Fermi contact contribution

The and operators determine the isotropic and anisotropic parts of the hyperfine coupling constant (eq. (10.11)), respectively. The latter contribution averages out for rapidly tumbling molecules (solution or gas phase), and the (isotropic) hyperfine coupling constant is therefore determined by the Fermi-Contact contribution, i.e. the electron density at the nucleus. 

The concept of spin-polarization has been found to be extremely useful for understanding the magnetic HFCs of organic radicals which are dominated by the Fermi contact contribution. The situation for transition metal complexes is rather different in several respects. The idea of spin-polarization is relatively simple and is best... 

Evaluation of trends in /pp coupling constants in solid-state 31P NMR spectra of P-phospholyl-NHPs allowed one to establish an inverse relation between the magnitude ofM and P-P bond distances [45], The distance dependence of. /pp is in line with the dominance of the Fermi contact contribution, and is presumably also of importance for other diphosphine derivatives. At the same time, large deviations between lJvv in solid-state and solution spectra of individual compounds and a temperature dependence of lJ77 in solution were also detected (Fig. 1) both effects... 

Since 3dyz/4s admixture is symmetry-forbidden for these radicals, the Fermi contact contribution to the isotropic coupling, As, must be entirely from spin polarization,... 

In aliphatic and cycloaliphatic compounds, vicinal carbon-proton coupling constants 3Jch are related to the dihedral angle 0, as known from the Karplus-Conroy relation for iJ[iH. The Fermi-contact contribution to 3JCH as a function of the dihedral angle 0 calculated for propane [131] is displayed in Fig. 3.15, and the Karplus relation given by eq. (3.17) can be derived ... 

Scalar Pauli computations and ZORA calculations with spin-orbit yield quite similar results, Table III, although the latter includes spin-orbit effects whereas the former does not. However, we note from a direct inspection of the ZORA calculations that the spin-orbit contributions are small (not shown in the table). The U-F bond is mostly po- and type and should only have very little s character at the fluorine center. Hence, Fermi contact contributions are small, and spin-orbit is not relevant here, according to the qualitative discussion above. 

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. 

FC = Fermi contact contribution OB = orbital contribution SD = spin-dipolar contribution. 

A very detailed study of 3/hcoh and other related coupling constants has recently been conducted.75 Zhao et al. performed DFT calculations on a series of aldopyr-anosyl model structures, many of which were deoxygenated at C-3, C-4, and/or C-6, so as to eliminate any undesired hydrogen bonding.75 DFT calculations were carried out with (a) only the Fermi contact contribution included and (b) non-Fermi contact terms included as well. For non-anomeric protons, inclusion of only the Fermi contact term resulted in a generalized Karplus equation ... 

In a reprise, almost 40 years later, Barfield has clarified the situation by a study of the structural dependencies of 4/hccch in propanic and allylic systems by DFT/FPT methods, which were used to obtain the Fermi-contact contributions to the couplings.154 The theoretical contributions to the coupling constants were dissected according to dependences on various molecular properties, including the y>i and torsion angles, the central C-1-C-2-C-3 bond angle 02, and the C-l-C-3 distance rC-i,c-3- Barfield has published a very revealing 3D plot of 4/hccch as a function of both 1 and y>3 (Fig. 10). 

The Fermi contact contribution to a coupling constant, V(A-B), is proportional to the product of the 5-electron densities at the coupled nuclei, sA(0)sB(0). (11-17) Both the orbital and dipolar contributions are proportional to the product of the one-centre integrals (r 3)A and (r 3)B, where (r 3)A and (r 3)B are the expectation values of r for valence shell p orbitals on atoms A and B respectively. (14-17) Thus one can write the total coupling constant... 

In 1971, Maciel et al. (40) reported /(C-C) values calculated using the finite perturbation technique (FPT) in conjunction with molecular orbital theory at the INDO level of approximation. The calculations were carried out on more than 75 molecules and only the Fermi contact contribution was evaluated. Molecules with strained rings were not considered. Reasonable agreement with experiment was realized and it was observed that computed /(C-C) values were approximately related to Pj(C)aS(C)b- In addition, it was found that computed /(C-C) and... 

MO calculations on a small number of molecules for which experimental data were available at that time. Only the Fermi contact contribution was considered and although agreement with experiment is rather poor, it is interesting that no correlation between calculated /(N-C) values and Pj(N)jiC) was found. This result is in contrast to the calculated results obtained for carbon-carbon coupling constants. More recent INDO-FPT calculations on a series of amine derivatives indicate that the Fermi contact contribution to /(N-C) is related to Pj(N)s(C) in this class of structurally similar compounds. (96) The results of these calculations are illustrated in Fig. 3. (... 

Two groups of workers (110, 118, 119) have carried out sum-overstate INDO calculations, which also indicate that the orbital and spin-dipolar contributions are significant across the C=N triple bond. Calculated results for /(N-C) in acetonitrile are summarized in Table IX. Although there is lack of agreement in the total. /(N-C) calculated, the Fermi contact contribution is consistently positive while the other two mechanisms give rise to negative contributions. 

The absolute value of /(N-C) in oximes and imine derivatives is generally less than 5 Hz. MO calculations (20, 104) successfully indicate that the Fermi contact contribution to /(N-C) in these compounds is small. This result appears to be quite general for molecules which contain nitrogen lone pairs with considerably s-character. (20) Pyridine... 

Values of /(C-N) across the triple bond in nitriles and isonitriles are negative. (106, 109) In both acetonitrile and methylisocyanide the Fermi contact contribution to /(N-C) is predicted to be positive and, for the methylisocyanide, quite large. The orbital and spin-dipolar mechanisms are predicted to make a negative contribution thus it appears that the latter two mechanisms are important for coupling across triple bonds. 

For the isonitriles, /(N-C) across the single bond is negative (109) the absolute value appears to increase as the 5-character of the C-N single bond increases. The Fermi contact contribution is expected to dominate this latter coupling. 

If the nitrogen has a lone-pair with considerable 5-character, and hence resembles the nitrogen atom in oximes or imines, lI/(N-C)l is generally less than 4 Hz. The Fermi contact contribution to these coupling constants is predicted to be small. (20, 104) (See ref. 20 for a reasonable explanation .)... 

INDO-FPT calculations of the Fermi contact contribution to 3/(N-C) in the peptide fragment [20], by Solkan and Bystrov, (127) find that... 

Calculated values (Fermi contact contribution only) of X(C-X) in a number of aliphatic methyl-X compounds are given in Table XIII. (23) As X increases in atomic number from 3 (Li) to 9 (F), X(C-X) increases, reaching a maximum for X = CHP and then rapidly decreases and becomes negative for X = OH and X = F. The experimental results discussed in this review qualitatively verify these predictions. 

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