Diamagnetic spin-orbit contribution

Recalling that A x (B x C) = B (A C) — C [A B) this term (called the diamagnetic spin-orbit contribution, DSCf ) reads as... 

As to the integrals involved, the Fermi contact contribution (just the value of the wave function at the nucleus position) is the easiest to compute. Assuming that states are Slater determinants, the diamagnetic spin-orbit contribution... 

Ramsey theory (p. 666) diamagnetic effect (p. 668) paramagnetic effect (p. 668) coupling constant (p. 668) direct spin-spin interaction (p. 669) diamagnetic spin-orbit contribution (p. 669) paramagnetic spin-orbit (p. 670) spin-dipole contribution (p. 670)... 

The total spin-spin coupling tensor includes (see, e.g Vahtras et al. 1992b) the so-called diamagnetic spin-orbit contribution - - obtained as the expectation value of the... 

According to NMR theory [30], contributions to spin-spin coupling come from paramagnetic spin-orbital (PSO), diamagnetic spin-orbital (DSO), Fermi contact (FC), and spin-dipolar (SD) interactions [30] ... 

It follows from Table V that spin-orbit effects are relevant for the heavy metal shieldings and, since the spin-orbit contribution does not always have the same sign, for the relative chemical shifts. In this connection, it is interesting to note that the ZORA spin-orbit numbers are shifted as compared to their Pauli spin-orbit counterparts. This effect can be attributed, at least partly, to core contributions at the metal while scalar contributions of the core orbitals are approximately accounted for by the frozen core approximation (6,7), spin-orbit contributions of the core orbitals are neglected. Hence, the more positive (diamagnetic) shieldings from the ZORA method are due to spin-orbit/Fermi contact contributions of the s orbitals in the uranium core. 

The diamagnetic spin-orbital (DSO) contribution to the spin-spin coupling constants is usually small, but nonnegligible, especially for the proton-proton coupling constants. 

Computation of the spin-orbit contribution to the electronic g-tensor shift can in principle be carried out using linear density functional response theory, however, one needs to introduce an efficient approximation of the two-electron spin-orbit operator, which formally can not be described in density functional theory. One way to solve this problem is to introduce the atomic mean-field (AMEI) approximation of the spin-orbit operator, which is well known for its accurate description of the spin-orbit interaction in molecules containing heavy atoms. Another two-electron operator appears in the first order diamagnetic two-electron contribution to the g-tensor shift, but in most molecules the contribution of this operator is negligible and can be safely omitted from actual calculations. These approximations have effectively resolved the DET dilemma of dealing with two-electron operators and have so allowed to take a practical approach to evaluate electronic g-tensors in DET. Conventionally, DET calculations of this kind are based on the unrestricted... 

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 atom is diamagnetic the orbital contribution to the magnetic moment is always zero because the charges are equal and opposite while the masses are identical the spin contribution is also zero in zero field since, if the spin momenta are parallel, the spin magnetic moments are opposed, while if the spin momenta are antiparallel there is no preferred direction and the time average of the magnetic moment in any particular direction is zero. 

Recalling that Ax (B xC)= B(A C)-C(A-B) this term (called the diamag- diamagnetic netic spin-orbit contribution, DSO ) reads as spin-orbit... 

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... 

Table 5 Comparison of Spin Densities, Orbital Energies (eV), and g-Tensor Contributions (Relativistic Mass Correction [RMC], Diamagnetic Spin-Orbit [DSO], and Paramagnetic Spin-Orbit [PSO] Contributions) of the DPNO Radical in Water, Obtained from COSMO, D-COSMO-RS, and from COSMO Emplo3dng Additionally the Supermolecule Approach (B3LYP/IGLO-11)...

The contribution of the Fermi contact term to J(NN) in both trans- and C/S-N2H2 was computed using the scanning molecular orbital method, a special approach within the Har-tree-Fock framework [4]. The diamagnetic spin-orbital (DSO) contribution to J(HH) in N2H2 was calculated at the ab initio SCF level of theory [5]. 

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