Local orbital moments

The eigenvalue equation corresponding to the Hamiltonian of Eq. [57] can be solved self-consistently by an iterative procedure for each orientation of the spin magnetization (identified as the z direction). The self-consistent density matrix is then employed to calculate the local spin and orbital magnetic moments. For instance, the local orbital moments at different atoms i are determined from... 

The magnetic moments of the Ni clusters are dominated by the contribution from surface atoms.48,69 The analysis of Wan et al. indicates that the orbital and spin local moments of cluster atoms with atomic coordination 8 or larger are similar to those in the bulk (p spin 0.55 and orb 0.05 pB) 73 that is, the orbital moment is almost quenched for internal cluster atoms. In contrast, there is a large enhancement of the spin and orbital moments for atoms with coordination less than 8. This enhancement increases with the coordination deficit, and it is larger for the orbital moment. Wan et al.48 also analyzed the quantum confinement effect proposed by Fujima and Yamaguchi,56 i.e., the... 

In the model of localized magnetic moments for the spin-only state (orbital moment is quenched) the interrelation between the effective magnetic moment and the moment in the magnetically ordered state is given by... 

Neutron diffraction experiments (522) indicate that there is no localized atomic moment in ordered FeAl. This result implies that s-p bonding between unlike atoms is considerably less stable relative to the iron d levels than that between like atoms, so that the localized, iron kg orbitals are filled. Since aluminum is electropositive with... 

CASSCF wave functions with their own sets of optimized orbitals, which where then not orthogonal to each other. The CAS State interaction CASSI, method made it possible to compute efficiently first and second order transition density matrices for any type of CASSCF wave functions [16, 17]. The method is used to compute transition dipole moments in spectroscopy and also in applications where it is advantageous to use localized orbitals, for example in studies of charge transfer reactions [18]. Today, the same approach is used to construct and solve a spin-orbit Hamiltonian in a basis of CASSCF wave functions [19]. 

Localized orbital methods, 227 Moments of inertia, 300 qeiec, partition function, 302 ... 

The energy diagram may be derived equally well starting with any orbital choice, but the three canonical ones are the simplest to use. We shall outline the derivation starting with the most localized orbitals. If for the moment spin is ignored, the four configurations if (l) if (2), if (l)Xfc(2), and... 

Within the framework of the local density method, which is strictly an orbital theory, the antiferromagnetic state can be attained by reducing the symmetry constraints imposed on spin-polarized calculations, hence allowing the spin orbitals to localize and local magnetic moments to persist, if it is variationally favorable to do so. While I do not know of any formal justification for this type of symmetry breaking (one cannot just mix determinants within DFT to obtain proper spin and space eigenfunctions), the results discussed below for Cr2, M02, and Mn2 certainly indicate that it is a reasonable approach. A rough rationalization can be obtained if one reasons... 

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