Energy-Band Structure of a Hypothetical Carbon Metal

Energy bands are derived for a hypothetical crystal composed of carbon atoms arrayed in a single face-centered-cubic lattice by the method of orthogonalized plane waves (OPW). The bands are compared with those of diamond which have been obtained by Herman. It is shown that the hypothetical crystal is an almost perfect metal. A potential for atomic carbon in the ${}_{}{}^3{}_{}{}^{}P$ ground-state is computed within the framework of Slater's free-electron-exchange approximation. An analytical approximation to this potential is provided. Results of a general symmetry analysis, appropriate for application of the OPW method to any f.c.c. lattice, are given. The cohesive energy of the metallic crystal relative to that of diamond is discussed within the approximation employed.