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Within this paper we outline a method able to generate truly minimal basis sets which describe either a group of bands, a band, or even just the occupied part of a band accurately. These basis sets are the so-called NMTOs, Muffin Tin Orbitals of order N. For an isolated set of bands, symmetrical orthonormalization of the NMTOs yields a set of Wannier functions which are atom-centered and localized by construction. They are not necessarily maximally localized, but may be transformed into those Wannier functions. For bands which overlap others, Wannier-like functions can be generated. It is shown that NMTOs give a chemical understanding of an extended system. In particular, orbitals for the pi and sigma bands in an insulator, boron nitride, and a semi-metal, graphite, will be considered. In addition, we illustrate that it is possible to obtain Wannier-like functions for only the occupied states in a metallic system by generating NMTOs for cesium. Finally, we visualize the pressure-induced s to d transition.
We present the results of a combined study by band theory and angle resolved photoemission spectroscopy (ARPES) of the purple bronze, Li$_{1-x}$Mo$_{6}$O$_{17}$. Structural and electronic origins of its unusually robust quasi-one dimensional (quasi-1
A method to calculate the crystal field parameters {it ab initio} is proposed and applied to trivalent rare earth impurities in yttrium aluminate and to Tb$^{3+}$ ion in TbAlO$_3$. To determine crystal field parameters local Hamiltonian expressed in
We study Bose-Hubbard models on tight-binding, non-Bravais lattices, with a filling of one boson per unit cell -- and thus fractional site filling. At integer filling of a unit cell neither symmetry breaking nor topological order is required, and in
We develop a strong coupling approach towards quantum magnetism in Mott insulators for Wannier obstructed bands. Despite the lack of Wannier orbitals, electrons can still singly occupy a set of exponentially-localized but nonorthogonal orbitals to mi
We study the electronic properties of GaV4S8 (GVS) and GaTaSe8 (GTS), two distant members within the large family of chalcogenides AM4X8, with A={Ga, Ge}, M={V, Nb, Ta, Mo} and X={S, Se}. While all these compounds are Mott insulators, their ground st