J. Phys. Chem. 1993,97,10937-10941
Theoretical Studies of the Structure of Ti&+ Surrounded by Metal Atoms
10937
Cluster: Existence of
Cl2 Cage
Structure
Arshad Khan Chemistry Department, The Pennsylvania State University, DuBois, Pennsylvania I5801 Received: June 29, 1993’
.
The structure of Ti&+ cluster (cationic Ti met-car) was obtained by examining a large number of possible structures, ranging from regular to distorted dodecahedron with varied interatom distances and optimizing geometry by applying the Zerner’s intermediate neglect of differential overlap self-consistent field unrestricted Hartree-Fock (ZINDOSCF UHF) method. Each of the two isomers that we characterized has the same basic structure, that is, 12 carbon atoms form a closely packed hollow polygonal structure (a distorted icosahedron) surrounded by 8 titanium atoms. Recently reported photodissociation results on metcars can be well explained by these structures.
Introduction Recent experiments by Castleman and co-workers’ suggested the existence of highly stable metal-carbon clusters (met-cars) such as Ti&ll2 and Ti&’*+. It was postulated that each of these met-cars has a regular dodecahedral cage structure with 12 pentagonal rings of titanium and carbon atoms.’ Each pentagonal ring structure was considered to be formed by two titanium and three carbon atoms. To establish the structure of these clusters, we examined theoretically a large number of possible geometries ranging from regular dodecahedral structures with the same C-C and C-Ti distances to ones with different interatom distances. Even though most of these starting geometries did not show any convergenceduring geometry optimizationprocess by the ZINDO SCF UHF method, two of the distorted structures did provide stable geometries (isomers) for the cluster. These calculations were performed by using the ZINDO seriesof programs developed by Zerner and co-workers.2-5 The basis sets which were used in these calculations are obtained by the linear combination of Slatertype orbitals with different exponents. Two such functions are used for each of the valence s and p orbitals on C and Ti, and three such functions are used for each of the d orbital on Ti. Since some of the parameters used in geometry optimization were obtained by fitting experimental results, this method can give quite reliable molecular structures with the advantage of a much smaller amount of computation time compared to ab initio calculations.6 Our test results on known Ti organometallics together with the available experimental results are presented in Table I. A good agreement between the experimental and the theoretical results suggests the reliability of the method for determining the structure of metcars. Recently, ZINDO has also been applied7 to calculations on the structure and spectra of c 6 0 and C70 cage molecules. A good agreement between the calculated and available experimental results further suggests the reliability of the method for determining cage structures. Parametrization for Ti and Reliability Tests. Reparametrization of the resonance integral for Ti was needed, as ZINDOs predicted Ti-C distances in Ti organometallics were about 0.3 A longer than those of experiments. The detailed discussion of these parameters (0) for the resonance integral can be found elsewhere.6Q The j3 value for the atomic d orbital was varied in such a way as to obtain a T i 4 distancein Ti(C&C&)d molecule within around 0.1 A of the experimental value. A /3 value of -33.0 eV was obtained and used in our structure calculations. Different test results are given under Table I together with the reported experimental values. It should be pointed out that the Abstract published in Advance ACS Abstracts, October 1, 1993.
0022-365419312097-10937$04.00/0
TABLE I: Calculated Distances (A)and Organometallics Together witb the Available xperimental for Ti ~~ults. compound lengths and angles theory expt T ~ ( C H Z C ~ H ~ ) ,T~ i 4 (av) nearest atoms 2.26 2.14 Ti-C (av) second nearest atoms 2.88 2.88 f l i C C (smallest) 86 88 others (av) 104 107 LCTiC (av) 108 108 Ti2(C5H5),C5HJ0 Ti-C (nearest) 2.16 2.19 others (av) 2.49 2.38
?? !
Ti(C~H~)zC12ll
Ti-Ti fliTiC C-C (av) LCCC (av) T i 4 (av) C-C (av) LCCC (av)
3.48 45
1.43 108 2.49 1.44 108
3.34 44
1.40
108 2.37 1.37 108
C’s in first two compounds are a-bonded atoms, and C’s in the third compound are bonded to Ti by the r-electroncloud of the cyclopentadienyl (CP) ring.
discrepancy between the experimentand the theory is small enough to rely on the calculated structure.
Results and Discussions The results of our calculations were quite unexpected and surprising. Each of the two stable isomers of the cationic metcar (Ti&+) has the same basic structure, a distorted icosahedral structure of 12 carbon atoms surrounded by eight Ti atoms (Figures 1-3). While one of the isomers has a cubic arrangement (slightly distorted) of Ti atoms (cubic isomer, Figures 1 and 2), the second isomer (Figure 3) has a noncubic arrangement of Ti atoms (noncubicisomer) and is more stable than the cubic isomer by about 119 kcallmol. Even though both the doublet and the quartet states of these cationic met-cars give almost the same structure, the doublet state is more stable than the quartet state by about 18 kcaljmol. Detailed structural features of doublet isomers of cationic metcars are presented below. Cubic Cationic Ti Met-car. Figure 1 shows the doublet structure for the cationic Ti metcar in which each atom is represented by a number or a letter. The carbon atoms 1O+h and 1li-1 are shown with letters for clarity. Figure 2 represents a space-fill model (based on van der Waals radii of Ti and C atoms) of the same cluster where Ti atoms are shown by dark filled circles and the C12 cage structure is shown as a shaded interior. Mulliken charge on the Clz cage structure is about -2.0 and the rest of the charge (+3) lies on eight Ti atoms in the 0 1993 American Chemical Society
10938 The Journal of Physical Chemistry, Vol. 97, No. 42,1993
Khan
Figure4. Optimized C Istructure ~ shown in absence of metal atoms and representing a highly symmetrical icosahedron with each C atom bonded to five nearest neighbors at a distance of around 1.58 A. Figme 1. Cubic isomer of Ti&+ presented with eight titanium atoms at comers of a distorted cube (shown by dotted lines) surrounding a distorted icosahedral carbon cage structure.
--"=
Figme 2. Cubic isomer O f Ti&+ presented in a space-filled model with metal atoms shown by dark filled circles surrounding the shaded interior of the carbon cage structure.
1
Figme 3. Noncubic isomer of Ti&12+ presented with eight titanium atoms surrounding a distorted icosahedral carbon cage structure; it is more stable than the cubic isomer.
cationic metcar and suggest a significantionic characterin metalcarbon bonds. We also examined whether Cl2 or its ionic forms can exist by itself without having metal atoms around. These resulted in stable Cl2 (Figure 4) and its ionic forms, like C1z2having icosahedral structures of high symmetry. Each icosahedron represents a hollow carbon cluster of 20 triangular faces in which each C has five nearest members at a distance of around 1.6 A. The bond angle C-C-C belonging to the same triangular face is around 60' and two adjacent faces is around 108'. In Table IIa-c, Ti3.9 A and bond index close to zero) and two T i 4 bonds at a distance of around 2.3 A. In noncubic isomer the Ti atoms 2,5,6, and 7 are involved in the Ti-Ti bond formation at around 2.90 A with a bond index of 1.0 (single covalent bond) and are shown with solid lines in Figure 3. The Ti atom 4 has three weak bonds with Ti atoms 1, 3, and 8 at distances of 3.76,3.84, and 3.52 A with bond indices of around 0.1, 0.1, and 0.2 respectively. Each of the Ti atoms 1,3, and 8 has only a weak Ti-Ti bonding with the atom 4 at the abovementioned distance. In addition, in the noncubic isomer each of the Ti atoms 1,3,4,6, and 8 is bonded to three C atoms and each of the rest (Ti atoms 2,5, and 7) is bonded to four C atoms at
The Journal of Physical Chemistry, Vol. 97, No. 42, 1993 10939
Structure of the Ti&12+ Cluster
TABLE 11
TABLE II1
(a) Calculated Ti-C Distances in Cubic Isomer (Figure 1)' cubic
atom
face of Ti8 1234 1234 1476 1476 2385 2385 2165 2165 3478 3478 5678 5678
Ti-C dist from C atoms in column 1 (A) (1) 2.34 (3) 2.36 (1) 2.36 (7) 2.34 (3) .. 2.34 (5) 2.35 (5) 2.35 (1) .. 2.33 (41 2.23 (3) 2.33 (5) 2.35 (8) 2.35 2.34 0.03
(2) 2.34 (4) 2.21 (4) 2.24 (6) 2.34 (2) 2.35 (8) 2.34 (2) 2.35 (6) 2.36 (7) 2.37 (8) 2.34 (6) 2.33 (7) 2.32 2.32 0.04
.,
(3) 3.80 (1) 3.83 (7) 3.85 (1) 3.81 (5) 3.80 (3) 3.78 (1) 3.77 (5) 3.80 (3) 3.83 (7) 3.79 (7) 3.78 (5) 3.80 3.80 0.02
(4) 3.69 (2) 3.80 (6) 3.82 (4) 3.70 (8) 3.80 (2) 3.81 (6) 3.79 (2) 3.80 (8) 3.81 (4) 3.66 (8) 3.79 (6) 3.78 3.77 0.05
(b) Calculated Ti-Ti Distances (A) in Cubic Isomer (Figure l)b Ti Ti-Ti dist from Ti in column 1 atom (1)
(2) 3.96 (2) 4.01 (2) 3.96 (4) 3.94
(3) (5)
(7)
av SD
(4) 4.02 (4) 3.92 (6) 3.95 (6) 4.03
(6) 3.95 (8) 3.93 (8) 4.02 (8) 3.93
3.96 0.04 (c)
(12)
(1) 3.30 2.38 3.87 2.39 3.97 2.34 3.39 4.58 4.68 3.63 4.92 4.50
(2) 3.74 2.64 2.35 4.26 4.66 3.70 2.33 2.34 3.63 4.46 4.53 3.57
(3) 2.38 3.62 2.33 3.95 3.27 4.92 4.50 3.39 2.38 4.68 3.89 4.58
(4) 2.39 3.62 3.93 2.35 2.37 3.87 4.77 4.79 3.63 3.57 3.89 4.77
(5) 4.70 3.64 4.52 3.74 4.29 2.34 2.34 3.57 4.48 2.66 3.71 2.34
(6) 4.78 3.89 3.78 4.76 4.75 3.79 2.40 2.39 3.87 3.88 3.77 2.38
(7) 4.25 4.45 3.69 4.64 3.68 4.51 3.58 2.33 2.60 3.62 2.31 2.34
(8) 3.86 4.60 4.88 3.17 2.33 3.80 4.58 4.52 3.63 2.36 2.39 3.46
Zalculated Ti-Ti Distances (A) in Noncubic Isomc:r (Figure 3)b Ti Ti-Ti dist from Ti in column 1 atom (1) (2) (3) (4) . . (5)
(6) (7)
(2) 4.56 (3) 4.36 (4) 3.84 (8) .. 3.52 (6) 2.87 (7) 2.88 (8) 4.46
(4) 3.76 (5) 4.33 (7) 4.52
(5) 4.36 (6) 2.87
(7) 4.38
(8) 4.63
(7) 4.36
(c) Calculated C-C Distances in Noncubic Isomer (Figure 3) C dist (A) from C atoms in column 1 atoms (12) 1.58 (14) 1.69
(13) 1.57 (15) 1.60
(17) 1.73
Calculated C-C Distances in Cubic Isomer (Figure 1)'
C atoms (9)
(a) Calculated T i 4 Distances in Noncubic Isomer (Figure 3)' C Ti-C dist from C atoms in column 1 (A) atom ___
dist (A) ( W 1.59 (11) 1.60
(1Of) 1.58 (lli) 1.58
(log) 1.59 (llj) 1.58
UOh)
1.60 (111) 1.60
(10) 2.22 (Ilk) 2.21
(18) 1.69 (19) 1.54
,I Av representsan average of Ti-C values in each of columns 3-6. SD representsthe standard deviation from each average. Av representsan average over all the nearest-neighbor Ti-Ti distances presented in this table, and SD is the standard deviation from the average. The other C atomsare each bonded similarlywith four nearest neighbors at a distance ranging from 1.58 to 1.60 A (shown with solid lines in Figure 1) and the fifth member at a distanceranging from 2.20 to 2.30 A (shown with C-C dotted lines). around 2.4 A. From this analysis we can say that Ti atoms 1, 3, and 8 are most weakly held in the noncubic metcar isomer followed by atom 4 which is less strongly held than the other Ti atoms. In cubic isomer, on the other hand, such a remarkable variation in Ti bond strengths are not expected as each Ti atom is similarly bonded to C atoms and has no bonding with other Ti atoms. Carbon Cage Structure and Possible Mechanism of Met-car Formation. We already pointed out that 12 carbon atoms form a highly symmetrical icosahedral structure in absence of metal atoms around it and distortion of the carbon cage in met-car is due to interaction of metal atoms with the carbon cage. The studies of relative stabilities of various ionic species of this cage structure suggest that the singlet or triplet state of the neutral
There are three distinct lengths with average values of around 2.38, 3.68, and 4.61 A with standard deviations of about 0.09,0.19, and 0.17, respectively. There are three distinct Ti-Ti distances of around 2.87, 3.70, and 4.44 A with standard deviations of about 0.00,0.14, and 0.10
respectively. structure has themaximumstability. Theneutral Cl2 cage (singlet or triplet) is more stable than the ionic Clz- (doublet), C12+ (doublet) and C1z2-(singlet) cage structures by around 59, 129, and 289 kcal/mol. Figure 4 represents the neutral carbon cage structure where solid lines represent C-C bonds. Different bond lengths and angles for this cage structure are presented in Table IV. We should point out that each of the neutral as well as ionic carbon cage structure has almost identical structural features,
10940 The Journal of Physical Chemistry, Vol. 97, No. 42, 1993
Khan
TABLE Iv: Calculated C-C Distances (A)and Some of tbe Angles (dea) in CIZIcosahedron (Figure 4) atoms
dist from C atoms in column 1
(9) (10) (11) (12) (13) 1.59 1.59 1.62 1.54 (15) 1.54 (16) i.62 117) i .62 (18) 1.54
5
angles (14) 1.62 (19) 1.62
9-14-19 = 108 9-14-18 = 108 10-1413 = 104 10-14-18 = 108 13-14-19 104 9-14-10 = 59 10-14-19 = 61 19-14-18 59
etc. Figure 5. Dodecahedral structureof metcar, proposed by Castleman and
co-workers, is presented.
(20) 1.54 (16) (17) (20) 1.59 1.62 (17) (18) (20) 1.62 1.59 (18) (19) (20) 1.59 1.59 (19) (20) 1.62
av = 1.58 A
SD = 0.03
that is, each carbon atom in it is bonded to five nearest neighbors at distances of around 1.58 A and bond angles are around 60° and 108O. The C122- ion among all these species shows the maximum symmetry with each C-C bond length of around 1.59 A and bond angles of around 60° and 108O with standard deviations of around 0.00. Even though an icosahedral carbon cage structure is made up of triangular faces of carbon atoms, each carbon atom in it is also involved with pentagonalring formation with other carbon atoms. For example, the carbon atom 14 is bonded with each of the carbon atoms 9, 10, 13, 18,and 19 (Figure 4) at a distance of around l.58A. Eachoftheseatoms,inadditiontoitsinvolvement with triangular faces, is also involved in pentagonal ring formation. The carbon atom 14, for example, is part of a pentagonal ring defined by atoms 9,12,17,18,and 14 and a second ring defined by atoms 10, 11, 12, 13, and 14. Some of the pentagonal ring angles (around 108O) and triangular face angles (around 60°) are presented in Table IV. Even though the 60' bond angles may result in certain bond strains, the 108O angles are the favorable ones and are presumably responsible for the overall stability of this cluster. The stability of a C12 cage structure (Figure 4) relative to larger ones, such as CM,could not be established from the present theoretical studies. We can, however, postulate that the larger fullereneshaving only five- and six-memberedrings will be more stable than the smaller C12 structure having three- and fivemembered rings. The abundance of C a cluster formation in most experiments1>l7may also suggest a greater stability of CM fullerene structure compared to the smaller C12 cage structure. We, therefore, can predict that these C12 hollow cage structures can be seen at lower temperatures without having metal atoms around them. The C-C distance in this structure (Figure 4), as already mentioned, is around 1.58 A and is somewhat longer than that in cyclopropane. It should be pointed out that the ZINDO SCFcalculationpredicts a C-C distancein cyclopropane to be around 1.49 A and compares quite well with that given by the ab initio calculation at 6-31G* level (1.497 A) or the experiment (1.50&.Is It is interesting to point out a remarkable structural similarity between carbonyl groups in F e ~ ( C 0 ) ~and z C12 group in Ti&+ clusters. As in the titanium cluster, 12 carbon atoms in carbonyl groups form a distorted icosahedral cage structure.19 While the eight metal atoms in Ti met-car remain outside of the distorted Clz cage structure, in carbonyl the three metal atoms remain inside of the cage.
On the basis of the present study, we can postulate a possible mechanism of or TisC12+cluster formation. The existence of a highly symmetrical icosahedral C12 cage structure in the absence of metal atoms and the distortion of this cage structure in the metcar may suggest that the major part of the carbon cage formation takes place prior to the attachment of metal atoms. Since the reaction of titanium atoms with any hydrocarbon molecule such as CH4, C2H2, etc., yields the same Ti8C12cluster,' we can expect a free-radical mechanism of the carbon cage formation. The growth of the carbon clusters is presumably terminated at different stages by the metal-carbon bond formation which prevents other C atoms from forming bonds and hence may add to the stability of these smaller cage structures. On the basis of our proposed mechanism, we can also expect other metal-carbon clusters in which either larger carbon cage structures (having five- and six-memberedrings) or condensation multicage str~ctures13~ may form. In the latter case of multicage formation the smaller C12 icosahedron may share one, two, or more atoms giving rise to C23, C22, C21, etc., which may be stabilized by metal atoms around them. The experimentally observed larger metal-carbon clustersmmay bedue to these larger carbon cage or multicage structures surrounded by metal atoms. Dodecahedral Structure vs Carbon Cage with Metal Atoms Around. The instability of the regular dodecahedral structure (having the sameTi-C and C-C distances)' of TisC12 or Ti&+, compared to the distorted icosahedral carbon cage structure surrounded by Ti atoms, can be explained by taking into account the remarkable differences in properties of Ti and C atoms. For example, the electronegativityvalues of Ti and C are 1 .5 and 2.5 eV and the first ionizationenergy values2' are 6.82and 1 1.26eV, respectively. These differences in properties suggest that the Ti-C and C-C distances are unlikely to be the same. Indeed, the closest Ti-C distances in Ti organometallics range from around 2.1 to 2.4 A and C-C range from around 1.3 to 1.5 A. Besides, the Ti-C bond energies in Ti organometallicsrange from around 184to 286 kJ/molIMand is significantlylower than thoseof C-C bonds, which range from around 348 to 840 kJ/mol (singletriple bond). Hence, on the basis of the known Ti organometallic data, wecansay that carbon atoms by clusteringamongthemselves may achieve stability by overcoming bond strains in theicosahedral structure. During the geometry optimization of TisC12+ from a regular dodecahedral structure, the titanium atoms are expected to move away from the carbon atoms, so as to have Ti-C distances greater than those of C-C in a pentagonalring (of a dodecahedron) allowing a greater interaction among the carbon atoms, which will bring them closer together forming a distorted icosahedral cage with metal atoms lying outside of it. While in the dodecahedral structure' each Ti atom has three Ti-C bonds (Figure 5 ) , in our optimized structures (Tables IIa and IIIa and Figures 1 and 3), we can expect two to four such bonds (at around 2.3 A) and an increased number of C-C bond formation. Since the bondenergyof C-Cisgreaterthan that ofTi4,agreaterstability
Structure of the Ti&+
Cluster
is achieved in a carbon cage formation (surrounded by Ti atoms) from a regular dodecahedron. A careful examinationof the results of recent photodissociation studiesZZon different metcars will also provide a strong support for our structure rather than the dodecahedral structure (Figure 5). These studies suggest that titanium, vanadium, iron, and chromium met-cars dissociate by losing metal atoms successively without the elimination of carbon atoms. Under their experimental conditions iron met-cars lost up to six, chromium up to seven, and titanium or vanadium up to three metal atoms. Even though most of our results are based on Ti met-cars, our preliminary results on iron and vanadium metcars suggest similar basic structures (Figures 1-3), and hence we can postulate that all the metcars may have the same basic structure (also expected from the experiments of Castleman and co-workers). It is interesting to point out that a regular (all bond lengths same) or a distorted dodecahedral structure (which accommodates the bond length variations) of metcar cannot account for successive dissociation of metal atoms (upto seven) without any elimination of carbon atoms. By referring to Figure 5, a dodecahedral structure, we can say that after the photodissociation of metal atoms 1, 2, and 3 (Ti or any other metal atom, M), if the metal atom 4 dissociates, it must carry two C atoms with it no matter whether the M-C bond is weaker or stronger than a C-C bond. Hence, the observation of the dissociation of up to seven metal atoms without theelimination of carbon atoms cannot beexplained by a regular or a distorted dodecahedral structure. On the other hand, the metcar structure with eight metal atoms (M) lying outside of the carbon cage (as in Figures 1-3) can explain all the experimental results. Since the metal atoms lie outside, any number of them can be dissociated without the elimination of C atoms provided that the M-C bonds are significatly weaker than the C-C bonds. This may be the case with most metal atoms used in photodissociation experiments, except Zr, which is known to give stronger M-C bonds*3dcompared to Ti in the same organometallics (having same ligands and similar bonding) and hence can explain why most photodissociated Zr atoms carry carbon atoms.22 How many C atoms will becarried by the metal will depend upon how many of them are closely linked with the metal in the cluster and the available energy in appropriate vibrational mode. A similar bond energy comparison for other metal atoms (in the same organometallic) suggest that the M-C bond is the weakest for chromium, followed by iron and vanadium.13c Even though we could not get any direct comparison (based on same organometallics) of Ti-C energy with V-C, FeC, or Cr-C, we expect that the Ti-C bond energy will be close to that of V-C in met-cars and hence may explain why a larger number of metal atoms were eliminated from the Fe and Cr met-cars (six to seven M atoms) compared to Ti or V met-cars (three M atoms) under the same experimental conditions. In cationic Ti met-car since the noncubic structure is significantly more stable than the cubic structure we expect a larger proportion of noncubic isomer formation in the experiment compared to the cubic isomer. As we already pointed out, the three Ti atoms (1, 3, and 8 in Figure 3) in the noncubic isomer are most weakly held
The Journal of Physical Chemistry, Vol. 97, No. 42, 1993 10941 among all the Ti atoms and hence during photodissociation these atoms are expected to leave more readily than the others. The experimental observation of the ease of the removal of three Ti atoms in cationic Ti met-car supports our structure of cationic metcar. Hence, on the basis of our calculations as well as experimental evidence, we can suggest that the metcar structure has a distorted icosahedral carbon cage surrounded by metal atoms.
Acknowledgment. We thank B. May and A. W. Castleman for giving us the coordinates of their proposed Ti&2 dodecahedral structure and G. L. Geoffroy for a key reference on structures of Ti organometallic compounds. We also acknowledge helpful discussions with W. D. Edwards and assistance of A. Buckvich and W. Skrzypek with some of our calculations and graphics. All of our quantum mechanical calculationswere performed by using an IBM ES/3090-600S computer at the facilities of the Pennsylvania State University Center for Academic Computing and the molecular models were obtained by using Alchemy I1 series of programs from Tripos Associates, Inc. References and Notes (1) Guo, B. C.; Kerns, K. P.; Castleman, Jr., A. W. Science 1992, 255, 1411. (2) Zerner, M. C. Quantum theory project; University of Florida, Gainsville, FL 32611. (3) Zerner, M. C.; Loew, G. H.; Kirchner, R. F.; Muller-Westerhoff,U. T. J . Am. Chem. SOC.1980, 102, 589. (4) Culberson, J.; Knappe, P., Rosch, N.; Zerner, M. C. Theor. Chim. Acta 1987, 71, 21. (5) Bacon, A. D.; Zerner, M. C. Theor. Chim. Acta 1979,53, 21. (6) a) Zerner, M. C. In: Reviews in Computational Chemistry; Lipkowitz, K.B.,Boyd,D.B.,Eds.;VCHPublishers: New York, 1991;p313. b)Stewart, J. J. P. In: Reviews in Computational Chemistry; Lipkowitz, K . B., Boyd, D. B., VCH Publishers: New York, 1990; p 45. (7) Bendale, R. D.; Baker, J. D.; Zerner, M. C. Int. J. Quantum. Chem: Quantum Chem. Symp. 1991,25, 557. ( 8 ) Zerner, M. C.; Loew, G. H.; Kirchner, R. F.; Mueller-Westerhoff, U. T. J. Am. Chem. SOC.1980, 102, 589. (9) Bassi, I. W.; Allegra, G.; Scordamaglia, R.; Chioccola, G. J. Am. Chem. SOC.1971, 93, 3788. (10) Pez. G. P. J. Am. Chem. SOC.1976. 98. 8072. (1 1j Clearfield, A.; Warner, D. K.; Molina, C.H. S.; Ropal, R.; Bernal, I. Can. J . Chem. 1975, 53, 1622. (12) Lucas, C. R.; Green, M.; Forder, R. A.; Prout, K. J . Chem. Soc., Chem. Commun. 1973, 97. (13) Pruchnik, F. P.; Duraj, S. A. Organometallic Chemistry of the Transition Elements; Plenum Press: New York, 1990; (a) pp 518, 607, (b) pp 160, 170, (c) p 150, (d) p 202, (e) pp 54, 528. (14) Sinanoglu,0.;Wiberg, K. B. Sigma Molecular Orbital Theory;Yale University Press: New Haven, CT, 1970; p 186. (15) Kroto, H. W.; Heath, J. R.; O'Brien, S. C.; Curl, R. F.; Smalley, R. E. Nature 1985, 318, 162. (16) Hopkins, J. B.; Langridge-Smith,P. R.; Morse, M. D.; Smalley, R. E.J . Chem. Phys. 1983, 78, 1627. (17) Kroto, H. R. Nafure 1987, 329, 529. (18) Hehre, W. J.; Radom, L.; Schleyer, P. R.; Pople, J. A. Ab initio Molecular Orbital Theory; John Wiley & Sons: New York, 1986. (19) Dorn, H.; Hanson, B. E.; Mortell, E. Inorg. Chim. Acta 1981, 54, L71. (20) Wei, S.; Guo, B. C.; Purnell, J.; Buzza, S.; Castleman, Jr., A. W. Science 1992. 256. 818. (21) Handbook of Chemistry and Physics, 66th 4.;Weast, R. C., Ed.; Chemical Rubber: Boca Raton, FL, 1985. (22) Pilgrim,J. S.and Duncan, M. A. J . Am. Chem. SOC.1993,115,4395.
