Particularly with transition and noble metals in mind, the authors analyze the pressure in a solid in terms of the (bulk) wave functions evaluated at the surface of the atomic (Wigner-Seitz) sphere. The partial pressures (angular-momentum decomposed) are further split into a number of terms to which some physical significance can be attributed. Calculations within the local-density scheme are presented for copper, silver, and gold over a large range of volumes. It is argued that one term presents a strong pairwise repulsion between full d shells, balances (at equilibrium) by a strong inward pressure due to the sp electrons. The latter is interpreted as a volume force driven by the atomic pseudopotential including the sp hybridization with the d states. The application of this picture to the understanding of surface instabilities in these metals is mentioned, but details of such investigations are given elsewhere. Also the observation that Cu, Ag, and Au in compounds where the d shells are kept out of contact tend to have substantially smaller volumes is understood from the present analysis.
 

Physical Review B, 32 6145-56, 1985.