LIII. The cohesive energy of metallic magnesium

Summary The method of Wigner and Seitz is applied to metallic magnesium, using an ion-core field of the Hartree type. Two alternative self-consistent fields in the metal are considered, and the wave functions and energies are found not to differ significantly in the two cases. The total energy of the metal is obtained as the sum of four terms: the eigenvalue of the Schrödinger equation for the lowest state, and the Fermi, exchange, and correlation energies. The free-electron approximation is used to evaluate the latter two terms, but, in the case of the Fermi energy, both the free-electron value and a modification of this using the effective electronic mass at the zone centre are considered : the effective mass being calculated by a method due to Bardeen. The energy of the valence electrons in a free atom is obtained by a self-consistent field calculation, and, in addition, an estimate is made of the correlation energy of these electrons. It is pointed out that the method employed in the latter case appears to be inapplicable to beryllium, so that the true correlation energy may differ significantly from the estimated value. However, the calculated values of the lattice constant, cohesive energy, and compressibility are found to be in fair agreement with experiment, and a discussion of the effects of the various approximations is given.