Theory of the Spin Susceptibility of an Inhomogeneous Electron Gas via the Density Functional Formalism

1975 ◽  
Vol 53 (14) ◽  
pp. 1385-1397 ◽  
Author(s):  
S. H. Vosko ◽  
J. P. Perdew
Keyword(s):  
Density Functional ◽  
Electron Gas ◽  
Local Approximation ◽  
Spin Susceptibility ◽  
Functional Formalism ◽  
Exchange Correlation ◽  
The Density Functional Theory ◽  
Interacting Systems ◽  
Core Electrons ◽  
Variational Expression

The density functional theory of Hohenberg, Kohn, and Sham has been used to derive an exact variational expression for the spin susceptibility (χ) of an inhomogeneous electron gas. This variational expression allows one to simultaneously treat band and exchange correlation effects among the conduction electrons and, furthermore, includes the influence of core electrons on the latter. The use of a simple trial function and a local approximation for the exchange correlation functional in the variational expression results in a simple formula for χ (lower bound). The above approach is developed in parallel and compared with the self consistent single particle equations for a magnetized paramagnetic system including exchange correlation. These equations are used to obtain explicit expressions for the paramagnetic response functionals for noninteracting and interacting systems.

Influence of nonlocality in the spin–spin interaction functional on the Pauli susceptibility of Li, Na, and K

1981 ◽  
Vol 59 (4) ◽  
pp. 500-505 ◽  
Author(s):  
A. H. MacDonald ◽  
K. L. Liu ◽  
S. H. Vosko ◽  
L. Wilk
Keyword(s):  
Spin Density ◽  
Density Functional ◽  
Alkali Metals ◽  
Spin Exchange ◽  
Local Approximation ◽  
Spin Interaction ◽  
Functional Formalism ◽  
Exchange Correlation ◽  
Experimental Values ◽  
Pauli Susceptibility

Two suggested nonlocal approximations for the spin–spin exchange-correlation interaction functional of the spin-density functional formalism have been applied to the calculation of the Pauli susceptibility, χp, of the alkali metals. The nonlocal approximations were found to imply values of the density-functional Stoner parameter, I, typically ~ 3% lower than values implied by the more usual local approximation. This qualitative trend was found to be supported by comparison of available experimental values of χp with new more accurate theoretical values for the local approximation to χp.

Non-local exchange-correlation effects on the spin susceptibility and thermal density of states of Cu

1977 ◽  
Vol 55 (22) ◽  
pp. 1991-2012 ◽  
Author(s):  
K. L. Liu ◽  
A. H. MacDonald ◽  
S. H. Vosko
Keyword(s):  
Density Of States ◽  
Single Particle ◽  
Density Functional ◽  
Local Approximation ◽  
Spin Susceptibility ◽  
Spin Interaction ◽  
Correlation Effects ◽  
Local Exchange ◽  
Exchange Correlation ◽  
Non Local

A variational-principle–spin-density-functional approach has been used to investigate the importance of non-local exchange-correlation effects on the spin magnetic susceptibility χp, of Cu. These effects are contained in two functionals, one of which gives the exchange-correlation part of the effective single-particle potential while the other gives an effective spin–spin interaction. For the former functional we have compared two empirically based choices with the commonly used local approximation. The differences between these single-particle potentials are shown to be of the same magnitude as the lowest order density gradient corrections to the local approximation and produce appreciable (~ 5%) effects on the single-particle density of states at the Fermi surface and on the density functional analog of the Stoner parameter I through changes in the single particle spin magnetization. To assess the importance of these non-local corrections, we have calculated the exchange-correlation contributions to the electronic thermal density of states by the density functional theory and find that they are necessary to bring theory and experiment into agreement. The non-local effects of the spin–spin interaction functional on I are investigated by using several non-local approximations based on calculations of the wave vector dependent spin susceptibility for the uniform electron gas system. On the basis of these investigations we conclude that non-local exchange-correlation effects on χp will be significant for d-band metals, especially those with a highly enhanced χp. Numerical techniques useful for finding Fourier series representations of translationally invariant functions with cubic symmetry, important in this work, are discussed in an Appendix.

Density functionals beyond the local approximation

1991 ◽  
Vol 334 (1635) ◽  
pp. 481-490 ◽  
Keyword(s):  
Density Functional ◽  
Correlation Energy ◽  
Local Density ◽  
Local Approximation ◽  
Density Functionals ◽  
Current Effort ◽  
Functional Theory ◽  
Quasi Particle ◽  
Exchange Correlation ◽  
The Density Functional Theory

A review of the current effort in improvement over the local density approximation is given. Within the density functional theory, the exchange-correlation energy and potential may be unambiguously defined. Based on the field theoretical expressions for them, approximations for classes of systems and approxim ate evaluations for specific solids are critically reviewed. Further lines of development are discussed. Relation to the quasi-particle energies is explored.

MAGNETIC MAP OF MnNi ALLOYED MONOLAYER ON Cu(001) SUBSTRATE: AB-INITIO CALCULATIONS

2010 ◽  
Vol 09 (06) ◽  
pp. 619-622
Author(s):  
BOTHINA A. HAMAD
Keyword(s):  
Density Functional ◽  
Theoretical Study ◽  
Magnetic Moments ◽  
Generalized Gradient ◽  
Functional Theory ◽  
Exchange Correlation ◽  
Generalized Gradient Approximation ◽  
Exchange Correlation Potential ◽  
The Density Functional Theory ◽  
Correlation Potential

In this work, a theoretical study of the structural, electronic and magnetic properties are presented for Mn 0.5 Ni 0.5 alloyed overlayer adsorbed on Cu (001) surface. The calculations were performed using the density functional theory (DFT) and the exchange-correlation potential was treated by the generalized gradient approximation (GGA). The system was fully relaxed except for the central layer, which yields to outward relaxations and inward Mn and Ni surface atoms, respectively in the ferromagnetic and antiferromagnetic configurations. The in-plane ferromagnetic configuration was found to be more stable than the antiferromagnetic one by 25 meV/atom. The local magnetic moments of Mn atoms were found to be about 4 μ B , whereas those of the Ni atoms where found to be 0.46 μ B .

Ab InitioCalculation of the Spin Susceptibility for the Alkali Metals Using the Density-Functional Formalism

1975 ◽  
Vol 35 (25) ◽  
pp. 1725-1728 ◽  
Author(s):  
S. H. Vosko ◽  
J. P. Perdew ◽  
A. H. MacDonald
Keyword(s):  
Density Functional ◽  
Alkali Metals ◽  
Spin Susceptibility ◽  
Functional Formalism

scholarly journals Structural and piezoelectric coefficients of AlP under pressure

2018 ◽  
Vol 6 (2) ◽  
pp. 53
Author(s):  
Salah Daoud ◽  
Rabie Mezouar ◽  
Abdelfateh Benmakhlouf
Keyword(s):  
Density Functional ◽  
Structural Parameters ◽  
Generalized Gradient ◽  
Aluminum Phosphide ◽  
Functional Theory ◽  
Exchange Correlation ◽  
Generalized Gradient Approximation ◽  
Zinc Blende ◽  
Density Functional Perturbation Theory ◽  
The Density Functional Theory

The present work aims to investigate the structural parameters and the piezoelectric coefficients of cubic zinc-blende Aluminum phosphide (AlP) under high pressure up to 21 GPa, using plane wave-pseudopotential (PW-PP) approach in the framework of the density functional theory (DFT) and the density functional perturbation theory (DFPT) with the generalized gradient approximation (GGA) for the exchange-correlation functional. The results obtained are analyzed and compared with other data of the literature. The structural parameters and the piezoelectric coefficients calculated here agree well with other data of the literature. We found also that both the direct and converse piezoelectric coefficients increase with increasing pressure up to 21 GPa. 

Magic Clusters in SixMg3 (x=1-10) Series: Potential Building Motifs for Inorganic Nanomaterials

2013 ◽  
Vol 24 ◽  
pp. 77-84 ◽  
Author(s):  
Debesh Ranjan Roy
Keyword(s):  
Density Functional ◽  
Alkaline Earth ◽  
Shell Closure ◽  
Generalized Gradient ◽  
Functional Formalism ◽  
Exchange Correlation ◽  
Generalized Gradient Approximation ◽  
Magic Clusters ◽  
Inorganic Nanomaterials ◽  
The Stability

A detail investigation on the stability and electronic properties for a series of bimetallic (semiconductor-alkaline earth) clusters, viz., SixMg3(x=1-10) is performed in search for the exceptional or unusual stable motifs. A standard generalized gradient approximation (GGA) exchange-correlation functional, as proposed by Perdew, Burke and Ernzerhof (PBE) is employed for this purpose under the density functional formalism. The magic stability of the concerned clusters is explained using the jellium and aromaticity models. It is evident from the present study that the magic stability of Si7Mg3cluster arises due to the jellium shell closure whereas the same for Si4Mg3originates from the σ dominated aromaticity over its π counterpart.

Exchange-correlation effects on the dynamical spin susceptibility of a homogeneous electron gas

1991 ◽  
Vol 69 (5) ◽  
pp. 573-580 ◽  
Author(s):  
K. L. Liu
Keyword(s):  
Local Field ◽  
Electron Gas ◽  
Spin Susceptibility ◽  
Wave Number ◽  
Large Wave ◽  
Limiting Behavior ◽  
High Frequencies ◽  
Exchange Correlation ◽  
Dynamical Spin ◽  
Local Field Factor

We study the wavevector- and frequency- dependent exchange-correlation local-field factor, [Formula: see text], of the dynamical spin susceptibility, [Formula: see text], of a homogeneous electron gas. For high frequencies we calculate [Formula: see text] diagrammatically to second order in the Coulomb interaction, and consequently find that [Formula: see text] varies as q−2 ω−1/2 for large ω and finite q. We also consider an interpolation formula for [Formula: see text], that yields the exact small- and large- wave-number limits. Making use of these results and the Kramers–Kronig relation, we construct an approximate local-field factor that has the correct limiting behavior for both low and high frequencies.

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