values) and electron affinities (EAvalues), direct bandgaps and bandwidths of the valence and conduction bands of syndiotactic and isotactic poly(phenylsilane) together with those obtained from syndiotactic and isotactic poly(methylsilane) [13] and polysilane [13] are collected in Table 1. As can be seen, the IP values of both s-PHPhS (7.63 eV) and iPHPhS (7.64 eV) are almost equal. This result was also observed for syndiotactic (8.06 eV) and isotactic (8.06 eV) poly(methylsilane) [13] and suggests that tacticity has no significant effect on the IP values of organopolysilanes. On the other hand, while the IP values of both poly(methylsilanes) are very similar to that of polysilane (8.01 eV), both poly(phenylsilanes) present a lowering of almost 0.4 eV with respect to polysilane. This different behaviour is due to the appearance of the antibonding interaction between silicon and carbon atoms in poly(phenylsilanes) which produces the destabilization of the HOCO, which is located at k = + ~r/a. This decrease of 0.4 eV is in good agreement with the UPS ionization potentials reported by Takeda et al. [9]. These authors show that in going from poly(dimethylsilane) to poly(methylphenylsilane) a decrease of 0.6 eV in the IP value is observed. The incorporation of a phenyl group in polysilane produces an increase of the EA value. This is an
110 TABLE 1. VEH values calculated for Koopmans' ionization potential (IP) and electron affinity (EA), direct bandgap (Es), bandwidth of the highest occupied or valence band (BW-VB) and bandwidth of the lowest unoccupied or conduction band (BW-CB). All the values are in eV Polymer
IP a
EA a
Eg
BW-VB
BW-CB
Syndiotactic poly(phenylsilane) Isotactic poly(phenylsilane) Syndiotactic poly(methylsilane) b Isotactic poly(methylsilane) b Polysilane b
7.63 7.64 8.06 8.06 8.01
4.09 3.87 4.46 4.19 3.58
3.55 3.77 3.60 3.87 4.50
1.92 1.96 3.30 3.32 4.10
1.30 1.23 1.69 1.52 3.45
"IP and E A values are those obtained for an isolated polymeric chain and no factor has been subtracted to take into account the polarization energy of the lattice, bValues from ref. 13.
expected feature since, as well as for poly(methylsilanes) [13] and unlike polysilane, where the LUCO located at k = 0 comes from the antibonding interaction of the 3p~ orbitals of silicon, in phenylated polymers there is a bonding interaction of carbon 2s with silicon 3s orbitals at the edges of the Brillouin zone which stabilize the crystal orbital at k = +~r/a where the LUCO is now located. In contrast to that found for the IP value, the value calculated for the EA of s-PHPhS (4.09 eV) is 0.22 eV higher than that of i-PHPhS (3.87 eV). This feature is similar to that observed for syndiotactic (4.46 eV) and isotactic (4.19 eV) poly(methylsilane) for which a difference of 0.27 eV was obtained [13]. In both cases, the difference between the EA calculated for syndiotactic and isotactic polymers arises from the fact that in the LUCO of isotactic polymers there is a large contribution from silicon 3s orbitals which produces an increase of the antibonding interactions between silicon atoms along the chain. The difference between the EA values calculated for poly(phenylsilane) and poly(methylsilane) is a consequence of the antibonding interactions between carbon 2s orbitals that take place among the carbons that compose the phenyl group. The decrease of the IP together with the increase of the EA determine that the direct bandgaps calculated for s-PHPhS (3.55 eV) and i-PHPhS (3.77 eV) show an important decrease with respect to that calculated for polysilane (4.50 eV). These values are similar to those obtained for syndiotactic (3.60 eV) and isotactic (3.87 eV) poly(methylsilane) because the decrease of the IP values of poly(phenylsilanes) are compensated by the decrease of the EA values. These trends correlate with reported experimental data from UV absorption spectra of films of poly(methylphenylsilane) [18] and poly(dimethylsilane) [19] which show that the absorption maxima of both polymers coincide (3.63 eV). In conclusion, we stress that the effects of phenyl substitution in polysilane are a decrease of the IP value and an increase of the EA value and, as a consequence, a decrease of the bandgap value. It is also pointed out that the effect in the bandgap value is similar to that obtained previously for methyl substitution. The trends
observed in this study are in good agreement with reported experimental data.
Acknowledgements This research was supported by the Generalitat Valenciana and DGICYT Projects PB91-0935 and OP900042. M.C.P. is grateful to the Ministerio de Educaci6n y Ciencia of Spain for a Doctoral Grant. We thank the Servei d'Inform~tica de la Universitat de Valencia for the use of their computing facilities.
References 1 Proc. Int. Conf. Science and Technology of Synthetic Metals (ICSM '90), Tiibingen, Germany, Sept. 2-7, 1990, Synth. Met., 41-43 (1991); Proc. Int. Conf. Science and Technology of Synthetic Metals (ICSM '92), Gi~teborg, Sweden, Aug. 12-18, 1992, Synth. Met., 55-57 (1993). 2 R.D. Miller and J. Michl, Chem. Rev., 89 (1989) 1359. 3 J.M. Zeigler and F.G. Fearon (eds.), Silicon-Based Polymer Science. A Comprehensive Resource, Advances in Chemistry Series, Vol. 224, The American Chemical Society, Washington, DC, 1990. 4 A. Diaz and R.D. Miller, J. Electrochem. Soc., 132 (1985) 834. 5 K. Yokoyama and M. Yokoyama, Solid State Commun., 70 (1989) 241. 6 R.D. Miller and R. Sooriyakumaran, Z Polym. Sci., Potym. Lett. Ed., 25 (1987) 321. 7 K. Song, R.D. Miller, G.M. Wallraff and J.F. Rabolt, Macromolecules, 24 (1991) 4084. 8 W.J. Welsh, J.R. Damewood, Jr. and R.C. West, Macromolecules, 22 (1989) 2947. 9 K. Takeda, H. Teramae and N. Matsumoto, J. Am. Chem. Soc., 108 (1986) 8186; K. Takeda, M. Fujino, K. Seki and H. Inokuchi, Phys. Rev. B, 36 (1987) 8129. 10 J.W. Mintmire and J.V. Ortiz, Polym. Prepr., 31 (1990) 234. 11 J.M. Andr6, J.L. Br6das, J. Delhalle, D.J. Vanderveken, D.P. Vercauteren and J.G. Fripiat, in E. Clementi (ed.), MOTECC90 (Modem Techniques in Computational Chemistry), ESCOM Science Publishers, Leiden, 1990, Ch. 15, p. 745.
111 12 R. Crespo, M.C. Piqueras, E. Ortf and J.L. Br6das, Synth. Met., 41-43 (1991) 3457. 13 R. Crespo, M.C. Piqueras, E. Ortf and F. Tom,is, Synth. Met., 54 (1993) 173. 14 E. Ortf, R. Crespo, M.C. Piqueras, F. Tomfis and J.L. Br6das, Synth. Met., 55-57 (1993) 4419; R. Crespo, M.C. Piqueras, E. Ortf and F. Tomiis, Synth. Met., 55-57 (1993) 4425. 15 J.M. Andr6, J. Delhalle and J.L. Br6das, Quantum Chemistry Aided Design of Organic Polymers. An Introduction to the Quantum Chemistry of Polymers and its Applications, World Scientific Publishing, Singapore, 1991, Ch. 2, p. 77.
16 J.T. Nelson and W.J. Pietro, Z Phys. Chem., 92 (1988) 1365; J.V. Ortiz and J.W. Mintmire, Z Am. Chem. Soc., 110 (1988) 4522. 17 M.J. Frisch, M. Head-Gordon, H.B. Schlegel, K. Raghavachari, J.S. Binkley, C. Gonzalez, D.J. DeFrees, D.J. Fox, R.A. Whiteside, R. Seeger, C.F. Melius, J. Baker, R. Martin, L.R. Kahn, J.J.P. Stewart, E.M. Fluder, S. Topiol and J.A. Pople, Gaussian 88, Gaussian, Inc., Pittsburgh, PA, 1988. 18 L.A. Harrah and J.M. Zeigler, Macromolecules, 20 (1983) 823. 19 F.C. Schilling, F.A. Bovey, D.D. Davis, A.J. Lovinger and R.B. MacGregor, Jr., Macromolecules, 22 (1989) 4645.
107
VEH electronic band structure of poly(phenylsilane) R. Crespo, M.C. Piqueras, E. O r t f a n d F. T o m , i s Departament de Qulmica Flsica, Universitat de Valdncia, Dr. Moliner 50, E-46100 Burjassot, Valencia (Spare)
Abstract The electronic structure of all-trans syndiotactic and isotactic poly(phenylsilane) has been calculated using the valence effective Hamiltonian (VEH) method. The effects of attachment of the phenyl group on the electronic properties of polysilane are analysed in detail. The VEH results show a decrease of ionization potential and an increase of electron affinity which determine an important reduction of the bandgap. These features are correlated with tr-~- and tr*-~r* interactions between the silicon backbone and the phenyl group.
Introduction Conjugated polymers have been intensively investigated in recent years because of their interesting electronic properties and potential useful applications [1]. These polymers resemble both organic molecular solids with van der Waals contacts between chains and onedimensional semiconductors. Most of the studies on conjugated polymers have been focused on Tr-conjugated systems; polyacetylene, polythiophene and polyaniline are examples of the most investigated ones. Recently, similar electronic properties have been recognized in tr-conjugated polymers, particularly in polysilanes which are high-molecular-weight polymers the backbone of which consists entirely of silicon atoms [2]. These findings together with the development of soluble polysilanes have led to widespread interest in their application as precursors of silicon carbide, polymerization catalysts, photoresists and photoconductors [3]. One of the more interesting features of polysilanes is their unusual electronic spectra. In this context, the thermochromic behaviour of symmetrically substituted poly(di-n-alkylsilanes) in solution and in the solid state has been widely documented [2, 3]. Furthermore, although aryl substituents linked to the silicon backbone by saturated chains have very little effect on the electronic properties, significant spectral changes occur when the aromatic group is directly bonded to the silicon backbone. It has been reported that the oxidation and ionization potentials of poly(methylphenylsilane) films are lower than those presented by simple alkylsubstituted derivatives [4, 5]. Moreover, the electronic spectrum of diaryl-substituted polysilanes shows that the maximum of absorption is located at 390-400 nm [6] while that presented by
0379-6779/93/$6.00
dialkyl-substituted polysilanes in an all-tram conformation appears at 350-380 nm in the solid state [7]. This bathochromic shift has been attributed to the mixing of the tr and ~r* orbitals of the silicon backbone with the ~- and ~r* orbitals of the aromatic substituents. Furthermore, the presence of the two aromatic substituents favours the trans conformation of the polymer backbone, even in solution. In this context, molecular mechanics calculations including full geometry optimization on oligomers of poly(methylphenylsilane) and poly(silastyrene) suggest that the planar zigzag conformation of the backbone is preferred over transgauche or gauche-gauche conformations in both syndiotactic and isotactic isomers [8]. Theoretical calculations on the electronic structure of phenyl derivatives of polysilane have shown that the valence band displays interactions between or electrons of the silicon backbone and ~" electrons of the phenyl group [9, 10]. However, there is a little controversy about the composition of the conduction band. Takeda et al. [9] predict that this band mainly results from the ~-* states of phenyl groups, while Mintmire and Ortiz [10] obtain tr*-w* interactions similar to those observed in the valence band. In this paper, we investigate the effect of phenyl substitution on the electronic structure and optical properties of polysilane. We focus on two structural isomers of poly(phenylsilane), syndiotactic and isotactic. For this purpose, we have used the valence effective Hamiltonian (VEH) technique [11] to calculate the one-dimensional electronic band structure of these polymers in their all-trans conformation. The VEH approach has been successfully applied to silicon-containing polymers [12, 13] and has been shown to provide accurate predictions of essential electronic properties, including
© 1993- Elsevier Sequoia. All rights reserved
108
the energies of the lowest optical transitions [14]. This feature is a clear indication that the VEH technique includes part of the electron-hole correlation into virtual one-electron levels [15].
Results and discussion
The geometrical parameters used to build up the unit cells employed in the electronic band structure calculations have been obtained by optimizing the geometries of both isomers of the closely related molecule 1,2,3-triphenyltrisilane at the ab initio level. We have followed this methodological approach as previous studies on n-oligosilanes have demonstrated that the geometrical parameters calculated for trisilane are almost identical to those obtained for longer n-oligosilanes [16]. This same approach has been previously applied to methyl-substituted polysilanes [13] for which it was found that the calculated electronic properties were in excellent agreement with reported experimental data. All the optimization calculations have been performed using the 3-21G* basis set as implemented in the GAUSSIAN 88 program [17]. This basis has been shown to provide accurate geometrical parameters, particularly those directly related to the silicon atoms [16]. The geometries have been fully optimized maintaining the three HSiC planes parallel to each other (see Fig. 1) in order to reproduce the environment of the -SiHPhunits in the polymer. We have optimized both the up-down-up (R~=Ph, R 2 = H ) and the up-up-up (R~ = H, R2 = Ph) isomers of 1,2,3-triphenyltrisilane because they reproduce accurately the environment of syndiotactic and isotactic poly(phenylsilane), respectively. These isomers only differ in the position of the central phenyl group with respect to the plane of the
R,~ ...-R1
YT ,,...i--"z H
(a)
si
H~si/ / '-Ph H
xp
Ph
Ph
Ph
H
(b)
~Si
,/H / '-Ph H
H
Ph
H
Fig. 1. Geometric parameters used to build up the unit cells of syndiotactic poly(phenylsilane) (a) and isotactic poly(phenylsilane) (b). Distances are in .~ and angles in degrees. Parameters not directly related to silicon atoms are not indicated.
silicon backbone. The parameters chosen to build up the unit cell of the corresponding polymer are those calculated for the central silicon atom. Figure I displays the geometrical parameters obtained for the unit cells of syndiotactic and isotactic poly(phenylsilane). The attachment of phenyl groups induces minor changes on the Si-Si bond length with respect to that obtained for polysilane (2.3456/~) [13]. However, the changes produced in the SiSiSi bond angle are more acute (from 110.91 ° in trisilane to 113.88 ° and 113.26 ° in 1,2,3-triphenyltrisilane isomers) because of the steric hindrance that the phenyl groups in positions 1 and 3 produce. These features are similar to those observed in methyl-substituted oligosilanes [13]. As can be seen, the geometries calculated for both isomers of 1,2,3-triphenyltrisilane are almost identical, except for that which concerns the CSiSi and HSiSi bond angles. While in the up--down-up isomer both angles are very similar (109.29 ° and 108.39°), in the up-up-up isomer the interaction between the three phenyl groups produces an increase of the CSiSi angle (112.84 °) and, as a consequence, a decrease of the HSiSi angle (105.45°). The VEH band structure calculated for syndiotactic poly(phenylsilane) (s-PHPhS) is displayed in Fig. 2. In order to provide an easy comparison, we have also included the band structure previously reported for polysilane [13] and the one-electron energy levels diagram of benzene. All the band structure calculations have been carried out assuming an all-trans conformation of the silicon backbone and taking into account the helical symmetry these polymers present. The energy levels of benzene have been obtained from VEH calculations based on ab initio 3-21G geometry. The band structures calculated for isotactic poly(phenylsilane) (iPHPhS) and s-PHPhS display similar features when the translational unit cell is used. As can be seen in Fig. 2, the band structure of sPHPhS looks quite different from that calculated for polysilane because of the great number of bands that the phenyl group incorporates into the electronic structure. However, the four bands displayed by polysilane can be clearly differentiated in s-PHPhS. Going from the bottom to the top of the valence band structure of s-PHPhS, the first three bands are very narrow because they are localized in the phenyl group and correlate with the lals and lelu levels of benzene. The next four bands (from 4 to 7) come from the le2g and 2alg levels of benzene and the first band of polysilane (which is mainly composed of silicon 3s orbital and weak contributions from hydrogen ls orbitals). A strong interaction of the polysilane band with one of the le2s levels and with the 2alg level is observed. This interaction produces a drastic narrowing of the polysilane band and a shift of the le2g level to lower energies at k = 0, and of the 2a18 level to higher energies at k = + 7r/a.
109 _ _ LUMO
~UCO CO - 0 4J -r-I C'D
653
25
-
HOMO
-0 5O
-
-
_
_
(_1
75
W-I
O0
f
J
lelg
2e2g la2u 2e lblu lb2a 2~lu
J
-1 25 0.0 (a)
le2u '
LUCO - -
E ©-0 4-J co
2blu"
lg
le2g
I
I
I
0.5 k (~/a)
I
.0
0.0 (b)
I
- -
lelu
- -
lalg
I
0.5 k (~/a)
~.0 (c)
Fig. 2. VEH band structures calculated for polysitane (a) and syndiotactic poly(phenylsilane) (b), and V E I l molecular orbital distribution obtained for benzene (c). Energies are in atomic units. Unoccupied bands and molecular levels with energies larger than 0.0 a.u. are not shown. VB denotes valence band and CB denotes conduction band. H O C O (HOMO) and L U C O (LUMO) denote the highest occupied and lowest unoccupied crystal (molecular) orbital, respectively.
The upper band of this group (7) is the first that presents significant contributions from hydrogen ls orbitals of the phenyl group. Bands 8 to 12 correlate with the lblu, lb2u, 2elu and one of the 2e2g orbitals of benzene. The most important contributions to these bands come from C - H interactions. These bands are located at the same energies as their analogue C - H bands in poly(methylsilane) [13]. The next band (13) correlates with the la2u orbital of benzene, which is the first rr orbital. This band presents weak contributions from the silicon 3px orbital (see Fig. 1 for assignment of axes). The 14th band corresponds to the second band of polysilane and results from the bonding interaction of the silicon 3pz orbital with the hydrogen and carbon atoms attached to silicon. As discussed for the first band of polysilane, the width of this band (14) presents a drastic reduction (with respect to that displayed for polysilane), which is more accentuated because of the greater proximity of the adjacent bands. The next three bands (from 15 to 17) come from the lel, levels of benzene (Tr orbitals) and the third band of polysilane (valence band). The central band (16) correlates with the antisymmetric leag level and displays a narrow width as a consequence of the nonparticipation of the 2px orbital of the carbon attached to the silicon atom. The other two bands mainly result from the interaction between the symmetric le,g level of benzene and the 3px orbital of the silicon atom. Bands 15 and 17 correspond, respectively, to the bonding and antibonding interaction between silicon and carbon atoms. As a result, the valence band (17) suffers a shift to higher energies with respect to that of polysilane.
The next four bands (from 18 to 21) are the first unoccupied ones and lie at negative energies and mainly correspond to the antibonding picture of the last four occupied bands. Bands 18 and 19 correlate with bands 17 and 16, respectively, while bands 20 and 21 correspond to bands 14 and 15, respectively. The VEH values obtained for Koopmans' ionization potentials (IP values) and electron affinities (EAvalues), direct bandgaps and bandwidths of the valence and conduction bands of syndiotactic and isotactic poly(phenylsilane) together with those obtained from syndiotactic and isotactic poly(methylsilane) [13] and polysilane [13] are collected in Table 1. As can be seen, the IP values of both s-PHPhS (7.63 eV) and iPHPhS (7.64 eV) are almost equal. This result was also observed for syndiotactic (8.06 eV) and isotactic (8.06 eV) poly(methylsilane) [13] and suggests that tacticity has no significant effect on the IP values of organopolysilanes. On the other hand, while the IP values of both poly(methylsilanes) are very similar to that of polysilane (8.01 eV), both poly(phenylsilanes) present a lowering of almost 0.4 eV with respect to polysilane. This different behaviour is due to the appearance of the antibonding interaction between silicon and carbon atoms in poly(phenylsilanes) which produces the destabilization of the HOCO, which is located at k = + ~r/a. This decrease of 0.4 eV is in good agreement with the UPS ionization potentials reported by Takeda et al. [9]. These authors show that in going from poly(dimethylsilane) to poly(methylphenylsilane) a decrease of 0.6 eV in the IP value is observed. The incorporation of a phenyl group in polysilane produces an increase of the EA value. This is an
110 TABLE 1. VEH values calculated for Koopmans' ionization potential (IP) and electron affinity (EA), direct bandgap (Es), bandwidth of the highest occupied or valence band (BW-VB) and bandwidth of the lowest unoccupied or conduction band (BW-CB). All the values are in eV Polymer
IP a
EA a
Eg
BW-VB
BW-CB
Syndiotactic poly(phenylsilane) Isotactic poly(phenylsilane) Syndiotactic poly(methylsilane) b Isotactic poly(methylsilane) b Polysilane b
7.63 7.64 8.06 8.06 8.01
4.09 3.87 4.46 4.19 3.58
3.55 3.77 3.60 3.87 4.50
1.92 1.96 3.30 3.32 4.10
1.30 1.23 1.69 1.52 3.45
"IP and E A values are those obtained for an isolated polymeric chain and no factor has been subtracted to take into account the polarization energy of the lattice, bValues from ref. 13.
expected feature since, as well as for poly(methylsilanes) [13] and unlike polysilane, where the LUCO located at k = 0 comes from the antibonding interaction of the 3p~ orbitals of silicon, in phenylated polymers there is a bonding interaction of carbon 2s with silicon 3s orbitals at the edges of the Brillouin zone which stabilize the crystal orbital at k = +~r/a where the LUCO is now located. In contrast to that found for the IP value, the value calculated for the EA of s-PHPhS (4.09 eV) is 0.22 eV higher than that of i-PHPhS (3.87 eV). This feature is similar to that observed for syndiotactic (4.46 eV) and isotactic (4.19 eV) poly(methylsilane) for which a difference of 0.27 eV was obtained [13]. In both cases, the difference between the EA calculated for syndiotactic and isotactic polymers arises from the fact that in the LUCO of isotactic polymers there is a large contribution from silicon 3s orbitals which produces an increase of the antibonding interactions between silicon atoms along the chain. The difference between the EA values calculated for poly(phenylsilane) and poly(methylsilane) is a consequence of the antibonding interactions between carbon 2s orbitals that take place among the carbons that compose the phenyl group. The decrease of the IP together with the increase of the EA determine that the direct bandgaps calculated for s-PHPhS (3.55 eV) and i-PHPhS (3.77 eV) show an important decrease with respect to that calculated for polysilane (4.50 eV). These values are similar to those obtained for syndiotactic (3.60 eV) and isotactic (3.87 eV) poly(methylsilane) because the decrease of the IP values of poly(phenylsilanes) are compensated by the decrease of the EA values. These trends correlate with reported experimental data from UV absorption spectra of films of poly(methylphenylsilane) [18] and poly(dimethylsilane) [19] which show that the absorption maxima of both polymers coincide (3.63 eV). In conclusion, we stress that the effects of phenyl substitution in polysilane are a decrease of the IP value and an increase of the EA value and, as a consequence, a decrease of the bandgap value. It is also pointed out that the effect in the bandgap value is similar to that obtained previously for methyl substitution. The trends
observed in this study are in good agreement with reported experimental data.
Acknowledgements This research was supported by the Generalitat Valenciana and DGICYT Projects PB91-0935 and OP900042. M.C.P. is grateful to the Ministerio de Educaci6n y Ciencia of Spain for a Doctoral Grant. We thank the Servei d'Inform~tica de la Universitat de Valencia for the use of their computing facilities.
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