Adiabatic-connection fluctuation-dissipation DFT for the structural properties of solids-the renormalized ALDA and electron gas kernels

We present calculations of the correlation energies of crystalline solids and isolated systems within the adiabatic-connection fluctuation-dissipation formulation of density-functional theory. We perform a quantitative comparison of a set of model exchange-correlation kernels originally derived for the homogeneous electron gas (HEG), including the recently-introduced renormalized adiabatic local-density approximation (rALDA) and also kernels which (a) satisfy known exact limits of the HEG, (b) carry a frequency dependence or (c) display a 1/$k^2$ divergence for small wavevectors. After generalizing the kernels to inhomogeneous systems through a reciprocal-space averaging procedure, we calculate the lattice constants and bulk moduli of a test set of 10 solids consisting of tetrahedrally-bonded semiconductors (C, Si, SiC), ionic compounds (MgO, LiCl, LiF) and metals (Al, Na, Cu, Pd). We also consider the atomization energy of the H$_2$ molecule. We compare the results calculated with different kernels to those obtained from the random-phase approximation (RPA) and to experimental measurements. We demonstrate that the model kernels correct the RPA's tendency to overestimate the magnitude of the correlation energy whilst maintaining a high-accuracy description of structural properties.Comment: 41 pages, 7 figure

GW quasiparticle band structures of stibnite, antimonselite, bismuthinite, and guanajuatite

We present first-principles calculations of the quasiparticle band structures of four isostructural semiconducting metal chalcogenides A$_2$B$_3$ (with A = Sb, Bi and B = S, Se) of the stibnite family within the G$_0$W$_0$ approach. We perform extensive convergence tests and identify a sensitivity of the quasiparticle corrections to the structural parameters and to the semicore $d$ electrons. Our calculations indicate that all four chalcogenides exhibit direct band gaps, if we exclude some indirect transitions marginally below the direct gap. Relativistic spin-orbit effects are evaluated for the Kohn-Sham band structures, and included as scissor corrections in the quasiparticle band gaps. Our calculated band gaps are 1.5 eV (Sb$_2$S$_3$), 1.3 eV (Sb$_2$Se$_3$), 1.4 eV (Bi$_2$S$_3$) and 0.9 eV (Bi$_2$Se$_3$). By comparing our calculated gaps with the ideal Shockley-Queisser value we find that all four chalcogenides are promising as light sensitizers for nanostructured photovoltaics.Comment: 11 pages, 5 figures. Revised manuscript - includes spin-orbit interactio

Simple vertex correction improves GW band energies of bulk and two-dimensional crystals

The GW self-energy method has long been recognized as the gold standard for quasiparticle (QP) calculations of solids in spite of the fact that the neglect of vertex corrections and the use of a DFT starting point lacks rigorous justification. In this work we remedy this situation by including a simple vertex correction that is consistent with an LDA starting point. We analyse the effect of the self-energy by splitting it into a short-range and long-range term which are shown to govern respectively the center and size of the band gap. The vertex mainly improves the short-range correlations and therefore has a small effect on the band gap, while it shifts the band gap center up in energy by around 0.5 eV in good agreement with experiments. Our analysis also explains how the relative importance of short- and long-range interactions in structures of different dimensionality is reflected in their QP energies. Inclusion of the vertex comes at practically no extra computational cost and even improves the basis set convergence compared to GW. The method thus provides an efficient and rigorous improvement over the GW approximation and sets a new standard for quasiparticle calculations of solids

GW quasiparticle bandgaps of anatase TiO2 starting from DFT+U

We investigate the quasiparticle band structure of anatase TiO2, a wide gap semiconductor widely employed in photovoltaics and photocatalysis. We obtain GW quasiparticle energies starting from density-functional theory (DFT) calculations including Hubbard U corrections. Using a simple iterative procedure we determine the value of the Hubbard parameter yielding a vanishing quasiparticle correction to the fundamental band gap of anatase TiO2. The band gap (3.3 eV) calculated using this optimal Hubbard parameter is smaller than the value obtained by applying many-body perturbation theory to standard DFT eigenstates and eigenvalues (3.7 eV). We extend our analysis to the rutile polymorph of TiO2 and reach similar conclusions. Our work highlights the role of the starting non-interacting Hamiltonian in the calculation of GW quasiparticle energies in TiO2, and suggests an optimal Hubbard parameter for future calculations.Comment: 8 pages, 3 figures, 1 tabl

Hubbard U-corrected Hamiltonians for non-self-consistent random-phase approximation total energy calculations : a study of ZnS, TiO2, and NiO

In non-self-consistent calculations of the total energy within the random-phase approximation (RPA) for electronic correlation, it is necessary to choose a single-particle Hamiltonian whose solutions are used to construct the electronic density and noninteracting response function. Here we investigate the effect of including a Hubbard-U term in this single-particle Hamiltonian, to better describe the on-site correlation of 3d electrons in the transition metal compounds ZnS, TiO2, and NiO. We find that the RPA lattice constants are essentially independent of U, despite large changes in the underlying electronic structure. We further demonstrate that the non-self-consistent RPA total energies of these materials have minima at nonzero U. Our RPA calculations find the rutile phase of TiO2 to be more stable than anatase independent of U, a result which is consistent with experiments and qualitatively different from that found from calculations employing U-corrected (semi)local functionals. However we also find that the +U term cannot be used to correct the RPA's poor description of the heat of formation of NiO

Rare-earth transition-metal magnets at finite temperature : self-interaction-corrected relativistic density functional theory in the disordered local-moment picture

Atomic-scale computational modeling of technologically-relevant permanent magnetic materials faces two key challenges. First, a material's magnetic properties depend sensitively on temperature, so the calculations must account for thermally-induced magnetic disorder. Second, the most widely-used permanent magnets are based on rare-earth elements, whose highly-localized 4f electrons are poorly described by standard electronic structure methods. Here, we take two established theories --- the disordered local moment picture of thermally-induced magnetic disorder and self-interaction-corrected density-functional theory --- and devise a computational framework to overcome these challenges. Using the new approach, we calculate magnetic moments and Curie temperatures of the rare-earth cobalt (RECo5) family for RE=Y--Lu. The calculations correctly reproduce the experimentally-measured trends across the series and confirm that, apart from the hypothetical compound EuCo5, SmCo5 has the strongest magnetic properties at high temperature. An order parameter analysis demonstrates that varying the RE has a surprisingly strong effect on the Co--Co magnetic interactions determining the Curie temperature, even when the lattice parameters are kept fixed. We propose the origin of this behavior is a small contribution to the density from f-character electrons located close to the Fermi level

Temperature-dependent magnetocrystalline anisotropy of rare earth/transition metal permanent magnets from first principles : the light RCo5 (R = Y, La-Gd) intermetallics

Computational design of more efficient rare earth/transition metal (RE-TM) permanent magnets requires accurately calculating the magnetocrystalline anisotropy (MCA) at finite temperature, since this property places an upper bound on the coercivity. Here, we present a first-principles methodology to calculate the MCA of RE-TM magnets which fully accounts for the effects of temperature on the underlying electrons. The itinerant electron TM magnetism is described within the disordered local moment picture, and the localized RE-4f magnetism is described within crystal field theory. We use our model, which is free of adjustable parameters, to calculate the MCA of the RCo5 (R=Y, La-Gd) magnet family for temperatures 0–600 K. We correctly find a huge uniaxial anisotropy for SmCo5 (21.3MJm−3 at 300 K) and two finite temperature spin reorientation transitions for NdCo5. The calculations also demonstrate dramatic valency effects in CeCo5 and PrCo5. Our calculations provide quantitative, first-principles insight into several decades of RE-TM experimental studies