J. Phys. Chem. 1988, 92, 1365-1371 parison to experiment) are due mainly to the neglect of dynamic electron correlation effects (GVB includes only "static" electron correlation effects) as opposed to the basis set truncation. Note that basis set truncation errors are generally much smaller for GVB than for the higher level wave functions including dynamic electron correlation effects. The values of Re and k , calculated with U H F and GVB are of similar accuracy (except for Na2 where U H F is especially poor). In each case, GVB leads to a cohesive energy (0,)that is substantially larger than the U H F value. Although atomization energies are seriously underestimated at the GVB level for both the M2 diatomic molecules and the MN ring clusters, the cohesive energies of the MN ring clusters with respect to dissociation into diatomic molecules MN
-
(N/2)M2
should be much more accurate due to similar dynamic electron correlation energies (per atom or valence electron) for the M, ring cluster and the Mz diatomic molecule. 2. CUI+,Agz', Au2+,Li2+,and Nu2+. For Cu2+,Ag2+,Au2+, Li2+,and Na2+,the GVB results are compared with the available experiment results in Table VIII."*'5-18,27~44 The GVB values of De for Cu2+,Ag2+, Li2+,and Na2+are too small by 32 f 4%, 28 f 275, 5.6%, and 5.9%, respectively (for Au2+,there is no available experimental data). Values of Re and k, have not been determined experimentally for Cuz+, Ag2+,or Au2+. The GVB values of k, for Liz+ and Na2+ are too large by 1.6 f 1.1% and 0.5 f 0.8%, respectively. The GVB values of Re for Li2+ and Na2+ are too large by 2.2 f 0.4% and 1.9 f 0.9%. For Cu2+and Ag2+,the errors in the GVB De values (in comparison to experiment) are mainly due to the neglect of core-core and core-valence electron correlation effects.'' For Liz+, almost (42) Langhoff, S. R.; Bauschlicher, Jr., C. W.; Walch, S.P.; Laskowski, B. C. J. Chem. Phys. 1986,85, 7211. Walch, S.P.; Bauschlicher, Jr., C. W.; Langhoff, S.R. J . Chem. Phys. 1986,85, 5900. (43) Konowalow, D. D.; Olson, M. L. J . Chem. Phys. 1979, 71, 450. Konowalow, D. D.; Rosenkrantz, M. E.; Olson, M. L. J. Chem. Phys. 1980, 72, 26 12. (44) Carter, E. A,, Gcddard 111, W. A., unpublished.
1365
all of the discrepancy between the listed GVB results and the experimental results can be removed with basis set improvements (such as optimizing the p basis scale factor and adding a set of d function^).'^*^^ Appendix D. Localization Transition for Lie The ground-state local electronic structure of each of the Cul0, A&, Ags, Agio, Aula, L&, Lila, LiI4,and Naloring clusters involves valence orbitals centered at bond midpoints for lattice constants ( a )equal to the respective bulk metal nearest-neighbor distances.25 However, in each case, for sufficiently large uniform expansions of the lattice there is a sharp transition from the bond-centered state to the atom-centered state (having valence s orbitals centered at the atoms in the limit as a approaches infinity). GVB-PP potential energy curves showing this localization transition for the Lis ring cluster are presented in Figure 13 for both the low-spin ( S = 0) ground state and the valence electron high-spin state ( S = 4). Results for these GVB-PP states and also for the U H F and GVB-CI(SCF) bond-centered (ground) states are given in Table IX for Lis. The localization transition occurs at a = 1 . 4 2 = ~ ~4.424 8, and at a = 1.374 = 4.457 8, for low-spin Lis and high-spin Lis, respectively. This localization transition is similar to the Mottz metal-insulator transition (both are sharp transitions as a function of a). For one-dimensional monovalent metals, the high-density (bond-centered) states are insulators since there is only one site (bond midpoint) per electron; hence all sites are filled. However, for two- and three-dimensional metals and alloys, analogous localization transitions-triangle-centered to atom-centered for 2D and tetrahedron-centered to atom-centered for 3D,14 both ~ ~ Li-are expected to be true metaloccurring at a = 1 . 4 for insulator transitions since in each case the number of sites per electron is greater than one (two sites/electron for 2D and up to five sites/electron for 3D). Registry No. Cu, 7440-SO-8; Ag, 7440-22-4; Au, 7440-57-5; Li, 7439-93-2; Na, 7440-23-5. (45) Konowalow, D. D.; Rosenkrantz, M. E. Chem. Phys. Lerr. 1979,61, 489.
Mechanism of Extensive Electron Delocalization in Linear Polysilanes Joel T. Nelson and William J. Pietro* Department of Chemistry, University of Wisconsin-Madison, Madison. Wisconsin 53706 (Received: July 20, 1987)
All-electron ab initio electronic structure calculations at the Hartree-Fock/3-21G* level were performed on linear polysilane oligomers, H(SiH2),H of up to n = 6 silicon atoms. Trends in the calculated HOMO-LUMO gap correlate well with trends in the experimental optical transition frequencies. In all cases, the highest n = 1 occupied molecular orbitals are u bonding while the lowest n - 1 unoccupied molecular orbitals are ?r bonding. The u bonding orbitals expand into a high-energy valence band as the chain grows. The atomic orbitals contributing to this band are predominantly located on the silicon atoms, although considerable H 1s interactions are present. This may account for the great variability observed in the physical properties of various long-chain alkyl- and arylpolysilanes. The present calculations also indicate no 3d orbital participation in any of the occupied or n - 1 unoccupied molecular orbitals.
Introduction Long-chain polysilanes comprise a new and exciting class of inorganic polymers.' Synthetic techniques for the formation of peralkyl- and perarylpolysilanes having degrees of polymerization
of up to several thousand are now known.2 One of the most intriguing properties of long-chain polysilanes is their ability to be oxidatively doped with TCNE or TCNQ forming stable, colored, charge-transfer systems3 It has recently been discovered
(1) For recent reviews, see: (a) West, R. C. J . Organomet. Chem. 1986, 300,327-346. (b) Wat, R. C. In Comprehensive Organometallic Chemistry; Wilkinson, G., Stone, F. G. A., Abel, E. W., Us.Pergamon: ; Oxford, 1983; Vol. 9, pp 365-397.
(2) Trefonas, P.; Djurovich, P. I.; Zhang, X.-H.; West, R. C.; Miller, R. D.; Hofer, D. J . Polym. Scf., Polym. Left. Ed. 1983, 21, 819-822. (3) (a) Sakurai, H.; Kira, M.; Uchida, T. J. Am. Chem. SOC.1973, 95, 68264827. (b) Traven, V. F.; West, R. C. J. Am. Chem. SOC.1973, 95, 6824-6825. (c) Nelson, J. T.; Pietro, W. J., unpublished results.
0022-3654/88/2092-1365%01.50/0
0 1988 American Chemical Society
1366 The Journal of Physical Chemistry, Vol. 92, No. 5, 1988 TABLE I: HF/3-21G* Optimized Geometric Parameters for H(SiH,).H (n = 2-5) Polyeilanes’ molecule Si2H6
Darametef rSiSi rSiH
LHSiSi Si3H8
rSiSi rSiH.
rSiHb rSiH,
LSiSiSi
LH,SiH, LH,SiSi LH,SiH,
value
molecule
Darameterc
2.343 1.477 110.3
SipHlo
rsiai,
2.345 1.480 1.477 1.478 1 1 1.2 108.0 110.0 108.4
Si5HI2
rsiai, LSi,Si,Si, rSisSib rsiGi,
LSi,Si,Si, LSi,Si,Si, (Si7H4)k
rSSi rSiH
LSiSiSi LHSiH
Nelson and Pietro TABLE II: Eigenvalues and Types of Interaction for Near Fermi Level Molecular Orbitals
value 2.346 2.346 11 1.2
molecule Si2H6
2.346 2.346 1 11.2 1 11.2 2.264 1.493 1 19.0 100.35
“Bond lengths are in angstroms, angles in degrees. bFully optimized geometry of nll-trans-polysilane using the effective core potential method with the LP-31 basis set (see ref 15). CThe notation for the symmetry-equivalent atoms is as follows:
that the high molecular weight polymers become electrically semiconductive when doped with AsF, or SbF5, with holes being the charge carriers.Ia This is truly unique. Of the few known polymeric conductors,4 all are believed to conduct via extensively delocalized ?r electrons (such as in poly(su1fur nitride), (SN),,5 polyacetylene, (CH),? polypyrrole,’ etc.) or via electrons delocalized in overlapping transition metal d orbitals (such as in Krogmann’s salt, K2Pt(CN)4-Bro,3S).However, polysilanes, being completely saturated systems, must conduct through extensive u delocalization. It has been speculated that the silane backbone is considerably polarizable, suggesting polysilanes should be excellent candidates for nonlinear optical ~ t u d i e s . ~ Previous theoretical studies have been undertaken at various levels lower than the present contribution. These have ranged from parametrized ~emiempirical~~~~-’*J~J~ and tight-binding band calculation^'^ to more rigorous pseudopotential m e t h o d ~ ’ ~which J ~ only explicitly include valence electrons in the SCF procedure. Due to the high density of states near the HOMO and LUMO levels, small geometry changes could quite possibly affect the energy ordering of the molecular orbitals (MO’s).’O At the HF/3-21G* level, (4) Miller, J. S., Ed. Exrended Linear Chain Compounds; Plenum: New York, 1982; Vol. 1-3. ( 5 ) Labes, M. M.; Love, P.; Nichols, L. F. Chem. Reo. 1979, 79-1-15. (6) MacDiarmid, A. G.; Heeger, A. J. Synrh. Mer. 1979/80, 1, 101-1 18. (7) Diaz, A. F.; Kanazawa, K. K.; Gardini, G. P. J . Chem. SOC.,Chem. Commun. 1979, 635-636. (8) (a) Krogmann, K.; Hauser, H.-D. Z.Anorg. Allg. Chem. 1968,358, 67-81. (b) Abys, J. A.; Enright, N. P.; Gerdes, H.M.; Hall, T. L.; Williams, J. M. Inorg. Synrh. 1979, 19, 1-57. (c) Miller, J. S.Science 1976, 194, 189. (d) Bernasconi, J.; Breusch, P.; Kuse, D.; Zeller, H. R. J . Phys. Chem. Solids 1974, 35, 145-157. (9) (a) Bigelow, Richard W.; McGrave, Kathleen, M. J. Polym. Sci., Polym. Phys. Ed. 1986, 24, 1233-1245. (b) Kajzar, F.;Messier, J.; Rosillo, C. J. Appl. Phys., 1986, 60, 3040-3044. (10) Hale, P. D.; Pietro, W. J.; Ellis, D. E.; Ratner, M. A,, submitted for publicat ion. (1 1) Damewood, James, R.; West, Robert Macromolecules 1985, 18, 159-1 64. (12) Takeda, K.; Matsumoto, N.; Fukuchi, M. Phys. Reu. B Condens. Marrer 1984, 30, 5871-5876. (13) Takeda, K.; Teramae, H.; Matsumoto, N. J . Am. Chem. SOC.1986, 108, 8186-8190. (14) Klingensmith, K. A.; Downing, J. W.; Miller, R. D.; Michl, J. J . Am. Chem. SOC. 1986, 108, 7438-7439.
molecular orbital
irreducible representation
eigenvalues, eV
LUMO I LUMO HOMO HOMO - 1 HOMO - 2
5azy 5% Sal, 4% 3%
t4.2 +4.0 -1 1.o -12.9 -13.7
LUMO t 1 LUMO HOMO HOMO - 1 HOMO - 2
5b1 1 2a1 8b2 1l a , 4bl
LUMO t 2 LUMO t 1 LUMO HOMO HOMO - 1 HOMO - 2 HOMO - 3 LUMO t 3 LUMO t 2 LUMO + 1 LUMO HOMO HOMO - 1 HOMO - 2 HOMO - 3 HOMO - 4
+
+ + +
LUMO 4 LUMO t 3 LUMO 2 LUMO 1 LUMO HOMO HOMO - 1 HOMO - 2 HOMO - 3 HOMO - 4 HOMO - 5
Si-Si
Si-H
U*
U*
lr
U*
U
U
a*
U
lr*
U
+3.8 +3.4 -10.5 -1 1.5 -12.8
a a
U*
U
U
5% 14a, 13bu 13a, 12a, 12b, 4b,
+3.7 +3.6 +2.9 -10.1 -11.5 -11.7 -12.8
a
U*
lr
U*
7r
U
U
U
14b2 7bl 19al 18a, 13b2 17al 16al l2b2 6bl
t3.7 +3.7 t3.5 +2.6 -9.8 -11.3 -11.6 -11.7 -12.8
a
U*
lr
U*
H
U*
7b, 7% 20a, 20b, 19bu 19a, 18b, 18a, 17b, 17a, 6b,
+3.7 +3.7 +3.5 +3.4 t2.4 -9.6 -11.1 -1 1.4 -1 1.7 -11.9 -12.8
U
U U
U U
U U
a
U
U
U
U U U
U U
a
U*
lr
U*
a
U*
a
U*
lr
U
U
U
U
U U
U
U U
all electronic interactions are explicitly calculated, enabling quantitative determination of the energy and atomic orbital composition of each occupied MO, as well as the ground-state geometry of the molecule. The nature of the bonding interactions as well as the energy ordering of the low-energy virtual orbitals has not been well-characterized. While at the Hartree-Fock (HF) level it is not possible to assign an exact energy ordering of the LUMO states, it nevertheless provides qualitative information concerning the atomic orbital contributions to those low-energy unoccupied MO’s. The magnitude of the Si-H interactions can likewise be accurately determined. It is quite possible that the magnitude of such interactions in the high-energy occupied manifold account for the great variability observed in the physical properties of various high molecular weight alkyl- and aryl-substituted polysilanes. Computational Methods
Closed-shell restricted Hartree-Fock calculations were performed on a VAX 8600 computer using the GAUSSIAN 82 system of programs.” Full geometry optimizations were performed on the linear polysilane oligomers, H(SiH,),H for n = 2-4, using a 3-21G* split-valence basis set which has a complete set of six supplementary d Gaussians. The 3-21G* basis set has been shown (15) Teramae, H.; Yamabe, Y.; Imamura, A. Theor. Chim. Acto 1983, 64, 1-12.
(16) Bigelow, Richard W. Chem. Phys. Leff. 1986, 126, 63-38. (17) Binkley, J. S.; Frisch, M. J.; DeFrees, D. J.; Drishnan, R.; Whiteside, R. A.; Schlegel, H. B.; Fluder, E. M.; Pople, J. S.GAusslAN 82; CarnegieMellon University: Pittsburgh, PA, 1982.
Electron Delocalization in Linear Polysilanes
The Journal of Physical Chemistry, Vol. 92, No. 5, 1988 1367 I
I
n
TABLE 111:
Calculated and Experimental Ionizdtion Potentials for Silane Oligomers,H(SiH2),,H IP,eV
n
exptl'
calcdb
2
10.75
11.0
3
10.09 10.97
10.5 11.5
4
9.85 10.65 11.12
10.1 11.5 11.7
9.61 10.25 10.70 11.oo
9.81 11.3 11.6 11.7
5
"See ref 28.
Koopmans' theorem ionization potentials.
to produce calculated geometries in excellent agreement with experimental structures for molecules containing second-row elements.18 For H(SiH2)5Honly bond lengths and angles to heavy atoms were optimized; bond lengths and angles to hydrogen were fixed at those values obtained from the smaller oligomers. For H(SiH2)6H,only a single-point calculation was performed. Bond lengths and angles were fixed at those values obtained from the smaller oligomers. All oligomers were constrained to maintain the all-trans configuration. Results and Discussion Optimized bond lengths and angles for H(SiH2),H ( n = 3-5) are presented in Table I. Energy eigenvalues, irreducible representations, and types of interactions for the few highest occupied and lowest unoccupied molecular orbitals of each oligomer are shown in Table 11. Comparison of Koopmans' theorem ionization potentials with photoelectron spectroscopy data is shown in Table 111. In the 3-21G* basis set the valence atomic orbitals (3s and 3p for silicon, 1s for hydrogen) are split into outer and inner shells of one and two Gaussian expansions, respectively. This gives the basis set great flexibility in that the size of an atomic orbital is actually optimized during the S C F procedure. Unfortunately, split-valence LCAO combinations are quantitatively difficult to interpret. For this reason, the values in Table IV, the 4a Salg, and 5% M O s for disilane, are condensed atomic orbital coe#cients in the respective molecular orbitals. These condensed coefficients are simply the sums of the outer and inner valence orbital coefficients. It is important to note that in all of the molecular orbitals in Table IV the inner and outer Gaussians have the same sign, since condensed orbital coefficients can occasionally be misleading when the inner and outer Gaussian have opposite signs. Attempts to explain interesting effects concerning silicon compounds frequently invoke controversy over d orbital participation.98*12,16s'9*23 It is therefore important to note that our calculations fail to indicate any nonnegligible d orbital involvement in the occupied or the low-energy unoccupied manifold of any of the oligomers calculated in this contribution. Consequently, our results indicate no d orbital participation in the mechanism of electrical conductivity in polysilanes. In a supplemented basis set, such as 3-21G*, there are six d Gaussians. Three of them, d,, d,, and dyz,have the familiar "four-leaf clover" shape, while the remaining three, dX2,dyz, and dZ2, more closely resemble p functions in shape, with the exception that they do not change (18) Retro, W. J.; Francl, M. M.;Hehre, W. J.; DeFrees, D. J.; Pople, J. A.; Binkley, J. S. J . Am. Chem. SOC.1982, 104, 5039-5048. (19) Halevi, E. A,; Winkelhofer, G.; Meisl, M.; Janoschek, R. J Orgunomet. Chem. 1985, 294, 151-161. (20) Bock, H.;Ensslin, W. Angew. Chem., Inr. Ed. Engl. 1985, 10, 404-405. (21) Nelson, J. T.; Fleck, L. E.; Pietro, W. J., manuscript in preparation (22) Shizuka, H.; Sato, Y.; Veki, Y.;Ishikawa, M.; Kumada, M. J . Chem. SOC.,Faraday Trans. 1 1984,80, 341-357. (23) Berkovitch-Yellin; Ellis, D. E.;Ratner, M. A. Chem. Phys. 1981, 62, 21-3.5.
WIUWIK
.-llICllD*
rnrirr
Figure 1. Model for conduction mechanism via extensive u delocalization in infinite-chain polysilanes.
phase through the nodal plane. Any equally weighted linear combination of these latter three d orbitals results in the formation of an additional s function. Consequently, whenever symmetry allows for s orbital mixing, these three d orbitals will necessarily attain nonzero coefficients. Therefore, the d orbital coefficients presented in Table IV have been corrected so as to represent true d symmetry contributions. Any combinations of d2, d?, and d,z leading to pseudes formation have been subtracted out. The result is that, in each of the three molecular orbitals presented in Table IV, only one d atomic function actually contributes (d,Z, d,z, and d,, respectively), and does so negligibly. Indeed, it has been previously shown that d orbitals are not important in describing bondii:g and reactivity in disilane, as is best demonstrated by the negligible difference (3 kcal/mol) in calculated hydrogenation energies obtained by using 3-21G and 3-21G* basis sets.'* In dimethyl sulfone, a typical hypervalent molecule, this difference is 97 kcal/mol.'* Although d orbital supplementation does produce a small but nonnegligible geometric change in Si2H6(Ars,-sl = 0.04 A, ArS,-H= 0.01 A),'8 this is entirely due to pseudo-s contribution as described earlier. Valence Band Structure in Linear Polysilanes The conductivity model we are employing assumes that extensive electron delocalization occurs along the chain axis and is mediated by substantial overlap between occupied molecular orbitals constituting adjacent Si-Si u bonds, as illustrated in Figure 1. Accordingly, analysis of the calculated electronic structure of disilane reveals two occupied molecular orbitals (4al, and 5al of Si-Si u symmetry, both of which exhibit considerable amplitu e along the Si-Si interatomic axis. The atomic orbital contributions to these two molecular orbitals, as well as the LUMO, appear in Table IV. We will focus primarily on the Sa,, M O since our model asserts that this orbital gives rise to the conduction band in the long-chain polymer. It is important at this point to contrast the u system of disilane with that of ethane. The Sal, MO of disilane is analogous to the 3al, occupied M O of ethane; however, their energies and radial extents are significantly different. First, the Salg M O of Si2Hs is the HOMO and is considerably higher in energy (by 1.9 eV) than the rest of the orbitals in the occu ied manifold, whereas in C2H6the 3al, M O is the third hig est occupied. (The HOMO is leg.) Second, the 5al, M O of Si2H6 is much more diffuse than the 3a,, M O of C2H6,as shown by the orbital amplitude contour diagrams in Figure 2. The high energy and large radial extent of the 5al, Si2H6HOMO support the assertion that end-on overlap of adjacent Si-Si u molecular orbitals is responsible for valence band formation in long-chain polysilanes. The highest two molecular orbitals of trisilane, Si3Hs, are of a l and b2 representations and are both u bonding between the central and terminal silicon atoms. (See Figure 3 for orbital contour diagrams.) The lower energy a, M O is composed primarily of a 3sp, hybrid on the central silicon (the chain axis is parallel to the y coordinate axis and lies in the yz plane) overlapping in a bonding fashion with an in-plane p function on each terminal silicon, as illustrated in the LCAO dissection in Figure 3C. The b2 HOMO is composed of a pure 3p, atomic orbital on the central silicon bonding with a 3sp3 hybrid on each terminal silicon (Figure 3B). Referring to the energy level diagram in Figure 6b, it can be seen that these two molecular orbitals are
d
R
1368 The Journal of Physical Chemistry, Vol. 92, No. 5, 1988
Nelson and Pietro
TABLE I V LCAO Coefficients for Disilane Molecular Orbitals
Si" MO
eigenvalue, eV
type
3s
3P*
4a1, 5a1,( HOMO) 5e,( LUMO)
-20.6 -1 1.o 4.0
SiSi u bond SiSi u bond SiSi u bond
0.407 0.134
0.050 0.537
H"
3Px
3PY
3db
1s
0.893
0.013(dZz) 0.090(dZ2) 0.095 (d,)
0.150 0.199 0.525.
OThese are condensed orbital coefficients, that is, the sum of the coefficients of the outer and inner valence shells. bThese numbers represent a combination of all six d orbital coefficients corrected for pseudo-s formation (see text).
si-
-SI
A n
B C
P'
JoCo
n
0 SI-
n
Figure 2. Orbital amplitude contours and LCAO dissections for (A) 5al, (HOMO), (B) 5% (LUMO) of Si2H6,and (C) 3al, of C2H6. Outermost contour represents J, = 0.03, and each subsequent contour is spaced by 0.03.
energetically well above the rest of the MO's in the occupied manifold. The electronic structure of tetrasilane, Si4HI0,has the three highest occupied molecular orbitals all involved with the Si-Si Q network, and at this point it becomes clear that a well-defined set of n - 1 high-energy u molecular orbitals, all directed along the oligomeric backbone, is forming as the chain grows. Orbital amplitude contours and LCAO dissections for these three MO's appear in Figure 4, and the valence manifold energy level diagram is included in Figure 6. Incrementing the chain by one more silyene unit (-SiH2-) adds another member to this high-energy set of u bonding orbitals. This trend suggests that the set of n - 1 high-energy u orbitals will expand into a quasi-continuum of finite width as the chain length approaches infinity. This conclusion is in accord with photoelectron studies indicating the highest several molecular orbitals of polysilanes are essentially Si-Si bonding,*O as well as with recent ab initio and semiempirical s t ~ d i e s . ~ - 'The ~ resulting quasi-continuum becomes a valence band and mediates charge transport when nonstoichiometricallyoxidized by p-type dopants. Such an effect is a direct consequence of the relatively high energy
C Figure 3. Orbital amplitude contour and LCAO dissections for (A) 12a, (LUMO), (B) 8b2 (HOMO), and (C) l l a , (HOMO - 1) of Si,H,. Outermost contour represents J, = 0.03, and each subsequent contour is spaced by 0.03.
and highly diffuse nature of the Si-Si u bond, as detailed earlier for disilane, and is not realized in polyethylene. Conduction Band Structure As alluded to earlier, the level of the present calculations precludes definite energy ordering of the LUMO states. It is nonetheless possible to .make qualitative statemenets concerning their nature. For each oligomer calculated, the n - 1 LUMO states, also being highly delocalized, are composed primarily of in-phase combinations of out-of-plane p orbitals on each Si (the remaining contribution consisting of Si-H antibonding interactions); only slightly higher in energy (ca. 0.5 eV) were the strongly destabilizing Si-Si u* MO's. This ordering is essentially in accord with recent minimal basis CND0/2(S+DES CI) calculations
The Journal of Physical Chemistry, Vol. 92, No. 5, 1988 1369
Electron Delocalization in Linear Polysilanes .,......'..
various donor and acceptor species bound to a disilane linkage. In all cases where the disilane functioned as an acceptor, a shortening of the Si-Si bond length was noted. This would be expected if the LUMO was indeed significantly bonding in character. The results of a recent experiment performed by Shizuka and co-workers22is also in accord with our claim. Shizuka's experiment involved examining the charge transfer (CT) fluorescence of two aromatic disilanes, mesitylpentamethyldisilane (l),in which the disilane substituent is normal to the ring plane, and phenylpentamethyldisilane (Z), where the disilane group and the ring are coplanar. The experiment entailed the excitation of a ring T-T* transition, an intramolecular CT to a state localized on the disilane, followed by an intense fluorescence. Charge-transfer fluorescence was observed only in the case of 2. The CT mechanism cannot be via the Si-Si B* orbital, since it is incapable of overlap with the aromatic 7r* system in 1. Shizuka therefore suggests a ring 2pa* Si 3d CT methanism; a silicon-centered d orbital has proper symmetry to overlap with the aromatic a* systems efficiently in 2 but not in 1. We propose, however, that ring disilane CT fluorescence actually occurs through aromatic a* overlap with the two lowest (nearly degenerate) unoccupied Si 3p7r). These two Si-Si 3pa bonding orbitals (ring 2pa* M O s are perpendicular to one another and would have analogous symmetry to a silicon d orbital a t the point of attachment to the ring. Accordingly, these orbitals would be capable of efficient interaction with the aromatic a* system in the in-plane 2 configuration but not in the out-of-plane 1 configuration, as illustrated in Figure 7. The important conclusion is that there is both an experimental and a theoretical precedence for the existence of a low-energy virtual a bonding manifold in polysilanes. This is very exciting, for it implies the possibility of creating novel electrically conductive n-doped polysilanes. Although cyclic polysilanes are readily red ~ c e dexperimental ,~~ attempts to reduce linear polysilanes, even under rather mild conditions such as cyclic v ~ l t a m m e t r y have ,~~ resulted in degradation of the polymer. A reasonable explanation for this apparent anomaly is a result of (1) the very high density of LUMO states" and (2) the presence of the low-energy B* manifold. Quite likely in the long-chain polymer, the 7r and t ~ * bonds overlap, precluding the possibility of selectively populating the a band only. Thus, any attempt to reduce linear polysilanes will likely significantly populate strongly destabilizing B* orbitals, resulting in degradation of the polymer.
._.._.....' .
A
-
-
C Figure 4. Orbital amplitude contour and LCAO dissections for (A) 13a, (HOMO), (B) 12a, (HOMO - l), and (C) 12bl (HOMO - 2) of Si4HI0. Outermost contour represents # = 0.03, and each subsequent contour is spaced by 0.03.
n
Significance of the Si-H Interactions In both the n - 1 highest occupied and n - 1 lowest unoccupied orbitals significant Si-H interactions are present. A close examination of Figure 4 reveals an apparent anomaly in the order of the MO's for tetrasilane. The lowest energy member of this set, 12b,, has a nodal plane passing through the two central silicon atoms, whereas 12a,, the next higher energy MO, is nodeless about all four silicons. The reason for this counterintuitive ordering is revealed by rotating the contour plane of Figure 4 to include a terminal silicon and its two out-of-plane hydrogens. Figure 5 clearly shows that the 12b, MO involves strong B bonding interactions between the terminal silicons (Si,) and their out-of-plane hydrogens, while the 12, MO is only weakly Si,-H bonding. The anomalous ordering therefore arises from the fact that the high-energy set of Si-Si B bonding molecular orbitals is coupled strongly with the Si-H B system. This implies that physical properties of polysilanes should be governed to some extent by the nature of the side chain groups. Diaz and co-workers have recently demonstrated that the electrochemical properties of polysilanes are largely determined by the nature of the side groups.2s Substituent studies on the electronic spectra of silane polymers afford a similar conclusion.2 We therefore propose that polysilanes with large aromatic substituents, being quite readily
'..___--Figure 5. Orbital amplitude contour and LCAO dissections for (A) 12a, (HOMO - 1) and (B) 12b, (HOMO - 2) of Si4Hlo. Outermost contour represents 9 = 0.03, and each subsequent contour is spaced by 0.03.
performed by Bigelow which suggest that the LUMO of H(SiH2)9H is composed of similar orbital interactions as reported above, however the dominant interaction being Si-H antibonding.16 Others have suggested the LUMO states are primarily B * ~ in nature. Importantly, there is both theoretical and experimental evidence which suggest the presence of a low-energy a manifold. In a separate contribution2*we have performed calculations on
-
~
-
~
~
~
~
(24) Carberry, E.; West, R. C.; Glass, G. E. J. Am. Chem. SOC.1969, 91, 5446-545 1. ( 2 5 ) Diaz, A.; Miller, R. D. J . Electrochem. SOC.1985, 132, 834-837.
1370 The Journal of Physical Chemistry, Vol. 92, No. 5, 1988 a -
b -
Si2H6
s i 3Hg
Nelson and Pietro
Si4H10
+3.8
5bl +3.7 +3.6
+3.4
-d
C -
e -
Si6H14
Si5H12
5au 14ag
+3.5
14b2 7b 1 19a1
+2.6
18a 1
+3.7
12al
+2.9
UNOCCUPIED MAN I FOLD
_________--
-
- - - ---
-12.9-
-13.7
8b2
-12.8
4b1
--eg
-
-3e
20ag 20bu
+2.4
19bu .-
-9.6
19ag
-12.8
6% 6a
---------________ 9.8
-10.5
t3.5 +3.4
13bu
HIGH-ENERGY OCCUPIED MAN I FOLD -10.1
+3.7
13b2
13ag
-12.8
4bg
-13.0
4a u
-13.2 -13.3
;ii
-13.3
llbu
-13.5
loa1
-13.4
llag
-13.9
3b 1
-12.8 -12.9 -13.2 -13.3
6bl 4a2
"
5b ;1 ::
-l3'-16b:
9
Figure 6. Energy level diagram for polysilane oligomers H(SiH2),H with n = (a) 2, (b) 3, (c) 4, (d) 5 , and (e) 6 . All energies are in eV.
0
maximizing electrical conductivity?J4 Enhanced photoconductivity in aromatic polysilanes has recently been observed and is under current investigation in our laboratories.26
/
Trends in Electronic Spectra
A
0
-
Figure 7. (A) Orbital interactions involved in a ring 2pa* Si 3sa* CT mechanism. CT fluorescencewould be expected only for 1. (B) Orbital Si 3pn CT mechanism. CT interactions involved in a ring 2pn* fluorescence is expected only for 2. Shizuka's experimental results support this mechanism.
-
oxidized, will show enhanced electrical conductivity. Important also is that bulky aromatic substituents would tend to sterically enforce a nearly all-trans conformation, a crucial requirement for
The trends in the electronic spectra of polysilanes have been well-characterized, The increasing red shift of the first electronic transition with increasing chain length is remarkably similar to that of conjugated polyenes and led to the introduction of the concept of a d e l ~ c a l i z a t i o n . ~Bigelow16 ~ and Halelo have each recently reported calculations on silane oligomers using methods specifically parametrized for predicting optical transitions. These, along with our results, are presented in Table V. Although electronic and geometric relaxation effects preclude accurate agreement of the wavelengths of electronic transitions (26) Bartz, J. A., private communication. (27) (a) W a t , R.C.; Carberry, E. Science 1975,189, 179-186. (b) West, R. C . Pure Appl. Chem. 1982,54, 1041-1050. (c) Sakurai, H. J . Orgammer. Chem. 1980, 200, 261-286. (28) Bock, H.; Ennslin, W.; FehEr, F.; Freund, R. J . Am. Chem. Soc. 1976, 98, 668-674.
J . Phys. Chem. 1988, 92, 1371-1377
TABLE V: Calculated and Observed Optical Transitions in Polysilane Oligomers, H(SiH2)fl nm calcdb
, , ,X n
exptl"
2 3 4 5 6
