Cohesive Energy of Noble Metals

Abstract

The method, developed by Kuhn and Van Vleck, and later simplified and extended by Brooks, for calculating the cohesive energy of monovalent metals, is here further extended to include the effects of the deviation of the effective ion-core potential from pure hydrogenic form in the vicinity of the surface of the $s$-sphere. A formula is derived for calculating the logarithmic derivative of the wave function at the surface of the $s$-sphere. From the logarithmic derivatives of the $s$- and $p$-functions the ground-state energy and the Fermi energy can be evaluated. The method thus extended is applied to the calculation of the cohesive energy of the monovalent noble metals. For these metals, the repulsion between ion cores is important. Combining the repulsive energy, which is calculated by Fuchs with a modified Thomas-Fermi method, with the energy of valence electrons calculated by the present method, we obtain the total cohesive energy of copper. Since there is no calculation of the repulsive energy for silver and gold, the ion cores are assumed to be rigid and the energies of the valence electrons at the observed lattice spacings are determined and considered as the approximate total energies. The cohesive energies calculated at the observed lattice spacings with the rigid ion-core assumption are 61.7 for Cu, 55.8 for Ag, and 49.2 for Au in comparison with the experimental values of 81.2, 68.0, and 92.0 respectively. Here the energy unit is kcal/mole.