Calculating of the Cohesive Energy of Diamond

Abstract

It is well known that a satisfactory value for the binding energy of the hydrogen molecule may be calculated using a wave function which has the form of a Heitler-London (HL) function built on non-orthogonal orbitals. However, Slater has shown that a HL function built on orthogonal orbitals fails to yield any binding for the hydrogen molecule, but binding may be achieved by mixing with the HL function an ionized-molecule function which assigns two electrons to one atom and none to the other. Satisfactory results may also be achieved using a Hund-Mulliken (HM) function which may be built on either orthogonal or nonorthogonal orbitals, since the wave functions resulting in these two cases may be shown to be identical.The present calculation shows that the situation for diamond is entirely analogous to that for the hydrogen molecule in that the usual formulation of the Slater-Pauling (SP) directional theory of valence, which is a generalization of the HL method using orthogonal orbitals, fails to yield any binding, but satisfactory results are achieved when this theory is reformulated to allow ionization to be introduced into the bonds. It is also shown that for the observed value of the lattice parameter, which is the only value for which the calculations have been performed, satisfactory results are also achieved using a wave function which is built on orthogonal HM orbitals, each of which, like its counterpart in the hydrogen molecule case, is spread out over a pair of bonded atoms.As a by-product of the main calculation, the total exchange energy of Bloch-type functions belonging to the valence bands of diamond is calculated and found to be essentially equal to the value obtained using free-electron functions.