*
S. Satpathy, V. P. Antropov, O. K. Andersen, O. Jepsen, O. Gunnarsson, and A. I. Liechtenstein
Max-Planck-Institut für Festkörperforschung, Stuttgart
*

We discuss the geometries of crystalline fcc C_{60}
for three cases of directional order, the hypothetical uni-directional
structure with space group Fm3, the bi-directional structure
P4_2/mnm) which is the ordered version of the structure observed
for alkali doped compounds at room temperature, and the
quadri-directional, low-temperature structure (Pa3) of pure
C_{60}. Analytical, parameter-free expressions for the
t1u-wavefunctions are derived and used to obtain analytical
conduction-band Hamiltonians for all three structures. The interactions
with other subbands are included in numerical tight-binding calculations
with a basis of 60 radial carbon orbitals per molecule. Ab initio
density functional (LDA) calculations are performed for uni-directional
fcc C_{60} and RbC_{60} for different lattice constants.
We use the
linear muffin-tin orbitals (LMTO) method in the atomic-spheres
approximation (ASA) with carefully chosen interstitial spheres. The LDA
bands are compared with photoemission and inverse photoemission data for
C_{60}. For RbC_{60} we find that the alkali atom is
fully ionized and that the doped electron occupies the
t_{1u}-band in a rigid-band
like fashion. Tight-binding theory explains why, and indicates that
this holds generally for A_{n-x}B_{x}C_{60}
with n\leq 3. The
LDA calculation shows that, for a given structure, the conduction band
scales uniformly in energy when, due to doping, the lattice constant a
is changed. The
energy scale behaves like
W~d(a)\exp[-d(a)/0.58 A ] where d
is the shortest distance between atoms belonging to different
molecules. Both the
LDA-LMTO and the tight-binding conduction-bands are well fitted by the
t1u-Hamiltonians. For a=14.1 A the density of states for a
conduction-band occupation of 3 electrons is 15, 17, and 21
el./(mol.eV) for the uni-, bi-
and quadri-directional structures, respectively. The calculated Stoner
exchange parameter is less than half the inverse density of states per
spin and atom, but the Coulomb self-energy for a molecular orbital
is presumably larger than the t1u-bandwidths, which are 0.52eV
(uni), 0.64eV (bi), and 0.44eV (quadri) for a=14.1 A . The LDA value
(0.58 A ) for the decay of the
inter-molecular hopping was used together
with experimental data for Tc vs. a for K_{3-x}Rb_{x}C60
compounds in the McMillan formula. The assumptions that the
Coulomb-interaction mu*, the electron-phonon interaction
V_{e-ph}, and the average phonon frequency omega are * all*
independent of a were found to be inconsistent.

Phys. Rev. B **46**, 1773 (1992).

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