We describe the screened Korringa-Kohn-Rostoker (KKR) method and the thirdgeneration linear muffin-tin orbital (LMTO) method for solving the single-particle Schrödinger equation for a MT potential. In the screened KKR method, the eigenvectors c RL,i are given as the non-zero solutions, and the energies ε i as those for which such solutions can be found, of the linear homogeneous equations: RL K a R ′ L ′ ,RL (ε i ) c RL,i = 0, where K a (ε) is the screened KKR matrix. The screening is specified by the boundary condition that, when a screened spherical wave ψ a RL (ε, r R ) is expanded in spherical harmonics Y R ′ L ′ (r R ′ ) about its neighboring sites R ′ , then each component either vanishes at a radius, r R ′ =a R ′ L ′ , or is a regular solution at that site. When the corresponding "hard" spheres are chosen to be nearly touching, then the KKR matrix is usually short ranged and its energy dependence smooth over a range of order 1 Ry around the centre of the valence band. The KKR matrix, K (ε ν ) , at a fixed, arbitrary energy turns out to be the negative of the Hamiltonian, and its first energy derivative,K (ε ν ) , to be the overlap matrix in a basis of kinked partial waves, Φ RL (ε ν , r R ) , each of which is a partial wave inside the MT-sphere, tailed with a screened spherical wave in the interstitial, or taking the other point of view, a screened spherical wave in the interstitial, augmented by a partial wave inside the sphere. When of short range, K (ε) has the two-centre tight-binding (TB) form and can be generated in real space, simply by inversion of a positive definite matrix for a cluster. The LMTOs, χ RL (ε ν ) , are smooth orbitals constructed from Φ RL (ε ν , r R ) andΦ RL (ε ν , r R ) , and the Hamiltonian and overlap matrices in the basis of LMTOs are expressed solely in terms of K (ε ν ) and its first three energy derivatives. The errors of the single-particle energies ε i obtained from the Hamiltonian and overlap matrices in the Φ (ε ν )-and χ (ε ν ) bases are respectively of second and fourth order in ε i − ε ν . Third-generation LMTO sets give wave functions which are correct to order ε i − ε ν , not only inside the MT spheres, but also in the interstitial region. As a consequence, the simple and popular formalism which previously resulted from the atomic-spheres approximation (ASA) now holds in general, that is, it includes downfolding and the combined correction. Downfolding to few-orbital, possibly short-ranged, low-energy, and possibly orthonormal Hamiltonians now works exceedingly well, as is demonstrated for a high-temperature superconductor. First-principles sp 3 and sp 3 d 5 TB Hamiltonians for the valence and lowest conduction bands of silicon are derived. Finally, we prove that the new method treats overlap of the potential wells correctly to leading order and we demonstrate how this can be exploited to get rid of the empty spheres in the diamond structure.

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

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A revisited electronic structure study of iron pyrite, FeS2, has been performed using a new Tight-Binding Linear Muffin-Tin Orbital (TB-LMTO) technique in which the radii of overlapping MT spheres are determined from a full potential construction. The interstitial spheres were chosen to provide an efficient packing of space while ensuring that the overlap between the spheres remain small. We have found that this treatment of interstitial spheres results in a dramatic improvement in the description of the electronic structure and the binding energy curves for FeS2 in comparison with a previous LMTO calculation. In particular, the energy band gap, the equilibrium lattice constant and the bulk modulus are all in much better agreement with experimental observations. Moreover, the calculated equation of state is in excellent accord with recent measured P- V data up to pressures of 15GPa with overall deviations of less than 10%. The predicted reflectivity spectrum of FeS2 as a function of pressure gives the observed behaviour of the optical edge. The bonding behaviour the orthorhombic marcasite phase of FeS2 is also discussed within this new TB-LMTO formalism.