AN ENERGY-INDEPENDENT METHOD OF BAND-STRUCTURE CALCULATION FOR TRANSITION METALS

The hybrid nearly-free-electron tight-binding first-principle schemes of Hubbard and Jacobs are investigated further, using the Korringa, Kohn and Rostoker equations as starting point. An improved energy-independent model Hamiltonian is presented, which is both more rapidly convergent in reciprocal lattice space and much less sensitive to the choice of splitting parameter than that proposed recently by Hubbard and Dalton. The validity of the approximations made is then tested by calculating the band structures of face-centred cubic copper and iron from first principles. The energy levels of Burdick and Wood are found to be reproduced with a root-mean-square accuracy of better than 0·01 ryd in both cases, with the use of only a 9 × 9 model Hamiltonian matrix. When a hybrid nearly-free-electron tight-binding model Hamiltonian is used as an empirical interpolation scheme, the expressions derived here show explicitly how the parameters describing both the hybridization and the tight-binding overlap integrals may be expressed in terms of only two constants, namely the energy ε0 and width Γ of the resonance associated with the d bands.