Orbital ordering

The so-ealled Slater-Condon rules express the matrix elements of any one-eleetron (F) plus two-eleetron (G) additive operator between pairs of antisymmetrized spin-orbital produets that have been arranged (by permuting spin-orbital ordering) to be in so-ealled maximal eoineidenee. Onee in this order, the matrix elements between two sueh Slater determinants (labelled >and are summarized as follows ... 

When you request an orbital, yon can use the cardinal number of the orbital (ordered by energy and starting with number=l) or an offset from either the highest occupied molecular orbital (HOMO) or the lowest unoccupied molecular orbital (LL MO). Offset from the HOMO are negative and from the LUMO are positive. Often these frontier orbitals are the ones of most chemical interest. 

During the endeavor to understand and explain the PT physically, a lot of effort has been spent on secondary problems. Even worse, an orbital ordering rule that has no general validity, has been assumed to be of central relevance. It has often been said that the structure of the neutral atoms is of primary importance for the periodic system. This is true, though in a modified sense ([34], p 653). 

Conjugated chains, 14, 46 Correlation diagrams, 44, 50 Cyclobutadiene, 171 Cyclobutane, 47, 222 orbital ordering, 26 through-space interactions, 26 Walsh orbitals, 27 Cyclobutene, 200 Cyclohexane, 278 Cyclohexene (half-boat), 274 Cyclopen tadiene, 225 Cvclopen tadienone, 269 Cyclopentadienyl anion, 237 Cyclopentane, 254 Cyclopen ten e, 241 Cyclopropane, 41, 47, 153 construction of orbitals, 19, 22 Walsh orbitals, 22, 36, 37 Cyclopropanone, 48, 197 bond lengths, 38 Cyclopropen e, 49, 132 reactivity, 40... 

Pentadienyl radical, 240 Perturbation theory, 11, 46 Propane, 16, 165 n-Propyi anion conformation, 34 n-Propyl cation, 48, 163 rotational barrier, 34 Propylene, 16, 139 Protonated methane, 72 Pyrazine, 266 orbital ordering, 30 through-bond interactions, 27 Pyridine, 263 Pyrrole, 231... 

Liechtenstein AI, Anisimov VI, Zaanen J (1995) Density-functional theory and strong interactions orbital ordering in Mott-Hubbard insulators. Phys Rev B 52(8) R5467... 

Functional Theory and Strong Interactions Orbital Ordering in Mott-Hubbard Insulators. 

It has been postulated on the basis of the crystal structure of [Mn (tpp)(02 )], that the peroxide ligand in Fe(III)-peroxo porphyrin species is coordinated in a side-on bidentate manner (Scheme 2) (8). Interestingly, based on the deuterium NMR studies the [Mn tppXOa )] complex was characterized as the Mn(II)-superoxo species (55). This discrepancy has been explained by an alteration of the normal d orbital ordering, where the highest energy d orbital is a d 2- -02 hybrid not the (8). These examples show that... 

The electrochemistry of dioxoruthenium(VI) and dioxoosmium(VI) complexes with polypyridyl and macrocyclic tertiary amine ligands has been extensively studied by cyclic voltammetric techniques. In general, cA-dioxo species have higher reduction potentials than the corresponding trans-Aiaxo species. " " For the trans-Aioxo species, the d, orbital ordering... 

Moritz, G., Hess, B.A., Reiher, M. Convergence behavior of the density-matrix renormalization group algorithm for optimized orbital orderings. J. Chem. Phys. 2005,122(2), 024107. 

Iwasa Y, Takenobu T (2003) Superconductivity, Mott-Hubbard states, and molecular orbital order in intercalated fullerides. J Phys Condens Matter 15 R495-R519... 

Kadomtseva et al. (2000) measured thermal expansion and longitudinal and transverse magnetostriction in pulsed magnetic fields up to 25 T in Lai - Sr MnOj single crystals (x = 0.1,0.125 and 0.15). The results were ascribed to a suppression of the O phase and field-induced transitions to a new orbital-ordered ferromagnetic state. 

We found that these more sophisticated spin-coupled calculations, which used larger basis sets with polarization functions on all of the atoms and which allowed the a orbitals to relax, produced a picture of bonding in the 7t-electron system of benzene which is practically identical to that described earlier. As before, we found six equivalent spin-coupled orbitals which are transformed into one another by successive C6 rotations. The overlaps between the orbitals, ordered cpa to cp6 around the ring, are reported in Table 1. In this case, the electron correlation effects incorporated in the spin-coupled model provide an energy improvement over the SCF description of 170 kJ mol - with a further lowering of 20 kJ mol -1 on including spin-coupled ionic structures. 

Orbital Ordering and the Cooperative Jahn-Teller Effect in Single Crystals of the Magnetic Perovskite La7/8Sr1/8Mn03... 

Fig. 1. Schematic view of the antiferrodistorsive orbital ordering of the 3z2-r2 orbitals in the a0 0-plane of LaMn03, taken from Ref. [6]. The orbital ordering along the cG-axis repeats the same pattern. The index o of the lattice parameters refers to the orthorhombic unit cell of LaMn03. The orbitals in this figure and in the subsequent figures of this article are not drawn on scale with respect to the lattice parameters.

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