A quantum mechanical investigation of the cohesive forces of metallic copper

Abstract

The calculations of Wigner and Seitz have shown that the Bloch theory is capable of yielding, at any rate roughly, the lattice energy, lattice constant, and compressibility of the metal sodium, and it seems probable that their method could be applied with equal success to the other alkalis. On the other hand, no calculations have as yet been made for the noble metals. Such a calculations is given in this paper. The noble metals differ from the alkalis in having cores which are much larger compared with the atomic volume than those of the alkalis, and the main purpose of this paper is to see whether direct interaction between the pressibility, etc. We have also attempted to find out why the noble metals have the face-centred cubic structure, while the alkalis are body-centred. In 2 we calculate the wave functions and energies of the valence electrons (4s) of metallic copper. We chose copper for this calculation, because a self-consistent field due to Hartree is available. Wigner and Seitz did not use the self-consistent field for sodium, but a half empirical potential function for the sodium ion, calculated by Prokofjew from the observed term values. This potential therefore includes implicitly the exchange interaction between the valence electrons and the inner shells, so far as this may be represented by an electrostatic potential. With the self-consistent field the exchange has to be taken into account explicitly; we have done this by solving approximately, instead of the simple Schroedinger equation, Fock’s wave equation, which includes the exchange. Apart from this the calculation in 2 is entirely analogous to that of Wigner and Seitz. It will be shown that for copper this calculations given at least the right order of magnitude for the lattice constant and for the heat of vaporization, but a totally incorrect value for the compressibility.