Cohesive Energy of Metallic Beryllium

A manageable expression for calculating the total energy of a solid is given in the Hartree-Fock approximation when one-electron wave functions are given by the APW method. The lattice sum in the expression is written down exactly, with the use of the structure constants in the KKR method. The total energy of metallic beryllium is computed from the APW functions obtained from the band structure calculation, in which the shape of the Fermi surfaces was in good agreement with the experiments. The result is quite favorable, as an approximation which neglects the correlation energy. We find that the cohesive energy of beryllium comes mainly from the difference in the Hartree-Fock energy in the atom and the solid. The exchange operator in real solid is found to depend on the wave number very slightly. The exceptionally high cohesive energy of beryllium is closely correlated with the formation of the bonding charge reported previously.