Electronic structures of ${\mathrm{K}}_3$${\mathrm{C}}_{60}$, ${\mathrm{RbK}}_2$${\mathrm{C}}_{60}$, ${\mathrm{Rb}}_2$${\mathrm{KC}}_{60}$, ${\mathrm{Rb}}_3$${\mathrm{C}}_{60}$, ${\mathrm{Rb}}_2$${\mathrm{CsC}}_{60}$, and ${\mathrm{Cs}}_3$${\mathrm{C}}_{60}$ crystals

The electronic structures of ${\mathrm{K}}_3$ ${\mathrm{C}}_{60}$, ${\mathrm{RbK}}_2$ ${\mathrm{C}}_{60}$, ${\mathrm{Rb}}_2$ ${\mathrm{KC}}_{60}$, ${\mathrm{Rb}}_3$ ${\mathrm{C}}_{60}$, ${\mathrm{Rb}}_2$ ${\mathrm{CsC}}_{60}$, and ${\mathrm{Cs}}_3$ ${\mathrm{C}}_{60}$ in the fcc lattice are calculated by means of a first-principles orthogonalized linear combination of atomic orbitals method. The band structures and the density of states for these six isoelectronic crystals are all very similar. High numerical precision is achieved by employing a large number of k points in the 1/24 of the Brillouin zone. The minute difference in the density of states at the Fermi level ${\mathit{E}}_{\mathit{F}}$, N(${\mathit{E}}_{\mathit{F}}$), is delineated and carefully analyzed. With the exception of the hypothetical ${\mathrm{Cs}}_3$ ${\mathrm{C}}_{60}$, there exists an approximate linear relationship between N(${\mathit{E}}_{\mathit{F}}$) and the lattice constant with a slope of 14 states/eV ${\mathrm{C}}_{60}$ per Å. Using the electron-phonon coupling parameters suggested by Schluter et al. and the usual McMillan formula, the superconducting temperatures for these crystals are estimated for a range of parameters. The set of parameters that yield ${\mathit{T}}_{\mathit{c}}$ in best overall agreement with the experimental values for the first five crystals are identified. Our results are also compared with other current theoretical calculations.