Session X11 - Theory: Electronic Structure III.
ORAL session, Thursday afternoon, March 15
Room 204, Washington State Convention Center

[X11.001] Semicore electrons without self-interactions: exact-exchange calculations for GaN, ZnO, and ZnS

We study theoretically electronic and structural properties of semiconductors with localized semicore 3d electrons (GaN, ZnO, ZnS) using exact-exchange density-functional methods(M. Staedele, M. Moukara, J. Majewski, P. Vogl, and A. Goerling, Phys. Rev. B 59), 10031 (1999), and references therein. in order to avoid well-known self-interaction errors that plague standard local-density (LDA) and generalized-gradient approximations. A plane-wave basis set and consistent EXX pseudopotentials were employed in the calculations. The 3d electrons were explicitly treated as valence states. Compared with the LDA, the EXX approach leads to lower (\approx 1 eV) d band energies and much higher (1.5 - 2 eV) band gaps than the local-density methods, improving the agreement with the available experimental data. EXX lattice constants are found to be only slightly larger (\approx 2 %) than the experimental ones. We also compare with results obtained by treating the 3d electrons as core electrons.

[X11.002] Fermi-surface dependent nonlocal contributions in the electronic structure of magnetic transition metals

We consider an approach which separates the exchange-correlation nonlocal potential into two parts: one, which depends only on the local electronic density and another which includes contributions determined by density variations at large distances and by the structure of levels near the Fermi surface. The exchange self-energy is taken into account exactly and correlation is treated by the set of GW diagrams. In this set we pick the contribution from the electron pole and the contribution from the integration over the imaginary axis. The interplay between these two contributions strongly influences the screening of the interaction in various metals. The approach is self-consistent and allows us to calculate the total energy. The proposed technique was used to study the electronic structure, the total energy and magnetic properties in transition metals. It is demonstrated that this technique produces a better than LDA description of the FM phase of Gd, whereas for FM Fe it gives results similar to LDA. We compare this approach with the GW and the "exact" screened exchange techniques and discuss ways to improve it.

[X11.003] Adiabatic spin dynamics from time-dependent spin density functional theory

The adiabatic spin dynamics (ASD) \footnote Q. Niu and L. Kleinman, Phys. Rev. Lett. 80, 2205 (1998) approach to the calculation of spin excitations in magnetic materials requires as inputs both the energy of a given spin configuration and the Berry curvature computed from the spin dependence of the adiabatic wave function. In this paper we describe a time-dependent spin density functional approach to the calculation of the Berry curvature in the linear response regime (small deviations from equilibrium). This approach completely bypasses the need for a knowledge of the adiabatic wave function. We derive a gradient expansion for the kinetic and exchange-correlation contributions to the Berry curvature tensor. In addition to the ordinary antisymmetric part, a symmetric component of the curvature appears naturally in our formalism. We show that this component describes dissipation and leads to damping of spin waves - a feature that is absent in the conventional ASD approach.

[X11.004] Describing exchange-correlation beyond semilocal approximations: Implementation of the adiabatic-connection fluctuation-dissipation theorem and application to H_2 and Be_2.

In studies of molecules and solids using density-functional theory, one often achieves a useful accuracy within the local-density or generalized gradient approximations for exchange-correlation (XC). Yet both fall short of giving total energies with chemical accuracy and do poorly for Van der Waals systems. Systematic improvements are expected from the (in principle exact) representation of the XC energy through the adiabatic-connection fluctuation-dissipation theorem (ACFDT). There the electronic pair-correlations are obtained by a coupling-strength integration of the dynamical density response. We present our implementation of the ACFDT formalism within the plane-wave pseudopotential method. We illustrate the accuracy of this method for He and H_2, treating exchange terms exactly, and examine approximations for the dynamical response. Furthermore, we evaluate the binding energy of the H_2 and Be_2 dimers using the random phase approximation with a local correction for short-range correlations.

[X11.005] Initial-state dependence in time-dependent density functional theory

In time-dependent density functional theory, the exchange-correlation potential depends on both the complete history (memory) of the density and the initial state. The adiabatic local density approximation (ALDA) ignores both these effects. There have been several attempts to construct approximate functionals with memory, but almost no investigation of initial-state effects. We show (1) that there is no initial-state dependence for one electron (non-trivial), (2) that the initial-state dependence can be made arbitrarily large for two or more electrons, and (3) that most, if not all, initial-state effects can be absorbed into a pseudo-prehistory of the density.

[X11.006] Dynamic effects in time-dependent density functional theory

The time-dependent Schrödinger equation is solved exactly for a simple model system: two electrons in a harmonic potential with a time-dependent force constant. The exact Kohn-Sham wavefunction is constructed. The time-dependent exchange-correlation energy is calculated and compared with the (almost) exact value for the ground-state energy functional evaluated on the instantaneous density. The difference is due to dynamic effects, which are absent from any adiabatic approximation. Such dynamic effects are important and significant for all the time-dependent quantities we calculate and their implications for time-dependent density functional theory are discussed. The time-dependent correlation energy is shown to sometimes become positive, to apparently scale to a constant function of scaled time in the high-density limit, and to have a strong non-locality in time. The dynamical correlation potential appears to have a first-order contribution.

[X11.007] Dispersion forces in density functional theory: van der Waals correlations without wavefunctions

Dispersion or vdW forces are important in the description of soft matter including polymers and biomolecules. These forces arise from long-ranged, geometry-dependent electronic correlations, missed by local and gradient density functionals. It is widely believed that the RPA and related many-body approaches capture vdW forces adequately, and methods have recently been advanced to streamline the exact evaluation of RPA-style energies. These approaches still require the evaluation of a selfconsistent set of time-dependent one-body wavefunctions or equivalent, however, and for large systems one would hope to avoid this detail. Here we explore methods which generate vdW correlations via direct use of groundstate densities and potentials to approximate response functions, rather than approximating the xc energy density as in the LDA. Issues include low-density cutoffs and their avoidance via exact constraint conditions, and the need for ``seamless" functionals that describe all force contributions even when charge densities overlap.

[X11.008] Investigation of the Inverse Radius of the Exchange Hole (a Local Exchange Energy Density) for Two Simple Systems

We investigate an explicitly known expression for a local exchange energy density (the inverse radius of the exchange hole) in the slowly varying limit for two simple model systems. The idea is to extract coefficients in a series expansion in the local electron density, thus giving a local gradient expansion (involving the density and its gradients and laplacians). This approach is different from the very successful traditional GGA's which are derived using non-local transformations that preserve the value of the total exchange energy, but drop the locality of the GGA functionals. The investigated systems are based on harmonic and cosinusoidal potentials respectively, and while extracting higher order coefficients in the local gradient expansion for the harmonic system, we find a singular behavior (a logarithmic divergence). This result is further investigated and discussed, comparing the two different model systems.

[X11.009] Slater Averaged Pseudopotential and Its Inprovements

We demonstrate that the optimized effective potential method(OEP), which can be viewed as a way for constructing orbital independent potential from the known orbital dependent potentials, is valid for pseudopotentials. It is further on proved that for most group I and II elements as well as the elements with large radius, the Slater averaged pseudopotential, which is local and orbital independent, is applicable with very good transferability. A Heine-Abarenkov(HA) correction is proposed to make the pseudopotential workable for other elements, especially the first row atoms. Further on, the combination of the Slater averaged potential and the Bachelet-Hamman-Schluter(BHS) construction produces a new family of first principle norm-conserving pseudopotentials.

[X11.010] Density-functional wavelet calculations of polarizability of atomic clusters with many electrons

We report the results of a study of the polarizability of GaAs clusters using new algorithms for multiresolution analysis (MRA). These new algorithms enable, for the first time, fully systematic all-electron calculations of systems with large numbers of electrons within density functional theory. We present the first wavelet calculations, to our knowledge, of electric polarizability and of systems beyond diatomic molecules.

[X11.011] Density functional wavelet calculation of solid state systems

We present, to our knowledge, the first all-electron wavelet calculations of the electronic structure of solids within density functional theory. To make these calculations competitive with traditional approaches, we employ recent developments in algorithms for multiresolution analysis (MRA) which speed density functional calculations by three to four orders of magnitude[1,2]. MRA provides a fully systematic, integrated treatment of core and valence electrons and is ideal for exploring the limits of the accuracy of density functional theory in the calculation of EELS spectra, which involve matrix elements between the core and valence states. We shall present results for EELS spectra as well as the resolution of technical issues which arise in carrying out solid-state calculations within a wavelet-like basis.

[1] ``Multiscale computation with interpolating wavelets,'' by Ross A. Lippert, T.A. Arias and Alan Edelman, Journal of Computational Physics, 140:2, 278--310 (1 March 1998). Preprint: http://xxx.lanl.gov/abs/cond-mat/9805283 .

[2] ``Multiresolution analysis of electronic structure: semicardinal and wavelet bases,'' T.A. Arias, Reviews of Modern Physics 71:1, 267--311 (January 1999). Preprint: http://xxx.lanl.gov/abs/cond-mat/9805262 .

[X11.012] A multi-resolution density-matrix scheme for electronic structure calculations

A multi-resolution density-matrix wavelet scheme for electronic structure calculations is proposed. The multi-resolution properties of the wavelet representation makes the scheme highly attractable compared to more conventional density-matrix methods. A separable multi-dimensional biorthogonal interpolating multi-wavelet and scaling representation of the Hamiltonian operator is introduced in which individual operator elements can be calculated locally at any scale. Issues regarding this represenation are discussed, such as its close relation with finite-difference schemes. A method for constructing the density matrix by means of a polynomial expansion of the density matrix in terms of the Hamiltonian operator within a grand canonical ensamble is introduced. The general properties regarding the efficiency of the multi-resolution representation in comparison with a real-space represenation is analyzed. Within the multi-resolution wavelet representation it is found that the sparsity of the density matrix is preserved for both localized systems with short-range correlations as well as for itinerant systems with long-range correlations. This is not possible within a conventional real-space representation.

[X11.013] Thomas-Fermi charge mixing for obtaining self-consistency in density functional calculations.

It is well known that when any one of the dimensions of a unit cell is large, the charge mixing converges slowly in a self-consistent density functional calculation. The problem of the charge density shifting from one end to the other has been called charge sloshing. This is mainly caused by the low frequencies components of the charge density. The problem becomes severe when the system is inhomogeneous where no model is available to approximate the dielectric function of the system. A new charge mixing scheme is tested here, which uses the Thomas-Fermi-von Weizsacker equation to solve the charge density response function to the potential. This is done each self-consistent iteration. We compare this new method with the commonly used Pulay and modified Broyden techniques, and find significant improvement for large dimension systems. We also compare a method that minimizes the DFT functional directly with a Grassmann conjugate gradient algorithm that updates the charge density and associated potential with every update of the wavefunctions.

[X11.014] The ABINIT software project

The computation of electronic structure, total energy, forces and many related properties of condensed matter, thanks to density-functional theory (DFT), is a field in constant progress. A DFT software project that wants to stay at the frontier of knowledge cannot be the work of a single individual, neither of a small group. Also, up-to-date software engineering concepts can considerably ease the harmonious development of such software.

The ABINIT project relies upon these ideas : concepts of reliability, portability, readability and freedom of sources are emphasized, in the course of developping a sophisticated plane-wave pseudopotential code. More than 200 automated tests secure existing capabilities despite heavy development efforts and the associated bug generation; thanks to MAKE and PERL scripts, and CPP directives, the unique set of Fortran90 source files (about 100000 lines) can generate sequential (or parallel) object code for many platforms, under Unix/Linux, DOS/Windows and MacOS; strict coding rules have been followed to make the source readable. Moreover, the whole package is distributed under the GNU General Public Licence, often nicknamed 'copyleft' (see http://www.pcpm.ucl.ac.be/ABINIT).

Part X of program listing