Paramagnetic Spin-Orbit Term

There are no simple rules, but usually the most important contribution to Jab comes from the Fermi contact term ( /Jg), the next most important is paramagnetic spin-orbit term other terms, including the mixed contributions are of little importance. Let us consider the... 

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. 

There are no simple rules, but usually the most important contribution to Jab comes from the Fermi contact term (7jg), the next most important is paramagnetic spin-orbit term J, other terms, including the mixed contributions 7 , are of little importance. Let us consider the Fermi contact coupling mechanism between two protons through a single bond (the coupling constant Jab denoted qs Jhh)- The proton and the electron close to it prefer to have opposite spins. Fig. 12.17. Then the other electron of the bond (being closer to the other nucleus) shows the other nucleus the spin of first nucleus, so the second nucleus prefers to have the opposite... 

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)). 

An increasing interest is being paid to spin-spin couplings between directly bonded two carbon nuclei. Four important papers by Cremer and coworker have been devoted to the mechanisms governing NMR spin-spin coupling and to the question if one can derive the information on the Jt character of a CC bond with the help of this parameter. An analysis of the spin-dipole and paramagnetic spin orbital transmission mechanisms led the authors to the conclusion that these terms are a sensitive indicator of the Jt character of a CC bond. 

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

Tormena et have analysed the dependence of paramagnetic spin-orbit (PSO) and spin-dipolar (SD) terms oi J(F,F) on F-C-F bond angle in CF2H2. The authors predicted on the basis of qualitative analysis that isotropic J(F.F) coupling should depend on the relative orientation of the C-F bonds containing coupled nuclei and the eigenvectors of second-rank tensor of the PSO and SD contributions. This relationship was validated by the calculations at the SOPPA(CCSD)/EPR-in//MP2/EPR-III level with DALTON program. 

Calculation of nuclear spin-spin coupling constants have begun to appear recently.[101-118] There are four terms which contribute diamagnetic spin-orbit, paramagnetic spin-orbital, spin-dipole, and Fermi contact terms. Often, the Fermi contact term dominates the coupling interaction and several workers have calculated J( B- H) and V( C- H) values at the B3LYP level... 

EOM-CC), to projected coupled cluster theory with all single and double excitations (CCSD) ° As an additional requirements there are (e) the use of enough large basis sets with augmented basis functions to obtain reliable evalution of paramagnetic spin-orbit (PSO) and spin-dipole (SD) terms (f) the inclusion of vibrational corrections for the SSCC, and (g) the consideration of solvent effects on SSCCs. " The latter two requirements concern the comparison of calculated and measured SSCCs. 

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