Photoemission spectra and band structures of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>d</mml:mi></mml:math>-band metals. VII. Extensions of the combined interpolation scheme

Abstract

The combined interpolation scheme for face-centered-cubic $d$-band metals has been extended to higher energies (\ensuremath{\sim} 1.6 Ry above the Fermi level) by inclusion of more plane waves in the basis set. Momentum matrix elements are evaluated for Cu from $k$-space derivatives of the Hamiltonian, and are used to calculate the imaginary part of the dielectric constant ${\ensuremath{\epsilon}}_{2}$. Good agreement with the first-principles results of Janak, Williams, and Moruzzi is obtained. Momentum matrix elements corresponding to normal emission from Cu(111) and Cu(100) are calculated and are shown to be consistent with elementary atomic-dipole selection-rule considerations. The occurrence of hybridization nodes in the momentum matrix elements is reported and discussed.