Calculation of 19F and 29Si NMR Shifts and Stabilities of F

3584

J. Phys. Chem. C 2007, 111, 3584-3590

Calculation of

19F

and

29Si

NMR Shifts and Stabilities of F- Encapsulating Silsesquioxanes

J. A. Tossell* Department of Chemistry and Biochemistry, UniVersity of Maryland, College Park, Maryland 20742 ReceiVed: September 1, 2006; In Final Form: December 20, 2006

Hartree-Fock and density functional theory techniques have been used to calculate the structures, the stabilities in aqueous and toluene solutions, and the 19F and 29Si NMR shifts of F- encapsulating double-ring geometry silsesquixoanes DnR with n ) 3-6. We find for the fluorides that the encapsulation free energy is most negative for the double four-ring (D4R) cage, in which the most stable geometry has F- in the center. For n ) 5, 6 (and for an opened version of the double five-ring, D5R, cage), the most stable geometry has Fbonded to a single apex Si atom, with a bond distance around 1.76 Å. The 19F NMR is somewhat deshielded relative to that of the Si(OH)4F- monomer for all of the apex bonded F- DnR species and is very strongly deshielded for the central F- encapsulating DnR species with n ) 3, 4. The Si is slightly deshielded by the presence of F- for the DnR with central F- ions, while in the apex-bonded larger double rings, n ) 5, 6, the Si directly bonded to F- is substantially shielded. The energetic results help to explain why fluorides, as mineralizing agents, increase the yield of zeolites and mesoporous silicas with D4R rings, and the NMR results provide a means for ascertaining double-ring size and the position of F- within the double-ring cage.

Introduction A cage molecule has both an inside and an outside. An atom, ion, or molecule within a cage affects the characteristics of the cage and is itself modified by the cage. Either type of modification may be important in the overall properties of the system. Some silsesquioxane molecules, with the general formula (RSiO1.5)n and double four-ring (D4R) cage structures, have been found to encapsulate F- ions at their centers.1,2 In zeolites and mesoporous silicas, F- is found either at the centers of D4R cages as in octadecasil3 or near one of the apical Si atoms in larger cages.4-11 In slightly different reaction systems, encapsulated F- has not been characterized, but the yield of D4R cages in the synthesized zeolite or mesoporous silica is greatly increased by the presence of fluorides in the reaction mixture.12 The presence of such D4R is correlated with a low density, a large void space, and consequently a high internal surface area of the mesoporous solid,13 increasing their capabilities as catalysts. In order to design such low-density mesoporous solids, it is important to understand which types of silsesquioxane cages can incorporate F-, how the properties of the F- are affected, and how the internal and external properties of the silsesquioxane cages are affected. This work is a continuation of our previous research on DnR silsesquioxane and aluminosilicate species.14,15 Those studies primarily examined structures, relative stabilities of different isomers of the Al-containing species, IR spectra, and Al, Si, and O NMR. The field of silsesquioxanes has recently become a very active one for theoretical study. The structural and electronic properties of both H-terminated16 and methylterminated17 silsesquioxanes have been studied. The IR spectra have been measured and calculated for F- encapsulated in the D4R sites in octadecasil.18 Catlow and co-workers have carried out a number of studies19-22 using both classical atomistic simulation methods and quantum chemical methods. They have * Corresponding author. E-mail: [email protected].

computationally established the stability of F- encapsulated in the D4R cage in octadecasil and the true Si-F bond distances present in five-coordinate SiO4/2F- species in zeolites and have determined part of the energetics for the oligomerization of silicate units to produce ring structures. More recently, interatomic potentials for polyhedral oligomeric silsesquioxanes (POSS) have been developed by two groups23,24 in preparation for large scale molecular dynamics (MD) simulations. The previous work most closely related to the present is a study of both endohedral and exohedral complexes of D4R species containing F- (as well as noble gases and cations).25 However, this work considered only D4R species, took no account of solvation, and presented no NMR calculations. Attfield et al.21 also studied the positioning of F- (ion-pair, central cage, and apical cage) computationally, but the particular structures they considered all yielded apical F positions. This group had previously confirmed20 the central positioning of Fin models for octadecasil. Another related work26 considered the 19F NMR spectra of F- encapsulated in D4R with varying mixtures of Si and Ge as the tetrahedral atoms, obtaining calculated F NMR spectra that matched well against experimental results. Only for the all-Si species did the F- occupy a central position. Another more general study27 explored the complexation of anions (as large as ClO4-) within neutral cryptands and uncovered some interesting general results on the size of basis set superposition errors (BSSEs) and the magnitudes of different components in the interaction energies. Comparison will be made with the results of these papers later in this manuscript. This work focuses upon two main questions: (1) how does the size of the silsesquioxane cage influence its interaction energy with F-, and (2) how are the NMR shifts of the F- ion influenced by incorporation? Our goals are to determine if the increase in yield of the D4R species in the presence of fluorides in the reaction mixtures can be extended to other types of silsesquioxane cages and if F NMR can be used as a diagnostic of the nature of Si-F bonding within the silsesquioxane cage.

10.1021/jp065695q CCC: $37.00 © 2007 American Chemical Society Published on Web 02/14/2007

F- Encapsulating Silsesquioxanes

J. Phys. Chem. C, Vol. 111, No. 9, 2007 3585

Figure 1. Calculated geometries for various F- encapsulating silsesquioxanes from Table 1, identified by formula and structure type, with atoms labeled.

For the octahydrosilsesquioxane D4R complex with F-, Si8O12H8F-, we have also examined a number of other structural and electronic properties. The lowest energy isomer of this molecule, of D4h symmetry with F- at the center of the cage, is shown in Figure 1.

Morokuma,37 as implemented in the GAMESS code by Chen and Gordon,38 was also employed for qualitative analysis of the results as was the natural chemical shielding analysis developed by Weinhold et al.39 Results

Computational Methods methods28

We use standard molecular quantum mechanical from both the Hartree-Fock (HF) theory and the density functional theory (DFT). Since the molecules considered are quite large and since low symmetry isomers must be considered for many of them, we have used 6-31G* HF calculations to obtain initial equilibrium geometries and have then refined many of them at the 6-311+G(2d,p) B3LYP29 level. 19F NMR shieldings have been calculated from an average of HF and B3LYP calculations employing the 6-311+G(2d,p) basis set and the GIAO method.30 We have previously established the accuracy of this averaging approach.31 An important aspect of the calculations is the incorporation of solvation contributions to the free energy of the molecules, both in water and in organic solvents such as toluene, using the CPCM32 version of the polarizable continuum method.33 BSSEs were evaluated using the counterpoise method.34 The BSSE effects were found to be large for the 6-31G* bases and an order of magnitude smaller for the 6-311+G(2d,p) bases. All calculations were done with GAUSSIAN03,35 and the molecules were visualized using GaussView.36 The energy decomposition scheme of Kitaura and

Calculated NMR Properties for F- Encapsulated in DnR. In Figure 1, we show representative F- encapsulating silsesquioxane complexes of both the high-symmetry central-F type (e.g., Si8O12H8F-, a D4R(H) species) and the low-symmetry apically-bonded-F type (e.g., Si10O15H10F-, a D5H(OH) species). 4R(OH), D3R(H), D5R(H) apical, D5R(H) central, and the OH- version of the D4R(H) species are also shown. We also show a cluster derived from silicalite-1, Si10O27H14F-, which can be seen as a D5R(OH) in which two four-rings have been opened along an edge to give six-rings. Other naming systems for such silsesquioxanes also exist. For example, our D4R could also be identified as a [46] and the D5R could be identified as a [4552], specifying the identities and numbers of various size rings binding the polyhedra, a nomenclature often used for zeolites. Calculated 19F NMR shieldings, shifts (referenced to CCl3F), and spans (separations of the largest and smallest components of the shielding tensor, designated Ω) are given in Table 1, and 29Si NMR shieldings and shifts (referenced to Si(CH3)4) are given in Table 2. Reaction free energies for the Fencapsulation reactions in water and toluene are given in Table

3586 J. Phys. Chem. C, Vol. 111, No. 9, 2007

Tossell

TABLE 1: Calculated 19F NMR Shieldings, Isotropic Shifts, and Spansa for Reference Species and for Ring and Double-Ring Silsesquixone Species with -H or -OH Termination type

1/2(σHF + σB3LYP)

formula

δF shift

ΩF span 90.1 0 109.5 81.9 92.4 110.2 111.3 55.8 6.8

104.7 27.8

reference free FM(OH) 3R(OH) 4R(OH) 5R(OH) 6R(OH) D3R(H) D4R(H)

CCl3F FSi(OH)4FSi3O9H6FSi4O12H8FSi5O15H10FSi6O18H12FSi6O9H6FSi8O12H8F-

203.8 480.2 318.6 271.6 291.1 291.4 294.0 163.8 242.2

D5R(H) D5R(H) central F D6R(H) D6R(H) central F D3R(OH) D4R(OH)

Si10O15H10FSi10O15H10F-

258.0 317.0

0 -276.4 -114.8 -67.5 -87.3 -87.7 -90.2 +40.0 -38.4 exp ) -26 R ) Ph -54.2 -112.6

Si12O18H12FSi12O18H12F-

272.5 374.1

-68.7 -170.8

Si6O15H6FSi8O20H8F-

173.7 263.1 265.2

+30.0 -59.3 exp ) -38 silicalite -61.4

276.5

-72.7

252.8

-49.0

D5R(OH) Si10O25H10Fopened Si10O27H14FD5R(OH) opt. R(Si-F) ) 1.749 X-ray R(Si-F) ) 1.916

87.9 22.6

45.1 0.7 79.7 101.5

exp ) -64 silicalite-1

a Given in ppm, average of HF and B3LYP GIAO calculations using 6-311+G(2d,p) bases evaluated at 6-31G* HF geometries.

TABLE 2: Calculated 29Si NMR Shieldings and Chemical Shiftsa molecule

σSi

δSi

Si(CH3)4 3R(OH) 3R(OH)FD3R(H) D3R(H)FD4R(H) D4R(H)FD5R(H) D5R(H)Fcentral F apex F opened D5H(OH) opt. R(Si-F) ) 1.749

386.0 474.0 2 × 465.1, 517.1 457.6 463.3 470.1 470.4 473.7

0 -88.0 2 × -79.1, -131.1 -71.6 -77.3 -84.1 -84.4 -87.7

474.6 469 to 475, 515.1 474 to 489, 525.8

-88.6 -83 to -89, -129.1 -88 to -103, -139.8

a Given in ppm, relative to Si(CH3)4 for ring and double-ring species 6-31G* optimized geometries and 6-311+G(2d,p) HF GIAO.

3. For each property, we have also obtained results for several simpler silicate-F compounds, involving monomers and singlering silicate oligomers. For example, we have calculated geometries, energetics, and NMR shieldings for Si4O12H8F-, a complex of F- with the single four-ring siloxane with a -OH termination of the Si atoms, in our notation, a 4R(OH). Note that all of the complexes of F- with DnR which we have considered here are endohedral complexes in which the F- is inside the DnR, sometimes designated as F-@DnR. Structures and energetics of exohedral complexes have been studied by Park et al.25 An overview of the optimized geometries obtained is that the most stable position for the F- is at the center of the DnR for small values of n (3 and 4) but singly bonded to an apex Si atom for large values of n (5 and 6). We have also optimized geometries with symmetry constraints for a number of com-

plexes, holding the F- in the center of the cage. For some cases, like the D5R(H) species, optimized energies for the central and apical positions are quite similar (within about 2 kcal/mol) while for n ) 6 the energies are quite different (with the apically bonded isomer more stable by about 15 kcal/mol). The 6-31G* HF and 6-311+G(2d,p) B3LYP methods yield very similar geometries, despite their significantly different formation energies (before BSSE corrections). Si-O distances are systematically about 0.005 Å longer at the 6-311+G(2d,p) B3LYP level, but trends, for example, in Si-O distances versus n and in distances from F- to the cage Si or O atoms versus n, are essentially the same. The distances we quote will be those from the 6-31G* HF calculations unless otherwise noted. For example, in Si8O12H8F-, we obtain average Si-O distances of 1.633 and 1.638 Å at the 6-31G* HF and 6-311+G(2d,p) B3LYP levels while the reported experimental value for the average Si-O distance in the phenylated D4R is 1.625 Å.1 For the case of the F- encapsulating cluster in silicalite-1, we started with the X-ray geometry of Aubert et al.,11 truncated it to a Si10O27H14F-1 cluster, and optimized it at the 6-31G* HF level. Aubert et al.11 describe this cluster as a [415262] cage, consisting of four-, five-, and six-rings. However, it can also be seen as derived from a [4552] D5R(OH) cluster by hydrolyzing two Si-O-Si linkages, thus converting five four-rings into one four-ring and two six-rings. At the top of Table 1 are the calculated shielding for the reference compound CCl3F and the shielding and shift for the free fluoride ion. Referenced to CCl3F, we find free F- strongly shielded, with a shift of -276.4 ppm. For the Si(OH)4Fmonomer, the calculated shift is -114.8 ppm. Youngman and Sen40 assign a F NMR peak in fluorinated amorphous SiO2 at -136 ppm to a “SiO4/2F” species (a five-coordinate Si species with four bridging O atoms and one F, nonbonding to other tetrahedral centers) in reasonable agreement with our calculated value of -114.8 for the monomeric species. For the single ring nR(OH) complexes, all of which have five-coordinate Si, the calculated shifts are -67 to -90 ppm. Early studies of F in high-silica zeolites often produced such values, such as the range -64 to -75 reported by Delmotte et al.4 or the range -56 to -78 reported by Koller et al.5 The larger double-ring species, DnR, n ) 5, 6, in their lowest energy isomers have the Fbonded to one apex Si and have calculated shifts from -54 to -69 ppm, in the same range observed in most high-silica zeolites, which probably have F singly bonded to Si within large silsesquioxane-like cages. However, for a species like our D4R(H) species Si8O12H8F-, but with phenyl replacing H, the experimental shift1 of -26 ppm compares reasonably well with the calculated value of -38.4 ppm. For this species, the crystal structure indicates that the F- is indeed at the center of the D4R. For the D4R species in octadecasil, the F NMR shift is reported as -38 ppm,3,18 while for the D4R(OH) species Si8O20H8F-, we calculate -58.3 ppm. Pulido et al.26 obtained a calculated F shift for a similar species of -36 ppm, somewhat less shielded than our result (and in better apparent agreement with experiment) probably mainly because they used a pure DFT method. They report 182 ppm as their calculated 19F NMR shielding in the reference compound CCl3F while we obtain 203.8 ppm, and the experimental value is usually given as 195.631a ppm. For a species like the opened D5R(OH), which we model by the species Si10O27H14F-, we calculate a shift of -72.7 ppm at our optimized geometry, while the experimental shift4 is -64 to -70 ppm, depending on the countercation. The X-ray data indicates that the F is singly bonded to an apex Si atom in this

F- Encapsulating Silsesquioxanes

J. Phys. Chem. C, Vol. 111, No. 9, 2007 3587

TABLE 3: Calculated Energetics (in kcal/mol) for Formation of Encapsulated F- in Double-Ring Silsesquioxanes in Aqueous and Toluene Solutionsa ∆E host D3R(H) D4R(H) D5R(H) central F apex F D6R(H) central F apex F D4R(OH) opened D5H(OH) a

∆EBSSE

HF B3LYP 6-31G* 6-311+G(2d,p)

∆Ecorr HF

∆∆GCPCM

B3LYP ∆GVRT

aq

org

∆Gaq

HF

B3LYP

B3LYP

HF

B3LYP

-86.6 -113.1

-47.3 -76.0

+46.5 +45.6

+4.7 +4.4

-40.1 -42.6 -67.5 -71.6

+10.3 +12.4

+72.0 +34.4 +42.2 +75.1 +36.5 +20.0

+39.7 +15.9

+4.6 -18.6

+2.1 -22.7

-103.0 -105.4

-68.6 -69.6

+41.5 +41.7

+4.3 +4.3

-61.5 -64.3 -63.8 -65.3

+12.0 +13.3

+78.2 +37.4 +28.7 +74.5 +36.6 +24.1

+25.9 +22.5

-12.1 -13.9

-14.9 -15.4

-84.8 -100.1 -114.5 -100.1

n.a. -65.8 n.a. n.a.

+37.7 +38.4 +45.4 +41.8

n.a. +4.3 n.a. n.a.

-47.1 n.a. -61.7 -61.5 -69.1 n.a. -58.3 n.a.

≈12 ≈13 +13.7 ≈+12

+83.1 +75.5 +78.3 +79.8

n.a. ≈+27 n.a. n.a.

≈+6 ≈-12 -18.1 ≈-7

n.a. ≈-12 n.a. n.a.

+41.3 +36.6 +37.3 +39.2

HF

∆Gorg

≈+48 ≈+27 +22.9 ≈+34

6-31G* HF and 6-311+G(2d,p) B3LYP level for energies, 6-31G* HF for gas-phase VRT free energies, 6-31G* HF for CPCM free energies.

structure.7 Artificially increasing the Si-F distance from its calculated value to its X-ray value,11 that is, from 1.749 to 1.916 Å, changes the shift from -72.7 to -49.0 ppm. As Catlow and co-workers have discussed,21 the X-ray structure suffers from averaging so the real apical Si-F distance is close to 1.76 Å. Thus, the energy optimized structure gives a better value of the F NMR shift than the reported X-ray structure. Thus, although the shifts of those species with F- singly bonded to the five-coordinate Si in a ring or cage structure are always in the range of -50 to -90 ppm, the situation is quite different for those species which have the central F- weakly interacting with a large number of Si atoms. If n is small enough, then the shifts of these species can even be positive, for example, +40 ppm for the D3R(H)F-, while if n is large, the shielding can be very negative, for example, -170.8 ppm for the D6R(H)F- species constrained by symmetry to have the F- in the middle. Note that this geometry is actually a local minimum on the potential energy surface, not a saddle point. Thus, for central positions in DnR with large n, the F approaches the shielding of free F-, but for small n, it is very strongly deshielded. However, note that (as we will discuss later on the basis of the energetics given in Table 3) the encapsulated Fcomplex is actually unstable in solution for the DnR with n ) 3 and the most stable isomers for n ) 5, 6 have F- bonded to a single apical Si rather than in a central position. For F- singly bonded to an apical Si in both single nR and DnR, there is a tendency toward increased shielding or a more negative shift as the ring or cage size increases or equivalently as the separation of the F- from the other atoms of the ring or cage increases. For example, the shift of F- bonded apically to Si goes from -67.5 to -90.2 ppm in the single nR(OH) compounds as n goes from 3 to 6, while the F shift goes from -54.2 to -68.7 ppm for the DnR(H) species as n increases from 5 to 6. Basically, the less the F- interacts with atoms other than the Si it is directly bonded to, the more shielded it becomes. This suggests that the 19F NMR shift may be a useful diagnostic of cage size. Potentially useful information is also present in the anisotropy of the components of the 19F shielding tensor. We calculate an extremely large value of the span of this tensor of 109.5 ppm for Si(OH)4F- and an extremely small value of 6.8 ppm for Si8O12H8F-.1 These cases represent the two extreme bonding situations: the first is a F singly bonded to five-coordinate Si with no perturbing atoms on the other side of the F, and the second is a F- weakly interacting with many cage atoms in a highly symmetric environment. For all of the central cage environments with n ) 3-6, the spans of the 11F NMR shielding tensor are small (e56 ppm), while for the apical bonded

geometries for n ) 5, 6, the spans increase to the high 80 ppm’s. Koller et al.5 have reported span values of 80-87 ppm for a number of F-containing zeolites, which on the basis of their isotropic 19F NMR shifts are expected to have F bonded to apical Si. However, they report a much smaller span of 52 ppm for silicalite-1. The calculated spans show systematic trends with ring and cage size, as do the shifts. As the size of the single or double ring increases, the span increases, tending toward a limiting value of around 110 ppm. Double rings which are just large enough for the apical F isomer to be the most stable, for example, D5H(H), have a considerably lower calculated span of 87.9 ppm. Thus, the span (which can be measured from the magic angle spinning, MAS, NMR) will also be diagnostic of ring size. Calculated 29Si NMR shieldings and shifts are given in Table 3. Here, we concentrate upon the change in 29Si shift when Fis added to the parent silsesquioxane or silicate. Addition of F- to 3R(OH), forming a single five-coordinate Si bonded to four O atoms and one F atom, causes a substantial shielding of the five-coordinate Si, taking it from -88.0 in Si(OH)4 to -131.1 ppm in Si(OH)4F-. Such highly shielded values for fivecoordinate Si are quite typical.5 For the n ) 3, 4 DnRF- where the F- occupies a central position, the addition of F- produces only a slight shielding of the Si, on the order of 1 ppm. For the (more stable) isomer of D5R(H)F-, in which the F- is bonded to a vertex Si atom, that five-coordinate Si is changed to δ ) -129.1. For the opened D5H(OH)F- species, the Si bonded to F- is again increased in shielding to -139.8. Koller et al.5 found that for a series of high-silica zeolites in which the 19F NMR shifts were -56 to -78, indicative of Si-F bonding to a fivecoordinate Si, the corresponding 29Si NMR shifts were -140 to -150, compared to a range of -98 to -117 ppm in the F--free zeolites. The magnitude of shielding increase is similar to that which we calculated, roughly 40-50 ppm. For the D4RF- species observed by Bassindale et al.,2 the change in the Si NMR shift compared to that of the free D4R is less than 1 ppm, consistent with our small calculated shielding increase of only a few tenths of a ppm. Calculated Energetics for the Encapsulation of F-. The interaction energies and BSSE values in Table 3 for the reaction

DnR + F- w DnRF-

(1)

first show that the BSSE is extremely large for the 6-31G* HF calculation and an order of magnitude smaller for the 6-311+G(2d,p) B3LYP calculation. This is, of course, due to the very limited stability of the last electron in F-. A closer analysis of the BSSE calculations shows that the BSSE arises almost

3588 J. Phys. Chem. C, Vol. 111, No. 9, 2007

Tossell

entirely from the stabilization of F- in the presence of the orbitals of the DnR. Such large BSSEs have been seen previously by Johansson et al.27 in their studies of F- encapsulated in cryptands. Additional calculations with intermediate size basis sets indicate that it is the neglect of diffuse functions in the small basis calculations of either the HF type or the B3LYP type which is responsible for most of the BSSE. However, after the BSSE correction is made, the 6-31G* HF and 6-311+G(2d,p) B3LYP results are actually in good agreement for interaction energies as well as structures. The BSSE corrected interaction energies are most negative for the n ) 4 case, indicating a stabilization of the D4R because of Fencapsulation. However, the interaction energies are only slightly less negative for n ) 5, 6. Unfortunately, the D4R(OH) and opened D5R(OH) structures were too large for the 6-311+G(2d,p) B3LYP optimization. The total free energy change for eq 1 in solution is given as the sum of the BSSE corrected gas-phase energy change, the gas-phase vibrational, rotational, and translational (VRT) free energy change, and the solvation free energy change calculated using the CPCM method:

∆Gsolution ) ∆Ecorr + ∆GVRT + ∆∆GCPCM

(2)

The gas-phase temperature-dependent VRT free energy, ∆GVRT (including the zero point vibrational energy), is always substantially positive (10-14 kcal/mol). This is mainly due to the reduction in the number of moles from the reactant to the product side of eq 1. The reaction free energy of solvation is highly positive (70-80 kcal/mol for aqueous solvation and around 35-40 kcal/mol for toluene solvation) primarily because of the loss of the solvation free energy of F-, which is only partially balanced by the solvation free energy of the much larger DnRF- product. Summing all of these terms, we obtain the change in free energy for these encapsulation reactions in water or toluene. The free energies are most negative for the D4R ring in both water and toluene, but only for toluene as the solvent is the overall free energy change negative. Of course, the synthesis procedure2 for these F- encapsulating silsesquioxanes typically involves solutions of the silanol reactant in toluene and the ammonium fluoride reactant in tetrahydrofuran (THF) with a little water. Thus, the energetics calculated for toluene are the most meaningful for comparing the usual synthetic methods. For the free DnR cage compounds, our calculations at the 6-311+G(2d,p) B3LYP level give a lowering in the energy per SiO1.5H unit of only -1.57, -1.57, and -1.82 kcal/mol for the DnR, n ) 4-6, compared to the energy of the D3R, Si6O9H6. Thus, the free double six-ring is slightly more stable than the double four-ring, but this stability difference can be reversed, even overwhelmed, by the encapsulation of F-. Such small energy differences between the various double-ring types are consistent with the small energy differences observed by Piccione et al.41 between different pure-silica zeolites and with the weak correlation to the ring type (or loop configuration) observed. This provides a simple explanation for the more favorable synthesis of less dense D4R-containing SiO2 mesostructures in the presence of F-. Preliminary 6-31G* HF Energetic Results for OH- and Cl Encapsulation. We have also done a preliminary study on the interaction of OH- and Cl- with the silsesquioxanes using only the 6-31G* HF method (with BSSE corrections) to evaluate geometries and energies. The gas-phase energies are given in Table 4. An important qualitative difference from the Fcomplexes is that we do not see a change from the central to

TABLE 4: Energy Changes (in kcal/mol) Calculated at the 6-31G* HF Level (with BSSE Corrections) for the Encapsulation of F-, Cl-, and OH- by Silsesquioxanes DnR in the Gas Phase n/X-

F-

Cl- all central

OH- all apical

3 4 5 6

-40.1 central -67.5 central (-63.7 MP2) -63.8 apical -61.7 apical

+199.6 +29.2 -5.7 -21.6

+2.7 -67.9 -58.5 -55.3

the apical coordination of the anion as we increase n. For OH-, the most favorable coordination geometry is always apical with a close attachment to one of the Si atoms, while for Cl-, the most favorable coordination is always central. This result has been tested by starting the geometry optimizations from several different starting geometries. For the D4R, the stabilization due to OH- is very similar to that from F- in the gas phase. We would also anticipate that the ∆GVRT terms would be quite similar, but the magnitude of the positive ∆∆GCPCM term will be a little smaller since the solvation free energy of OH- is a little smaller than that of F- (-106.7 vs -112.1 kcal/mol). Thus, OH- encapsulation will also favor the formation of D4R. Since the energetics are similar for encapsulation of F- or OH- in the D4R, they will compete for such sites, so that OHencapsulation will be more prominent at high pH. One important difference may be that the OH- encapsulation in the D4R produces five-coordinate Si atoms which may be more susceptible to a reaction, giving the defects that plague the products of OH- assisted synthesis. F- occupies the central position in the D4R, and so all of the Si atoms remain four-coordinate. Xiao and Lasaga42 have shown that hydrolysis of Si-O-Si linkages in alkaline conditions proceeds with a little activation barrier once one of the Si centers becomes five-coordinate. Therefore, the OH- encapsulating cages, with OH- bonded to an apical Si to form a five-coordinate species, should be more reactive toward hydrolysis, which will produce the nonbonding oxygen (NBO) common in mesoporous silicas synthesized by the OH- route. Qualitative Interpretations of Stabilities and Shieldings. While our primary focus is on accurate calculation of stabilities and NMR shieldings, it is worthwhile to also attempt some qualitative analysis of the stabilities and shieldings. To this end, we have performed a Kitaura-Morokuma energy decomposition analysis on Si8O12H8F- as well as calculating the potential at the center of the cage both for the optimized geometry of Si8O12H8 and for the geometry of the fragment Si8O12H8 within the complex Si8O12H8F-. Merz-Kollman charges43 appropriate for the generation of electrostatic (ES) potentials have also been determined. We find that at the 6-31G* HF level (without BSSE corrections) the Si8O12H8 group within the Si8O12H8F- complex is higher in energy than free Si8O12H8 by about 30 kcal/mol; that is, it is substantially strained. However, the accompanying geometric distortion brings the Si’s in toward the center of the cage (by about 0.05 Å) and pushes the O’s out (by about 0.08 Å), causing the ES potential calculated at the cage center to beome more positive by about 0.095 au, giving an additional stabilization of a central negative charge of about 55 kcal/mol. Thus, the energy required for cage distortion is overbalanced by the enhanced ES interaction. Calculating the ES potentials from the Merz-Kollman atomic charges and atom distances to the center gives ES potentials at the center within 10% of those calculated directly from the electron density. The Kitaura-Morokuma analysis for Si8O12H8F- supports the predominance of ES interactions with the ES term constituting about 93% of the total interaction energy, while the EX

F- Encapsulating Silsesquioxanes (exchange or Pauli repulsion), PL (polarization), CT (charge transfer), and MIX terms constitute about -39% (i.e., with opposite sign), 20%, 22%, and 3% of the total, respectively. These are similar to the results found by Johansson et al.27 for stable compounds of anions with cryptands, with ES terms dominating EXs and fairly small geometric strain energies. To qualitatively analyze the 19F NMR shieldings, we have used the 6-31G* HF method to simplify the analysis and have performed a natural chemical shielding analysis39 for the DnRFcomplexes with n ) 3-5. The calculated total shieldings with these smaller basis sets are 225, 308, and 352 ppm for the central F complexes with n ) 3, 4, 5, respectively. These 6-31G* HF shielding values for the central F’s show the same trend as the more accurate results given in Table 1, that is, greater shielding as n increases. A decomposition of the shielding over the localized molecular orbitals (MOs) indicates that most all of this trend arises from changes in the paramagnetic contributions for the F 2s and 2p valence orbitals, which become more negative as n decreases. This is consistent with the NBO charges on the F which become more negative as n increases, with values of -0.74, -0.81, and -0.86 for n ) 3, 4, 5, respectively, indicative of weaker interaction and less CT to the silsesquioxane cage for larger values of n. Conclusions F- adopts two distinctly different geometries when encapsulated in double-ring silsesquixoane cages, either a central position or an apical position strongly bonded to a single Si of the cage. This choice of course depends upon the energetics of the two isomers, which is a strong function of the size of the DnR: larger n rings favor apical sites. The maximum stabilization is found for n ) 4, where the F- occupies a central site, but the stabilizations for larger n are only slightly smaller. When the F- is bonded to a single apical Si, its NMR properties (and that of the Si) are fairly similar to those in a simple monomeric species like Si(OH)4F-. However, there are subtle but systematic changes in both the 19F NMR shift and the span, depending upon the size of the cage. Thus, with a sufficient database of experimental 19F NMR and crystal structures and/or calculated 19F NMR and structures, it would be possible to determine the location of the F- from its NMR alone. When the F- is at the center of a smaller DnR it can be strongly deshielded, and its NMR span is substantially reduced. The formation of the D4RF- species Si8O12H8F- is correctly predicted to be thermodynamically favorable in a toluene but not a water solution. The favorability of encapsulation is greatest for the D4R, although the encapsulation of F- in the double five- and six-rings is only 5-6 kcal less favorable. Energetics for encapsulation of F- and OH- are very similar for the D4R so that F- and OH- will compete for this location. The mechanism for the formation of low-density mesoporous silicas using F- as mineralizer has been discussed by Corma and Davis12 and Zones et al.44 We hope that the energetics calculated in this paper will help to refine the proposed mechanisms. The favorability of the encapsulation process is primarily a result of a stabilizing ES interaction between the (strained) Si8O12H8 cage and the F-. Qualitatively, interaction of the Fwith the cage is responsible for the deshielding of the 19F NMR. However, it is apparent that a more detailed study of both the energetics and the source of the NMR deshielding would be desirable. Acknowledgment. This work was supported by NSF Grant EAR-0001031 and DOE Grant DE-FG02-94ER14467.

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