A method for 3D interpolation between hard spheres is described. The function to be interpolated could be the charge density between atoms in condensed matter. Its electrostatic potential is found analytically, and so are various integrals. Periodicity is not required. The interpolation functions are localized structure-adapted linear combinations of spherical waves, socalled unitary spherical waves (USWs), centered at the spheres where they have cubic-harmonic character. Input to the interpolation are the coefficients in the cubic-harmonic expansion of the target function at and slightly outside the spheres; specifically, the values and 3 first radial derivatives. To fit this, we use USWs with 4 negative energies. Each interpolation function is actually a linear combination of these 4 sets of USWs with the following properties: (1) It is centered at a specific sphere where it has a specific cubic-harmonic character and radial derivative. (2) Its value and first 3 radial derivatives vanish at all other spheres and for all other cubic-harmonics. It is therefore highly localized. Explicit expressions are given for these value-and-derivative (v&d) functions and their Coulomb potentials in terms of the USWs and their structure matrix, including those with zero energy, as well as for integrals over the interstitial of the v&d functions and of their products. Use of point- and space-group symmetries can significantly reduce matrix sizes and the number of v&d functions. For open structures, additional constraints are needed to pinpoint the interpolated function deep in the interstitial. This requires the USW set at one extra energy. As examples, we consider a constant density and the valence-electron densities in zinc-blende structured Si, ZnSe, and CuBr.
The most popular electronic structure method, the linear muffin-tin orbital method (LMTO), in its full-potential (FP) and relativistic forms has been extended to calculate the spectroscopic properties of materials form first principles, i.e, optical spectra, x-ray magnetic circular dichroism (XMCD) and magneto-optical kerr effect (MOKE). The paper describes an overview of the FP-LMTO basis set and the calculation of the momentum matrix elements. Some applications concerning the computation of optical properties of semiconductors and XMCD spectra of transition metal alloys are reviewed.
We have examined a method of direct extraction of accurate tight-binding parameters from an ab-initio band-structure calculation. The linear muffin-tin potential method, in its full-potential implementation, has been used to provide the hamiltonian and overlap matrix elements in the momentum space. These matrix elements are Fourier transformed to real space to produce the tight-binding parameters. The feasibility of this method has been tested on the intermetallic alloy NiAl, using spd orbitals for each atom. The parameters generated for this alloy have been used as input to a real-space calcu…
We present a new full-potential method to solve the one-body problem, for example, in the local density approximation. The method uses the augmented plane waves (APWs) and the generalized muffin-tin orbitals (MTOs) together as basis sets to represent the eigenfunctions. Since the MTOs can efficiently describe localized orbitals, e.g, transition metal 3$d$ orbitals, the total energy convergence with basis size is drastically improved in comparison with the linearized APW method. Required parameters to specify MTOs are given by atomic calculations in advance. Thus the robustness, reliability, ea…
We present the formalism and demonstrate the use of the overlapping muffin-tin approximation (OMTA). This fits a full potential to a superposition of spherically symmetric short-ranged potential wells plus a constant. For one-electron potentials of this form, the standard multiple-scattering methods can solve Schrödingers' equation correctly to 1st order in the potential overlap. Choosing an augmented-plane-wave method as the source of the full potential, we illustrate the procedure for diamond-structured Si. First, we compare the potential in the Si-centered OMTA with the full potential, and …
A mixed basis all-electron full-potential method, which uses two kinds of augmented waves, the augmented plane waves and the muffin-tin orbitals simultaneously, in addition to the local orbitals, was proposed by Kotani and van Schilfgaarde in Phys. Rev. B81, 125117(2010). We named it the PMT method. In this paper, this mixed basis method is reformulated on the basis of a new formalism named as the 3-component formalism, which is a mathematically transparent version of the additive augmentation originally due to Soler and Williams in Phys. Rev. B47, 6784(1993). Atomic forces are easily derived …
We present a self-consistent electronic structure calculation method based on the {\it Exact Muffin-Tin Orbitals} (EMTO) Theory developed by O. K. Andersen, O. Jepsen and G. Krier (in {\it Lectures on Methods of Electronic Structure Calculations}, Ed. by V. Kumar, O.K. Andersen, A. Mookerjee, Word Scientific, 1994 pp. 63-124) and O. K. Andersen, C. Arcangeli, R. W. Tank, T. Saha-Dasgupta, G. Krier, O. Jepsen, and I. Dasgupta, (in {\it Mat. Res. Soc. Symp. Proc.} {\bf 491}, 1998 pp. 3-34). The EMTO Theory can be considered as an {\it improved screened} KKR (Korringa-Kohn-Rostoker) method which …
We have developed the quasiparticle self-consistent GW (QSGW) method based on a recently developed mixed basis all-electron full-potential method (the PMT method), which uses the augmented plane waves (APWs) and the highly localized muffin-tin orbitals (MTOs) simultaneously. We call this PMT-QSGW. Because of the two kinds of augmented bases, we have efficient description of one-particle eigenfunctions in materials with small number of basis functions. In QSGW, we have to treat a static non-local exchange-correlation potential, which is generated from the self-energy. We expand the potential in…
Based on the exact muffin-tin orbitals (EMTOs), we developed a first-principles method to calculate the current operators and investigated the anomalous Hall effect in bcc Fe as an example, with which we successfully separated the skew scattering contribution from the side jump and intrinsic contributions by fitting the scaling law with the introduction of sparse impurities. By investigating the temperature dependence of the anomalous Hall effect in bulk Fe, we predicted a fluctuated anomalous Hall angle as a function of temperature when considering only phonons, which, in the future, can be m…
This paper summarises the theory and functionality behind Questaal, an open-source suite of codes for calculating the electronic structure and related properties of materials from first principles. The formalism of the linearised muffin-tin orbital (LMTO) method is revisited in detail and developed further by the introduction of short-ranged tight-binding basis functions for full-potential calculations. The LMTO method is presented in both Green's function and wave function formulations for bulk and layered systems. The suite's full-potential LMTO code uses a sophisticated basis and augmentati…
Full charge self-consistence (CSC) over the electron density has been implemented into the local density approximation plus dynamical mean-field theory (LDA+DMFT) scheme based on a full-potential linear muffin-tin orbital method (FP-LMTO). Computational details on the construction of the electron density from the density matrix are provided. The method is tested on the prototypical charge-transfer insulator NiO using a simple static Hartree-Fock approximation as impurity solver. The spectral and ground state properties of bcc Fe are then addressed, by means of the spin-polarized T-matrix fluct…
We present a formulation of the so-called Fermi sea contribution to the conductivity tensor of spin-polarized random alloys within the fully relativistic tight-binding linear muffin-tin-orbital (TB-LMTO) method and the coherent potential approximation (CPA). We show that the configuration averaging of this contribution leads to the CPA-vertex corrections that are solely due to the energy dependence of the average single-particle propagators. Moreover, we prove that this contribution is indispensable for the invariance of the anomalous Hall conductivities with respect to the particular LMTO rep…
In a recent article [1], the FEAST algorithm has been presented as a general purpose eigenvalue solver which is ideally suited for addressing the numerical challenges in electronic structure calculations. Here, FEAST is presented beyond the "black-box" solver as a fundamental modeling framework which can naturally address the original numerical complexity of the electronic structure problem as formulated by Slater in 1937 [2]. The non-linear eigenvalue problem arising from the muffin-tin decomposition of the real-space domain is first derived and then reformulated to be solved exactly within t…
In a recent paper by Jones et al., it is argued, based on FP-LAPW band-structure calculations, that previous calculations of ground-state properties for actinides, using the FP-LMTO method implemented by J. M. Wills, are in error. We demonstrate in this paper that the conclusions of Jones et. al. are unfounded. Calculations using the FP-LMTO method are compared with calculations performed with the FP-LAPW method and, in contradiction to statements by Jones et. al., they agree very well. The limitation of the present implementation of the spin-orbit coupling is discussed, where especially the 6…
Interface by definition is two-dimensional (2-D) as it separates 2 phases with an abrupt change in structure and chemistry across the interface. The interface between a metal and its nitride is expected to be atomically sharp, as chemical gradation would require the creation of N vacancies in nitrides and N interstitials in metal. Contrary to this belief, using first-principles density functional theory (DFT), we establish that the chemically graded Ti/TiN interface is thermodynamically preferred over the sharp interface. DFT calculated N vacancy formation energy in TiN is 2.4 eV, and N inters…
The essential features of a full potential electronic structure method using Linear Muffin-Tin Orbitals (LMTOs) are presented. The electron density and potential in the this method are represented with no inherent geometrical approximation. This method allows the calculation of total energies and forces with arbitrary accuracy while sacrificing much of the efficiency and physical content of approximate methods such as the LMTO-ASA method.
We investigate the elastic and isotropic aggregate properties of ferromagnetic bcc iron as a function of temperature and pressure by computing the Helmholtz free energies for the volume-conserving strained structures using the first-principles linear response linear-muffin-tin-orbital method and the generalized-gradient approximation. We include the electronic excitation contributions to the free energy from the band structures, and phonon contributions from quasi-harmonic lattice dynamics. We make detailed comparisons between our calculated elastic moduli and their temperature and pressure de…
The ab initio linear muffin-tin-orbital (LMTO) formalism and the semi-empirical method of the Intermediate Neglect of the Differential Overlap (INDO) based on the Hartree-Fock formalism are combined for the study of the hole polarons (a hole trapped nearby the cation vacancy) in a cubic phase of KNbO3 perovskite crystals. The 40-atom and 320-atom supercells were used, respectively. We predict existence of both, one-site and two-site (molecular) polarons with close optical absorption energies (0.9 eV and 0.95 eV). The relevant experimental data are discussed.
We present a new all-electron, augmented-wave implementation of the GW approximation using eigenfunctions generated by a recent variant of the full-potential LMTO method. The dynamically screened Coulomb interaction W is expanded in a mixed basis set which consists of two contributions, local atom-centered functions confined to muffin-tin spheres, and plane waves with the overlap to the local functions projected out. The former can include any of the core states; thus the core and valence states can be treated on an equal footing. Systematic studies of semiconductors and insulators show that t…
The muffin-tin model of an effective-mass electron interacting with magnetic ions in semiconductors is extended to incorporate electrostatic potentials that are present in the case of Mn-based III-V compounds (${Ga}_{1-x} {Mn}_x {N}$, ${Ga}_{1-x} {Mn}_x {As}$). Since the conduction band electron is repelled from negatively charged magnetic ions and attracted by compensating donors, the \emph{apparent} value of the s-d exchange coupling $N_0 α$ is reduced. It is shown that the magnitude of this effect increases when x diminishes. Our model may explain an unusual behavior of electron spin splitt…
We present one-dimensional KKR method with the aim to elucidate its linear features, particularly important in optimizing the numerical algorithms in energy bands computations. The conventional KKR equations based on the multiple scattering theory as well as novel forms of the secular matrix with nearly linear energy dependency of the eigenvalues are presented. The quasi-linear behaviour of these eigenvalue functions appears after (i) re-normalizing the wave functions in such a way that 'irregular' solutions vanish on the boundary of the 'muffin-tin' segments and (ii) integrating the full Gree…
Using the tight-binding linear muffin-tin orbitals method, the soft x-ray fluorescence K-emission spectra of boron in MgB_2, excited close to the absorption edge, are estimated. In the calculations the angle of incidence between the direction of the incoming photon and the hexagonal axis of the specimen is 60 degrees and 75 degrees. Comparison with experiment is possible in the former case where good agreement is found. Furthermore, another resonant feature below the Fermi energy is predicted for the larger angle. This feature can be related to the excitations to the antibonding B pi-band in t…
We discuss an efficiency of various band structure algorithms in determining the Fermi surface (FS) of the paramagnetic ErGa3. The linear muffin-tin orbital (LMTO) in the atomic sphere approximation (ASA) method and three full potential (FP) codes: FP-LMTO, FP linear augmented plane wave (FLAPW), and FP local orbitals (FPLO) methods are employed. Results are compared with electron-positron (e-p) momentum densities reconstructed from two dimensional angular correlation of annihilation radiation (2D ACAR). Unexpectedly, none of used modern FP codes is able to give satisfying description of the e…
