Crystal Structures of the Simple Metals: Role of Correlation and Exchange

Abstract

Using a momentum-independent pseudopotential, we have derived an expression for the contribution of correlation and exchange to the structure-dependent part of the cohesive energy. Our only approximation consists of replacing the exact dielectric matrix by the Hartree dielectric matrix in the correlation-and-exchange term of Cohen's dielectric formulation for the ground-state energy of a nonuniform, many-electron system. The nature of, and the justification for this approximation are discussed. The correlation-and-exchange part of the structure-dependent energy is shown to be separable into two parts, one part arising from the random-phase approximation to the Hartree dielectric matrix and the other part arising from the local field corrections. Each of these two terms constitutes a significant correction to the structure-dependent energy calculated in the Hartree approximation. The sum of the two terms very nearly cancels in some regions of wave-number space, but the local field term dominates in the most important region. An explicit illustration of the determination of the crystal structure with correlation and exchange included is given with a momentum-independent pseudopotential appropriate to Zn.