J. Phys. Chem. 19!42,96,9095-9097
9095
Asymmetric Localization of Titanium in C2* Brett I. Dunlap, Code 6179, Naval Research Laboratory. Washington, D.C. 20375-5000
Oliver D. Hiiberlen, and Notker Riiscb* Lehrstuhl fiir Theoretische Chemie, Technische Universitcit Miinchen, W-8046 Garching, Germany (Received: July 20, 1992: In Final Form: September 22, 1992)
Linear combination of Gaussian-type orbital (LCGTO) local density functional (LDF) calculations on the@ & iT endohedral fullerene complex suggest that the titanium atom is too small to fill completely the interior volume of the tetrahedral c28 fullerene and the titanium atom is attracted a significant distance, 0.5 A, toward one of u e four corners of the tetrahedron. This may be one reason why is experimentally less abundant and stable than U@C=, which has a larger endohedral atom.
When C,, was determined to be unusually abundant in certain mass spectra because it was a spherical shell of threefold-coordinated carbon atoms (a fullerene), the molecule was postulated to be able to trap atoms inside.' Soon experimental evidence was found for trapping a lanthanum atom2 The technology for preparing macroscopic amounts of empty fullerenes3has recently been modified to create endohedral complexes with an increasing number of metal atoms and cluster^."^ The host fullerenes for these complexes are the size of Cso and larger. A guest atom has enough room to 'roll around" on the inside surface in these large cage^,^^^ but it might be forced to occupy the central position inside smaller fullerenes. C2*is the smallest experimentally important f~1lerene.l~Recent experimental and theoretical work suggests that c28 is tetrahedral and tetra~a1ent.I~Thus, one expects that four hydrogen atoms bind on the outside of c28 or that a single tetravalent guest atom M is able to stabilize the corresponding M a c 2 8 complex, where the @ notation has been used to indicate the endohedral complex! Experiment suggests that stabilization, as measured by enhanced abundances, of this fullerene by tetravalent atoms increases in the order Ti@Cz8< Zr@Czs< Hf@C28< U@cm" Because titanium is smaller and affords significantly less stabilization than the other endohedral tetravalent atoms in the study, it might be that titanium has its equilibrium position a significant distance from the center of c28. Here, this possibility is studied theoretically using the first-principles hear combination of Gaussian-type orbitals (LCGTO) local density functional (LDF) method.I6 Figure 1 shows the proposed15tetrahedral structure for CZs. It contains three symmetry-inequivalent sets of atoms. The four symmetry-equivalent 'black" (b) atoms mark the corners of the tetrahedron defining the head end of threefold symmetry axes, C3(h). Toward the opposite (tail) end of each threefold axis, C3(t), is the center of a hexagon formed by a ring of carbon atoms. The rest of the cage, apart from these four hexagons, is composed of pentagons. Around the perimeter of the four hexagons the other two types of symmetry-inequivalentatoms alternate. The 'white" (w) set of atoms forms six nearest-neighbor pairs, the midpoints of their bonds defining an octahedron. These "white" pairs join two pentagons containing a 'black" comer atom. The 12 'gray" (8) atoms are never nearest neighbors to each other. The intersection of a plane formed by a 'black", "white", and 'gray" atom on an equator of the fullerene is indicated in Figure 1 by the dashed line. This plane, shown in Figure 2, includes examples of all symmetry axes for this tetrahedral fullerene. There are six equivalent planes of this type; each can be specified by a pair of 'black" atoms or a pair of neighboring 'white" atoms. In the previous ab initio study of Ti@C28and Z T @ C ~the ~, endohedral atom was constrained to lie at the center of the cluster, *Author to whom correspondenceshould be addressed. Tel.: (++49+89) 3209 3616. Fax: (++49+89) 3209 3622. E-mail:
[email protected].
0022-3654/92/2096-9095%03.00/0
TABLE I: Geometries of Tetnbedrnl cu4 method molecule d k dw d,
HF HF HF empirical
c28
1.440
1.412
Ti@C2* 1.453 1.432 Zr@C28 1.456 1.441 CZ
1.465
1.452
1.527 1.492 1.511 1.490
rbx fh 1.939 1.961 1.949 1.959 2.514
The three unique bond distances connect nearcst-neighbor black and gray (db),gray and white (dp), and white and white (d,) atoms of Figure 1. Two other distances are ntcessary to uniquely specify the geometry of the cage, e.g., the distance of the center of the hexagons (rbex)and of the black atoms (rb)from the molecular center. The results are obtained from HartretFock optimizations (HF)ISband, in this work, using an empirical potential (empirical).l' All distances are in A.
i.e., at the intersection of the three axes in Figure 2. In that study, the geometry of the empty and two endohedral complexes were optimized in tetrahedral symmetry at the Hartree-Fock (HF) level of theory using a double zeta basis.lsb The results of these optimizations are given in Table I, where they are compared with the optimized empirical potential. (228 geometry used for the cage in this work. Five distances are necessary to completely specify the tetrahedral c28 structure unless a constraint is placed on the structure such as requiring the six atoms in each hexagon to be coplanar. We take these distances to be the three unique nearest-neighbor distances, dbg, dP, and d,, and the distances from the center to the center of a hexagon, rhcx,and from the center to a black atom, fb. The H F re$ults (Table I) show that the fullerene distorts somewhat as the endohedral atom is varied or removed. We expect variations of similar magnitude as an endohedral titanium atom moves about near the center of the cage. In our study of such motions for titanium, we kept the structure of the cage fixed at the empirical geometry which is close to the H F shell geometry with the titanium atom at the center. For this fixed geometry of the cage, we computed the LCGTO-LDF potential energy as the titanium atom is moved away from the center in both directions along each symmetry axis in Figure 2. Actually, only one end of any C2axis has to be explored because tetrahedral symmetry requires the other two C2 axes to be perpendicular to the first. However, both the head and tail ends of the C3 axis have to be investigated. The local density approximation used in this work is the V~sko-Wilk-Nusair'~functional form for the exchangacorrelation potential that interpolates between the essentially exact Ceperley-Alder free-electron gas calculation^'^ in the completely ferromagnetic and completely paramagnetic limits. The starting orbital basis set for carbon, a 9s/5p/ld basis,20was augmented with a d exponent of 0.621(all exponents are given in au) and contracted to an atomic 5s/4p/ Id basis according to a spin-restricted calculation. The starting orbital basis set for titanium, a 14s/lOp/Sd basis,22was augmented with one s (0.205), two p 0 1992 American Chemical Society
Letters
9096 The Journal of Physical Chemistry, Vol. 96, No. 23, 1992 TABLE II: LCGTO-LDF Results for the Motion of Titanium inside Cma rq, A Eq,eV ur,cm-' d(nn), A c 2 0.48 -1.83 542 1.97 (w) C3(h) 0.52 -2.05 54 1 2.00 (b) C3(t) 0.47 -1.68 524 2.06 (w) center 600 ib 2.42 (w) 513 ie
d(nnn), A 2.15 (8) 2-05 (8) 2.09 (g) 2.46 (g)
A
D
Q(Ti), e
1.83 2.82 2.02
1.49 1.29 1.53 1.45
0.00
OThe center is a position of unstable equilibrium, relative to which titanium is stabilized by E, at a radial distance rq out the three different high-symmetry axes (see Figure 2). The vibrational frequencies along these axes at the minima are 0,. The imaginary frequencies at the center are along the twofold and threefold axes, respectively. From these extrema, the distances to the nearest neighbor, d(nn), and the next-nearest neighbor carbon atoms, d(nnn), and the 'color" of these neighbors are listed followed by the total molecular dipole moment p (oriented along the direction of the displacement) and the Mulliken charge of thetitanium atom Q(Ti).
0.4 -
0 7 Y
0.0 -0.4 -
-
-0.8' -0.8
i
1
I
-0.4
I
I
I
0.0
I
I
I
0.4
'
0.8
Figure 3. Contour plot of the LCGTO-LDF potential energy in the plane of Figure 2. The various stationary points with respect to the motion 'on global minimum, A local maximum, the shell" are marked as follows: 0 saddle point. The contour spacing is 0.05 eV with the lowest contour shown for -2.0 eV.
+
Figure 1. Structure of the tetrahedral c 2 8 fullerene. The plane shown in Figure 2 is indicated by dashed lines.
t c2
Figure 2. Equatorial plane of tetrahedral c 2 8 in which the location of the titanium atoms has been varied. Also shown are the symmetry axes that lie in the plane and the various stationary points on the axes.
(0.061 1,O.156), and a d exponent (O.072)F3J4 The titanium orbital basis set was contracted in analogous fashion to a 7s/6p/3d basis. The 9 carbon and the 15 titanium s orbital exponents were scaled by 2 and 2/3 to generate atom centered s-type parts of the charge density and exchange-correlation fitting basis, respect i ~ e l y .The ~ ~ 5 carbon p and the 11 titanium p orbital exponents were scaled in the same way to generate the atom centered r2-type fitting basis functions, respectively. To fit angular variations around both types of atom a geometric series of 5 ptype fitting exponents, 0.1,0.25,0.625, 1.5625, and 3.90625, was used in both fitting bases.26 The calculations were performed from the origin out past each minimum along the various symmetry axes of Figure 2 in steps
of 0.2 au. The results of these calculations are summarized in Table 11. At the center, the titanium atom is unstable with respect to outward displacements along both symmetry axes, as indicated by the two imaginary vibrational frequencies. The radial equilibrium positions reqall occur near a shell of radius 0.5 A about the origin. In contrast to the case of an alkali metal ion inside the much more symmetric buckminsterfullerene, C60,e* where there are little or no barriers to tangential motion, we find here large tangential forces near this shell inside c28 as can be seen from the contour plot of the potential energy in Figure 3. The binding energy of Ti@C28 with respect to Ti d2s2and c28 is quite large, 11.22 eV, even if one takes into account that the LDF approximation tends to overestimate binding energies.27 We calculate an ionization potential of 7.38 eV for the minimum geometry, slightly reduced from that of the Tdstructure, 7.59 eV. The resulting nearest-neighbor titanium-carbon distances (Table 11) are rather short compared to those typically found between titanium and carbon atoms in cyclopentadienyl rings which are about 2.35 A.28 An example is ( V ~ - C ~ H ~ ) ~ T ~ ( C O ) ~ . ~ ~ But the titanium-carbon distances in Ti@c28are quite similar to the T i 4 0 distance in the same compound29as well as the T i 4 distance in C13TiCH3. Experimentally, this latter distance has been determined to be 2.05 A;30an LCGTO-LDF calculation of this compound yields 2.00 A23which may be taken to indicate the accuracy of the computed bond distances. On the C3(h) axis the minimum is a true (global) minimum. On the C3(t) the radial minimum is actually a maximum with respect to the tangential motion "on the shell"; when motion in three dimensions is allowed, it is a saddle point. On the C2 axis there is a single minimum indicated by the symmetry-equivalent circular marks on this axis in Figure 3. The top and bottom contours about this axis are also contours in the two perpendicular tangential directions about either point, and the minimum energy outside the C,axis lies in between the other two minimal values along the C3 directions. Figure 3 and its six equivalent counterparts show that the potential energy surface of titanium inside c 2 8 in the neighborhood of the shell of radius 0.5 A has four global
Letters minima and four local maxima on the four threefold axes as well as six saddle points on the three twofold axes. The titanium atom is strongly localized in one of the four symmetry-equivalent C,(h) wells. The tangential vibrational frequency "on the shell" is approximately 200 cm-'. The WKB approximation of the tunneling probability between any two of the four C3(h) wells is about Therefore, the resultant splitting of the fourfold degenerate vibrational ground state is negligible, on the order of lo4 cm-'. Inspection of the oneelectron orbitals reveals that the bonding of the metal to the CB cage is to due to the interaction with x-type orbitals of the cage. Significant interaction occurs between Ti 3d orbitals and appropriate orbitals of c28,but also some overlap between Ti 4s (and even 4p) orbitals and orbitals of the shell is found. The shape of most orbitals does not change much when titanium is displaced from the center to its minimum energy location on the C3(h)axis, except for additional interaction of Ti 3d orbitals with high-lying shell orbitals derived from the orbitals 7t, and 16t2 of tetrahedral
[email protected] cage x orbitals lie energetically just below the HOMO l l a l , which retains its predominant carbon r character. A further consequence of this geometry change occurs in the manifold of unoccupied states. The nearest-neighbor T i 4 distance is quite large when titanium is located at the center of C28, 2.42 A; the orbital interaction is therefore correspondingly weak. As a result, one finds only a small HOMO-LUMO gap, 1.07 eV, the LUMO being the metal-cage antibonding Ti 3d ligand-field levels which are essentially degenerate (48e) - ~ ( 1 % = ~ )0.04 eV). This finding may be taken as an indication that the interaction of the metal and the six quasi-octahedrally coordinated C2moieties is comparable to that with the four tetrahedrally coordinated C4 units. However, when titanium is displaced to the C3(h) minimum, the strong additional Ti(3d)X interaction mentioned above shifts the corresponding antibonding ligand-field levels toward higher energies so that the LUMO 31e of Ti@C28is essentially identical to that of the empty CB cage, 8e. The HOMO-LUMO gap opens to 1.74 eV and the ligand-field splitting of the unoccupied Ti 3d manifold increases to about 0.8 eV. These differences in the spectrum of the one-electron levels between the tetrahedral and the C3(h) configuration will be reflected in the optical spectrum which may afford an experimental verification of the off-center location of the titanium. The Mulliken charge on the titanium atom is roughly 1.5 au, independent of the location of the atom. The fact that the direction of the dipole moment also follows the titanium atom suggests a picture in which the metal atom is viewed as giving up its charge to be spread all over the fullerene rather than being restricted to the carbon atoms that are nearest to it. This picture further suggests the possibility for a reasonably strong coupling between the titanium motion and light. All-electron LDF total energy calculations were used to study the interaction between tetrahedral c28 fullerene and an endohedral titanium atom. LDF potential energies as a function of the radial displacement from the center out any of the six twofold axes toward a C2 bond center, out any of the four three-fold axes C3(t) toward a C6 hexagonal center, and out any of the four threefold axes C3(h) toward a C4 tetrahedral corner suggest that
The Journal of Physical Chemistry, Vol. 96, No. 23, 1992 9097
the interaction between the carbon shell and the titanium atom is quite asymmetric. In the lowest-energy configuration the titanium atom is displaced about 0.5 A from the center toward one corner of the tetrahedron of carbon atoms. Such a large displacement precludes a significant amount of tunneling from one such minimum to any of the three other symmetry-equivalent minima and the asymmetry may be verifiable spectroscopically. Acknowledgment. This work was supported by the Deutsche Forschungsgemeinschaft (N.R.), by the Fonds der Chemischen Industrie (N.R.), and by the U S . Office of Naval Research through the Naval Research Laboratory (B.I.D.). The stay of B.I.D. at the TU MBnchen, where most of this work was done, was made possible through a NATO travel grant (CRG 920132).
References and Notes (1) Kroto, H. W.; Heath, J. R.; OBrien, S. C.; Curl, R. F.; Smalley, R. E. Nature 1985, 318, 162. (2) Heath, J. R.; OBrien, S. C.; Zhang, Q.; Liu, Y.; Curl, R. F.; Kroto, W.; Tittel, H. W.; Smalley, R. E. J. Am. Chem. Soc. 1985, 107, 7779. (3) Kritschmer, W.;Lamb, L. D.; Fostiropoulos, K.; Huffman, D. R. Nature 1990, 347, 354. (4) Chai, Y.; Guo, T.; Jin, C.; Haufler, R. E.; Chibante, L. P. F.; Fure, J.; Wang, L.; Alford, J. M.; Smalley, R. E. J. Phys. Chem. 1991, 95, 7564. (5) Alvarez, M. M.; Gillan, E. G.; Holczer, K.; Kaner, R. B.; Min, K. S.; Whetten, R. L. J. Phys. Chem. 1991, 95, 10561. (6) Johnson, R. D.; de Vrie-s, M. S.;Salem, J.; Bethune, D. S.;Yannoni, C. S. Nature 1992, 355, 239. (7) Weaver, J. H.; Chai, Y.; Kroll, G. H.; Jin, C.; Ohno, T. R.; Haufler, R. E.; Guo, T.; Alford, J. M.; Coccicao, J.; Chibante, L. P. F.; Jain, A.; Palmer, G.; Smalley, R. E. Chem. Phys. Lett. 1992, 190, 460. (8) Shinohara, H.; Sato, H.; Ohkohchi, M.; Ando, Y.; Kodama, T.; Shida, T.; Kato, T.; Saito, Y. Nature 1992, 357, 52. (9) Cioslowski, J.; Fleischmann, E. D. J. Chem. Phys. 1991, 94, 3730. (10) Bakowies, D.; Thiel, W. J . Am. Chem. SOC.1991, 113, 3704. (11) Schmidt, P. P.; Dunlap, B. I.; White, C. T. J. Phys. Chem. 1991,95, 10537. (12) Ballester, J. L.; Dunlap, B. I. Phys. Reu. A 1992, 45, 7985. (13) Dunlap, B. I.; Balleater, J. L.; Schmidt, P. P. J. Phys. Chem., in press. (14) Zhang, Q.L.; O'Brien, S.C.; Heath, J. R.; Liu,Y.; Curl, R. F.; Kroto, H. W.; Smalley, R. E. J. Phys. Chem. 1986, 90, 525. (15) (a) Guo, T.; Diener, M. D.; Chai, Y.; Alford, M. J.; Haufler, R. E.;
McClure, S.M.; Ohno, T.; Weaver, J. H.; Scuseria, G. E.; Smalley, R. E. Science 1992, 257, 1661. (b) Guo, T.; Scuseria, G. E.; Smalley, R. E., unpublished work. (16) Dunlap, B. I.; Rbch, N. Adu. Quantum Chem. 1990, 21, 317. (17) Brenner, D. W. Phys. Rev. B 1990, 42, 9458. (18) Vosko, S. H.; Wilk, L.; Nusair, M. Can. J . Phys. 1980, 58, 1200. (19) Ceperley, D. M.; Alder, B. J. Phys. Rev. Lett. 1980, 45, 566. (20) van Duijneveldt, F. B. IBM Research Report Nr. RJ 945, 1971. (21) Huzinaga, S., Ed. Gaussian Basis Sets for Molecular Calculations; Elsevier: New York, 1984. (22) Wachters, A. J. H. J. Chem. Phys. 1970,52, 1033. (23) Knappe, P.; Rbch, N. J . Organomet. Chem. 1989, 359, C5. (24) Knappe, P. Dissertation, Technical University Munich, 1990. (25) Dunlap, B. I.; Connolly, J. W. D.; Sabin, J. R. J . Chem. Phys. 1979, 71, 3396, 4993. (26) JiSrg, H.; Rosch, N.; Sabin, J. R.; Dunlap, B. I. Chem. Phys. Lett. 1985,114, 529. (27) Parr, R. G.; Yang, W. Density Functional Theory for Atoms and Molecules: Oxford Universitv Press: New York. 1989. (28) Thewalt, U. Gmelin 'Handbook of Inorganic Chemistry: Orgamtitanium Compounds, Part 4; Springer-Verlag: Berlin, 1984. (29) Atwood, J. L.; Stone, K. E.; Alt, H. G.; Hrncir, D. C.; Rausch, M. D. J. Orgonomet. Chem. 1977, 132, 367. (30)Briant, P.; Green, J.; Haaland, A.; Mollendal, H.; Rypdal, K.; Tremmel, J. J. Am. Chem. SOC.1989, 1 1 1 , 3434.
