Fermi contact coupling constant

The isotropic (Fermi contact) coupling constant is defined in terms of the unpaired spin density at a nucleus ... 

Many theoretical calculations of the molecular constants have been described, using a variety of models for the electronic structure. We do not intend to go into the details here, except to note that one of the simplest models of the excited electronic states of H2 describes them as an Hj core coupled with a Rydberg electron. In this connection it is significant to note that the Fermi contact interaction constant fy for the c3nu state of H2 is very close to the value determined for Hj itself, described in chapter 11. 

Fermi contact coupling mechanism between two protons through a single bond (the coupling constant Jab denoted as 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... 

Fermi-contact coupling. The through-bond coupling between the average electron spin and a nuclear spin 7 has a rank-0, isotropic component A (hyperfine Fermi constant) which is proportional to the spin density in the i orbital of the atom carrying the I spin ... 

Gaussian computes isotropic hyperfine coupling constants as part of the population analysis, given in the section labeled "Fermi contact analysis the values are in atomic-units. It is necessary to convert these values to other units in order to compare with experiment we will be converting from atomic units to MHz, using the following expressions ri6ltYg ... 

The spin Hamiltonian operates only on spin wavefunctions, and all details of the electronic wavefunction are absorbed into the coupling constant a. If we treat the Fermi contact term as a perturbation on the wavefunction theR use of standard perturbation theory gives a first-order energy... 

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. 

A completely different type of property is for example spin-spin coupling constants, which contain interactions of electronic and nuclear spins. One of the operators is a delta function (Fermi-Contact, eq. (10.78)), which measures the quality of the wave function at a single point, the nuclear position. Since Gaussian functions have an incorrect behaviour at the nucleus (zero derivative compared with the cusp displayed by an exponential function), this requires addition of a number of very tight functions (large exponents) in order to predict coupling constants accurately. ... 

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... 

From the isotropic coupling constant one may calculate C12, the fractional occupancy of the nitrogen s orbital, which is equal to AUo/Ao. The term Ao is the Fermi contact interaction for an unpaired electron in a pure nitrogen 2s orbital. For NO2 the value of ci2 = 56.5/550 = 0.103. The fraction of the unpaired electron associated with the N nucleus is then... 

The correlation between the X-ray crystallographic data of the W—CN bond lengths and the first-order coupling constants between the 183W and 13C in the equatorial cyano ligands, as predicted by the Fermi-contact term (51), is fairly good (see Table III). This illustrates the increase in cis W—CN bond length induced by increased donor... 

Fermi contact interaction. The coupling constant of the Fermi contact term for the nucleus N has the form127 ... 

Classical shielding arguments indicate an electron-rich phosphorus atom, or equally, an increase in coordination number. The silicon atom seems also to be electron-rich, while the carbon has a chemical shift in the range expected for a multiply bonded species. The coupling constant data are difficult to rationalize, as it is not possible to predict the influence of orbital, spin-dipolar, Fermi contact, or higher-order quantum mechanical contributions to the magnitude of the coupling constants. However, classical interpretation of the NMR data indicates that the (phosphino)(silyl)carbenes have a P-C multiple bond character. 

Figure 3.12 Total spin-spin coupling constant J(H-H) (squares) and PSO (triangles), DSO (circles), and Fermi contact (diamonds) contributions as a function of the H- -H distance in the dihydrogen-bonded complex CNH- -HLi. (Reproduced with permission from ref. 21.)...

The coupling interaction between directly bonded N—H is generally dominated by the Fermi contact term, as evidenced by the dependence of 7( N—H) on the amount of s character in the bond. Table 15 lists some illustrative N—H coupling constants, determined under comparable solvent conditions, as a function of the s character in the bonding orbitals. 

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 ... 

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