Polarization orbital

A set of polarized orbital pairs is described pictorially in figure B3.1.6. In each of the tln-ee equivalent temis in the above wavefunction, one of the valence electrons moves in a 2s+a2p orbital polarized in one direction while the other valence electron moves in the 2s - a2p orbital polarized in the opposite direction. For example, the first temi (2s - a2p )a(2s+a2p )P - (2s-a2p )P(2s+a2p )a describes one electron occupying a 2s-a2p polarized orbital while the other electron occupies the 2s+a2p orbital. The electrons thus reduce their... 

Ebert, H., and Battocletti, M., 1996, Spin and orbital polarized relativistic multiple scattering theory - with applications to Fe, Co, Ni and Fe cCoi- c , Solid State Commun. 98 785. 

SPIN AND ORBITAL POLARIZED RELATIVISTIC MULTIPLE SCATTERING THEORY... 

One-dimensional model Onsanger cavity field Onsanger equation Orbital polarization Ordered phase Ordered state... 

Keywords Orbital mixing. Orbital amplitude. Orbital phase. Orbital polarization. Orbital deformation, Regioselectivity, Stereoselectivity, n Facial selectivity... 

The n orbital amplitudes of ethene are identical on both carbons. Unsymmetrical substitutions polarize the n orbital. Electron acceptors or electrophiles attack the carbon with the larger r amplitude. The polarization of frontier orbitals is important for regioselectivities of reactions. Here, mechanism of the n orbital polarization of ethene by methyl substitution [4] is described (Scheme 5). 

The relative magnitudes of the resulting average mixing coefficients Ay and Ay per and Bi average AO, respectively, give a measure of the polarity of the Bi — Bi MOs. In simple cases (say, HC1) the concepts of orbital polarity and electron polarity (as a measure of ionicity) coincide. The extension of the latter inference to more complicated molecular systems is far from trivial, although such a conclusion is commonly accepted for qualitative purposes. 

A little reflection shows that the commutation relationships, recognized as one of the fundamental differences between classical and quantum systems, are common to all forms of angular momentum, including orbital, polarization and spin. It is of interest to note that the eigenvalues for all forms of angular momentum can be obtained directly from the commutation rules, without using special differential operators. To emphasize the commonality, angular momentum M of all forms will be represented here by three linear operators Mx, My and Mz, that obey the commutation rules ... 

The calculations discussed above considered spin magnetic moments but not the orbital magnetic moments. However, it is known that orbital correlation has a strong effect in low-dimensional systems, which leads to orbital polarized ground states.67-69 Based on this fact, Guirado-Lopez et al.69 and... 

The intraatomic d-d electron-electron interaction includes Coulomb and exchange interactions, and it is responsible for orbital and spin polarization. To account for orbital polarization, the idea of the LDA + U method was followed.70 A generalized Hartree-Fock approximation including all possible pairings was then used to write... 

Fig. 11 0 Competition by ligands for Ihe ir bonding d orbilul of a central metal atom. Relative overtop is symbolized by the shaded areas, (a) Equal aod strong tr bonds resulting from equal and good overlap of Ihe two carbon monoxide sr orbitals with the meial J orbital (b) Superior overlap of carbon monoxide t orbital wilh polarized metal d orbiial compared lo poorer overlap between ligand <1 and metal d orbitals. Polarization (mixing of higher energy wave functions) occurs so as to maximize total overlap Recall that the overlap integral includes both spatial and intensive properties Ihe represemation above is a graphic simplification.

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Conclusions We have established that the light Br and Rb isotopes presented here have very large quadrupole deformations of s 0.4 and moments of inertia close to the rigid body values. The odd proton in the 431 3/2+ Nilsson orbit polarizes and stabilizes the y-soft, shape coexistent Se and Kr cores into definite prolate triaxial shapes. This effect sets in at rather low spin and seems to be intimately connected with the suppression of pairing correlations near the N = Z = 38 gap developing at 82 = 0.4. We thus face a cumulative suppression of both proton and neutron pairing correlations in the same oscillator shell, a fairly unique feature in the periodic table. 

It has been pointed out by several authors that the population of rota-tionally aligning high-j orbitals may provide a sensitive probe of the triaxiality parameter y and could be used to trace the evolution of y with angular momentum [BEN83], [FRA83], [LEA83]. These observations are based on. the fact that a particle (hole) in a high-j orbital polarizes the core toward... 

Finally, the orbital polarization functions and the chemical potential can be expressed as ... 

The spin-dynamic interpretation is that the up spin associated with the p orbital polarizes (unpairs) the paired spins on s and h. This is of course dynamically incorrect because the electron spin magnetic moments are not large enough to produce the observed polarization. 

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