Fermi contact field

The isotropic Fermi contact field B, which arises from a net spin-up or spin-down -electron density at the nucleus as a consequence of spin-polarization of -electrons by unpaired valence electrons [63] ... 

Both terms originate from the same set of dipoles. Bdip is the direct dipolar field of the moments surroimding the muon. We will return to it shortly. The term Bcon is called the Fermi contact field and is produced by the net spin density of conduction electrons in contact with the muon. The spin polarization of the conduction electrons in turn is induced by the dipole moments on lattice sites. One finds... 

Saturation values T —> 0) of the measiued local magnetic field the calculated dipolar field and the extracted Fermi contact field for Dy, Ho and Er according to Schreier et al. (2000a) corresponding values lor Gd are... 

Spc is the so-called Fermi contact field [21] and represents the most important contribution to the field This field is the direct coupling... 

Owing to the fact that the exchange interaction between the spin-up polarized d-shell and the spin-up s-electron is attractive, while that between the spin-up d-shell and the spin-down s-electron is repulsive, the radial parts of the two s-electrons distort, one being closer to the nucleus and the other being more distant. As a consequence, the spin density with spin-down is enhanced at the nucleus. The direction of the Fermi contact field is antiparallel to this spin, and consequently the Fermi contact field is negative by defintion, which means anti-parallel to the magnetic moments of the d-electrons. 

In contrast to the EFG analyzed before, aU of these expectations from ligand field theory are largely confirmed by the DFT calculations. Despite the fact that the S = 2 state has a smaller prefactor for the isotropic Fermi contact term, the core polarization in the presence of four unpaired electrons is much larger and, consequently, the isotropic Fe-HFC is predicted to be roughly a factor of two larger in magnitude for as compared to 2g. Similarly, the dipolar MFCs are comparable for both spin states, which must be due to a considerable contribution from anisotropic covalency in the 5 = 2 species which partially compensates for the smaller prefactor. 

Although attempts have been made to correlate the hyperfine field of a mixed-valence compound with the weighted mean of the Fermi contact-interaction field H, = 220 < Sz > kOe , the orbital and spin-moment contributions Hl and Hd, which may be comparable to H, at Fe(II) ions, make any such correlations dubious ... 

In addition to the isomer shift and the quadrupole splitting, it is possible to obtain the hyperfine coupling tensor from a Mossbauer experiment if a magnetic field is applied. This additional parameter describes the interactions between impaired electrons and the nuclear magnetic moment. Three terms contribute to the hyperfine coupling (i) the isotropic Fermi contact, (ii) the spin—dipole... 

We have previously defined the one-electron spin-density matrix in the context of standard HF methodology (Eq. (6.9)), which includes semiempirical methods and both the UHF and ROHF implementations of Hartree-Fock for open-shell systems. In addition, it is well defined at the MP2, CISD, and DFT levels of theory, which permits straightforward computation of h.f.s. values at many levels of theory. Note that if the one-electron density matrix is not readily calculable, the finite-field methodology outlined in the last section allows evaluation of the Fermi contact integral by an appropriate perturbation of the quantum mechanical Hamiltonian. 

The pseudocontact term Afipo,ar is due to the valence electrons of the shift reagent SR they cause an additional intramolecular field in the adduct S + SR, shielding or deshielding the nucleus i in the molecule S. The Fermi contact term Afon ac accounts for interaction between the nucleus i and the field of the unpaired electrons of the paramagnetic additive SR which may be delocalized within the adduct S + SR [103]. 

Barone and coworkers250 also determined EPR hyperfine splittings nN of the radical 40 at the UMP2/DZ + P level of theory using the Fermi contact operator and a finite field method with an increment size of 0.001 a.u. Expectation values of aN, < aN >, at higher temperatures T were calculated by assuming a Boltzmann population of vibrational levels according to equation 23 ... 

The Fermi contact constant for the k state was not determined because the low field transitions could not be observed. The overall behaviour of the parameters can be understood in terms of the sag and npn orbitals. The Fermi contact constant, which is proportional to the unpaired electron density at the nucleus, is determined almost entirely by the lsag electron. The nearly constant value of iy is consistent with the 1 so g electron being essentially unaffected by the npnu electron. The orbital... 

---