The band structure of aluminium III. A self-consistent calculation

Abstract The main feature of the present recalculation of the band structure is a careful consideration of the potential on which it is based. An effective potential acting on a conduction electron is defined intuitively so as to include the effects of correlation and exchange. This grafts the Bohm & Pines theory of a free-electron gas (Pines 1955) on to the Hartree—Fock treatment of the effect of the ion cores. Correlation and exchange effects among the conduction and ion-core electrons have been calculated, and the variation of the potential in the regions about half-way between the atoms has also been calculated and taken into account. Achieving self-consistency in the contribution to the potential due to the conduction electrons has not been difficult. Because of various approximations, including those in the potential, the calculated energy values are judged to be correct to about 0·03 Ry. The results are found to agree satisfactorily with the model of the band structure obtained in I by noting that the effective Fermi level for electrons and holes in the band structure may not be the same due to additional correlation effects.