Neglect of spin-orbit coupling

A formal definition of is thus necessary to apply the no-pair approximation 

A different approach is chosen when the screening of nuclear potential due to the electrons is incorporated in /z . Transformation to the eigenspinor basis is then only possible after the DHF equation is solved which makes it more difficult to isolate the spin-orbit coupling parts of the Hamiltonian. Still, it is also in this case possible to define a scalar relativistic formalism if the so-called restricted kinetic balance scheme is used to relate the upper and lower component expansion sets. The modified Dirac formalism of Dyall [24] formalizes this procedure and makes it possible to identify and eliminate the spin-orbit coupling terms in the selfconsistent field calculations. The resulting 4-spinors remain complex functions, but the matrix elements of the DCB Hamiltonian exhibit the non-relativistic symmetry and algebra. 

Both the 4-component and the DKH or NESC methods allow also for more advanced treatments of spin-orbit effects. It is possible to ignore spin-orbit coupling effects in the Hartree-Fock procedure but include them afterwards in 

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For the nonrelativistic case with neglect of spin—orbit coupling we separate the space and spin parts of the coordinate—spin representation of the orbital... 

The electric dipole moment operator is independent of spin and, in the absence of spin-orbit coupling, the spin part of the magnetic moment operator will have no influence on MCD. We shall therefore neglect the spin part of Eq. (8) until we come to spin-orbit-induced MCD in Section II.A.4. 

Table 1. M.O. energies (all in eV = 8065.48 cm-1) calculated for the uranyl ion, and in the first column, monatomic U+2 and oxygen atoms. The half-numbered quantum number is a> of linear symmetries. The two last columns give M.O. energies, neglecting effects of spin-orbital coupling, and hence characterized by X and parity...

Table 3. M.O. energies (all in eV) calculated for the uranium hexafluoride molecule. When effects of spin-orbit coupling are neglected, the symmetry types tlu,. .. of the point-group Oh are indicated. The quantum numbers y6, y7 and y8 refers to the corresponding double-group (used for describing relativistic effects) in which case the parity can be seen from the main component of the one-electron function given at first in parenthesis...

The direction of the magnetic field defines the space-fixed p = 0 (or Z) direction. Equation (8.239) represents a very simplified version, in that it neglects the nuclear and rotational Zeeman effects, as well as the second-order effects of spin-orbit coupling, none of which are negligible. Nevertheless (8.239) will allow us to derive theoretical values for the first-order effective g-factors, for comparison with the experimental spectra [43]. The required matrix elements of (8.239) in a case (b) hyperfine-coupled basis are as follows ... 

Neglecting any spin-orbit coupling, what would be the observed orbital angular momenta of octahedral-site Co, Ni, Ni, Cr, Cr +, Mn +, and Cu + cations. 

The structural similarity of MgAgAs-type compounds with Heusler alloys and with the transition-metal based half-metallic ferromagnets (de Groot et al. 1983) has provoked band-structure calculations of UNiSn (Mueller et al. 1987, Albers et al. 1987). Self-consistent-field scalar relativistic spin-polarized calculations neglecting the spin-orbit coupling revealed the following features of the valence band ... 

In this Section we consider briefly the spectroscopic consequences of the operation of the Jahn-Teller effect in the hexafluoro complexes of the 3d series. In this context we shall neglect the influence of spin-orbit coupling, which is small in the first transition series, and treat only the orbital degeneracies involved. 

Neglecting the spin-orbit coupling, the wavefunctions of the molecules, i.e. the molecular orbitals, are the product of a spatial part (Rj,ri) and a spin part. The spatial functions T> depend only on the position variables Rj of the nuclei and r, of the electrons, while the spin part depends only on the spin variables of the electrons (and in some cases of the nuclei). As long as no applied magnetic field is present... 

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