Operator paramagnetic spin-orbit

The Aa P term in eq. (10.68) gives the Paramagnetic Spin-Orbit operator. 

The paramagnetic spin-orbit operator, also called the orbital hyperfine... 

The equivalent of the spin-other-orbit operator in eq. (8.30) splits into two contributions, one involving the interaction of the electron spin with the magnetic field generated by the movement of the nuclei, and one describing the interaction of the nuclear spin with the magnetic field generated by the movement of the electrons. Only the latter survives in the Born-Oppenheimer approximation, and is normally called the Paramagnetic Spin-Orbit (PSO) operator. The operator is the one-electron part of... 

The expression for the contribution to the spin-orbit induced MCD intensity from perturbation of the ground state is somewhat reminiscent of an expression for the Ag quantity of EPR spectroscopy. The similarity lies in the paramagnetic term, Agp. This term is composed of integrals of a spin-orbit operator over molecular orbitals similar to the expression for the perturbation of the ground state in the presence of spin-orbit coupling (Eqs. 52-56). The paramagnetic contribution to Ag dominates for blue copper proteins and it was suspected that the MCD parameters and Amay have some sort of relationship. It was found that many of the terms that make large contributions to AgP do play a role in the MCD intensity but no simple relationship was found (160). 

From the three operators obtained by differentiating the Hamiltonian with respect to the nuclear magnetic moments (Equation (2.12)) only the singlet paramagnetic spin-orbital (PSO) operator... 

Paramagnetic Spin-Orbit (PSO) operator. The operator is the one-electron part of which in its time-independent form (setting A = 0 in eq. (8.81) can be written as ... 

The nonrelativistic limit of this operator yields the paramagnetic spin-orbit (PSO) contribution of Ramsey s theory. The remaining terms in eq. (4.10b) result in the ZORA relativistic spin-orbit Hamiltonian,... 

As mentioned above there are four main contributions to the nuclear spin-spin coupling constants the Fermi contact (FC), the paramagnetic spin-orbit (PSO), the spin-dipolar (SD) and the diamagnetic spin-orbit (DSO) contributions. The Fermi contact term is usually the most important of these and also the most sensitive to geometry changes [8]. The Fermi contact contribution arises from the interactions between the terms containing S(riM) and < (riN) in the operators Hon for nuclei N and M (see Eqn. (12)). 

The singlet paramagnetic spin-orbit (PSO) operator the triplet Fermi contact (FC) operator... 

Zeeman operator and the spin-orbit coupling (also called paramagnetic spin-orbit term). A ° and A/ are generally small and of opposite sign, so that their effects tend to cancel one another. For transition metal ions, the g-anisotropy and the deviation from the free electron value mainly come from the third contribution, which is usually the most difficult to calculate. Thus, a proper treatment of the spin-orbit coupling (SOC) is crucial for the g-tensor calculation. 

While the chemical interpretation of the e parameters is a matter of real concern to us, there are also several other difficulties which are, however, more apparent than real. Consider the question of the calculation of magnetic properties in transition metal complexes - paramagnetic susceptibilities and e.s.r. g values. In contrast to the study of eigenvalues for optical transition energies, these require descriptions of the wavefunc-tions after the perturbation by the ligand field, interelectron repulsion and spin-orbit coupling effects. In susceptibility calculations it is customary to use Stevens orbital reduction factor k in the magnetic moment operator... 

By virtue of the results obtained for BaF, these error margins appear to be somewhat too narrow. With empirical data extracted from molecular beam experiments, Kozlov [149] obtained in 1985 a value for the parity violating effective constant Wpy of 212 Hz and a value of 180 Hz with data derived from electron paramagnetic resonance (EPR) spectra of the matrix-isolated molecule. With a different method for the treatment of the spin-orbit interaction, Kozlov and Labzowsky [32] obtained in 1995 Wpy = 240 Hz and 210 Hz, respectively. The ab initio calculations performed by Kozlov, Titov, Mosyagin and Souchko [171] with RECPs, however, resulted in Wpv = 111 Hz on the self-consistent field (SCF) level and Wpy = 181 Hz on the SCF level with an effective operator technique designed to take... 

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