A short historical expose

Before going into the theory for the Exact Muffin-Tin Orbital method, I want to give a short historical overview of muffin-tin based methods. This is done in order to put the method, and the development of the quantities used in the method, in a historical context. 

The first method for solving the MST problem in angular momentum representation was made by Korringa [43] and Kohn and Rostocker [44] separately. The method came to be called the KKR method for electronic structure calculations and used the Green s function technique from Chapter 3 to solve the electronic structure problem. The separation into potential- and structure dependent parts made the method conceptually clean and also speeded up calculations, since the structural dependent part could be calculated once and for all for each structure. Furthermore, the Green s function technique made the method very suitable for the treatment of disordered alloys, since the Coherent Potential Approximation [45] could easily be implemented. 

With the later introduction of the Linear Muffin-Tin Orbital (LMTO) method [46, 47, 48, 49, 50], a formulation of the multiple scattering problem in terms of Hamiltonians was introduced. This provided another way to gain more knowledge about the KKR method, which, although elegant, was not so easily understood. In the LMTO method one had to use energy linearizations of the MTOs to be able to put it into a Hamiltonian formalism. The two methods (KKR and LMTO) were shown [51] to be very closely related within the Atomic Sphere Approximation (ASA) [46, 52], which was used in conjunction with the LMTO method to provide an accurate and computationally efficient technique. 

In 1984, it was also realized that it was possible to transform the original, so called bare (or canonical), structure constants into other types of structure constants using so-called screening transformations [53]. This allowed one to trans- 

Not until the so called third generation of LMTOs [58], was there a way to properly include the interstitial part of the muffin-tin potential and perform calculations without the ASA, in fact it was possible to perform calculations for exact muffin-tins using the Exact Muffin-Tin Orbitals (EMTO) method. Since the structural dependent part is called the slope matrix in the EMTO method, this is the name I will use for the rest of this thesis when discussing the EMTO method. 

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