J . Phys. Chem. 1994,98, 9222-9226
9222
Electronic Structure and Stability of closo-Heteroboranes, XYBJI, (n = 3-5; X, Y = N, CH, P, and SiH). An ab Initio MO Study? Eluvathingal D. Jemmis' and G. Subramanian School of Chemistry, University of Hyderabad, Central University P.O., Hyderabad 500 134, India Received: March 3, 1994"
Ab initio MO calculations a t the HF/6-31G* and MP2/6-31G* levels were carried out on five-, six-, and seven-vertex closo-heteroboranes with N, C H , P, and S i H as the heteroatoms (X, Y)capping the n-membered borocyclic ring B,H, ( n = 3-5). With unsymmetrical capping groups (X # Y), the hydrogens of the ring bend toward the cap that is smaller in size and provide less diffuse p,-orbitals. The stability and bonding in these molecules are explained using the compatibility of orbitals in overlap and the six interstitial electron rule. The five-vertex cages are seen to obey the classical 2c-2e bonding description, while the six- and seven-vertex cages are best described as three-dimensionally delocalized structures. Several thermochemical equations were derived to find the preferred combination of capping groups for a given borocyclic ring and the effect of a capping group combination as a function of ring size. In XzB,H,, the five-vertex cage finds nitrogen as a suitable partner, while S i H as a capping group fits the seven-vertex cage perfectly. Among the closo-heteroboranes of the type XYB,H, studied, HSi-(B,H,)-N (n = 3-5) is predicted to be the most preferred combination.
Introduction closo-Carboranes form one of the first classes of compounds studied extensively with heteroatoms incorporated into the boron cage.' Recent synthesis of closo-phosphaborane, 1,5-P2B3R3 [R = N(iPr)2],2 and 1,2-PzB4C143suggests that, apart from group IV elements like carbon, even group V elements can be incorporated into the boron cage. closo-l,2-Si~BloHloMe~ with an icosahedral framework is the only structure characterized among polyhedral silaboranes possessing cage structure^.^ Theoretical studies on small-vortex closo-silaboranes have been reported recently to aid further experimental inve~tigation.~ An equally interesting class of closo-heteroboranes would be of the general formula XYB,H,, where X and Y are group IV and/or V elements. There are a few examples of related isoelectronic compounds reported in the literature such as closo1-CH3-1-GaC&&,6 closo-l-Sn-2-[SiMe3]-2,3-C2B4H~,7 and ~loso-l-Si-2,3-[SiMe3]~-2,3-C~B4H4.~ In view of the current interest in the cage structures, we undertook a systematic study at a uniform level of theory to probe into the details of the bonding and stability of closo-heteroboranes (Figure 1) of the type XYB,H, ( n = 3-5; X, Y = N , CH, P, and SiH). These heteroboranes are seen to obey the six interstitial electron rule for three-dimensional delocalizationgand various other electroncounting schemed0 applicable for closed polyhedra. The structures with two dissimilar caps turn out to be of special interest with pronounced distortion of the exocyclic B-H bonds of the ring toward one of the capping groups. The concept of the compatibility of orbitals in overlapg (Scheme 1) is used in this paper to explain the geometries and to predict the best X, Y combination for a specific B,H, ring.
Method of Calculation All the structures considered in the present study (XYB,H,: n = 3-5; X, Y = N, CH, P, and SiH) were optimized initially using the HF/6-3 lG* basis" within the given symmetry restriction. Frequency calculations were performed at the same level to ascertain the nature of the stationary points. Minima were characterized as those structures with zero imaginary frequency R.Rao on his 60th birthday. Abstract published in Aduance ACS Abstracts, August 15, 1994.
t Dedicated to Professor C. N.
XZSSHS
Figure 1.
and transition states with one imaginary frequency. Single-point calculations at the MP2(FC)/6-31G* level12 were performed to estimate the effect of electron correlation on the relative energies. The total energies of all the structures are given in Table 1 along with their zero point energies and the number of imaginary frequencies. The geometries and the Mulliken population analysis obtained at the HF/6-31G* level (Tables 2 and 3) and energies obtained at the MP2/6-3 lG*//HF/6-31G* level will be used in the discussion unless otherwise specified. The heats of reaction in Tables 4 and 5 include zero point energies scaled by a factor
0022-3654/94/2098-9222$04.50/0 0 1994 American Chemical Society
The Journal of Physical Chemistry, Vol. 98, No. 37, 1994 9223
Structure and Stability of closo-Heteroboranes
TABLE 1: Absolute (hartrees) and Zero Point Energies (ZPE; kcal/mol) of clmeHeteroboranesOptimized at the HF/6-31G* Level molecule symm HF/6-31G* MP2/6-31G* ZPE (NIF)b -185.274 89 32.32 (0) NzBaHs D3h -184.716 95 47.32 (0) D3h -152.686 57 -153.182 46 CzB3Hs -757.702 94 27.09 (0) PzB3H3 D3h -757.226 99 35.95 (0) SizB3Hs D3h -654.657 01 -655.047 93 39.89 (0) CNBpH4 C30 -168.703 94 -169.230 91 29.78 (0) 9, -470.977 1 1 -471.490 84 NPB3Hp 37.23 (0) -455.443 46 CPB3H4 9, -454.960 23 -420.182 04 34.33 (0) NSiBnH4 C3, -419.694 88 41.64 (0) C3, -403.670 49 -404.123 52 CSiB3Hs 3 1.40 (0) C3, -705.939 56 -706.383 99 PSiBsH4 -210.592 39 40.52 (1) NzB4H4 D4h -209.904 98 -178.562 02 57.37 (0) CzB4H6 D4h -177.946 22 -783.095 61 37.32 (0) PzB4H4 D4h -782.508 82 46.43 (0) D4h -679.965 41 -680.501 35 SizB4H6 49.03 (0) Cb -193.928 32 -194.579 48 CNB4Hs 39.08 (0) Cb -496.214 70 -496.850 41 NPBdH4 47.35 (0) Cb -480.231 93 -480.832 79 CPB4Hs 44.10 (0) Cb -444.957 52 -445.569 24 NSiB4Hs 52.15 (0) CO, -428.963 28 -429.538 56 CSiBdH6 -731.806 33 42.11 (0) PSiB4Hs Cb -731.244 42 45.85 (2) D5h -234.990 99 -235.796 77 NzBsH, 65.16 (0) -203.836 01 CzBsH7 DSh -203.116 38 -808.426 77 46.57 (0) PzBsHs Dsh -807.748 48 57.09 (0) SizBsH7 Dsh -705.275 37 -705.899 73 -219.818 77 55.35 (2) CNBsH6 Csh -219.056 84 46.84 (0) C5u -521.380 88 -522.120 20 NPBsHs 55.98 (0) Cs, -505.438 98 -506.138 08 CPBsH6 52.73 (0) Cs, -470.162 62 -470.875 13 NSiB& 61.54 (0) Cs, -454.207 76 -454.878 75 CSiBsH7 51.96 (0) Cs, -756.521 25 -757.172 94 PSiBsH6 a Single-pointcalculation at the MP2(FC)/6-3 lG*//HF /6-31G* level. b NIF = number of imaginary frequencies. SCHEME 1
bond) has to be in the plane of the borocycle by symmetry (the molecule possesses a horizontal plane of symmetry; Figure 1). Depending on the size of the capping group and the diffuse nature of the p-orbital of the cap, the B-B distance of the borocycle varies to accommodate the E X bonding and strengthen its interaction with the cap (Scheme 1). For example, in the fivevertex cage, the B-B distance in c ~ o s o - N ~ Bis~calculated H ~ ~ ~ to be 1.775 A and, in closo-SizB3H~,it is 2.531 A (Table 2).17 This is because nitrogen with less diffuse p-orbitals than Si prefers a smaller ring to have optimum ring-cap overlap (Scheme 1b). On the other hand, Si, which is larger in size and has a more diffuse p-orbital, does not prefer this arrangement due to the ineffective overlap between the c a p r i n g s-orbitals (Scheme la). In fact, 2,3-SizB3H~is predicted to be more stable." The variations in the B-B bond lengths for closo cages based on the five-membered borocycle (Table 2) are also along the same directions, though much less dramatic. The B-B distance of 1.77 A calculated for clo~o-SizB,H7~ais more realistic than the value of 1.587 A calculated for closo-N2BsH, (this value is close to a normal B=B (1.533 A) observed for B2H2).I8 This indicates that a larger ring prefers a cap with more diffuse orbitals to have a favorable interaction (Scheme 1b). Nitrogen with contracted orbitals cannot optimize its interaction with the ring s-orbitals in the seven-vertexcage (Scheme IC),and hence the molecule is unstable (two imaginary frequencies; Table 1). Thus, for a given cap combination such as nitrogen, the variation in the B-B distances for the B3H3, B4H4, and BSHSrings are 1.775 to 1.647 to 1.587 A compared to the corresponding change of 2.531 to 1.888 to 1.775 A for the SiH caps. N2B,HS
+ Si2B3H,
+
-
N2B3H3+ Si2B5H,
(1)
HeH N2B4H4 Si2B4H6
+
N2B5H, Si2B3H,
C
a
H
H
b
d
of 0.89 to correct for the known deficiencies in this method." All calculations have been performed using the Gaussian 90 program package.14
Results and Discussion The bonding in closo-heteroboranes can be understood by considering the cage as arising from the interaction of a B,H, ring (n = 3-5) with capping groups (X, Y) on either sidegb(Figure 1). If the capping groups are the same on either side of the borocyclic ring (X2B,H, or Y2B,H,), the cage is described as a homocapped (symmetrically capped) closo-heteroborane. On the other hand, if the capping groups on the two sides of the borocyclic ring are different (XYB,H,), the cage is described as a heterocapped (unsymmetrically capped) closo-heteroborane. The stability of these arrangements depends on the size of the capping group and the diffuse nature of the p-orbital's of the cap. Bonding in Homocapped clos+Heteroboranes. In the homocapped closo-heteroboranes, the ring substituent (external B-H
AH = -200.3
+
N2B3H3 Si,B,H,
AH = -48.6
(2)
+
N2B4H4 Si2B4H6
AH = -1 51.7 (3)
The exothermicities of the above reactions, eqs 1-3, (kcal/ mol) further substantiate the fact that a three-membered borocycle finds nitrogen as a suitable partner while a capping group like SiH prefers a five-membered borocycle. Equation 1, where two unfavorable structures are changed to favorable ones, has maximum exothermicity. Equations 2 and 3 compare the octahedron and pentagonal bipyramidal structures with respect to the neighboring cage structures and hence are less exothermic. A similar rationale can be extended to show that carbon prefers the apical position in the five- and six-vertex cages but not in the seven-vertex cage (2,4-C2B~H7is the most stable arrangement).%Jg Bonding in Heterocapped closeHeteroboranes. The drawback due to the incompatibility of orbitals in overlap (ineffective overlap) between the ring and cap for a particular borocyclic ring and capcombination (Scheme la,c) discussed above can be turned to advantage by selecting different capping groups (X and Y), as in heterocapped closo-heteroboranes (Figure 1, right). Here, there is an additional possibility of enhancing the ring
t
X
I Y
X
Y
I
&
t
2A
AH1
TABLE 5 Heats of Reaction (kcal/mol) for RVertex (n = 5-7) Heterocapped cfoseHeteroboranes Calculated Using the Equations Below
+-+
X
->
2
b
I
I
I
X
Y
X
&
I
I
& . - > + t
I Y
Y
y'
Y
X
x'
x
Y
AH8
A+&
->
I Y
X
CH P
N N
P
CH
SiH SiH SiH
N
-2.7 -2.3 -0.9 -25.6 -10.4 -10.9
CH P
-2.7 -7.8 -4.9 -26.9 -8.2 -9.4
SiH SiH SiH SiH
-3.3 -9.5 -8.2 -31.5 -12.9 -11.9
very weak bonding interaction between them. On the other hand, the B-X and B-Y overlap populations are strongly positive (Table 3) with their magnitudes close to that of the normal B-X and B-Y single bonds. Hence, the bonding in five-vertex heterocapped closo-heteroboranes can be better described by classical 2c-2e bonding. Analogous homocapped closo-heteroboranes are also explained by a localized bonding picture.21 Unlike the case of the three-membered borocycle, the B-B distance in the fourmembered borocycle falls in the range 1.677-1.839 A and that in the five-membered ring falls in the range 1.606-1.743A. These are only slightly longer than the normal B-B bond distances. The variations in the B-X and B-Y bond distances follow the same pattern as seen in the tbp framework, and hencea similar rationale can be extended here also. The Mulliken overlap population for B-B is positive (Table 3) and substantial as are the B-X and B-Y overlap populations, indicating an equally strong bonding interaction between B-B, B-X, and B-Y pairs. So, the description of the bonding in the six- and seven-vertex cages as three dimensionally delocalized is appropriate for heterocapped closoheterob~ranes.~ Energetics of Heterocapped cfoso-Heteroboranes. The stabilities of the various heterocapped closo-heteroboranes can be estimated from the exothermicities of the following reactions in comparison to those for the reactions of the homocapped closoheteroboranes.16 NSiB,H,
NSiB,H, 2NSiB,H,
+ SiH,
-
+ NH,
-
-
+
Si2B3H5 NH, AH = 58.3 kcal/mol
(4)
+
N2B3H3 SiH,
Si,B,H5
+ N,B,H,
AH1
AH = -32.7 kcal/mol (5) AH = -25.6 kcal/mol (6)
For example, eq 4 clearly shows the preference of heterocapped closo-heteroborane in comparison to closo-SizB3H~.On the other hand, eq 5 predicts closo-N~B3H3to be more favored compared to NSiBsH4. Adding eqs 4 and 5 gives eq 6. Isodesmic equations such as eq 6 would help in predicting the stability of various heterocapped closo-heteroboranes in comparison to their corresponding homocapped closo-heteroboranes as shown in Table 4. This reveals that heterocapped closo-heteroboranes with HC, N , and P as capping groups are stabilized only marginally, while
+
I
I
Y
y'
Y
X'
Y'
CH
CH CH
P
P P
N N N N N N N
P
P
CH CH
SiH SiH SiH
N P P
CH CH SiH P P P
CH
P
CH
SiH SiH SiH
N
CH CH
SiH P
CH
P
N P N
CH SiH
N
N N N
MI -121.6 -101.1 -96.9 -76.5 -64.1 -63.1 -58.2 -57.6 -39.5 -38.8 -37.6 -37.0 -25.1 -20.6 -0.7
AH3
&f
I
Y
AH2 -76.8 -60.6 -58.9 42.7 -39.4 -39.7 -36.9 -37.4 -21.5 -21.8 -20.9 -21.2 -17.9 -16.1 -0.4
AH3 -44.9 -40.5 -38.1 -33.7 -24.7 -23.7 -21.2 -20.2 -17.9 -16.9 -16.8 -15.8 -6.8 -4.4 -1.0
SiH CH SiH P CH caps involving the SiH group are stabilized to a larger extent (Table 4). Secondly, the exothermicity of the reaction increases as the size of the borocyclic ring increases for a given cap combination. The only exceptions are the HC, SiH and P, SiH caps, where the six-vertex cage is seen to be the least stabilized. The HC, N and HSi, N caps show only a marginal change in the magnitude of the exothermicities of the reaction as a function of ring size, indicating that the ring size does not affect the stability dramatically in these two cases. On the other hand, the N, P and HC, P capped polyhedra are stabilized to some extent as the B,H, ring size increases, indicating the preference for four- and five-membered borocycles compared to the three-membered ones. Thelargest exothermicity is found for the HSi, N capcombination, which also has a maximum difference in the diffuse nature of their orbitals.15 To conclude, for a given ring the variations in the preferences of X, X vs X, Y cap are small. This is to be contrasted with the energetics of equations involving different rings, as discussed below. Comparison of Heterocapped closo Systems Based on Three-, Four-, and Five-MemberedBorocycles. The analysis done so far reveals the stability of heterocapped closo-heteroboranes in comparison to the homocapped closo-heteroboranes. In a similar fashion, it is possible to estimate the preference of a given heterocap combination for various rings by the equations shown in Table 5. The preference of nitrogen for a three-membered ring and of HSi for a larger ring is clearly seen from the exothermicities of these reactions. This is due to the larger size of the atom and the diffuse nature of the interacting orbitals. Similar trends are observed for other capping group and ring combinations. Maximum magnitudes in the exothermicity are obtained for comparisons involving three- and five-membered rings. Minimum differences are seen in equations involving three- and fourmembered rings. Given a ring combination, maximum differences are obtained where capping combinations involve both the first and second row elements. These equations provide a quantitative estimate and support the concept of the compatibility of orbitals in overlap.
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The Journal of Physical Chemistry, Vol. 98, No. 37, 1994
Conclusions. Unlike the case of the homocapped closoheteroboranes, the ring substituents in heterocapped closoheteroboranes are bent toward the cap that provides less diffuse orbitals. This out-of-plane bending increases as the size of the ring increases. The B-B distances in heterocapped closoheteroboranes fall generally between those of their homocapped analogs. The B-B distance decreases as the size of the ring increases to maximize the ring-cap orbital overlap. The B-Y distances are found to be relatively shorter in heterocapped closoheteroboranes compared to their homocapped analogs. From the Mulliken population analysis, it is clear that the out-of-plane bending of the ring hydrogens does not influence the B-X and B-Y bonding to the same extent. The bonding in the trigonal bipyramidal arrangement is better described by the electron precise 2c-2e bonds. The electronic structures of the octahedral and pentagonal bipyramidal arrangements justify their descriptions as three-dimensionally delocalized. In general, the stability of various heterocapped closo-heteroboranes and their bonding have been rationalized using thecompatibility oforbitals inoverlap and isodesmic equations. On the other hand, the preference of various caps for a particular borocycle and thevariation in bonding of a particular cap combination for varying borocyclic rings have been quantified using several thermochemical equations. Experimental studies along these directions would lead to unprecedented structural arrangements for heterocapped closoheteroboranes. Acknowledgment. The authors thank the Council of Scientific and Industrial Research, New Delhi, for financial support. References and Notes (1) (a) Grimes, R. N. Carboranes; Academic Press: New York, 1970. (b) Advances in Boron and the Boranes; Liebman, J. F., Greenberg, A., Williams, R. E., Eds.; VCH: New York, 1988. (c) Lipscomb, W. N. Boron Hydrides; Benjamin: New York, 1963. (2) (a) Wood, G. L.; Duesler, E. N.; Narula, C. K.; Paine, R. T.; NBth, H. J . Chem. SOC.,Chem. Commun.1987,496. (b) Dou, D.; Westerhausen, M.; Wood, G. L.; Linti, G.; Duesler, E. N.; NBth, H.; Paine, R. T. Chem. Ber. 1993, 126, 379. (3) (a) Haubold, W.; Keller, W.; Sawitzki, G. Angew Chem., Inr. Ed. Engl. 1988, 27, 925. (b) Solouki, B.; Bock, H.; Haubold, W.; Keller, W. Angew Chem., Int. Ed. Engl. 1990, 29, 1044.
. Jemmis and Subramanian (4) (a) Seyferth, D.; Biichner, K.; Rees, W. S.; Jr.; Davis, W. M. Angew Chem., Int. Ed. Engl. 1990,29,918. (b) Seyferth, D.; Biichner, K. D.; Rees, W. S.,Jr.; Wesemann, L.; Davis, W. M.; Bukalov, S. S.; Leites, L. A.; Bock, H.; Solonki, B. J. Am. Chem. SOC.1993, 115, 3586. ( 5 ) (a) Jemmis, E. D.; Subramanian, G.; Radom, L. J . Am. Chem. Soc. 1992, 114, 1481. (b) McKee, M. L. J . Phys. Chem. 1992, 96, 1679. (6) Grimes, R. N.; Rademaker, W. J.; Denniston, M. L.; Bryan, R. F.; Greene, P. T. J. Am. Chem. SOC.1972.94, 1865. (7) Hosmane, N . S.; de Meester, P.; Maldar, N. N.; Potts, S. B.; Chu, S. S. C.; Herber, R. H. Organometallics 1986, 5, 772. (8) (a) Hosmane, N. S.;de Meester, P.; Siriwardane, U.; Islam, M. S.; Chu, S.S . C. J . Chem. SOC.,Chem. Commun.1986, 1421. (b) Siriwardane, U.; Islam, M. S.;West, T. A.; Hosmane, N. S.;Maguire, J. A.; Cowley, A. H. J. Am. Chem. SOC.1987, 109, 4600. (9) (a) Jemmis, E. D.; Schleyer, P. v. R. J . Am. Chem. SOC.1982,104, 4781. (b) Jemmis, E. D. J . Am. Chem. SOC.1982, 104, 7017. (10) (a) Wade, K. Ado. Inorg. Radiochem. 1976,18, 1. (b) Wade, K. J. Chem. SOC.,Chem. Commun. 1971, 792. (c) Williams, R. E. Inorg. Chem. 1971,10,210. (d) King, R. B.; Rouvray, D. H. J . Am. Chem. SOC.1977,99, 7834. (e) Mingos, D. M. P. Nature, Phys. Sci. 1972,236,99. (0 Stone, A. J. Inorg. Chem. 1981,20, 563. (9) Zhao, M.; Gimarc, B. M. Inorg. Chem. 1993, 32, 4700 and references therein. (1 1) (a) Hariharan, P. C.; Pople, J. A. Theor. Chim. Acta 1971,28, 213. (b) For details of the basis set, see: Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab Initio Molecular Orbital Theory; Wiley: New York, 1986. (12) (a) Binkley, J. S.;Pople, J. A. Int. J . Quantum Chem. 1975,9,229 and references therein. (b) Moller, C.; Plesset, M. S.Phys. Rev. 1934, 46, 618. (13) Pople, J. A.; Krishnan, R.; Schlegel, H. B.; Binkley, J. S. Inr. J. Quantum Chem., Quantum Chem. Symp. 1979, 13, 225. (14) Frisch, M. J.; Head-Gordon, M.; Trucks, G. W.; Foresman, J. B.; Schlegel, H. B.; Raghavachari, K.; Robb, M. A.; Binkley, J. S.; Gonzales, C.; DeFrees, D. J.; Fox, D. J.; Whiteside, R. A.; Seeger, R.; Melius, C. F.; Baker, J.; Martin, R. L.; Kahn, L. R.; Stewart, J. J. P.; Topiol, S.; Pople, J. A. Gaussian 90; Gaussian Inc.: Pittsburgh, PA, 1990. (15) Atomic radii or the optimized exponents in a basis set indicate the expected trends of the diffuse nature of the orbitals (N < C < P < Si). (16) McKee, M. L. J . Phys. Chem. 1991, 95,9273. (17) Jemmis, E. D.; Subramanian, G. Ind. J . Chem. 1992,31A, 645. (18) The Carnegie-Mellon Quantum Chemistry Archive, 3rd ed.; Whiteside, R. A., Frisch, M. J., Pople,J. A., Eds.; Department of Chemistry,CarnegieMellon University: Pittsburgh, PA, 1983. (19) (a) Ott, J. J.; Gimarc, B. M. J . Am. Chem. Soc. 1986, 108, 4303. (b) Ott, J. J.; Gimarc, B. M. J . Comput. Chem. 1986, 7, 673. (20) Jemmis, E. D.; Pavan Kumar, P. N. V. P r o c l n d i a n Acad. Sci., Chem. Sci. 1984, 93,479. (21) (a) Takano, K.; Izuho, M.; Hosoya, H. J. Phys. Chem. 1992, 96, 6962. (b) Bader, R. F. W.; Legare, D. A. Can. J. Chem. 1992,70,651 and references therein.
