Energy Window Muffin Tin Orbitals (EWMTO) and Energy Window Linear Muffin Tin orbitals (EWLMTO) within the Atomic Sphere Approximation (ASA)

Abstract

In this work we propose two new, closely related, efficient basis sets for the electronic structure problem. The basis sets are based on the Muffin Tin Orbital (MTO) idea that the eigenstates of the Khon Sham (KS) Hamiltonian may we be expanded in terms of eigenstates of the spherically averaged KS Hamiltonian inside the so called Muffin Tin (MT) spheres and Bessel functions in the interstitial multiplied by appropriate spherical Harmonics. Here we use the fact that the solution to the finding the ground state electron density is most often found through an iterative process: where generically on the order of over twenty iterations are taken till the ground state electron density and energy converges to the lowest values allowed by the correlation and exchange functional. We use eigenstate information from the previous iteration loop to choose the energies of the basis set elements used to study the KS Hamiltonian. Furthermore within the Atomic Sphere Approximation (ASA) the energies of the Bessel functions do not matter, as they are cancelled out other than for boundary conditions, and are chosen at zero energy. This is an efficient method aimed at studying the electronic structure of materials with large unit cells especially if they are of close packed form where ASA is particularly accurate.