Other Muffin-Tin Orbital methods

In the BGFM, the ASA+M technique [57] is used to improve on the ASA energies. In the ASA+M, the multipole moments which are lost in the ASA (that is, all but the spherical l = 0 monopole moment) are added to the Madelung potential and energy. This significantly increases the accuracy [81], and makes the BGFM a reliable method in many cases [76, 82]. 

The LSGF method on the other hand is an order-IV method for calculation of the electronic system. It is based on a supercell (which may just be one unit cell) with periodic boundary conditions, see Fig.(4.5), and the concept of a Local Interaction Zone (LIZ), which is embedded in an effective medium, usually chosen to be the Coherent Potential Approximation medium (see next chapter). For each atom in the supercell, one uses the Dyson equation to solve the electronic structure problem as an impurity problem in the effective medium. The ASA is employed as well as the ASA+M correction described above. The total energy is defined to 

The LSGF method will be mentioned in the next chapter when I describe how to use it to correct the CPA method for some problems with charge transfer that appears when you calculate properties for alloys. 

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