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.

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.

Density Functional Calculations on Electronic and Magnetic Properties of Fe-Pt Systems

2005 ◽  
Vol 475-479 ◽  
pp. 3103-3106 ◽  
Author(s):  
You Song Gu ◽  
Jian He ◽  
Zhen Ji ◽  
Xiao Yan Zhan ◽  
Yue Zhang ◽  
...  
Keyword(s):  
Magnetic Properties ◽  
Magnetic Moment ◽  
Electronic Structures ◽  
Density Functional ◽  
Generalized Gradient ◽  
Functional Theory ◽  
Exchange Correlation ◽  
Generalized Gradient Approximation ◽  
Experimental Values ◽  
Pseudo Potential

The electronic structures and magnetic properties of Fe-Pt systems were calculated by CASTEP codes, which employed density functional theory, generalized gradient approximation (GGA), Perdew Burke Ernzerh exchange correlation, Pulay density-mixing scheme and Ultra Soft pseudo potential. The band structures and density of states (DOS) were calculated, together with band populations and magnetic properties. The calculated results of α-Fe show the validatiy of this method in predication magnetic properties. It is found that as the Pt concentration increases, Fe 4s and 3d electrons decrease while 4p electrons increase, and the magnetic moment of Fe atom increases. Pt atoms also contribute to the magnetic moment due to polarization. The calculated magnetization agrees with experimental values quite well.

Exact exchange-correlation potentials in spin-density functional theory and their discontinuities at unit electron number

2009 ◽  
Vol 87 (10) ◽  
pp. 1268-1272 ◽  
Author(s):  
John P. Perdew ◽  
Espen Sagvolden
Keyword(s):  
Density Functional Theory ◽  
Spin Density ◽  
Density Functional ◽  
Electron Number ◽  
Functional Theory ◽  
Exchange Correlation ◽  
Exchange Correlation Potential ◽  
Correlation Potential ◽  
Exact Exchange ◽  
Physical Consequences

The exact exchange-correlation potential of Kohn–Sham density functional theory is known to jump discontinuously by a spatial constant as the average electron number, N, crosses an integer in an open system of fluctuating electron number, with important physical consequences for charge transfers and band gaps. We have recently constructed an essentially exact exchange-correlation potential vxc for N electrons (0 ≤ N ≤ 2) in the presence of a –1/r external potential, i.e., for a ground ensemble of H+ ion, H atom, and H– ion densities. That construction illustrates the discontinuity at N = 1, where it equals IH – AH, the positive difference between the ionization energy and the electron affinity of the hydrogen atom. Here we construct the corresponding essentially exact spin-up and spin-down exchange-correlation potentials vxc,↑ and vxc,↓ of the Kohn–Sham spin-density functional theory, more commonly used for electronic structure calculations, for the ground ensemble with most-negative z-component of spin (or equivalently in the presence of a uniform magnetic field of infinitesimal strength). The potentials vxc, vxc,↑, and vxc,↓, which vanish as r → ∞ (except when N approaches an integer from above), are identical for 0 ≤ N ≤ 1 and for N = 2 but not for 1 < N < 2. We find that the majority or spin-down potential has a spatially constant discontinuity at N = 1 equal to IH – AH. The minority or spin-up potential has a discontinuity which is this constant in one order of limits, but is a spatially varying function in a different order of limits. This order-of-limits problem is a consequence of a special circumstance: the vanishing of the spin-up density at N = 1.

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