LCMTO secular matrix

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. 

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

Then the L"1 summations vanish and the LCMTO secular matrix reduces to... 

In Chap.5 we derive the LCMTO equations in a form not restricted to the atomic-sphere approximation, and use the , technique introduced in Chap.3 to turn these equations into the linear muffin-tin orbital method. Here we also give a description of the partial waves and the muffin-tin orbitals for a single muffin-tin sphere, define the energy-independent muffin-tin orbitals and present the LMTO secular matrix in the form used in the actual programming, Sect.9.3. 

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