Green's function multiple-scattering theory with a truncated basis set: An augmented-KKR formalism (original) (raw)
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Multiple-scattering theory with a truncated basis set
Physical Review B, 1992
Multiple-scattering theory (MST) is an extremely efficient technique for calculating the electronic structure of an assembly of atoms. The wave function in MST is expanded in terms of spherical waves centered on each atom and indexed by their orbital and azimuthal quantum numbers, 4' and m. The secular equation which determines the characteristic energies can be truncated at a value of the orbital angular momentum f,f or which the higher angular momentum phase shifts, 6s (E)E), are sufficiently small. Generally, the wave-function coefficients which are calculated from the secular equation are also truncated at Em~. Here we point out that this truncation of the wave function is not necessary and is in fact inconsistent with the truncation of the secular equation. A consistent procedure is described in which the states with higher orbital angular momenta are retained but with their phase shifts set to zero. We show that this treatment gives smooth, continuous, and correctly normalized wave functions and that the total charge density calculated from the corresponding Green function agrees with the Lloyd formula result. We also show that this augmented wave function can be written as a linear combination of Andersen s muffin-tin orbitals in the case of muffin-tin potentials, and can be used to generalize the muffin-tin orbital idea to full-cell potentials.
The Electronic Structure of the Copper Oxide Plane within the Green's Functions Projection Method
physica status solidi (b), 1991
The projection method for two-time Green functions is used to derive a self-consistent set of equations for the spectrum of the two-dimensional Emery model with infinite copper correlation. In the relevant parameter region near the filling n = 1 a charge-transfer gap is found, but in difference to the Gutzwiller approximation a finite bandwidth occurs at the transition point. The critical A , = cpcd at which the transition to metallic behaviour occurs is found to be approximately A , = 2t.
Angular momentum convergence of Korringa-Kohn-Rostoker Green's function methods
Journal of Physics: Condensed Matter, 2001
The convergence of multiple-scattering-theory-based electronic structure methods (e.g. the Korringa-Kohn-Rostoker (KKR) band theory method), is determined by l max , the maximum value of the angular momentum quantum number l. It has been generally assumed that l max = 3 or 4 is sufficient to ensure a converged ground state and other properties. Using the locally self-consistent multiple-scattering method, which facilitates the use of very high values of l max , it is shown that the convergence of KKR Green's function methods is much slower than previously supposed, even when spherical approximations to the crystal potential are used. Calculations for Cu using 3 l max 16 indicate that the total energy is converged to within ∼0.04 mRyd at l max = 12. For both face-centred cubic and body-centred cubic structures, the largest error in the total energy occurs at l max = 4; l max = 8 gives total energies, bulk moduli, and lattice constants that are converged to accuracies of 0.1 mRyd, 0.1 Mbar, and 0.002 Bohr respectively.
This Ph.D. thesis has been carried out in the period from 1999 till 2002. The work is organized as follows. After an introduction, concerning the goals and key ideas of this work, we review the density functional theory. This is followed by a look at how the electronic structure calculations are performed, in particular the LMTO method and the tetrahedron method. Next, a chapter is devoted to the calculation of maximally localized Wannier functions using a method proposed by Marzari and Vanderbilt. We then focus on the second quantized Hamiltonian, its matrix elements in Wannier representation and their evaluation within the atomic sphere approximation. By then, we will have all the pieces to perform many-particle calculations using this second quantized Hamiltonian with its matrix elements from first-principle, which will be dealt with in chapter 6. Finally, we present results for the 3d transition metals iron, cobalt, nickel and copper.
Physical Review B, 2008
The class of the Generalized Coherent Potential Approximations (GCPA) to the Density Functional Theory (DFT) is introduced within the Multiple Scattering Theory formalism with the aim of dealing with, ordered or disordered, metallic alloys. All GCPA theories are based on a common ansatz for the kinetic part of the Hohenberg-Kohn functional and each theory of the class is specified by an external model concerning the potential reconstruction. Most existing DFT implementations of CPA based theories belong to the GCPA class. The analysis of the formal properties of the density functional defined by GCPA theories shows that it consists of marginally coupled local contributions. Furthermore it is shown that the GCPA functional does not depend on the details of the charge density and that it can be exactly rewritten as a function of the appropriate charge multipole moments to be associated with each lattice site. A general procedure based on the integration of the 'qV' laws is described that allows for the explicit construction the same function. The coarse grained nature of the GCPA density functional implies a great deal of computational advantages and is connected with the O(N ) scalability of GCPA algorithms. Moreover, it is shown that a convenient truncated series expansion of the GCPA functional leads to the Charge Excess Functional (CEF) theory [E. Bruno, L. Zingales and Y. Wang, Phys. Rev. Lett. 91, 166401 ] which here is offered in a generalized version that includes multipolar interactions.
Strongly correlated electron ground-state energy approximations for Anderson-like models
Journal of Applied Physics, 1987
We report preliminary results of convergence properties for nonperturbative resolvent approximations to Anderson-like models of magnetic ions in metals. Our study is initially focused on the spin-! Anderson model for magnetic impurities, but the methods studied can include mUltiplet and crystal-field effects which are needed for more accurate descriptions of real systems. We will compare the nonperturbative Lanczos method (tridiagonalization) and similar truncation schemes to exact ground-state energies for the impurity model and assess the efficacy of these nonperturbative approaches to understanding the Anderson lattice, heavy fermions, and other strongly interacting electronic systems.
Self-interaction correction in multiple scattering theory
Physical Review B, 2005
We propose a simplified version of self-interaction corrected local spin-density (SIC-LSD) approximation, based on multiple scattering theory, which implements self-interaction correction locally, within the KKR method. The multiple scattering aspect of this new SIC-LSD method allows for the description of crystal potentials which vary from site to site in a random fashion and the calculation of physical quantities averaged over ensembles of such potentials using the coherent potential approximation (CPA). This facilitates applications of the SIC to alloys and pseudoalloys which could describe disordered local moment systems, as well as intermediate valences. As a demonstration of the method, we study the well-known alpha\alphaalpha-$\gamma$ phase transition in Ce, where we also explain how SIC operates in terms of multiple scattering theory.
Self-consistent GW: All-electron implementation with localized basis functions
Physical Review B, 2013
This paper describes an all-electron implementation of the self-consistent GW (sc-GW ) approach -i.e. based on the solution of the Dyson equation -in an all-electron numeric atom-centered orbital (NAO) basis set. We cast Hedin's equations into a matrix form that is suitable for numerical calculations by means of i) the resolution of identity technique to handle 4-center integrals; and ii) a basis representation for the imaginary-frequency dependence of dynamical operators. In contrast to perturbative G0W0, sc-GW provides a consistent framework for ground-and excited-state properties and facilitates an unbiased assessment of the GW approximation. For excited-states, we benchmark sc-GW for five molecules relevant for organic photovoltaic applications: thiophene, benzothiazole, 1,2,5-thiadiazole, naphthalene, and tetrathiafulvalene. At self-consistency, the quasi-particle energies are found to be in good agreement with experiment and, on average, more accurate than G0W0 based on Hartree-Fock (HF) or density-functional theory with the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional. Based on the Galitskii-Migdal total energy, structural properties are investigated for a set of diatomic molecules. For binding energies, bond lengths, and vibrational frequencies sc-GW and G0W0 achieve a comparable performance, which is, however, not as good as that of exact-exchange plus correlation in the random-phase approximation (EX+cRPA) and its advancement to renormalized second-order perturbation theory (rPT2). Finally, the improved description of dipole moments for a small set of diatomic molecules demonstrates the quality of the sc-GW ground state density.
Self-interaction correction to density-functional approximations for many-electron systems
The exact density functional for the ground-state energy is strictly self-interaction-free (i.e., orbitals demonstrably do not self-interact), but many approximations to it, including the local-spin-density (LSD) approximation for exchange and correlation, are not. We present two related methods for the self-interaction correction (SIC) of any density functional for the energy; correction of the self-consistent one-electron potenial follows naturally from the variational principle. Both methods are sanctioned by the Hohenberg-Kohn theorem, Although the first method introduces an orbital-dependent single-particle potential, the second involves a local potential as in the Kohn-Sham scheme. We apply the first method to LSD and show that it properly conserves the number content of the exchange-correlation hole, while substantially improving the description of its shape. We apply this method to a number of physical problems, where the uncorrected LSD approach produces systematic errors. We find systematic improvements, qualitative as well as quantitative, from this simple correction. Benefits of SIC in atomic calculations include (i) improved values for the total energy and for the separate exchange and correlation pieces of it, (ii) accurate binding energies of negative ions, which are wrongly unstable in LSD, (iii) more accurate electron densities, (iv) orbital eigenvalues that closely approximate physical removal energies, including relaxation, and (v) correct long-range behavior of the potential and density, It appears that SIC can also remedy the LSD underestimate of the band gaps in insulators (as shown by numerical calculations for the rare-gas solids and CuCl), and the LSD overestimate of the cohesive energies of transition metals. The LSD spin splitting in atomic Ni and s-d interconfigurational energies of transition elements are almost unchanged by SIC. We also discuss the admissibility of fractional occupation numbers, and present a parametrization of the electron-gas correlation energy at any density, based on the recent results of Ceperley and Alder.
Full-potential multiple scattering theory with space-filling cells for bound and continuum states
Journal of Physics: Condensed Matter, 2010
We present a rigorous derivation of a real space Full-Potential Multiple-Scattering-Theory (FP-MST) that is free from the drawbacks that up to now have impaired its development (in particular the need to expand cell shape functions in spherical harmonics and rectangular matrices), valid both for continuum and bound states, under conditions for space-partitioning that are not excessively restrictive and easily implemented. In this connection we give a new scheme to generate local basis functions for the truncated potential cells that is simple, fast, efficient, valid for any shape of the cell and reduces to the minimum the number of spherical harmonics in the expansion of the scattering wave function. The method also avoids the need for saturating 'internal sums' due to the re-expansion of the spherical Hankel functions around another point in space (usually another cell center). Thus this approach, provides a straightforward extension of MST in the Muffin-Tin (MT) approximation, with only one truncation parameter given by the classical relation l max = kR b , where k is the electron wave vector (either in the excited or ground state of the system under consideration) and R b the radius of the bounding sphere of the scattering cell. Moreover, the scattering path operator of the theory can be found in terms of an absolutely convergent procedure in the l max → ∞ limit. Consequently, this feature provides a firm ground to the use of FP-MST as a viable method for electronic structure calculations and makes possible the computation of x-ray spectroscopies, notably photo-electron diffraction, absorption and anomalous scattering among others, with the ease and versatility of the corresponding MT theory. Some numerical applications of the theory are presented, both for continuum and bound states.