The theoretical underpinnings of the linear combination of Gaussian-ty
pe orbitals (LCGTO) calculations of the density functional (DF) energy
of molecules and clusters are described. The generating function for
three-center integrals of arbitrary angular momenta is given in the so
lid-spherical-harmonic basis. Variational fitting is described and its
accuracy tested. The LCGTO-DF method is used to address questions rel
ated to the problem of how it is that the methods of cluster science,
i.e., high-energy beams or currents, can be used to make C-60 in bulk
quantities. In particular, it is shown that C-60 is neither especially
stable nor is it the only large, stable, perfectly round, approximate
ly sp(2) carbon molecule. (C) 1996 John Wiley & Sons, Inc.