Non-local Exchange-correlation Potentials Research Articles

Low-Order Scaling Quasiparticle Self-Consistent GW for Molecules.

Low-order scaling GW implementations for molecules are usually restricted to approximations with diagonal self-energy. Here, we present an all-electron implementation of quasiparticle self-consistent GW for molecular systems. We use an efficient algorithm for the evaluation of the self-energy in imaginary time, from which a static non-local exchange-correlation potential is calculated via analytical continuation. By using a direct inversion of iterative subspace method, fast and stable convergence is achieved for almost all molecules in the GW100 database. Exceptions are systems which are associated with a breakdown of the single quasiparticle picture in the valence region. The implementation is proven to be starting point independent and good agreement of QP energies with other codes is observed. We demonstrate the computational efficiency of the new implementation by calculating the quasiparticle spectrum of a DNA oligomer with 1,220 electrons using a basis of 6,300 atomic orbitals in less than 4 days on a single compute node with 16 cores. We use then our implementation to study the dependence of quasiparticle energies of DNA oligomers consisting of adenine-thymine pairs on the oligomer size. The first ionization potential in vacuum decreases by nearly 1 electron volt and the electron affinity increases by 0.4 eV going from the smallest to the largest considered oligomer. This shows that the DNA environment stabilizes the hole/electron resulting from photoexcitation/photoattachment. Upon inclusion of the aqueous environment via a polarizable continuum model, the differences between the ionization potentials reduce to 130 meV, demonstrating that the solvent effectively compensates for the stabilizing effect of the DNA environment. The electron affinities of the different oligomers are almost identical in the aqueous environment.

Hybrid-DFT + Vw method for band structure calculation of semiconducting transition metal compounds: the case of cerium dioxide

Hybrid functionals’ non-local exchange-correlation potential contains a derivative discontinuity that improves on standard semi-local density functional theory (DFT) band gaps. Moreover, by careful parameterization, hybrid functionals can provide self-interaction reduced description of selected states. On the other hand, the uniform description of all the electronic states of a given system is a known drawback of these functionals that causes varying accuracy in the description of states with different degrees of localization. This limitation can be remedied by the orbital dependent exact exchange extension of hybrid functionals; the hybrid-DFT + Vw method (Ivády et al 2014 Phys. Rev. B 90 035146). Based on the analogy of quasi-particle equations and hybrid-DFT single particle equations, here we demonstrate that parameters of hybrid-DFT + Vw functional can be determined from approximate theoretical quasi-particle spectra without any fitting to experiment. The proposed method is illustrated on the charge self-consistent electronic structure calculation for cerium dioxide where itinerant valence states interact with well-localized 4f atomic like states, making this system challenging for conventional methods, either hybrid-DFT or LDA + U, and therefore allowing for a demonstration of the advantages of the proposed scheme.

Topologicalα-Sn surface states versus film thickness and strain

The theoretical prediction that gray tin represents a strong topological insulator under strain [L. Fu and C.L. Kane, Phys. Rev. B 76, 045302 (2007)] is proven for biaxially strained $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{Sn}$ layers with varying thickness by means of a generalized density functional theory with a nonlocal exchange-correlation potential that widely simulates quasiparticle bands and a tight-binding method including intra- and interatomic spin-orbit interaction. Hydrogen-passivated surfaces are modeled by symmetric slabs. In contrast to the conventional picture of a topological insulator, we find topological gapless surface states below the strain-induced bulk gap, in agreement with photoemission studies. The topological surfaces states do not emerge out of the lower ${\ensuremath{\Gamma}}_{8}^{+}$ states but are strongly influenced by the inverted bulk ${\ensuremath{\Gamma}}_{7}^{\ensuremath{-}}$ band, i.e., lie within the negative bulk $sp$ gap. We show that the position of the Dirac point and the dispersion of the surrounding bands depend on the thickness of the $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{Sn}$ layer but are less influenced by strain. The resulting Fermi velocities agree well with available photoemission data.

Quasiparticle Self-Consistent GW Method Based on the Augmented Plane-Wave and Muffin-Tin Orbital Method

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 the highly localized MTOs. This allows us to make stable interpolation of the self-energy in the whole Brillouin zone. In addition, we have improved the offset-{\Gamma} method for the Brillouin zone integration, so that we take into account the anisotropy of the screened Coulomb interaction in the calculation of the self-energy. For GaAs and cubic SiO2 , we checked convergence of calculated band gaps on cutoff parameters. PMT-QSGW is implemented in a first-principles electronic structure package ecalj, which is freely available from github.

Ab-Initio Studies of Electronic and Spectroscopic Properties of MgO, ZnO and CdO

We present ab-initio calculations of excited-state properties within single-particle and two-particle approaches in comparison with corresponding experimental results. For the theoretical treatment of the electronic structure, we compute eigenvalues and eigenfunctions by using a spatially nonlocal exchange-correlation potential. From this starting point, quasiparticle energies within the fully frequency-dependent G(0)W(0) approximation are obtained. By solving the Bethe-Salpeter equation, we evaluate optical properties, including the electron-hole attraction and the local-field effects. The results are compared with experimental spectra from soft X-ray emission, as well as from X-ray photoelectron spectroscopy or ellipsometry measurements. In more detail, we compute the valence-band densities of states, bound excitons, and the dielectric function. For the latter, we discuss both the absorption edge and higher critical points.

Ab initiotheory of excitons and optical properties for spin-polarized systems: Application to antiferromagnetic MnO

We study quasiparticle and electron-hole pair excitations in the presence of spin polarization within the framework of many-body perturbation theory. The influence of magnetic ordering on linear optical response is examined in detail for collinear spins. Whereas Hedin's expression for the exchange-correlation self-energy in the $GW$ approximation remains diagonal with respect to the one-particle spin quantum number, the Bethe-Salpeter equation becomes more complex: The separation between triplet and singlet excitons no longer holds. The submatrices of the two-particle Hamiltonian are coupled by the matrix elements of the bare Coulomb potential which account for local-field effects. Therefore, the rank of the corresponding eigenvalue problem doubles. Numerical results are computed from first principles for the antiferromagnetic insulator MnO starting from electronic states obtained with nonlocal exchange-correlation potentials. The calculated electronic structure and optical absorption spectra including excitonic and local-field effects are compared with experimental data. The dominance of interatomic transitions between Mn atoms in the interband region of the optical absorption is revealed.

Band-theory calculation of image states on a metal surface.

A band-theory method is presented for the calculation of image states on a metal surface. It is modified from the film linearized augmented-plane-wave method for surface-electronic-structure calculations. A nonlocal exchange-correlation potential is incorporated to correct the long-range potential beyond the image plane, and a multiple-energy-parameter scheme is used to generate the basis in vacuum. A calculation on Ag(100) yields accurate binding energies, effective masses, and wave functions for the two lowest image states, which agree closely with the available experimental data.

A test of density functional theory for dative bonding systems

Density functional calculations are carried out for the H 3B—NH 3 system and compared with experimental and ab initio theoretical data. Calculations that use non-local exchange-correlation potentials are capable of providing excellent geometries, dative bond energies and dipole moments, as well as a adequate estimates of vibrational frequencies and barriers to internal rotations. The local density approximation can provide reasonable structure information, but significantly overestimates the dative bond energy, without perturbative non-local corrections.

Approximate nonlocal-exchange-correlation potential as the image potential for metals.

A method is presented for applying the concept of an exchange-correlation electric field due to the exchange-correlation hole when determining the approximated nonlocal-exchange-correlation (NLXC) potential in the surface region of a metal. Our approximation for the electron-hole separation based on the theory is proposed by Serena, Soler, and Garci\ifmmode\acute\else\textasciiacute\fi{}a. The NLXC potential obtained shows the correct classical imagelike limit outside the metal without any extra boundary conditions. The method presented is also applied to determining the NLXC potential of a one-dimensional metal-vacuum-metal (MVM) interface barrier. This method gives the physical background of the approach for a MVM barrier suggested by Garci\ifmmode\acute\else\textasciiacute\fi{}a and incorporates the classical multi-image potential in the NLXC potential of a MVM junction.

Self-consistent implementation of nonlocal exchange and correlation in a Gaussian density-functional method.

The gradient-expansion approximation (GEA) and the generalized gradient approximation (GGA) to nonlocal exchange energy in concert with the nonlocal correlation energy functional of Perdew [Phys. Rev. B 33, 8822 (1986)] are analyzed when implemented in a fully self-consistent way in conjunction with the Vosko-Wilk-Nusair parametrization for the local exchange-correlation energy. It is shown that the lowest-order gradient expansion, even with corrected asymptotic behavior in the large-density-gradient limit, is still unsatisfactory in the chemically important region of electron densities where the basic assumption of the GEA (\ensuremath{\Vert}\ensuremath{\nabla}n\ensuremath{\Vert}/2${\mathit{k}}_{\mathit{F}}$n1) breaks down. In contrast, the GGA expansion behaves better. A shift by a constant additive term of an effective one-body Kohn-Sham potential in concert with the GGA nonlocal functional provides, within the framework of density-functional theory, a way of interpreting excitation energies. The nonlocal functionals significantly improve binding energies. The resulting nonlocal exchange-correlation potential is state independent; thus the present method is convenient from the computational point of view. Applications are presented for a number of atoms and small molecules, including ${\mathrm{O}}_{2}$, ${\mathrm{Mg}}_{2}$, ${\mathrm{CH}}_{2}$, and for a transition-metal cluster, ${\mathrm{Ni}}_{4}$.

Non-local exchange-correlation potential at a metal surface from many-body perturbation theory

We report a first-principles evaluation of the exchange-correlation potential (V XC ) at a metal surface. An integral equation relating (V XC ) and the non-local electron self-energy (Σ XC ) is solved numerically for a free-electron metal surface, with use of a static approximation for Σ XC . The strongly-inhomogeneous nature of the electron density profile at the surface is treated exactly, i.e. without invoking the usual local density approximation. Our result for V XC has the correct image-like asymptotic behavior; it derives implicitly from a non-local exchange-correlation energy functional. We study the effect of non-locality on the position of the effective image plane (z O ) from an analysis of the image tail of V XC and also from linear-response theory. The difference in the values of z O obtained by both methods for low metallic densities is attributed to electron overlap effects. We also discuss the effects of V XC on image-potential induced surface states.

Non-local-density based self-consistent surface calculations. II. Bimetal interfaces

For pt.I see ibid., vol.10, p.567 (1977). The effect of a non-local exchange correlation potential on the charge density profile and electrostatic potential near an interface is investigated in the case of a metal-metal junction. A simple jellium model is considered, in which an approximate exchange correlation potential is constructed from the self-energy formalism as modified for interfaces. An extension of the Thomas-Fermi model of the electron gas is used as a first approximation to the self-consistent solution of the problem and the results compared with a self-consistent local-density calculation and some exact results for jellium interfaces. The model gives the correct qualitative features of the interface and at higher metallic densities the quantitative agreement is good.