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Register a new userImplementation of an all-electron GW Approximation using the Projector Augmented Wave method: I. Formulation and application to the electronic structure of semiconductors
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We have implemented the so called GW approximation (GWA) based on an all-electron full-potential Projector Augmented Wave (PAW) method. For the screening of the Coulomb interaction W we tested three different plasmon-pole dielectric function models, and showed that the accuracy of the quasiparticle energies is not sensitive to the the details of these models. We have then applied this new method to compute the quasiparticle band structure of some small, medium and large-band-gap semiconductors: Si, GaAs, AlAs, InP, SiMg$_2$, C and (insulator) LiCl. A special attention was devoted to the convergence of the self-energy with respect to both the {bf k}-points in the Brillouin zone and to the number of reciprocal space $bf G$-vectors. The most important result is that although the all-electron GWA improves considerably the quasiparticle band structure of semiconductors, it does not always provide the correct energy band gaps as originally claimed by GWA pseudopotential type of calculations. We argue that the decoupling between the valence and core electrons is a problem, and is some what hidden in a pseudopotential type of approach.
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A new implementation of the GW approximation (GWA) based on the all-electron Projector-Augmented-Wave method (PAW) is presented, where the screened Coulomb interaction is computed within the Random Phase Approximation (RPA) instead of the plasmon-pole model. Two different ways of computing the self-energy are reported. The method is used successfully to determine the quasiparticle energies of six semiconducting or insulating materials: Si, SiC, AlAs, InAs, NaH and KH. To illustrate the novelty of the method the real and imaginary part of the frequency-dependent self-energy together with the spectral function of silicon are computed. Finally, the GWA results are compared with other calculations, highlighting that all-electron GWA results can differ markedly from those based on pseudopotential approaches.
The so-called local density approximation plus the multi-orbital mean-field Hubbard model (LDA+U) has been implemented within the all-electron projector augmented-wave method (PAW), and then used to compute the insulating antiferromagnetic ground state of NiO and its optical properties. The electronic and optical properties have been investigated as a function of the Coulomb repulsion parameter U. We find that the value obtained from constrained LDA (U=8 eV) is not the best possible choice, whereas an intermediate value (U=5 eV) reproduces the experimental magnetic moment and optical properties satisfactorily. At intermediate U, the nature of the band gap is a mixture of charge transfer and Mott-Hubbard type, and becomes almost purely of the charge-transfer type at higher values of U. This is due to the enhancement of the oxygen 2p states near the top of the valence states with increasing U value.
We present valence electron Compton profiles calculated within the density-functional theory using the all-electron full-potential projector augmented-wave method (PAW). Our results for covalent (Si), metallic (Li, Al) and hydrogen-bonded ((H_2O)_2) systems agree well with experiments and computational results obtained with other band-structure and basis set schemes. The PAW basis set describes the high-momentum Fourier components of the valence wave functions accurately when compared with other basis set schemes and previous all-electron calculations.
The quasiparticle band structures of nonmagnetic monoxides, MO (M=Mg, Ca, Ti, and V), are calculated by the GW approximation. The band gap and the width of occupied oxygen 2p states in insulating MgO and CaO agree with experimental observation. In metallic TiO and VO, conduction bands originated from metal 3d states become narrower. Then the partial densities of transition metal e_g and t_2g states show an enhanced dip between the two. The effects of static screening and dynamical correlation are discussed in detail in comparison with the results of the Hartree-Fock approximation and the static Coulomb hole plus screened exchange approximation. The d-d Coulomb interaction is shown to be very much reduced by on-site and off-site d-electron screening in TiO and VO. The dielectric function and the energy loss spectrum are also presented and discussed in detail.
We construct a reference database of materials properties calculated using density-functional theory in the local or generalized-gradient approximation, and an all-electron or a projector augmented-wave (PAW) formulation, for verification and validation of first-principles simulations. All-electron calculations use the full-potential linearised augmented-plane wave method, as implemented in the texttt{Elk} open-source code, while PAW calculations use the datasets developed by some of us in the open-source texttt{PSlibrary} repository and the texttt{Quantum ESPRESSO} distribution. We first calculate lattice parameters, bulk moduli, and energy differences for alkaline metals, alkaline earths, and $3d$ and $4d$ transition metals in three ideal, reference phases (simple cubic, fcc, and bcc), representing a standardized crystalline monoatomic solid-state test. Then, as suggested by K. Lejaeghere {it et al.}, [Critical Reviews in Solid State and Material Sciences 39, p 1 (2014)], we compare the equations of state for all elements, except lanthanides and actinides, in their experimental phase (or occasionally a simpler, closely related one). PAW and all-electron energy differences and structural parameters agree in most cases within a few meV/atom and a fraction of a percent, respectively. This level of agreement, comparable with the previous study, includes also other PAW and all-electron data from the electronic-structure codes texttt{VASP} and texttt{WIEN2K}, and underscores the overall reliability of current, state-of-the-art electronic-structure calculations. At the same time, discrepancies that arise even within the same formulation for simple, fundamental structural properties point to the urgent need of establishing standards for verification and validation, reference data sets, and careful refinements of the computational approaches used.
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