Total energy and band structure of the 3d, 4d, and 5dmetals

The relative stability of crystal structures in the transition metals has been explained by Pettifor' using a model characterized by only two d-resonance parameters, from which the densities of states were obtained in a hybrid nearly-free-electron and tight-binding scheme. The simple approach of Pettifor worked surprisingly well considering that it was based on differences of the total oneelectron band-structure energies neglecting contributions to the total energy from the electrostatic double counting and the exchange and correlation terms. Subsequently, Andersen and co-workers ' and Heine demonstrated the cancellation of the double counting and exchangecorrelation terms provided that the electron potential is frozen from one structure to the other. This approach, referred to as Andersen's force theorem, was taken by Skriver, who used the linear muffin-tin orbital (LMTO) method to calculate the relative stability of all elements. Skriver went beyond the essentially canonical approximation employed by Pettifor including hybridization with sp bands. Skriver performed a self-consistent (SC) calculation for each element in the fcc structure, and then used the SC fcc potential to calculate the sum of one-electron energies for the bcc structure. The resulting difference of the band structure energies gave him the correct ordering of total energies between different structures for all elements except Au. In the present paper we present systematic calculations of the total energy of all the 3d, 4d, and 5d transition metals as well as the alkaline earth elements. Our calculations were performed by the semirelativistic augmented-plane-wave (APW) method in the muffin-tin approximation; they were done fully self-consistently for both the fcc and bcc structures without using the frozen potential procedure employed by Skriver. In this sense our calculations are similar to those of Davenport, Watson, and Weinert, who studied the Sd series by the linear augmented Slater-type-orbital method. Our results for the lattice parameters and bulk moduli agree with those of Moruzzi, Janak, and Williams with small differences due to neglect of relativistic effects in the latter calculations. This article is organized as follows. Section II describes the method of calculation and the approximations. Section III contains our results in comparison with values from the experiment and previous calculations. In Sec. IV we discuss trends in the band structure, and in Sec. V we summarize the results.