Despite the remarkable thermochemical accuracy of Kohn–Sham density‐functional theories with gradient corrections for exchange‐correlation [see, for example, A. D. Becke, J. Chem. Phys. 96, 2155 (1992)], we believe that further improvements are unlikely unless exact‐exchange information is considered. Arguments to support this view are presented, and a semiempirical exchange‐correlation functional containing local‐spin‐density, gradient, and exact‐exchange terms is tested on 56 atomization energies, 42 ionization potentials, 8 proton affinities, and 10 total atomic energies of first‐ and second‐row systems. This functional performs significantly better than previous functionals with gradient corrections only, and fits experimental atomization energies with an impressively small average absolute deviation of 2.4 kcal/mol.

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Density‐functional thermochemistry. III. The role of exact exchange

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

The exact density functional for the ground-state energy is strictly self-interaction-free (i.e., orbitals demonstrably do not self-interact), but many approximations to it, including the local-spin-density (LSD) approximation for exchange and correlation, are not. We present two related methods for the self-interaction correction (SIC) of any density functional for the energy; correction of the self-consistent one-electron potenial follows naturally from the variational principle. Both methods are sanctioned by the Hohenberg-Kohn theorem. Although the first method introduces an orbital-dependent single-particle potential, the second involves a local potential as in the Kohn-Sham scheme. We apply the first method to LSD and show that it properly conserves the number content of the exchange-correlation hole, while substantially improving the description of its shape. We apply this method to a number of physical problems, where the uncorrected LSD approach produces systematic errors. We find systematic improvements, qualitative as well as quantitative, from this simple correction. Benefits of SIC in atomic calculations include (i) improved values for the total energy and for the separate exchange and correlation pieces of it, (ii) accurate binding energies of negative ions, which are wrongly unstable in LSD, (iii) more accurate electron densities, (iv) orbital eigenvalues that closely approximate physical removal energies, including relaxation, and (v) correct longrange behavior of the potential and density. It appears that SIC can also remedy the LSD underestimate of the band gaps in insulators (as shown by numerical calculations for the rare-gas solids and CuCl), and the LSD overestimate of the cohesive energies of transition metals. The LSD spin splitting in atomic Ni and $s\ensuremath{-}d$ interconfigurational energies of transition elements are almost unchanged by SIC. We also discuss the admissibility of fractional occupation numbers, and present a parametrization of the electron-gas correlation energy at any density, based on the recent results of Ceperley and Alder.

Self-interaction correction to density-functional approximations for many-electron systems

Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

First-principles simulation, meaning density-functional theory calculations with plane waves and pseudopotentials, has become a prized technique in condensed-matter theory. Here I look at the basics of the suject, give a brief review of the theory, examining the strengths and weaknesses of its implementation, and illustrating some of the ways simulators approach problems through a small case study. I also discuss why and how modern software design methods have been used in writing a completely new modular version of the CASTEP code.

https://iopscience.iop.org/article/10.1088/0953-8984/14/11/301/pdf

First-principles simulation: ideas, illustrations and the CASTEP code

A scheme that reduces the calculations of ground-state properties of systems of interacting particles exactly to the solution of single-particle Hartree-type equations has obvious advantages. It is not surprising, then, that the density functional formalism, which provides a way of doing this, has received much attention in the past two decades. The quality of the energy surfaces calculated using a simple local-density approximation for exchange and correlation exceeds by far the original expectations. In this work, the authors survey the formalism and some of its applications (in particular to atoms and small molecules) and discuss the reasons for the successes and failures of the local-density approximation and some of its modifications.

The density functional formalism, its applications and prospects

Calculations of ground-state and excited-state properties of materials have been one of the major goals of condensed matter physics. Ground-state properties of solids have been extensively investigated for several decades within the standard density functional theory. Excited-state properties, on the other hand, were relatively unexplored in ab initio calculations until a decade ago. The most suitable approach up to now for studying excited-state properties of extended systems is the Green function method. To calculate the Green function one requires the self-energy operator which is non-local and energy dependent. In this article we describe the GW approximation which has turned out to be a fruitful approximation to the self-energy. The Green function theory, numerical methods for carrying out the self-energy calculations, simplified schemes, and applications to various systems are described. Self-consistency issue and new developments beyond the GW approximation are also discussed as well as the success and shortcomings of the GW approximation.

https://iopscience.iop.org/article/10.1088/0034-4885/61/3/002/pdf

The GW method

We present a method for calculating the core-level x-ray photoemission (XPS), the $3d\ensuremath{\rightarrow}4f$ x-ray absorption (XAS), the valence photoemission, and the bremsstrahlung isochromat spectra in a slightly modified Anderson impurity model of a Ce compound at zero temperature. Both the spin and orbital degeneracies of the $f$ level are included and the Coulomb interaction between the $f$ electrons is taken into account. The spectra are expressed in terms of a resolvent operator. A many-electron basis set is introduced, and the resolvent is obtained from a matrix inversion. The particular form of the Anderson model allows us to find a small but sufficiently complete basis set, if the degeneracy ${N}_{f}$ of the $f$ level is large. In particular, we consider the limit ${N}_{f}\ensuremath{\rightarrow}\ensuremath{\infty}$, and show that the method is exact for the XPS, XAS, and valence photoemission spectra in this limit. It is also demonstrated that for ${N}_{f}\ensuremath{\gtrsim}6$, the method provides accurate spectra. Analytical results are obtained for the valence photoemission spectrum ${\ensuremath{\rho}}_{v}(\ensuremath{\epsilon})$. The spectrum has a sharp rise close to the Fermi energy ${\ensuremath{\epsilon}}_{F}$, which goes over to a "Kondo peak" in the spin-fluctuation limit. An exact relation between ${\ensuremath{\rho}}_{v}({\ensuremath{\epsilon}}_{F})$ and the $f$-level occupancy ${n}_{f}$ is shown to be satisfied to within 10% for ${N}_{f}\ensuremath{\ge}6$. We discuss how core-level XPS spectra can be used to estimate the $f$-level occupancy ${n}_{f}$ and the coupling $\ensuremath{\Delta}$ between the $f$ level and the conduction states. We find that the values of ${n}_{f}$ and $\ensuremath{\Delta}$ obtained from core-level XPS are basically consistent with the other spectroscopies and the static, $T=0$ susceptibility. It is, therefore, possible to describe these experiments in the Anderson model, using essentially the same set of parameters for all the experiments. Typically, we find ${n}_{f}g0.7$ and $\ensuremath{\Delta}\ensuremath{\sim}0.1$ eV.

Electron spectroscopies for Ce compounds in the impurity model

The breakdown of the antiferromagnetism in the high-{ital T}{sub {ital c}} oxides is studied taking into account the 3{ital d} charge fluctuations. We point out a tendency towards the formation of charged magnetic domain lines if holes are introduced in such a state, which can be viewed as a generalization of soliton of the Su, Schrieffer, and Heeger to two dimensions. In the ground state these domain lines line up, explaining the incommensurate spin phase observed in the high-{ital T}{sub {ital c}}'s superconductors.

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Charged magnetic domain lines and the magnetism of high-tc oxides

Experimental studies of the superconductive properties of fullerides are briefly reviewed. Theoretical calculations of the electron-phonon coupling, in particular for the intramolecular phonons, are discussed extensively. The calculations are compared with coupling constants deduced from a number of different experimental techniques. It is discussed why ${\mathrm{A}}_{3}$${\mathrm{C}}_{60}$ are not Mott-Hubbard insulators, in spite of the large Coulomb interaction. Estimates of the Coulomb pseudopotential ${\mathrm{\ensuremath{\mu}}}^{\mathrm{*}}$, describing the effect of the Coulomb repulsion on the superconductivity, as well as possible electronic mechanisms for the superconductivity, are reviewed. The calculation of various properties within the Migdal-Eliashberg theory and attempts to go beyond this theory are described.

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Olle Gunnarsson

Papers

The density functional formalism, its applications and prospects

The GW method

Electron spectroscopies for Ce compounds in the impurity model

Charged magnetic domain lines and the magnetism of high-tc oxides

Superconductivity in fullerides