Abstract. The TB-LMTO-ASA method is reviewed and generalized to an accurate and robust TB-NMTO minimal-basis method, which solves Schrödinger's equation to N th order in the energy expansion for an overlapping MT-potential, and which may include any degree of downfolding. For N = 1, the simple TB-LMTO-ASA formalism is preserved. For a discrete energy mesh, the NMTO basis set may be given as:in terms of kinked partial waves, φ (ε, r) , evaluated on the mesh, ε0, ..., εN . This basis solves Schrödinger's equation for the MT-potential to within an errorn , as well as the Hamiltonian and overlap matrices for the NMTO set, have simple expressions in terms of energy derivatives on the mesh of the Green matrix, defined as the inverse of the screened KKR matrix. The variationally determined single-electron energies have errorsA method for obtaining orthonormal NMTO sets is given and several applications are presented.
OverviewMuffin-tin orbitals (MTOs) have been used for a long time in ab initio calculations of the electronic structure of condensed matter. Over the years, several MTO-based methods have been devised and further developed. The ultimate aim is to find a generally applicable electronic-structure method which is accurate and robust, as well as intelligible.In order to be intelligible, such a method must employ a small, singleelectron basis of atom-centered, short-ranged orbitals. Moreover, the singleelectron Hamiltonian must have a simple, analytical form, which relates to a two-center, orthogonal, tight-binding (TB) Hamiltonian.In this sense, the conventional linear muffin-tin-orbitals method in the atomic-spheres approximation (LMTO-ASA) [1,2] is intelligible, because the orbital may be expressed as:Here, φ RL (r R ) is the solution, ϕ Rl (ε ν , r R ) Y lm (r R ) , at a chosen energy, ε ν , of Schrödinger's differential equation inside the atomic sphere at site R for the single-particle potential, R v R (r R ) , assumed to be spherically symmetric