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The LCMTO Secular Matrix

Instead of applying tail cancellation as in Sect.2.1 where we derived the KKR-ASA equations, one may use the linear combination of muffin-tin orbitals (5.27) directly in a variational procedure. This has the advantages that it leads to an eigenvalue problem and that it is possible to include non-muffin-tin perturbations to the potential. According to the Rayleigh-Ritz variational principle, one varies y to make the energy functional stationary, i.e. [Pg.76]

Since the muffin-tin orbital is everywhere continuous and differentiable we may evaluate the integral over all space in (5.36) as a sum of integrals over all atomic polyhedra. After repeated use of the Bloch condition (5.28) and rearrangement of the lattice sums, we obtain the well-known result [Pg.76]

The LCMTO secular matrix is now simply obtained by inserting the one-centre expansion (5.29) into the matrix (5.37). We find [Pg.76]

If the cellular potential, which has not been specified so far in this section, is spherically symmetric and the cells approximated by spheres (or 2 [Pg.76]

Then the L 1 summations vanish and the LCMTO secular matrix reduces to [Pg.77]


In 1973 Andersen and Woolley [1.25] extended the LCMTO method to molecular calculations. At the end of their paper they introduced that choice of MTO tail, i.e. proportional to J = 9i/j/9E, which in a natural fashion ensured orthogonality to the core states and at the same time led to an accurate and elegant formulation of linear methods. The resulting, technique was immediately developed in a paper by Andersen [1.26] which, in a condensed form, contains most of what one need know about the simple concepts of linear band theory. Thus, we find here the KKR equation within the atomic-sphere approximation at this stage is called ASM the LCMTO secular matrix, latter called the LMTO matrix the energy-independent structure constants and the canonical bands and the Laurent expansion of the logarithmic-derivative function and the corresponding potential parameters. [Pg.21]


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LCMTO secular matrix

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