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Register a new userA wavelet-based Projector Augmented-Wave (PAW) method: reaching frozen-core all-electron precision with a systematic, adaptive and localized wavelet basis set
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Added by
Tonatiuh Rangel Gordillo
Publication date
2016
fields
Physics
and research's language is
English
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We present a Projector Augmented-Wave~(PAW) method based on a wavelet basis set. We implemented our wavelet-PAW method as a PAW library in the ABINIT package [http://www.abinit.org] and into BigDFT [http://www.bigdft.org]. We test our implementation in prototypical systems to illustrate the potential usage of our code. By using the wavelet-PAW method, we can simulate charged and special boundary condition systems with frozen-core all-electron precision. Furthermore, our work paves the way to large-scale and potentially order-N simulations within a PAW method.
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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.
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.
The detail structure of the wave function is analyzed at various refinement levels using the methods of wavelet analysis. The eigenvalue problem of a model system is solved in granular Hilbert spaces, and the trajectory of the eigenstates is traced in terms of the resolution. An adaptive method is developed for identifying the fine structure localization regions, where further refinement of the wave function is necessary.
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.
In order to increase the accuracy of the linearized augmented plane wave method (LAPW) we present a new approach where the plane wave basis function is augmented by two different atomic radial components constructed at two different linearization energies corresponding to two different electron bands (or energy windows). We demonstrate that this case can be reduced to the standard treatment within the LAPW paradigm where the usual basis set is enriched by the basis functions of the tight binding type, which go to zero with zero derivative at the sphere boundary. We show that the task is closely related with the problem of extended core states which is currently solved by applying the LAPW method with local orbitals (LAPW+LO). In comparison with LAPW+LO, the number of supplemented basis functions in our approach is doubled, which opens up a new channel for the extension of the LAPW and LAPW+LO basis sets. The appearance of new supplemented basis functions absent in the LAPW+LO treatment is closely related with the existence of the $dot{u}_l-$component in the canonical LAPW method. We discuss properties of additional tight binding basis functions and apply the extended basis set for computation of electron energy bands of lanthanum (face and body centered structures) and hexagonal close packed lattice of cadmium. We demonstrate that the new treatment gives lower total energies in comparison with both canonical LAPW and LAPW+LO, with the energy difference more pronounced for intermediate and poor LAPW basis sets.
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