# Bonding in Endohedral MetalЦFullerene Complexes f-Orbital Covalency in Ce@C28.

код для вставкиСкачатьBonding in Endohedral Metal-Fullerene Complexes: f-Orbital Covalency in Ce@C2s** By Notker Rosch,* Oliver D.Habevlen, and Brett I. Dunlap The technology for preparing macroscopic amounts of empty fullerenes[*]has been developed to furnish comparable quantities of host-guest complexes with one to three metal atoms inside the fullerene.[21The host fullerenes for these complexes are the size of C,, and larger, providing a single guest atom with a large volume in which to move a r o ~ n d . 1The ~ ~ smallest experimentally relevant fullerene, C,, ,[41forms endohedral compounds with uranium, hafnium, zirconium, and titanium, which were detected by mass spectr~metry.[~I These experiments indicate that the stabilization of this fullerene by tetravalent atoms, as measured by the relative abundance of the endohedral complexes, increases in the order Ti@C,, < Zr@ C,, < Hf(tr C,, < U(icC,,, where the (a notation indicates endohedral comp l e x e ~ . [ ’ ~The ” ~ proposed tetrahedral structure of C2,I5] is drawn in Figure 1. Inside C,,, titanium, the smallest of these Fig. 1. Structure of the tetrahedral fullerene C, . One of six symmetry-equivalent planes that contain two atoms of each of the three sets of symmetry-equivalent atoms I S indicated by solid and dashed lines. In this plane there are two threefold axes from the center to a black atom and one twofold axis from the center to the center of a bond connecting nearest-neighbor white atoms. Gray and white atoms alternate around the circumference of the four hexagons diametrically opposite the four black atoms. endohedral atoms, is strongly attracted (off-center by about 0.5 A) to one of the four “black” atoms, which form the corners of a tetrahedron, together with its three nearestneighboring “gray” atoms.[61 If a larger endohedral atom forms stronger simultaneous bonds to all four corners of the tetrahedron of black atoms, then the experimental trend in the stability of the M(k C,, complexes could be rationalized. Such bonding is facilitated by sp3 or sd3 (or even sf3) hybridization on the central atom. Alternatively, C,, may be stabilized by bonding between the endohedral atom and the six nearest-neighbor pairs of “white” atoms (see Fig. 1) that form an octahedron around the center of C,,. The radial distance from the center of C,, to the latter atoms is actually [‘I [**I Prof Dr. N . Rosch. Dip].-Phys. 0 . D. Hiberlen Lehrstuhl fur Theoretische Chemie der Technischen Universitdt Miinchen Lichtenbergstrak 4, D-W-8046 Garching ( F R G ) Dr. B. I. Duniap Theoretical Chemistry Section. Code 6179 Naval Research Laboratory Washington, DC 20375-5000 (USA) This work was supported by the Deutsche Forschungsgemeinschaft, the Fonds der Chemischen Industrie. and the U.S. Office of Naval Research through the Naval Research Laboratory. The stay of B. I. Dunlap at the T U Miinchen, during which this work was done, was made possible by a NATO travel grant (CRG 920132) about 0.1 A shorter than to the black atoms. If the sixfold coordination prevails. then metal-fullerene bonding would be facilitated by sp3d2 or sd2f3 hybridization on the central atom. The question of f orbital covalency in endohedral fullerene complexes, that is, whether the f orbitals of an endohedral atom contribute to the metal-cage bonding, however, cannot be decided by simply considering localized bonds to atoms (or combinations of atoms). If all possible valence orbitals (s, p, d, and f) of an endohedral f element atom, such as uranium, are employed in the bonding to the cage, then a maximum of 16 localized bonds can be formed. Group theory reveals that all these metal orbitals will be employed when localized bonds are formed to the sets of four black ( u , t,) and twelve white (or, alternatively, 2 t,). twelve gray) atoms ( a , e f , If a compound exhibits a sufficiently high symmetry then the bonding contributions can be isolated according to the irreducible representations of the molecular orbitals. Historically the di-x-[8]annulene complexes, [M(C,H,),] where M = Ce, Th, Pa, U, Np, and Pu, have provided fertile ground for such analyses.[’. ‘1 Due to the D,, symmetry, of all the metal atom valence orbitals only the f orbitals can contribute to an e3” HOMO. Indeed, calculations[’~1‘ and analysis of photoelectron spectraISclshowed an f orbital contribution to the metal-ring bonding in these sandwich complexes. Fullerenes are spheroidal shells of atoms often also having high symmetry. Endohedral fullerene complexes may thus be used to assess f orbital covalency with the help of symmetry arguments. At the center of buckminsterfullerene, icosahedral C,,, f orbitals can only contribute tog, and t,, molecular orbitals; at the center of tetrahedral C,,, only the f o r bitals of the s, p, d, and f valence atomic orbitals can contribute to a t , molecular orbital. The f electrons of Eu@ C,, und U(iiC,, remain localized on the metal atom, however,[91because the interior volume of C,, is too large to allow sufficient overlap between the central f orbitals and the n orbitals of the carbon frame. When the surface of a fullerene is approximated as a sphere with a fixed surface area per carbon atom, the usable interior volume of the fullerene is proportional to the number of carbon atoms to the power 2/3.[’01 In this approximation the interior of C,, is 40% smaller than the interior of C,, (51 YOsmaller than the interior of C,,), and even the f electrons of a lanthanide or an actinide atom might participate in the bonding. This spherical approximation provides yet another, unique way to analyze the electronic structure of fullerenes and endohedral fullerene complexes. The fullerenes can be viewed as spherical shells on which a single n orbital per carbon atom can delocalize forming molecular orbitals to be filled in the order s, p, d, f, etc., according to their nodal character.[“] Real spherical harmonics of rank 1 have 1 distinct nodal circles. On a fullerene shell these nodal lines must deform slightly to avoid atomic cores, thus lifting the m, degeneracy, but the fact that the HOMO and LUMO of C,, belong to an incompletely filled h shell ( I = 5 ) is obvious from contour plots of those orbitals.[”] This same spherical approximation applied to any isomer of C,, suggests that it can be viewed as having four electrons too few to complete its f shell. In particular. the HOMO group of tetrahedral C,,, 8a,, 14t,, and 71, (see Fig. 2), is ideally set up to overlap with f orbitals on the central atom. The bonding of a lanthanide atom inside C,, is best studied using a scaiar-relativistic extension[131of the first-principles linear combination of Gaussian-type orbitals local density functional (LCGTO-LDF) neth hod.^'^] This twocomponent approximation to the four-component Dirac + + + + determined by the empirical potential. The equilibrium position of Ce is at the center to an accuracy of 0.05 A. The vibrational frequency along the threefold axis is 360 cm and that along the twofold axis 350 cm- '. The binding energy ofCe@,C,, with respect to Ce f'd's' (theexperimental Ce ground state) and C,, ' A , is quite large, 13.7 eV. even if one takes into account that the L D F approximation tends to overestimate binding energies"'] and that the L D F ground state for Ce differs slightly from experiment. The electronic structures of the empty and tilled fullerene show that the spherical approximation is quite good in the case of CZ8.The energies of the one-electron orbitals of C,, and Ce@C,, show that two large gaps isolate the f-like orbitals (see Fig. 2). Of these, the 8ai and the three degenerate 14t, orbitals are singly occupied in the ground state of C,,. The entire set of corresponding f-like orbitals, 13ai, 20t2, and 71,, is completely filled in Ce(a,C,,. These f-like orbitals undergo strong downward shifts in energy due to the covalent metal-cage bonding. Similarly, the lower lying d-like orbitals, 13t, and 7e of C,,, are shifted even lower in energy (18t2 and 8e of Ce@C,,). These bonding interactions should be reflected in the photoelectron spectrum of the two fullerene compounds. We calcukdted (as a difference between two all-electron total-energy calculations) the first ionization potentials of C,, and Ce(niC2, to be 7.40 and 8.27 eV, respectively. In their photoelectron spectra both systems are expected to have a gap of similar size (about 2.4 eV) after the first three bands which correspond to the emission of an electron from the HOMO and from the second and third highest levels ( C 2 , : 8a,, 14t,, 7t,; Ce@C,,: 13at, 20t2, 7/,). These three orbitals each have significant Mulliken f electron population (approximately 0.1) on the Ce atom and lie within 1.2 eV of each other (see Fig. 2 and Fig. 3 a-c). These bonding f contributions are comparable to those found in uranocene [U(C,H8),].r71 ' I 1 8a, 6e 6t, = Fig. 2. One-electron energy level diagrams (LDF Kohn-Sham eigenvalues) for C,, and Ce:o C L x .The LUMOs are 8e and 10e. respectively. The empty fullerene has an open-shell quintet ground state; the levels 14/, and 8u, are half tilled. The spin-restricted levels are plotted for clarity of presentation; the splittings due to spin-polarization are very small asevery orbital is spread out evenly over a t least four different symmetry-equivalent atoms. The electronic structure is closed-shell. The Mulliken contribution of the cerium atom to of Ce,u each level is given in parentheses (in "A together with the appropriate angular momentum) where it is significant. form of the Kohn-Sham equations essentially takes into account the Darwin and mass-velocity We chose cerium as the endohedral atom because it can be tetravalent, because some aspects of its organometallic chemistry are strikingly similar to that of uranium,[71and because we have a good Gaussian basis set for all-electron quasi-relativistic LCGTO calculations with this We used an optimized empirical-potential geometry for Czs[t51that compares well with the cage geometries of TiGC,, and Zr@C,, optimized in tetrahedral symmetry at the Hartree-Fock level of theory.[5b1 We employed a L D F exchange-correlation potential that interpolates between the essentially exact free-electron gas calculations in the completely ferromagnetic and completely paramagnetic The starting orbital basis set for C (9~/5p),~""'was augmented with a d exponent of 0.6117b1 (all exponents are given in atomic units) and contracted to an atomic 5s/4p/l d basis according to a spin-restricted atomic calculation. The orbital basis set for Ce, 21s/16p/l 1d/9f,['3a1 was contracted similarly to an atomic 1Is/lOp/8d/5f basis. The 9 C s and the 21 Ce s orbital exponents were scaled by 2 and 2/3 to generate atom-centered s-type functions for the charge density and exchange-correlation fitting bases, respectively.[i81The 5 C p and the 16 Ce p orbital exponents were scaled in the same way to generate the atom-centered r2-type fitting basis functions. To fit nonspherical contributions around both types of atoms we employed additional fitting functions with higher angular momentum quantum numbers. A geometric series of 5 p-type fitting exponents, 0.1,0.25,0.625, 1.5625, and 3.90625, was used in both fitting bases of carbon.r18b1 These exponents were scaled by a factor of three to get f-type (the lowest nonzero angular momentum allowed by tetrahedral symmetry at the origin) fitting exponents for Ce that have radial maxima at the same distances. The symmetry of C,, is high enough that a rather complete picture of it may be formed by considering a special single slice through it. Such a plane is indicated by the bold solid and dashed lines in Figure 1. We studied the motion of a Ce atom along the symmetry axes shown in Figure 1 when the structure of the cage was kept fixed at the geometry .... .. . Fig. 3. Contour plots of the LDF one-electron orbitals with significant cerium character (in the plane defined in Fig. 1). The three highest occupied levels. a ) the 13u, orbital, b) the 20r, orbital. and c) the 7 f , orbital. exhibit Ce fcharacter as can be seen from the nodal patterns at the center of the plots. Orbitals with significant Ce d character are d) the 181, orbital and e) the 8r orbital. Thc LDF valence orbital with some Ce s character is f) the 1 2 a , orbital. The values of the 0.12 a.u., solid and dashed contour lines are f 0.015, _+ 0.03, _+ 0.06. and lines indicate valuesof opposite sign. The positions ofcarbon atoms in the plane and the midpoint between out-of-plane white atoms are indicated by black dots and an empty circle. respectively. Covalent orbitals with a similar amount of Ce d Mulliken population, the 181, and 8e orbitals, lie roughly 3 eV lower in one-electron energy and within 0.4eV of each other (see Fig. 2 and Fig. 3 d, e). The near degeneracy of these d shell orbitals indicates that the tetrahedral (four corners) and the octahedral (six pairs of bonds between white atoms) contributions to the ligand field are of comparable strength. Lower still in energy by 2 eV is the only valence orbital with significant Ce s character (0.04) (see Fig. 2 and Fig. 3f). The LUMOs of C,, and Ce(aC,, are rather similar in nature: they are cage orbitals. The metal-cage antibonding Ce f orbitals lie higher in energy (I~u,,22t,, and s t , ) and exhibit a ligand-field splitting of 0.26 eV. All other Ce valence orbitals are pushed to even higher energies than displayed in Figure 2. A picture of all the bonding contributions in Ce(+C,, is provided by the charge density difference map (Fig. 4)which is taken with respect to the charge density of the noninteracting fragments Ce and C2,. It is clear that cerium forms Fig. 4. Contour plot of the charge density difference for Cew C,, with respect to the noninteracting fragments Ce and C I S .The values of the contour lines are . and dashed lines indicate positive and 0.003 x 2.5” a.u. ( n = 0 ~ 3 ) Solid negative values. respectively. The positions of the cage atoms are marked as in Figure 3. strong bonds to the tetrahedral (black) atoms as well as to the pairs of octahedral (white) atoms (see Fig. 1). The bonds to the gray atoms are significantly weaker. The net Mulliken charge on the Ce atom is 1.1e. Our scalar-relativistic, all-electron, total-energy L D F calculations show that in contrast to titanium,I6]cerium is large enough to lie at the center of C,, . Because to a good approximation the fullerene is a spherical cage with frontier orbitals of F character, there is significant F covalency as indicated by Ce F population in the three highest occupied orbitals. These metal orbital contributions should be identifiable in variable-energy photoelectron spectra.[*‘] Due to its high symmetry CeGz C,, obviously provides an ideal case for a detailed analysis of the metalkage bonding in endohedral fullerene complexes. The general possibility of overlap characterized by rapid angular modulation will certainly also be found in less symmetric molecules. Strong bonds will arise when the valence orbitals of the enclosed system favorably complements the frontier orbital shell of the fullerene cage and have the proper radial extent, resulting in a closed-shell electronic structure. The isolobality principle[”I with its emphasis on orbital topology comes to mind. For example, in Sc,((r‘C,,r2e1 an i orbital of C,, with its six lobes in one plane might favorably match a molecular orbital of a Sc, cluster formed by an antibonding combination of three in-plane d orbitals. + Received: August 27, 1992 [Z 55391El German version: Angew. Clirin. 1993, 10.5. 78 [l] W. Kritschmer. L. D. Lamb. K. Fostiropoulos. Nurure 1990, 347, 354. [2] a)Y. Chai, T. Guo, C. Jin, R. E. Haufler. L. P. F. Chihante. J. Flure. L. Wang. J M. Alford, R. E. Smalley. J. Plijs. Cheni. 1991, 95. 7564: h) M. M. Alvarez, E. G. Gillan, K. Holczer, R . B. Kaner, K S. Min. R. L. Whetten. h i d . 1991, 95. 10561, c) R. D . Johnson. M . S. deVries, J. Salem. D. S. Bethune. C. S Yannoni, Nafure 1992, 355. 239: d ) J. H. Weaver. Y. Chai. G . H. Kroll, C. Jin. T R. Ohno. R. E. Haufler, T. Guo. J. M. Alford. J. Coceicao. L. P. F. Chihante. A. Jain, G. Palmer, R. E. Smalley. Chrni P h u . 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Quunfurn Chem. 1990. 21. 317. 1151 a ) D. W. Brenner, P / i m Re%..B 1990. 42. 9458; h) Representatives of the three sets of symmetry-equivalent carbon atoms (“black”. “gray”, and “white”. see Fig. 1 ) of tetrahedral C,, have the following coordinates (in A):(1.451,1.451. 1.451),(1.737.1.737.0.043)and(2.302.0.527.0S27). [I61 a ) D M. Ceperley, B. J. Alder. P/ivs. Rev. Let/. 1980, 45, 566: b) S. H. Vosko. L. Wilk. M. Nusair. Cum J P l i w 1980, 58, 1200. [17] a) F. B. van Duijneveldt. IBM Kes. K r p . K J 1971, 945; h) Guus.siun Busis Srrc {or Molecuiur Culculurrons (Ed.: S . Huztnaga). Elsevier. New York, 1984. [18] a ) B.I. Dunlap. J. W. D. Connolly, J. R. Sabin, J. Cheni. P h j ~ 1979, . 71. 3396. 4993: h) H. Jorg. N. Rosch, J. R. Sabin, B. I. Dunlap. CIimi.. P h w L r t f . 1985. 114, 529. [19] R. G. Parr. W. Yang, Drnsit?. Fzmcrionui Theorj,jor Aroms und Mokirles, Oxford University Press. New York, 1989. [20] a ) R. Hofmann. Anxew CJiein. 1982, 94, 725; Angcw. Chen7. h i . Ed. Engi. 1982. 21, 71 1: h) K. Wade. C/irm. Cominun. 1971. 792. c) D. M. P. Mingos. Notrrrr 1972. 236. 99. Organic Clathrate-Forming Compounds as Highly Selective Sensor Coatings for the Gravimetric Detection of Solvent Vapors** By Alberl EJiIen, Cluus Wimmrr, Edtvin Weber,* and Jocrchim Burgon* The need for chemical sensors“] to measure concentrations for medical purposes and industrial process control applications, for warning and safety systems, in environmental analysis, etc. is great.”] However, the properties of the [*] Prof. Dr. E. Weher, Dip1.-Chem. C . Wimmcr Institur fur Organische Chemie and Biochemie der Universitit Gerhard-Domagk-Strasse 1. D-W-5300 Bonn-1 (FRG) Prof. Dr. J. Bargon. DiplLChem. A. Ehlen lnstitut fur Physikalische und Theoretische Chemie der Uiiiversitiit Wegelerstrasse 12. D-W-5300 Bonn-1 (FRG) [**I This work was supported by the Fonds der Chemischen lndustrie.

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