Ground state, properties

In addition, we find that for Bloch states Pjk) the expectation value jkWzVEjk) 

A further consequence of the presence of the spin-orbit coupling for a spin-polarized solid is that its orbital angular momentum is quenched no more. This corresponds to the occurrence of a finite paramagnetic orbital current density jp, which can be obtained from the expression 

Here the direction and magnitude of jp are represented by arrows for the (001) plane with the z- and magnetization axes pointing upwards. At first sight the current density distribution seems to be rotational symmetric. However, a closer look reveals 

With the spin-orbit-induced orbital current density in magnetic solids there is obviously a finite orbital angular momentum density associated. The corresponding orbital magnetic moment /xorb can be obtained from the expression (Ebert et al. 1988a)  

The basic CDFT Hamiltonian in Equation (5.6) does not rule out the existence of a finite orbital magnetic moment in the nonrelativistic limit. With the help of model calculations, it could be demonstrated that this is not the case for bulk Fe, Co and Ni (Ebert et al. 1997a). Starting an SCF calculation with a finite spin-orbit-induced orbital current density and switching off the spin-orbit coupling during the SCF-cycle the orbital magnetic moment vanished (see also next section). 

For the sake of clarity we shall first discuss in Section 6.2.1 ground-state properties in the framework of the unrestricted Hartree-Fock approximation. In Section 6.2.2 the theory is extended to finite temperatures by using a functional integral formalism including spin fluctuations. Finally, in Section 6.2.3 we analyze the problem of electron correlations by exact diagonalization of the simpler single-band Hubbard model. 

Within a self-consistent mean-field approximation Eq. (1) can be rewritten as [10, 32] 

The number of electrons with spin a at the orbital a of atom i is given by 

Sp denotes the Fermi energy. The local magnetic moments are obtained from 

Notice that self-consistency is required for Eqs (2)-(5). The magnetic order is inferred from the spatial distribution of the moments /i/. In case of multiple self-consistent solutions for the magnetic order or when different atomic structures are involved, the corresponding free energies F = E — TS are compared. Then, the atomic and magnetic structure with lowest F is taken. At T = 0 the energy is given by 

The original material for the present chapter may be found in the papers by Eohenberg and Kohn [7.1], Kohn and Sham [7.2], Andersen [7.3], and Mackintosh and Andersen [7.4]. 

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In DFT, the electronic density rather than the wavefiinction is tire basic variable. Flohenberg and Kohn showed [24] that all the observable ground-state properties of a system of interacting electrons moving in an external potential are uniquely dependent on the charge density p(r) that minimizes the system s total... 

Singh D 1991 Ground-state properties of ianthanum treatment of extended-oore states Phys. Rev. B 43 6388... 

A. Ciach, J. S. Hoye, G. Stell. Microscopic model for microemulsion. I. Ground state properties. J Chem Phys 90 1214-1221, 1989. 

Ground State Properties of Titanium Dioxide Polymorphs... 

We have investigated ground state properties on a first principles basis. Total energy as well as magnetic moment (for FeaNi) were determined with the FLAPW method and the GGA introduced by Perdew and Wang in 1992 by employing the WIEN95 code developed by Blaha et al. 

We presented selected results from a new tight-binding total energy method that accurately predicts ground state properties of transition and noble metals, and successfully extended to transition metal carbides. 

O. B. Christensen and M. L. Cohen, Ground-state properties of small iron clusters , Phys. Rev. B47 13643 (1993). 

The effect of axial ligands on ground state properties of complexes with orbitally degenerate ground terms. G. A. Webb, Coord. Chem. Rev., 1969, 4,107-145 (151). 

Although magnetic properties of a number of plutonium compounds are known, it seems from the above discussion that the knowledge of the electronic ground state properties is very limited. Each compound represents a system of its own which has to be... 

A more complete coverage of the literature on electronic spectra of radicals is presented in our paper submitted for publication in Fortschr. Chem. Forsch. (Topics in Current Chemistry), where theafi initio studies are also reviewed and the existing open-shell computational procedures discussed. Recently we performed semiempirical all-valence-electron calculations on ground-state properties and electronic spectra of small radicals (Zahradnik, R., and P. Carsky, Theoret, Chim. Acta, 27, 121 (1972) and Carsky, P., M. Machacek, and R. Zahradnik, Coll. Czech. Chem. Commun., in press) and on equilibrium constants of dimerization reactions of small radicals (Zahradnik, R., Z. Slanina, and P. (5arsky, to be published). 

The ground-state properties of the [ZnFe3S4l+ and [CdFe3S4l+ clus-... 

Summary of Predicted and Observed Ground-State Properties of Protein-Bound... 

Summary of the Ground-State Properties of Representative Examples of Synthetic Single AND Double Cubanes Containing [MFejSJ Clusters and Rationalization in Terms of the... 

These limitations, most urgently felt in solid state theory, have stimulated the search for alternative approaches to the many-body problem of an interacting electron system as found in solids, surfaces, interfaces, and molecular systems. Today, local density functional (LDF) theory (3-4) and its generalization to spin polarized systems (5-6) are known to provide accurate descriptions of the electronic and magnetic structures as well as other ground state properties such as bond distances and force constants in bulk solids and surfaces. 

Suzumura, T., Nakajima, T. and Hirao, K. (1999) Ground-state properties of MH, MCI, and M2 (M—Cu, Ag, and Au) calculated by a scalar relativistic density functional theory International Journal of Quantum Chemistry, 75, lVJ-1. ... 

Takeuchi, N., Chan, C.T. and Ho, K.M. (1989) First-principles calculations of equilibrium ground-state properties of Au and Ag. Physical Review B - Condensed Matter, 40, 1565-1570. 

Ground State Properties and Zero-Field Splitting... 

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