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Developing the MTO Formalism

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Author:  O. K. Andersen, T. SahaDasgupta, R. W. Tank, C. Arcangeli, O. J 
















Description 
We review the simple linear muffintin orbital method in the atomicspheres approximation and a tightbinding representation (TBLMTOASA method), and show how it can be generalized to an accurate and robust Nth order muffintin orbital (NMTO) method without increasing the size of the basis set and without complicating the formalism. On the contrary, downfolding is now more efficient and the formalism is simpler and closer to that of screened multiplescattering theory. The NMTO method allows one to solve the singleelectron Schroedinger equation for a MTpotential in which the MTwells may overlap using basis sets which are arbitrarily minimal. The substantial increase in accuracy over the LMTOASA method is achieved by substitution of the energydependent partial waves by socalled kinked partial waves, which have tails attached to them, and by using these kinked partial waves at N 1 arbitrary energies to construct the set of NMTOs. For N=1 and the two energies chosen infinitesimally close, the NMTOs are simply the 3rdgeneration LMTOs. Increasing N, widens the energy window, inside which accurate results are obtained, and increases the range of the orbitals, but it does not increase the size of the basis set and therefore does not change the number of bands obtained. The price for reducing the size of the basis set through downfolding, is a reduction in the number of bands accounted for and unless N is increased a narrowing of the energy window inside which these bands are accurate. A method for obtaining orthonormal NMTO sets is given and several applications are presented. 

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