Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set

QUANTUM ESPRESSO is an integrated suite of computer codes for electronic-structure calculations and materials modeling, based on density-functional theory, plane waves, and pseudopotentials (norm-conserving, ultrasoft, and projector-augmented wave). The acronym ESPRESSO stands for opEn Source Package for Research in Electronic Structure, Simulation, and Optimization. It is freely available to researchers around the world under the terms of the GNU General Public License. QUANTUM ESPRESSO builds upon newly-restructured electronic-structure codes that have been developed and tested by some of the original authors of novel electronic-structure algorithms and applied in the last twenty years by some of the leading materials modeling groups worldwide. Innovation and efficiency are still its main focus, with special attention paid to massively parallel architectures, and a great effort being devoted to user friendliness. QUANTUM ESPRESSO is evolving towards a distribution of independent and interoperable codes in the spirit of an open-source project, where researchers active in the field of electronic-structure calculations are encouraged to participate in the project by contributing their own codes or by implementing their own ideas into existing codes.

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QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials

Multiwfn is a multifunctional program for wavefunction analysis. Its main functions are: (1) Calculating and visualizing real space function, such as electrostatic potential and electron localization function at point, in a line, in a plane or in a spatial scope. (2) Population analysis. (3) Bond order analysis. (4) Orbital composition analysis. (5) Plot density-of-states and spectrum. (6) Topology analysis for electron density. Some other useful utilities involved in quantum chemistry studies are also provided. The built-in graph module enables the results of wavefunction analysis to be plotted directly or exported to high-quality graphic file. The program interface is very user-friendly and suitable for both research and teaching purpose. The code of Multiwfn is substantially optimized and parallelized. Its efficiency is demonstrated to be significantly higher than related programs with the same functions. Five practical examples involving a wide variety of systems and analysis methods are given to illustrate the usefulness of Multiwfn. The program is free of charge and open-source. Its precompiled file and source codes are available from http://multiwfn.codeplex.com.

Multiwfn: a multifunctional wavefunction analyzer.

Recent extensions of the DMol3 local orbital density functional method for band structure calculations of insulating and metallic solids are described. Furthermore the method for calculating semilocal pseudopotential matrix elements and basis functions are detailed together with other unpublished parts of the methodology pertaining to gradient functionals and local orbital basis sets. The method is applied to calculations of the enthalpy of formation of a set of molecules and solids. We find that the present numerical localized basis sets yield improved results as compared to previous results for the same functionals. Enthalpies for the formation of H, N, O, F, Cl, and C, Si, S atoms from the thermodynamic reference states are calculated at the same level of theory. It is found that the performance in predicting molecular enthalpies of formation is markedly improved for the Perdew–Burke–Ernzerhof [Phys. Rev. Lett. 77, 3865 (1996)] functional.

From molecules to solids with the DMol3 approach

This article reviews the current status of lattice-dynamical calculations in crystals, using density-functional perturbation theory, with emphasis on the plane-wave pseudopotential method. Several specialized topics are treated, including the implementation for metals, the calculation of the response to macroscopic electric fields and their relevance to long-wavelength vibrations in polar materials, the response to strain deformations, and higher-order responses. The success of this methodology is demonstrated with a number of applications existing in the literature.

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Phonons and related crystal properties from density-functional perturbation theory

Several improvements of the tetrahedron method for Brillouin-zone integrations are presented. (1) A translational grid of k points and tetrahedra is suggested that renders the results for insulators identical to those obtained with special-point methods with the same number of k points. (2) A simple correction formula goes beyond the linear approximation of matrix elements within the tetrahedra and also improves the results for metals significantly. For a required accuracy this reduces the number of k points by orders of magnitude. (3) Irreducible k points and tetrahedra are selected by a fully automated procedure, requiring as input only the space-group operations. (4) The integration is formulated as a weighted sum over irreducible k points with integration weights calculated using the tetrahedron method once for a given band structure. This allows an efficient use of the tetrahedron method also in plane-wave-based electronic-structure methods.

Improved tetrahedron method for Brillouin-zone integrations

We propose a form for the exchange-correlation potential in local-density band theory, appropriate for Mott insulators The idea is to use the ``constrained-local-density-approximation'' Hubbard parameter U as the quantity relating the single-particle potentials to the magnetic- (and orbital-) order parameters Our energy functional is that of the local-density approximation plus the mean-field approximation to the remaining part of the U term We argue that such a method should make sense, if one accepts the Hubbard model and the success of constrained-local-density-approximation parameter calculations Using this ab initio scheme, we find that all late-3d-transition-metal monoxides, as well as the parent compounds of the high-${\mathit{T}}_{\mathit{c}}$ compounds, are large-gap magnetic insulators of the charge-transfer type Further, the method predicts that ${\mathrm{LiNiO}}_{2}$ is a low-spin ferromagnet and NiS a local-moment p-type metal The present version of the scheme fails for the early-3d-transition-metal monoxides and for the late 3d transition metals

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Band theory and Mott insulators: Hubbard U instead of Stoner I.

The minimal base of muffin-tin orbitals is transformed exactly into a tight-binding base. The linear transformations, the orbitals, and the Hamiltonian, overlap, and Green's function matrices are expressed in terms of one matrix, the canonical structure matrix ${S}_{\mathrm{ij}}$. It vanishes beyond second-nearest neighbors and is tabulated. Tight-binding two-center forms with transfer integrals proportional to ${S}_{\mathrm{ij}}$ are derived.

Explicit, First-Principles Tight-Binding Theory

verify this result half quantitatively using a model kit as analog computer. The different sizes of C and Si are simulated with tetrahedral joints whose arm lengths differ[*] and the atoms are joined by flexible bonds (bent bonds). In disilabicyclo[l .1 .O]butane C,Si,H, (2) the region between the two C atoms does have a high ELF value (Fig. 1 c and 1 d). This confirms the previously described bond.['] The relatively small region of high ELF values implies a weak bond, in agreement with the long bond length. The white ELF maximum is also clearly off the straight topological CC connecting line. Its position is remarkably close to that of the bent bond derived from the simple structural model.IZ1 As expected, there is no bond between the Si atoms (Fig. 1 d). on the Cray-2 in Stuttgart. Mr. M. Kohout (Universitat Stuttgart) contributed to the development of the program MEROP (for the calculation of the electron density and of ELF) and wrote the program MPLOT (for drawing the contour lines of Fig. 2). The methods for obtaining localized orbitals-often used in the chemistry of molecules to describe bonding-can be used in principle for solids as well (in methane and in diamond , for example). They can lead, however, to several equivalent sets of orbitals for a given structure and are non-unique in this case. This ambiguity occurs, for example, in monomeric monocycles such as benzene, or in an infinite polyene chain.\"] In solids ambiguity often arises on account of the higher coordination, and localized orbitals are therefore used only rarely. An analysis in positional space can nevertheless be performed when instead of the equivocal localized orbitals, the electron localization function (ELF) is used. In this work we have calculated ELF for crystalline solids for the first time. The electron localization function was introduced by Becke and Edgecombe as a measure of the probability of finding an electron in the neighborhood of another electron with the same spin.\"] ELF is thus a measure of the Pauli repulsion. The explicit formulation is given in Equation (a) The parameter K is the curvature of the electron pair density for electrons of identical spin, e(r) the density at (Y), and Kh the value of K in a homogeneous electron gas with density e. The ELF values lie by definition between zero and one. Values are close to 1 when in the vicinity of one …

Electron Localization in Solid-State Structures of the Elements: the Diamond Structure

Plots of the tight-binding (TB) orbitals recently derived by exact transformation of the conventional set of linear muffin-tin orbitals (LMTO's) are presented for crystalline silicon. The TB-LMTO's are found to be extremely compact. As a simple application we show how non-spherically-averaged charge densities may be obtained from standard LMTO calculations. For silicon this charge density is found to be in excellent agreement with the one obtained from a linear augmented plane-wave full-potential calculation. This is true even when the LMTO calculation employs the atomic-sphere approximation for the one-electron potential. A self-contained account of the TB-MTO formalism is presented and a simple way of including the quadratic energy dependence of the MTO's is derived.

Ole Krogh Andersen

Papers

Improved tetrahedron method for Brillouin-zone integrations

Band theory and Mott insulators: Hubbard U instead of Stoner I.

Explicit, First-Principles Tight-Binding Theory

Electron Localization in Solid-State Structures of the Elements: the Diamond Structure

Illustration of the linear-muffin-tin-orbital tight-binding representation: Compact orbitals and charge density in Si