J . Phys. Chem. 1994,98, 8693-8698
8693
A Quantum Mechanical Investigation of Silsesquioxane Cages Clarke W. Earley Department of Chemistry, University of Missouri-Kansas
City, Kansas City, Missouri 641 10
Received: June 4, 1994”
Electronic structure calculations have been performed on a series of molecular silsesquioxane cages [HSiOl,s], ( n = 4, 6 , 8, 10, and 12) using a b initio quantum mechanical methods to examine factors that determine the relatively stability of different sizes of silicon oxide cages. While previous a b initio studies have been reported on the relative stability of molecular silicate rings, silsesquioxane cages are expected to be better models for solid-state silicates due to their rigidity and more similar molecular environment. To determine the relative stability of silicate cages, calculated total energies a t optimized geometries (6-31G(d)//6-3 lG(d)) for a series of silsesquioxane cages were compared. Consistent with both experimental observations and prior theoretical investigations, molecules containing (Si-O-)3 rings were calculated to be significantly less stable than molecules containing only larger rings. Much smaller differences in relative stability were calculated to occur between larger cages that do not contain this type of ring.
Introduction The structural diversity of zeolites is well-known.’ To aid in understanding and classifying these structures, zeolites are often described in terms of “secondary building units” such as rings and cages.2 Inherent in this approach is the implicit assumption that the relative stability of different zeolite structures should be related to the relative stability of these building blocks. With few exceptions, these secondary building units consist of one or more rings1 which contain 4, 5, or 6 tetrahedral atoms (Si, Al, P, etc.) connected by an equal number of bridging oxygen atoms. Given their widespread occurrence in zeolites, it is not surprising that several theoretical studies3 of the relative stability of silicon oxides containing different ring sizes have been reported. Using the series of molecular rings [R2SiO], (R = H, OH) as models? the calculated relative stabilities of (Si-&)” rings obtained from previous theoretical investigations appear reasonable. For example, the cyclic trimer was calculated to be significantly less stable than any of the larger rings. This is the expected result, since three-membered rings5 are only rarely observed in zeolite materials.6 Much smaller differences were found between the larger rings, consistent with the structural diversity observed in solid-state silicon oxide structures. The use of molecular rings as models for solid-state materials has one potentially serious limitation: The inherent flexibility of rings contrasts to the rigidity of zeolites. For example, a study of the vibrational spectra of a series of cyclic dimethyl siloxane^^ determined that molecules larger than [MezSiO]3 could not be fit to any definite symmetry, which was interpreted to indicate that these molecules possess a high degree of flexibility. A theoretical investigation of H6Si303 indicated4athat, even in this molecule, only small energy differences were found upon distortion from the equilibrium geometry. In the majority of theoretical investigations reported to date, the flexibility of the rings investigated were artificially restricted by the use of C, symmetry constraints, with “n” set equal to the number of silicon atoms in the ring. However, the gas-phase electron diffraction data8 for the cyclic tetramer [H2Si0]4 indicate this molecule possesses S4 symmetry, with both silicon and oxygen atoms alternating above and below the Uh plane. A molecular mechanics study9 of nine conformations of the Me~Si404molecule correctly reproduced the& minimum and found the C4,isomer to be the highest energy conformation examined. It is unlikely that the most stable configurations for the remaining larger rings maintain the
* Abstract published in Aduance ACS Abstracts, July 15, 1994. 0022-3654f 94/2098-8693%04.50/0
arrangement of silicon and oxygen atoms imposed by the C , symmetry constraints either. These observations suggest that use of more rigid models might be advantageous. A few workers have performed quantum mechanical investigations on extended siliconoxide solids. Lacks and Goldon reportedlo calculations on quartz, cristobalite, and sodalite using a nonempirical ionic model which these workers modified to include effects of electron polarization. Ooms et al. have reported” extended Huckel calculational results comparing energies of different solid-state silicate structures. Hess and co-workers very recently reported12 results from a STO-3G calculation on solidstate silicalite and analcime using the periodic Hartree-Fock program CRYSTAL.13 Vetrivel and co-workers have reported14 a novel approach to examine reaction mechanisms in zeolites in which a limited number of atoms (C20) are treated using a STO3G or 3-21G basis set, and a much larger portion of the zeolite framework is modeled using point charges. In the present study, a theoretical investigation of the dependence of the relative stability of silicate rings on ring size has been performed using molecular silsesquioxane cages, with the aim of understanding factors that govern the relative stability of zeolites and related silicates. Calculations have been performed on silsesquioxane cages having the general formula [HSiO& A number of these molecular cages and closely related derivatives have been synthesized and characterized.15 Idealized geometric structures of cages with R = H are shown in Figure 1, and selected experimentally determined geometric parameters for several representative cages are summarized in Table 1. The existence of these molecular cages allows a direct comparison of the computational results with experimental values. In addition to being more rigid than single-ring systems, silsesquioxanes more closely approximate the molecular geometry around each silicon atom than is found insilicates [R2Si(OSi)2/2(rings) vs RSi(OSi)3/2 (cages) vs Si(OSi)4/2 (silicates)]. While a large number of calculations on disiloxanes and molecular siloxane rings have appeared, relatively few quantum mechanical calculations on molecular silsesquioxane cages have been reported. Calzaferri and Hoffman16 reported a study of the mechanism of substitution reactions on XsSi8012 (X = H, C1, and CHs) using the extended Huckel method. Carson et aI.l7 reported atomic charges in a CNDO/2 investigationof H8Si801Z. Mortlock et a1.18 correlated atomic charges from MNDO calculations with 29Si N M R chemical shifts for a series of silicate and aluminosilicate anions, including [(O)Si(p-0)1.,],* ( n = 6 and 8). Earley19 studied the relative stability of [R8A13ie_x012]X0 1994 American Chemical Society
8694
Earley
The Journal of Physical Chemistry, Vol. 98, Nc?. 35,1994
0
U
Osil Ool 5
D6h-H12sil 2O18
D2d-H12Si12018
Figure 1. Idealized geometries of silsesquioxanecages [HSiOl.s],, examined in this investigation. Large filled spheres represent silicon atoms, medium open spheres represent bridging oxygen atoms, and small lightly shaded spheres represent terminal hydrogen atoms.
TABLE 1: Selected Geometric Parameters from Experimentally Determined Structures for [RSiOl.& Cages n R molecule SiSi-OSib O-.@ ref 1.64 1.608 1.619 1.61 1.604 1.613 1.616 1.612, 1.601 1.604 1.611
131, 141 150.4 147.5 145 148.2 148.5 148.9 154.7, 149.5 155.0, 149.3 150.5
2.64 d 2.608 e 2.644 f 2.65 g 2.626 2.635 2.625 2.614 2.622
h i j
the computational effort required and accuracy of calculated energies. While the use of R = OH- might be preferable to using H-as the “capping”group, this substitution would result in systems that are simply too large to be conveniently examined using available computational resources at the desired level of theory. Geometric results for a range of silsesquioxane cages (see Table 1) suggest that substitution of different terminal groups has only minor consequences.
k
Computational Methodology
1
Calculations were performed primarily on a Digital Equipment Corporation ALPHA AXP-3000 using the G A M E S S program. ~~ A few calculations were performed on a CRAY-YMP4/464 using the G ~ u s S 1 ~ N - program. 92~~ For oxygen and hydrogen, the 6-3 1G(d) basis set of Pople et al. was ~ s e d , 2while ~ for silicon, Gordon’s 6-31G(d) basis set28was used. While this combination is the default 6-3 1G(d) basis set in the GAMESSprogram, GAUSSIAN-92 uses slightly different values for silicon.29 Perhaps the most important difference between these basis sets is the value used for the polarization exponent ( a d ) on silicon: Gordon’s basis set uses a value of a d = 0.395, while Pople’s basis set uses a value of a d = 0.45. Gordon’s parameters were chosen for the present investigation because calculations using this basis set on the H3SiOSiH3 molecule predicted30 a Si-0 bond length (1.638 A) and S i - o S i bond angle (153.4’) in somewhat better agreement with the gas-phase electron diffraction structure3l( 1.634 A and 144.1O , re~pectively).~~ To maintain consistency, the selected 6-3 1G(d) basis set was added as a “GENERAL” basis set in all GAUSSIAN-92 calculations. This basis set includes a set of six d-type polarization functions on both silicon and oxygen. Due to the size of the larger molecules, all calculations were performed using direct S C F procedures.33 Molecular geometries were fully optimized within the indicated symmetry constraints by optimization of Cartesian coordinates using Baker’s meth0d.3~ The convergence criteria used with the GAMESS program required that both the maximum and rms gradient components be less than 10-4 and l / 3 X 10-4 au, respectively (default values). Geometry optimizations with the GAuSSIAN-~~ program utilized the “Berny”optimization method35 and used slightly less stringent convergence criteria for these forces (4.5 X 10-4and 3.0 X 10-4au for maximum and rms forces, respectively). GAUSSIAN-92also examines the maximum and RMS calculated displacements of coordinates, which were required to be less than 1.8 X and 1.2 X l t 3 , respectively. Force calculations were performed on H4Si406, H6Si609, and the Oh isomer of H8Si8012 to characterize the stationary points obtained.
m
Average Si-Ob bond lengths in angstroms. Average S i - O b S i bond angles in degrees. Average nonbonding O--O distances in angstroms. Smolin, Yu. I.; Shepelev, Yu. F.; Ershov, A. S.; Hoebbel, D.; Wieker, W. Kristallografiya 1984,29,712.e Smolin, Yu. I.; Shepelev, Yu. F.; Pomes, R.; Hoebbel, D.; Wieker, W. Kristallografiya 1979, 24, 38. JHeyde, T. P. E.; Biirgi, H.-B.; Biirgy, H.; Tbrnroos, K. W. Chimia 1991, 45,38.g Larsson, K.Ark. Kemi 1960,Z6,203.I , Day, V. W.; Klemperer, W. G.; Mainz, V. V.; Millar, D. M. J . Am. Chem. SOC.1985,107,8262. Hossain, M. A.; Hursthouse, M. B.; Malik, K. M. A. Acta Crystallogr., Sect. B 1979,B35,2258. Fehrer, F.J.; Budzichowski, T. A. J. Organomet. Chem. 1989,373,153. Biirgi, H.-B.; Tbrnroos, K. W.; Calzaferri, G.; Biirgy, H. Inorg. Chem. 1993,32,4914. Baidina, I. A.;Podberezskaya, N. V.; Borisov, S. V.; Alekseev, V. I.; Martynova, T. N.; Kanev, A. N. Zh. Strukt. Khim. 1980,21,125. Clegg, W.; Sheldrick, G. M.; Vater, N. Acta Crystallogr., Sect. B 1980,B36, 3162.
(R = H, OH) cages using the AM1 method. Ahlrichs et a1.20 reported calculated total energies using a 3-21G basis set for the highly symmetric (H0)12Si12018, (H0)24Si24036, and (H0)12Al6P6O18 molecules. Hill and Sauer21 recently extended these results by performing calculations on the (H0)8Si8012, (H0)12Si12018, and (H0)24Si24036 cages using a more extensive basis set (double-zeta plus polarization on silicon, triple-zeta plus polarization on oxygen atoms). Kramer et a1.22 compared the total energies of these larger cages with the calculated total energy (3-21G basis set) of the (H0)4Si406 cage. Recently, Schriider and Sauer23examined the relative stability of two isomers of the double 6-ring (H0)12A12Silo0182-using a 3-21G basis set. In the present investigation, we have examined a series of hydrospherosilicates having the general formula [HSiOl& Previous computational st~dies392~ on compounds containing SiO S i groups (especially H3Si-OSiH3) have demonstrated that accurate reproduction of experimental results is quite difficult due to the flexibility of this linkage. All calculations reported in this work were performed a t the 6-31G(d)//6-31G(d) level, which was deemed to provide an acceptable compromise between
The Journal of Physical Chemistry, Vol. 98, No. 35, 1994 8695
Quantum Mechanics of Silsesquioxane Cages
TABLE 2 Calculated 631G(d)//6-31G(d) molecule HSi40.5 H6Si60g HeSis012
symb Td D3h
Cb
HnSi8012 HloSiloOls Dsh H12Sil2018 D6h H12Si12018 D u
Geometries for [HsiO1.sI, Cages
Si-@ 1.655(3R) 1.643(3R),1.634(4R) 1.642(3R),1.640 (3R),1.629(4R), 1.628(4R),1.623(5R) 1.630(4R) 1.629(4R),1.625(5R) 1.630(4R),1.624(6R) 1.629(4R),1.627 (4R),1.626 (4R), 1.624(5R)
selected geometric parameters0 Si-H Si-O-Sic 1.454 118 (3R) 1.456 131 (3R),139 (4R) 1.458,1.459,1.460 131 (3R),134 (3R),145 (4R), 165 (4R),154 (5R) 1.457 149 (4R) 1.459 152 (4R),155 (5R) 1.461 150 (4R),155 (6R) 1.460,1.461 157 (4R),152 (4R),159 (4R), 148 (5R)
OSi-Oe
105 (3R) 106 (3R),109 (4R) 106 (3R),109 (4R),110 (5R) 109 (4R) 109 (4R), 109 (5R) 110 (4R),109 (6R) 109 (4R),110 (5R)
Selected bond lengths in angstroms and angles in degrees. Symmetry constraints imposed on molecules during calculations. The "nR"identifier in parentheses following each value indicates the size of the (Si-O-)n ring. For molecules containing fused rings of differing sizes, the smaller of the two fused rings is indicated. For these three molecules, the Hessian matrices were positive definite, which verified that these optimizations had converged to local minima on the potential energy surface. Due to computational restraints, force calculations were not performed on the larger molecules. Since frequency calculations were not performed on all molecules, the total energies reported do not include in any corrections for zero-point vibrational energy.
Results and Discussion Geometries. Selected geometric parameters calculated at the 6-31G(d)//6-31G(d) optimized geometries obtained for each molecule included in this study are given in Table 2. These values are in reasonable agreement with previous experimental and theoretical results. Calculated silicon-oxygen bond lengths range from 1.623 to 1.655 A, with the longest s i - 0 bond lengths occurring in cage molecules containing three-membered rings. If these molecules areexcluded, Si-0 bond lengths range from 1.624 to 1.630 A, which is roughly 0.015 A longer than the S i 4 bond lengths observed experimentally (see Table 1). Although only limited structuraldata are available for the smallest silsesquioxane cages, comparison of the X-ray structures of tetraalkylammonium ~ a l t s 3of~ [06si6(P-o)9]6- and [ 0 ~ S i s ( ~ - O ) l # -suggests the calculated lengthening of the Si-0 bond lengths in threemembered rings is correct. This same result was observed in a gas-phase electron diffraction study of a series of cyclic dimethylsiloxanes,37 where the Si-0 bond in the cyclic trimer was found to be 0.023-0.025 A longer than in the larger ring systems. Observed Si-0 distances in the larger molecules ([Me,SiO],; n = 4, 5, and 6) were the same within the experimental limits. Comparison of experimental and calculated structures provides an estimate of the absolute errors in the geometries obtained in the present work. Experimentalstructures for twoofthemolecules examined in this work have been reported. Comparison of the calculated geometry for the 0,isomer of HsSi~Ol2with results from a recent low-temperature (100 K) X-ray diffraction structure determination for this m01ecule~~j indicates that the calculated Si-0 bond lengths are 0.01 1 A too long. The differences between the calculated 0-Si-0 and Si-OSi angles and the experimental values (109.6' and 147.5') are -0.5' and +1.6', respectively. Similar results are obtained for the Hl&iloOls molecule,l5k with the calculated Si-0 bond lengths 0.017-0.024 8, longer than the average values observed in the 180 K structure.38 The HloSiloOIS molecule presents an opportunity to compare the difference between Si-0 bond lengths and S i - O s i bond angles as a function of ring size, since this molecule contains both four- and five-membered rings. Experimentally determined values for Si-0 bond lengths in the five-membered rings ranged from 1.593 to 1.607A(average= 1.601 A),whichwereslightlyshorter than the Si-0 bonds connecting these rings, which ranged from 1.61 1 to 1.616 A (average = 1.612 A). This trend was correctly reproduced by the present calculations, with the Si-0 bonds within the five-membered rings calculated as being 1.625 A and the Si-0 bonds between rings calculated at 1.629 A. The Si-OSi
anglesobservedin thisexperimental structurerangedfrom 15 1.5' to 159.5' (average = 154.7') in the five-membered rings. These values are slightly larger than the observed S i - O s i angle in the four-membered rings, which ranged from 147.4' to 150.6' (average = 149.5'). While the calculated Si-OSi angles of 155.3' and 152.1', respectively, are both too large, the trend is reproduced correctly. Given the experimental results presented in Table 1, it appears that substitution at the fourth coordination site of the silicon atoms in these cages has only a minor influence on the molecular geometry. A further measure of the accuracy of the calculated geometries in the present investigation can be obtained by comparison of the calculated geometry of the D2d isomer of HI2Si12018with the solid-state structure of ( C ~ H S ) I ~ S This ~~~O~~. molecule was fou11d~~6to have approximate D u molecular symmetry, with S i 4 bond lengths ranging from 1.605 to 1.617 A, compared with 1.624-1.629 A in the present calculation on H12Si12018. The experimental S i - O s i bond angles ranged from 144.8' to 158.1' in the phenyl derivative, compared with a calculated rangeof 148.3'-159.4' in the hydride. A comparison between each of the different types of S i - O s i angles was also performed. The two smallest S i - O s i angles found experimentally (144.8O and 150.4') werealsocalculated to havethe smallest values (148.3' and 151.8'), although the two largest S i - O s i angleswerereversed(152.8'and 158.1' (experimental) vs 159.4' and 157.3' (calculated)). Comparison of results from the present study with previous computational investigations can be made for the D6a isomer of R12Si12OI8. Ahlrichs and co-workers20 performed calculations on this molecule using a 3-21G basis set with R = OH-. These workers calculated the 24 symmetry-equivalent Si-0 bond lengths within the two six-membered rings to be 1.632 A, while the 12 Si-0 bonds connecting these rings were calculated to be 1.620 A. In the present investigation, the opposite order of Si-0 bond lengths was observed. The calculated Si-0 bond lengths in the six-membered rings were found to be 1.624 A, while the Si-0 bonds connecting these rings were calculated to be slightly longer a t 1.630 A at the 6-31G(d)//6-31G(d) level of theory. A more significant difference between these two sets of calculations is found between the calculated S i - O s i bond angles. Ahlrichs and co-workers calculated the S i - O S i bond angle within the six-membered rings to be 150.6', while the S i - O s i bond angles between these two rings were calculated to be 170.4' (3-21G//3-21G). In the present investigation, the S i - O s i bond angles within the six-memberedrings werecalculated to be 155.3', and the S i - O s i bond angles between these rings were found to be 150.4'. Calculations on the Dah isomer of R12Si12018 cannot be compared directly with experiment results from molecular silsesquioxanes because the only molecules obtained experimentally have approximate D u symmetry. However, the calculated S i - O s i bond angle of 170.4' (at 3-21G//3-21G) in the fourmembered rings appears to be too large for this molecule. In
8696 The Journal of Physical Chemistry, Vol. 98, No. 35, 195'4 particular, note that none of the experimental Si-O-Si bond angles listed in Table 1 are larger than 155'. In addition, a gas-phase electron diffraction study3' of a series of cyclic dimethylsiloxanes ([MezSiO],) suggests that the Si-O-Si angle should increase slightly as the ring size increases from n = 4 to n = 6, which is the result found at the 6-3 lG(d)//6-31G(d) level. The Si-O-Si angle obtained from a crystal structure of ((CH3)3Si0)12Si606 (which contains the si606 six-membered ring) is only 160.2°.39 In this structure, the si606 ring is almost planar,40 presumably due to the steric bulk of the trimethyl siloxide groups, which is expected to increase the Si-&Si angle. Finally, it is known24b3h that the calculated Si-&Si angle in H3Si-OSiH3 using the 3-2 1G basis set is predicted to be significantly too large (calculated to be linear, compared with an experimental value of 144'). Given the above, it is felt that the 6-31G(d)//6-31G(dJ geometry provides a more accurate description of the geometry of this molecule. Recently, Hill and Sauer21 reported calculations on a series of hydroxysilsesquioxanes ([(HO)SiOl.&, n = 8, 12, and 24) utilizing a slightly larger basis set than used in the present investigation. These authors used4]a double-zeta plus polarization basis set (DZP) on the hydrogen and silicon atoms and a triplezeta plus polarization basis set (TZP) on the oxygen atoms. The molecular geometries obtained by these authors for the two smaller cages are generally in agreement with the present results. For the (H0)8Si8012 cage, the Si-0 bonds within the Si8012 cage range from 1.6 11 to 1.627 A, while the calculated Si-0 bonds in H8Si8OlZ are 1.630 A. In the (HO)8Si8012cage, the Si-04% bond angles range from 148.8' to 151.6', while the calculated angles in H8SisOlz are 149.1'. For the D6h RlzSi12018 cage, slightly larger differences between the two calculations are observed. For (H0)12Si1201sr the Si-0 bonds range from 1.609 to 1.618 A and the Si-0-Si angles range from 149.3' to 163.8'. In the present calculations on the D6h isomer of H12Si12018, the Si-0 bonds range from 1.624 to 1.630 A and the Si-O-Si bond angles range from 150.4' to 155.3'. The relatively minor differences in calculated geometries between the hydro- and hydroxysilsesquioxane cages support the idea that substitution on the terminal positions of these cages has only a minor effect on the molecular geometry. Hill and Sauer also performed calculations on the H8SisOl2 molecule using the same basis set. For this molecule, the calculated Si-0 bond length was 1.626 A and the Si-O-Si angle was 150'. The present results are in very good agreement with these values, with the Si-0 bonds calculated to be slightly longer (1.630A) and theSi-0-Siangleveryslightlymoreacute(149'). The Si-0 bond lengths calculated by Hill and Sauer appear to be in somewhat better agreement than those obtained in the present work, which are generally somewhat too long. However, the Si-O-Si bond angles calculated by Hill and Sauer appear to be slightly too large when compared with the Si-O-Si bond angles found experimentally (cf. Table 1). Notein particular the 163.8' angle found in (H0)12Si12018and the 162.0' angle found in the (HO)24Si24036 cage. Given the overall similarity of the calculated geometries and the fact that the basis set used in the present work is somewhat smaller than the Huzinaga DZP/TZP basis set used by Hill and Sauer, use of the double-zeta plus polarization basis set used in the present investigation would appear to be advantageous. Molecular Orbitals. The calculated energies of the "core" orbitals occur in the expected regions. The silicon "1s" orbitals were calculated to range from -68.859 to -68.863 au (-1874 eV), the oxygen "1s" orbitals ranged from -20.574 to-20.582 au (-560 eV), the silicon "2s" orbitals ranged from-6.201 to-6.207 au (-169 eV), and the silicon "2p" orbitals ranged from -4.307 to -4.315 au (-1 17 eV). These values are similar to the core orbital energies calculated for the disiloxane molecule (H3-
Earley
? I
I
2.
F C W
-24.0
L
[4]Td
[6]D3h
[8]'&
[8]oh
[10lD5h
[12lD6h
[12lD2d
Figure 2. Calculated valence molecular orbital energies (in eV) for silsesquioxane cages [HSiOl,s], at 6-3 lG(d)//6-31G(d) geometries. Values in brackets refer to number of silicon atoms in each cage.
SiOSiH3)24h and somewhat more negative than the experimental ESCA values reported for both d i ~ i l o x a n eand ~ ~ Si02 films.43 Calculated valence molecular orbital energies for each of the molecules included in this study are illustrated in Figure 2. A simple examination of the calculated basis function coefficients indicates that the valence molecular orbitals in these cages cannot be segregated into energy ranges corresponding to the discrete types of orbitals (oxygen lone pair, Si-H bonding, and Si-0 bonding) expected from simple Lewis structures. This contrasts with results from a previous extended Hiickel investigationl6 of the H8Si8012 molecule, which predicted the highest 24 orbitals to all bear oxygen lone-pair character and which predicted a relatively large separation in energy (ca. 2.3 eV) between the lowest of these orbitals and the next set of orbitals. However, this earlier study did note that these orbitals were perturbed by other interactions. Both the present work and the extended Hiickel investigation predict that the HOMO is of Azgsymmetry and has "pure" oxygen lone-pair character. The appearance of the molecular orbital diagram for HsSi~Ol2 is qualitatively similar to the photoelectron spectra of this molecule reported by Calzaferri and Hoffman,I6 although the calculated valence orbital energies are too negative. The reported first ionization energy was 10.7 eV, compared ,with a calculated HOMOenergyof-13.1 eV. At slightlystronger binding energies, a broad, intense band ranging from ca. 1 1.5 to 13.5 eV is observed in the PES spectra. This is followed by several smaller peaks between 14and 16 eV. Below theHOMO, thenext 19 calculated molecular orbital energies lie between -13.5 and-15.0 eV, which presumably correspond to the broad, most intense band in the PES spectra. At more negative energies, the calculated orbitals energies are not as close in energy, which is consistent with the smaller peaks observed in the PES spectra at higher binding energies. Relative Energies. While calculated total energies cannot be compared directly to any experimental measure, these values can be used to predict the relative stability of different molecules. Calculated relative energies for each silsesquioxane cage (normalized by the number of silicon atoms) are given in Table 3. These values are simply the calculated total energies divided by the number of silicon atoms and do not include corrections for zero-point vibrational energy. Results from frequency calcula-
Quantum Mechanics of Silsesquioxane Cages
TABLE 3 Calculated Total Energies for [HSiOl.& Cages molecule svm' total eneravb re1 enerap AH(hyd)d AHln' H4Si406 Td -1607.762 -16.5 -4.12 H&i609 Djh -2411.716 -7.56 +20.6 +3.44 H8Si8012 Cb -3215.639 -8.92 +38.4 +4.80 H8SisO12 -3215.652 -10.00 +47.0 +5.87 +62.2 +6.22 -4019.571 -10.34 Hl&iloOls Dsh +74.3 +6.19 -4823.485 -10.31 H12Si12018 D6h -10.53 +76.9 +6.41 -4823.489 H12Si12018 DU Symmetry constraints imposed on molecules during calculations. * Calculatedtotalenergies(inatomicunits) at 6-31G(d)//6-31G(d)level. c Calculated total energies (in kcal/mol) divided by number of silicon atoms, relative to &Si&. Calculated energy of the hydrolysisreaction given in eq 1 (in kcal/mol). e Calculated energy of the hydrolysisreaction given in eq 1 normalized by number of silicon atoms in cage (in kcal/mol of Si atoms). ~~
tions on the smaller molecules suggest that the calculated zeropoint energies per silicon atom remain roughly constant.44 These relative energies clearly show that cages containing threemembered rings are significantly less stable than cages containing only larger rings, consistent with previous experimental and theoretical works4 Calculated energy differences between the larger cages are much smaller. An equivalent means of evaluating the relative stability of these cages is by examination of the energies of isodesmic reactions,45 which are commonly used to estimate strain energy.46 In the present investigation, energies of the following reaction have been determined.
[HSiO,.,],
+ 1.5nH20 F! nHSi(OH),
Calculated energies for these reactions are given in Table 3. Hydrolysis of these cages is calculated to be an endothermic process for all molecules except HdSi406, consistent with the observed stability of molecular hydrosilsesquioxane cages. It should also be noted that the reverse of the reaction in eq 1 describes the self-condensation of HSi(OH)j, which is formally an intermediate in the synthesis of these cage molecules. The calculated relative instability of molecules containing threemembered rings is consistent with experimental observations. For example, while both a trigonal prismatic hexamer and a cubic octamer have been observed in freshly prepared aqueous silicate solutions, the cubic octamer is thermodynamically more stable, and at equilibrium only the cubic oligomer remains.47 Additionally, three-membered rings are only rarely observed in either natural or synthetic zeolites.6 The calculated relative instability of three-membered rings is also consistent with previously published4b~cab initio studies on [(H0)2SiO], rings using both STO-3G and 3-21G basis sets. To further assess the thermodynamic bias against three-membered rings, calculations were performed on two structural isomers of the H&i801z molecule. The experimentally observed oh structure contains only fourmembered rings, while the C2"isomer contains three-, four-, and five-membered rings. As expected, the Ohstructure was calculated to be the most stable isomer. Calculated relative energies of silsesquioxane cages that do not contain three-membered rings are quite similar and are small enough that different synthetic conditions can easily account for the diversity of structures observed. Interconversion between isomers is expected to involve a high activation energy since chemical bonds (Si-0) must be broken, and thus kinetic products can be quite stable. This conclusion is supported by the structural diversity of zeolites and the variety of molecular silsesquioxane cages isolated. For example, controlled hydrolysis of HSiCl3 results in a complex mixture of silsesquioxane cages [HSiOl,5],, where compounds with n = 8, 10, 12, 14, and 16 were characterized spectroscopically.~5~ Higher oligomers which were not fully characterized are also produced by this reaction. Further
The Journal of Physical Chemistry, Vol. 98, No. 35, 1994 8697 TABLE 4 Average Geometric Parameters for Different Rings Found in [HSiOl.& Cages ringo S i 0 Siaic ringd &Si-@ 3R/3R 1.655 117.8 3R 105.4 3R/4R 1.643 131.1 4R 109.3 3R/5R 1.640 133.5 5R 109.7 4R/4R 1.630 150.0 6R 109.0 4R/5R 1.626 153.2 av 108.8 4R/6R 1.624 155.3 5R/5R 1.624 149.5 av 1.631 av 147.0 Number of silicon atoms in two rings which contain bridging oxygen atom. Average S i 4 bond length (in angstroms). Average Si-oSi bond angle (in degrees). Number of silicon atoms in rings which contains both bridging oxygen atoms. e Average 0 4 - 0 bond angle (in degrees). (I
support for this proposal comes from a z9Si N M R study47 of an aqueous tetramethylammonium silicate solution. Only small differences in relative stability were calculated for cages that do not contain three-membered rings. As shown in Figure 1, two structural isomers are possible for the H&i12o18 molecule that do not contain three-membered rings. The D6h isomer can be described as a "double 6-ring" and is observed as a secondary building unit in solid-state zeolites. As noted above, the DZd isomer is the only structure that has been observed in molecular s i l s e s q u i ~ x a n e s .In~ ~the ~ ~present ~ ~ ~ ~ investigation, the D u isomer was calculated to be slightly more stable (2.6 kcal/ mol) than the D6h isomer, consistent with these experimental observations. Siloxane Bonds. Numerous experimental and theoretical i n v e s t i g a t i ~ n shave ~ ~ * demonstrated ~~~~~ that Si-0 bond lengths tend to increase with decreasing Si-oSi bond angles. This result was also obtained in the present investigation. In Table 4, average geometric parameters for each of the molecules included in this study are summarized. The differences between the three-membered rings and the larger rings are clearly evident from these results. The largest magnitude difference obtained from these results is the change in thecalculated S i - O s i angle, which is significantly moreacute in three-membered rings (ranging from 1So to -30' smaller) than found for the larger rings. Another significant difference is the calculated bond angles around each silicon atom. For each of the larger rings, the average 04-0 bond angles are within 0.So of the ideal tetrahedral angle. However, for the threemembered rings, this angle is over 4 O too small, which is consistent with the relatively high strain in this ring. Given the known flexibility of the Si-0-Si angle, it is not surprising that this angle changes significantly more than the 0-Si-0 angle. Geometric parameters for the larger rings are relatively similar. The most significant difference between the four-, five-, and sixmembered rings is a slight increase in the average Si-OSi bond angle along with a concomitant decrease in the average Si-0 bond length. The bond angles around silicon remain relatively constant in these larger rings.
-
Conclusions Quantum mechanical calculations on a series of molecular hydrospherosilicates having the general formula [HSiOl,5], have been performed a t the 6-3 lG(d)//6-3 1G(d) level. Detailed comparison of calculated geometries with experimental structures indicates that calculations using this basis set provide excellent prediction of geometries, with Si-0 bond lengths typically calculated to be approximately 0.015 A longer than found experimentally. Calculated Si-0-Si bond angles also appear to be quite accurate in these constrained systems. In agreement with both previous theoretical calculations and experimental observations, cages containing one or more threemembered rings are calculated to be significantly less stable than cages containing only larger rings. Calculated energies for cages
8698 The Journal of Physical Chemistry, Vol. 98, No. 35, 1994
containing only four-, five-, and/or six-membered rings are predicted to besimilar. While thedifferences incalculated relative stabilities in these cages containing only larger rings are small, they do appear to be correctly predicted by these calculations. In particular, the D2d isomer of H12Si12018 was calculated to be thermodynamically more stable than the D6h isomer, in agreement with the observed experimental structures.
Acknowledgment. This work was partially supported by the National Center for Supercomputing Applications under Grant CHE920020N and utilized the CRAY Y-MP41464 at the National Center for Supercomputing Applications, University of Illinois at Urbana-Champaign, Additional support for this project from the University of Missouri-Kansas City is gratefully acknowledged. References and Notes (1) Meier, W. M.; Olson, H. Atlas of Zeolite Structure Types; Butterworth: Stoneham, MA, 1988. (2) Cf.: (a) Dyer, A. An Introduction to Zeolite Molecular Sieves; Wiley: New York, 1988. (b) Zeolites: Facts, Figures, Future; Jacobs, P. A,, van Santen, R. A., Eds.; Elsevier: Amsterdam, 1989. (c) Szostak, R. Molecular Sieves: Principles of Synthesis and Identification; Van Nostrand Reinhold: New York, 1989. (d) Bhatia, S . Zeolite Catalysis: Principles and Applications; CRCPress: Boca Raton, FL, 1990;Chapter 2. (e) Introduction to ZeoliteScience and Practice; Bekkum, H., Flanigen, E. M., Jansen, J. C., Eds.; Elsevier: Amsterdam, 1991. (3) For reviews on application of quantum mechanical calculations to study of zeolites, see: (a) Sauer, J. Chem. Rev. 1989,89,199-255. (b) Beran, S. In Catalysis on Zeolites; Ka116, D., Minachev, Kh. M., Eds.; Akaddmiai Kiad6: Budapest, 1989; pp 1-42. (4) (a) Kudo, T.; Nagase, S. J. Am. Chem. SOC.1985,107,2589-2595. (b) van Santen, R. A,; Ooms, G.; den Ouden, C. J. J.; van Beest, B. W.; Post, M. F. M. In Zeolite Synthesis; Occelli, M. L., Robson, H. E., Eds.; ACS SymposiumSeries 398; American Chemical Society: Washington, DC, 1989; pp 617-633. (c) Kramer, G. J.; de Man, A. J. M.; van Santen, R. A. J . Am. Chem. SOC.1991, 113,64354441, ( 5 ) When looking at these systems, the size of the rings is typically given based on the number of tetrahedral atoms (Si, AI, P, etc.) in the ring. The total number of atoms in the ring (including oxygen atoms) is twice this number. (6) Lawton, S. L.; Rohrbaugh, W. J. Science 1990,247, 1319-1322. (7) Fogarasi, G.; Hacker, H.; Hoffmann, V.; Dobos, S. Spectrochim. Acta, Part A 1974,30A, 629-639. (8) Glidewell,C.; R0biette.A. G.; Sheldrick, G. M. J . Chem.SOC.,Chem. Commun. 1970, 931-932. (9) Grigoras, S.; Lane, T. H. J . Comput. Chem. 1988, 9, 25-39. (10) Lacks, D. J.; Gordon, R. G. Phys. Rev. B 1993, 48,2889-2908. (11) Ooms, G.; Santen, R. A,; Jackson, R. A.; Catlow, C. R. A. In InnwationinZeoliteMaterialsScience;Grobet, P. J., Mortier, W. J., Vansant, E. F., Schulz-Ekloff, G., Eds.; Elsevier: Amsterdam, 1988; pp 317-322. (12) (a) White, J. C.; Hess, A. C. J . Phys. Chem. 1993,97, 8703-8706. (b) Anchell, J. L.; White, J. C.; Thompson, M. R.; Hess, A. C. J . Phys. Chem. 1994, 98, 4463-4468. (1 3) Dovesi, R.; Pisani, C.; Roetti, C.; Causa, M.; Saunders, V. R. QCPE 1988, No. 577. (14) (a) Vetrivel, R.; Catlow, C. R. A. J. Phys. Chem. 1989, 93, 45944598. (b) Vetrivel, R.;Catlow, C. R. A.; Colburn, E. A.; Leslie, M. In Zeolites as Catalysts, Sorbents and Detergent Builders; Karge, H. G., Weitkamp, J., Eds.; Elsevier: Amsterdam, 1989; pp 409-419. (1 5 ) (a) Wiberg, E.; Simmler, W. Z . Anorg. Allg. Chem. 1955,282,330344. (b) Olsson, K. Ark. Kemi. 1958, 13, 367-378. (c) Larsson, K. Ark. Kemi. 1960,16,203-208,209-214,215-219. (d) Brown, J. F.J. Am. Chem. SOC.1965,87,4317-4324. ( e ) Frye, C. L.; Collins, W. T. J.Am. Chem. SOC. 1970,92, 5586-5588. (f) Hossain, M. A.; Hursthouse, M. B.; Malik, K. M. A. Acta Crysrallogr. 1979, 835, 2258-2260. (g) Clegg, W.; Sheldrick, G. M.; Vater, N. Acta Crystallogr. 1980,836, 3162-3164. (h) Agaskar, P. A.; Day, V. W.; Klemperer, W. G. J. Am. Chem. SOC.1987,109,5554-5556. (i) Feher, F. J.; Newman, D. A.; Walzer, J. F. J. Am. Chem. SOC.1989, 111, 1741-1748. (j) Heyde, T. P. E.; Biirgi, H.-B.; Biirgy, H.; TBrnroos, K. W. Chimia 1991, 45, 3 8 4 0 . (k) Biirgi, H.-B.; TBrnroos, K. W.; Calzaferri, G.; Biirgy, H. Inorg. Chem. 1993,32,4914. (16) Calzaferri, G.; Hoffmann, R. J . Chem. SOC.,Dalton Trans. 1991, 917-928. (17) Carson, R.; Cooke, E. M.; Dwyer, J.; Hinchliffe, A.; O’Malley, P. J.
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*
a.
