TY - JOUR

T1 - Generalisation of the modified tight-binding approximation in transition metals

AU - Entin-Wohlman, O.

N1 - Funding Information:
THE ADVANTAGE of the tight-binding approximation for the description of d-band transition metals and their compounds has long been recognized. In particular, a considerable effort was devoted to the calculation of the electron—phonon coupling in this approach \[1,2\]. Such a formulation was developed by Frohlich and Mitra \[3\]and Barisic \[4\]I.t was argued that with Bloch functions constructed from atomic orbitals, the modified tight-binding approximation (MTBA) is more appropriate for calculating the electron—phonon coupling than the ordinary Bloch formulation. In the MTBA, the Bloch functions are linear combinations of atomic orbitals centered around the instantaneous positions of the ions, so that the electrons are allowed to follow adiabatically the motion of the ions. In the Bloch picture~the atomic orbitals are centered around the equilibrium positions of the ions. As a result, the electron—phonon coupling constant involves gradients of matrix elements of the potential in MTBA, rather than matrix elements of the potential gradient as in the Bloch picture. Numerical calculations \[2\]of the transition temperature of several d-band metals revealed that the MTBA gave results which were in quantitative agreement with experiments. It was shown \[5,6\]that with Bloch functions based on orthogonal orbitals (with zero overlap between different sites), the two formulations of the electron—phonon coupling are equivalent. This holds as long as one stays within the adiabatic approximation, so that the additional terms in the kinetic energy arising in the MTBA (because of the operation of a/an on the * This work is supported by a grant from the National Council for Research and Development, Israel and the Kf\[( (Kernforschungszentrum, Karlsruh~G, ermany).

PY - 1980/6

Y1 - 1980/6

N2 - The modified tight-binding approach (MTBA) used in calculations of the electron-phonon coupling in d-band metals was criticized before because the non-orthogonality of the wavefunctions was not taken into account. It is shown that the wavefunctions can be made orthogonal to first order in the overlap integrals. The modifications thus introduced in the electron-phonon matrix element are derived, and their impact on former calculations done in the MTBA is discussed.

AB - The modified tight-binding approach (MTBA) used in calculations of the electron-phonon coupling in d-band metals was criticized before because the non-orthogonality of the wavefunctions was not taken into account. It is shown that the wavefunctions can be made orthogonal to first order in the overlap integrals. The modifications thus introduced in the electron-phonon matrix element are derived, and their impact on former calculations done in the MTBA is discussed.

UR - http://www.scopus.com/inward/record.url?scp=0019025798&partnerID=8YFLogxK

U2 - 10.1016/0038-1098(80)90116-7

DO - 10.1016/0038-1098(80)90116-7

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AN - SCOPUS:0019025798

SN - 0038-1098

VL - 34

SP - 879

EP - 881

JO - Solid State Communications

JF - Solid State Communications

IS - 11

ER -