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

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Bonding 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
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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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bonding, metalцfullerene, covalency, c28, complexes, orbital, endohedral
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