Simple approximate physical orbitals for GW quasiparticle calculations

Generating unoccupied orbitals within density functional theory (DFT) for use in GW calculations of quasiparticle energies becomes prohibitive for large systems. We show that, without any loss of accuracy, the unoccupied orbitals may be replaced by a set of simple approximate physical orbitals made from appropriately prepared plane waves and localized basis DFT orbitals that represent the continuum and resonant states of the system, respectively. This approach allows for accurate quasiparticle calculations using only a very small number of unoccupied DFT orbitals, resulting in an order of magnitude gain in speed.     

Accurate quasiparticle spectra from self-consistent GW calculations with vertex corrections

Self-consistent GW calculations, maintaining only the quasiparticle part of the Green's function G, are reported for a wide class of materials, including small gap semiconductors and large gap insulators. We show that the inclusion of the attractive electron-hole interaction via an effective nonlocal exchange correlation kernel is required to obtain accurate band gaps in the framework of self-consistent GW calculations. If these are accounted for via vertex corrections in W, the band gaps are found to be within a few percent of the experimental values.     

BaSe的准粒子能带结构

运用标准的准粒子GW方法重新考察了BaSe的准粒子能带结构.为便于比较，同时计算了局域密度近似(LDA)和广义梯度近似(GGA)下的能带.结果表明，LDA和GGA方法都不能准确描述这个材料的带隙.与实验测量值对比，其误差分别达到39.9%和32.6%.GW准粒子能带的结果则可以对其带隙作出大幅度的修正，得到与实验测量相当符合的理论结果.与已有的计算结果不同，B1结构BaSe准粒子能带具有Γ点直接带隙特性，表明在Ba价电子组态中考虑4d电子的作用至关重要. 关键词： BaSe GW 能带结构 带隙     

Electronic structure and the local electroneutrality level of SiC polytypes from quasiparticle calculations within the GW approximation

The most important interband transitions and the local charge neutrality level (CNL) in silicon carbide polytypes 3C-SiC and nH-SiC (n = 2?C8) are calculated using the GW approximation for the self energy of quasiparticles. The calculated values of band gap E _g for various polytypes fall in the range 2.38 eV (3C-SiC)-3.33 eV (2H-SiC) and are very close to the experimental data (2.42?C3.33 eV). The quasiparticle corrections to E _g determined by DFT-LDA calculations (about 1.1 eV) are almost independent of the crystal structure of a polytype. The positions of CNL in various polytypes are found to be almost the same, and the change in CNL correlates weakly with the change in E _g, which increases with the hexagonality of SiC. The calculated value of CNL varies from 1.74 eV in polytype 3C-SiC to 1.81 eV in 4H-SiC.     

Parameter-free quasiparticle calculations for YH3

Electronic structure calculations for YH3 within the local density approximation result in a metallic ground state with the bands at the Fermi energy overlapping by more than 1 eV, whereas a band gap of 2.8 eV is deduced from optical experiments. Here, we report the results of parameter-free GW calculations which predict a fundamental gap of 1 eV. When we take into account electric dipole matrix elements a large optical gap of almost 3 eV is obtained. A combination of photoemission and inverse photoemission spectroscopy could test the prediction of a small fundamental band gap.     

Conserving quasiparticle calculations for small metal clusters

A novel approach for GW-based calculations of quasiparticle properties for finite systems is presented, in which the screened interaction is obtained directly from a linear response calculation of the density-density correlation function. The conserving nature of our results is shown by explicit evaluation of the f-sum rule. As an application, energy renormalizations and level broadenings are calculated for the closed-shell Na₉ ⁺ and Na₂₁ ⁺ clusters, as well as for Na₄. Pronounced improvements of conserving approximations to RPA-level results are obtained.     

GW quasiparticle bandgaps of anatase TiO2 starting from DFT + U

We investigate the quasiparticle band structure of anatase TiO(2), 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 bandgap of anatase TiO(2). The bandgap (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 TiO(2) and reach similar conclusions. Our work highlights the role of the starting non-interacting Hamiltonian in the calculation of GW quasiparticle energies in TiO(2) and suggests an optimal Hubbard parameter for future calculations.     

Three-nucleon calculations for local potentials with the quasiparticle method

The three-nucleon system for energies below the breakup threshold is investigated with the help of the quasiparticle method. Two types of local potentials are used, namely purely attractive Yukawa potentials and the soft-core potentials of Malfliet and Tjon. The results obtained are compared with those of other calculations employing different methods.Presented at the symposium Theory of lightest nuclei, Liblice, Czechoslovakia, May 1974.     

First-principles calculations of quasiparticle excitations of open-shell condensed matter systems

We develop a Green's function approach to quasiparticle excitations of open-shell systems within the GW approximation. It is shown that accurate calculations of the characteristic multiplet structure require a precise knowledge of the self-energy and, in particular, its poles. We achieve this by constructing the self-energy from appropriately chosen mean-field theories on a fine frequency grid. We apply our method to a two-site Hubbard model, several molecules, and the negatively charged nitrogen-vacancy defect in diamond and obtain good agreement with experiment and other high-level theories.     

Editorial: Challenges and solutions in GW calculations for complex systems

We report key advances in the area of GW calculations, review the available software implementations and define standardization criteria to render the comparison between GW calculations from different codes meaningful, and identify future major challenges in the area of quasiparticle calculations. This Topical Issue should be a reference point for further developments in the field.     

Monte Carlo calculations of atoms and molecules

The variational and Green's function Monte Carlo (GFMC) methods can treat many interesting atomic and molecular problems. These methods can give chemical accuracy for up to 10 or so electrons. The various implementations of the GFMC method, including the domain Green's function method and the short-time approximation, are discussed. Results are presented for several representative atoms and molecules.     

Influence of an enlargement of the model space on number projected quasiparticle calculations

Results of number projected quasiparticle calculations for Sn isotopes in large and in small model spaces are compared when the force strengths and single-particle energies are determined consistently within each model space. When extending the model space, one observes that the model parameters extracted from the odd nuclei become more satisfactory. For even nuclei the collective states are not lowered in energy although electromagnetic transition rates increase considerably. Spectroscopic factors for one-nucleon transfer reactions change noticeably only for shells close to the Fermi level. Two-nucleon transfer cross-sections are strongly increased for ground state to ground state transitions only. We criticize a usual approximation formula for theL=0 two-nucleon transfer cross-section.     

Influence of an enlargement of the model space on number projected quasiparticle calculations

Results of number projected quasiparticle calculations for Sn isotopes in large and in small model spaces are compared when the force strengths and single-particle energies are determined consistently within each model space. When extending the model space, one observes that the model parameters extracted from the odd nuclei become more satisfactory. For even nuclei the collective states are not lowered in energy although electromagnetic transition rates increase considerably. Spectroscopic factors for one-nucleon transfer reactions change noticeably only for shells close to the Fermi level. Two-nucleon transfer cross-sections are strongly increased for ground state to ground state transitions only. We criticize a usual approximation formula for theL=0 two-nucleon transfer cross-section.     

Scattering factor calculations and dispersion corrections for heavy atoms

Reliable knowledge of the complex X-ray form factor (Re(f) and Im(f)) is required for crystallography, deformation density bonding studies and refractive index studies. Dispersion corrections are important in DAFS, MAD analyses and XAFS studies. Discrepancies between currently used theoretical approaches of 200% exist for numerous elements from 1 to 3 keV X-ray energies, and at higher energies these discrepancies can persist at the 10% level or more. This has suggested that new formulations and new experimental approaches are necessary. Recent tabulations improve upon the theoretical uncertainty in some of these regions by a factor of 10 and reduce the error of this approach to below one standard deviation. Recent experimental developments have begun to probe alternate theory, providing a tool to investigate the significance of relativistic corrections and convergence criteria across a range of atomic number. In part, this has revealed that more theoretical work will be required in future years. Recent advances permit new probes and insights into atomic and solid state physics, as well as to many X-ray optical applications. This paper discusses significant improvements upon the theoretical uncertainty in near-edge regions, reducing the error of this approach to less than one standard deviation.     

Relativistic calculations of inelastic collisions between electrons and atoms

The Feynman S-matrix formalism is used to consider the inelastic collisions of electrons with a hydrogen atom. The two leading Feynman diagrams are calculated, and the 1s-2s transition is treated in detail. Results are given for scattering amplitudes at energies of 1.0–8.0 (atomic units) and for various scattering angles, as well as the differential cross sections for direct scattering in the energy region 1.36–118.5 keV. On the basis of comparison with nonrelativistic calculations, we conclude that relativistic effects are appreciable and increase with energy. Total cross sections are calculated in both nonrelativistic and relativistic approximations. The difference between them increases with energy and is 15–20% for energies of 20–50 keV.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 7–12, August, 1977.     

Optical potential calculations for the 1s level in pionic atoms

The Ericson-Ericson optical potential for theπ-nucleuss-wave interaction was extended to be applicable also for light nuclei. In particular, terms of order A^?1 were evaluated and the (π2N) dispersion was considered. From comparison with experimental data we found that considerable improvement could be achieved by introducing terms of order A^?1. The (π2N) dispersion was found to be repulsive and of the same magnitude as the absorption. The (πN) scattering lengths were deduced to be α₃?α₁=0.258±0.008m _π ^?1 and α₁+2α₃=?0.018±0.008m _π ^?1 .     

Interaction of interstitial nitrogen atoms in Nb: Ab initio calculations

Ab initio calculations of pair nitrogen interstitials interaction in the first 12 coordination shells of a Nb crystal lattice are performed using the Vienna ab initio simulation package (VASP), and chemical and strain-induced contributions are analyzed. It is shown that rapidly decreasing chemical repulsion prevails in the nearest coordination shells, whereas strain-induced (elastic) interaction makes the main contribution in more distant shells.