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Register a new userComparison of the full-potential and frozen-core approximation approaches to density-functional calculations of surfaces
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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.
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We implement and benchmark the frozen core approximation, a technique commonly adopted in electronic structure theory to reduce the computational cost by means of mathematically fixing the chemically inactive core electron states. The accuracy and efficiency of this approach are well controlled by a single parameter, the number of frozen orbitals. Explicit corrections for the frozen core orbitals and the unfrozen valence orbitals are introduced, safeguarding against seemingly minor numerical deviations from the assumed orthonormality conditions of the basis functions. A speedup of over two-fold can be achieved for the diagonalization step in all-electron density-functional theory simulations containing heavy elements, without any accuracy degradation in terms of the electron density, total energy, and atomic forces. This is demonstrated in a benchmark study covering 103 materials across the periodic table, and a large-scale simulation of CsPbBr3 with 2,560 atoms. Our study provides a rigorous benchmark of the precision of the frozen core approximation (sub-meV per atom for frozen core orbitals below -200 eV) for a wide range of test cases and for chemical elements ranging from Li to Po. The algorithms discussed here are implemented in the open-source Electronic Structure Infrastructure software package.
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.
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).
The essential features of a full potential electronic structure method using Linear Muffin-Tin Orbitals (LMTOs) are presented. The electron density and potential in the this method are represented with no inherent geometrical approximation. This method allows the calculation of total energies and forces with arbitrary accuracy while sacrificing much of the efficiency and physical content of approximate methods such as the LMTO-ASA method.
We propose a method to decompose the total energy of a supercell containing defects into contributions of individual atoms, using the energy density formalism within density functional theory. The spatial energy density is unique up to a gauge transformation, and we show that unique atomic energies can be calculated by integrating over Bader and charge-neutral volumes for each atom. Numerically, we implement the energy density method in the framework of the Vienna ab initio simulation package (VASP) for both norm-conserving and ultrasoft pseudopotentials and the projector augmented wave method, and use a weighted integration algorithm to integrate the volumes. The surface energies and point defect energies can be calculated by integrating the energy density over the surface region and the defect region, respectively. We compute energies for several surfaces and defects: the (110) surface energy of GaAs, the mono-vacancy formation energies of Si, the (100) surface energy of Au, and the interstitial formation energy of O in the hexagonal close-packed Ti crystal. The surface and defect energies calculated using our method agree with size-converged calculations of the difference between the total energies of the system with and without the defect. Moreover, the convergence of the defect energies with size can be found from a single calculation.
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