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Register a new userComparison of Global and Local Adaptive Coordinates for Density Functional Calculations
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Authors
D. R. Hamann
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A globally-adaptive curvilinear coordinate formalism is shown to be easily convertible to a class of curvilinear transformations locally optimized around atom sites by a few parameters. Parameter transferability is established for a demanding test case, and the results of the two methods are shown to be comparable. Computational efficiencies realized in the local method are discussed.
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Localized basis sets in the projector augmented wave formalism allow for computationally efficient calculations within density functional theory (DFT). However, achieving high numerical accuracy requires an extensive basis set, which also poses a fundamental problem for the interpretation of the results. We present a way to obtain a reduced basis set of atomic orbitals through the subdiagonalization of each atomic block of the Hamiltonian. The resulting local orbitals (LOs) inherit the information of the local crystal field. In the LO basis, it becomes apparent that the Hamiltonian is nearly block-diagonal, and we demonstrate that it is possible to keep only a subset of relevant LOs which provide an accurate description of the physics around the Fermi level. This reduces to some extent the redundancy of the original basis set, and at the same time it allows one to perform post-processing of DFT calculations, ranging from the interpretation of electron transport to extracting effective tight-binding Hamiltonians, very efficiently and without sacrificing the accuracy of the results.
We scrutinize the accuracy of the pseudopotential approximation in density-functional theory (DFT) calculations of surfaces by systematically comparing to results obtained within a full-potential setup. As model system we choose the CO oxidation at a RuO2(110) surface and focus in particular on the adsorbate binding energies and reaction barriers as target quantities for the comparison. Rather surprisingly, the major reason for discrepancy does not result from the neglected semi-core state relaxation in the frozen-core approximation, but from an inadequate description of the local part of the Ru pseudopotential, responsible for the scattering of f like waves. Tiny, seemingly irrelevant, imprecisions appearing in these properties can have a noticeable influence on the surface energetics. At least for the present example, we obtain excellent agreement between both approaches, if the pseudopotential describes these scattering properties accurately.
We assess the validity of various exchange-correlation functionals for computing the structural, vibrational, dielectric, and thermodynamical properties of materials in the framework of density-functional perturbation theory (DFPT). We consider five generalized-gradient approximation (GGA) functionals (PBE, PBEsol, WC, AM05, and HTBS) as well as the local density approximation (LDA) functional. We investigate a wide variety of materials including a semiconductor (silicon), a metal (copper), and various insulators (SiO$_2$ $alpha$-quartz and stishovite, ZrSiO$_4$ zircon, and MgO periclase). For the structural properties, we find that PBEsol and WC are the closest to the experiments and AM05 performs only slightly worse. All three functionals actually improve over LDA and PBE in contrast with HTBS, which is shown to fail dramatically for $alpha$-quartz. For the vibrational and thermodynamical properties, LDA performs surprisingly very good. In the majority of the test cases, it outperforms PBE significantly and also the WC, PBEsol and AM05 functionals though by a smaller margin (and to the detriment of structural parameters). On the other hand, HTBS performs also poorly for vibrational quantities. For the dielectric properties, none of the functionals can be put forward. They all (i) fail to reproduce the electronic dielectric constant due to the well-known band gap problem and (ii) tend to overestimate the oscillator strengths (and hence the static dielectric constant).
Daubechies wavelets are a powerful systematic basis set for electronic structure calculations because they are orthogonal and localized both in real and Fourier space. We describe in detail how this basis set can be used to obtain a highly efficient and accurate method for density functional electronic structure calculations. An implementation of this method is available in the ABINIT free software package. This code shows high systematic convergence properties, very good performances and an excellent efficiency for parallel calculations.
Using density functional theory calculations, the ground state structure of BaFeO$_3$ (BFO) is investigated with local spin density approximation (LSDA). Cubic, tetragonal, orthorhombic, and rhombohedral types BFO are considered to calculate the formation enthalpy. The formation enthalpies reveal that cubic is the most stable structure of BFO. Small energy difference between the cubic and tetragonal suggests a possible tetragonal BFO. Ferromagnetic(FM) and anitiferromagnetic (AFM) coupling between the Fe atoms show that all the striochmetric BFO are FM. The energy difference between FM and AFM shows room temperature ferromagnetism in cubic BFO in agreement with the experimental work. The LSDA calculated electronic structures are metallic in all studied crystallographic phases of BFO. Calculations including the Hubbard potential $U,i.e.$ LSDA+$U$, show that all phases of BFO are half-metallic consistent with the integer magnetic moments. The presence of half-metallicity is discussed in terms of electronic band structures of BFO.
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