Anomalous Hall Coefficient in the f Electron System

We present an ab initio procedure for the construction of pseudopotentials accommodated to a crystal environment under study, which takes into account the response of the core charge density to the valence electrons of an atom in a bond. Within pseudopotential methodology, core electrons are treated differently from valence electrons; however, the core electrons are considered as ``frozen'' in space and independent of the atom's valence electrons after they were relaxed and adapted to a crystal-valence charge density. In this way the frozen-core approximation is removed despite the fact that the frozen-core technique is still used and no all-electron solid-state calculation is required. Since the all-electron core-valence response is taken into account properly, the treatment of nonlinear properties of exchange-correlation functionals is naturally included and corrections using model core charges for nonlinear functionals are eliminated. Contrary to standard pseudopotentials based on the atomic charge density of a free atom, the new all-electron pseudopotentials are functionals of the crystal charge density. Consequently, the intuitive ad hoc choice of occupation numbers, which is necessary for the construction of pseudopotentials by existing methods, is avoided and energy windows for pseudopotentials are put at optimum positions. In this paper, core-level shifts were calculated within the pseudopotential framework. The results of test calculations for diamond, silicon, nonmagnetic fcc $\ensuremath{\beta}$-Co, cubic TiC, and hexagonal ${\mathrm{TiS}}_{2}$ are presented.

Pseudopotential

Core charge

Valence electron

Jellium

10.1103/physrevb.58.12712

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Citations (38)

Ultrasoft pseudopotentials for lanthanide solvation complexes: Core or valence character of the 4f electrons

The Journal of Chemical Physics (2006)

Rodolphe Pollet Carine Clavaguéra Jean‐Pierre Dognon

The 4f electrons of lanthanides, because of their strong localization in the region around the nucleus, are traditionally included in a pseudopotential core. This approximation is scrutinized by optimizing the structures and calculating the interaction energies of Gd(3+)(H(2)O) and Gd(3+)(NH(3)) microsolvation complexes within plane wave Perdew-Burke-Ernzerhof calculations using ultrasoft pseudopotentials where the 4f electrons are included either in the core or in the valence space. Upon comparison to quantum chemical MP2 and CCSD(T) reference calculations it is found that the explicit treatment of the 4f electrons in the valence shell yields quite accurate results including the required small spin polarization due to ligand charge transfer with only modest computational overhead.

Pseudopotential

Core charge

Valence electron

10.1063/1.2191498

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Citations (19)

All-valence MO procedures

Lecture notes in chemistry (1976)

G. Wagnière

Core charge

Valence electron

10.1007/978-3-642-93050-8_5

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Citations (0)

ESCA

Elsevier eBooks (1971)

B.J. Lindberg

Valence electron

Electron spectroscopy

Core charge

10.1016/b978-0-408-70321-5.50006-6

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Effective shell charge of electrons on a sphere

Theoretica Chimica Acta (1983)

Hanno Ess�n

Valence electron

Core charge

Electron shell

Effective nuclear charge

Open shell

10.1007/bf01151614

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Valence and core region energies of atoms in Hartree–Fock theory

Canadian Journal of Chemistry (1992)

Sándor Fliszár N. Desmarais G. Dancausse

The subdivision of an atom into an inner core and an outer valence region reveals an interesting statistical aspect about the Hartree–Fock (HF) eigenvalues, ε i , and the electron populations in the valence region, [Formula: see text] namely [Formula: see text] where T v and [Formula: see text] are, respectively, the kinetic energy and the nuclear-electronic potential energy of the [Formula: see text] valence electrons, [Formula: see text] the interelectronic repulsion confined within the valence region, while [Formula: see text] is the repulsion between the core electrons and those of the valence region. This relationship (and a similar one for the core region) holds for any number of electrons arbitrarily assigned to the core, but is accurate only for HF (or near-HF) wave functions. This leads to a definition of the valence region energy, [Formula: see text] which, however, cannot be compared to the energy actually required for the removal of the outer electrons, because relaxation is not accounted for. An accurate energy expression has also been derived, [Formula: see text] which measures the actual withdrawal of the valence electrons. The latter expression requires the use of discrete values of N c , the number of electrons assigned to the core, namely N c = 2 for the first-row and N c = 10 e for the second-row elements. Keywords: atoms, core–valence separation.

Core charge

Valence electron

10.1139/v92-076

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Citations (3)