Hyperfine contact isotropic

Detection and measurement of the two isomeric forms in solution again is most convenient by proton NMR spectroscopy, in which the isotropic proton hyperfine contact shifts in the paramagnetic tetrahedral isomers make recognition easy, and the amount of the shift reflects the proportion of paramagnetic species in solution (107,110-116, 119). Other methods, including UV/vis spectroscopy (106, 112, 114, 116, 118, 119), magnetic moment determination (105, 106, 109, 110, 115,116,118,119), dipole moment measurement (106,109,114), and IR spectroscopy (118), have also been employed. 

The coupling of the unpaired electrons with the nucleus being observed generally results in a shift in resonance frequency that is referred to as a hyperfine isotropic or simply isotropic shift. This shift is usually dissected into two principal components. One, the hyperfine contact, Fermi contact or contact shift derives from a transfer of spin density from the unpaired electrons to the nucleus being observed. The other, the dipolar or pseudocontact shift, derives from a classical dipole-dipole interaction between the electron magnetic moment and the nuclear magnetic moment and is geometry dependent. 

The Fermi contact, or isotropic contact or isotropic hyperfine contact mechanism applies when there is finite unpaired electron density at the nucleus. This either adds to, or subtracts from the external field, depending upon the sign and magnitude of (the hyperfine coupling constant). 

The conditions necessary for observation of proton magnetic resonance spectra in paramagnetic systems are well established (1). Either the electronic spin-lattice relaxation time, T, or a characteristic electronic exchange time, Te, must be short compared with the isotropic hyperfine contact interaction constant, in order for resonances to be observed. Proton resonances in paramagnetic systems are often shifted hundreds of cps from their values in the diamagnetic substances. These isotropic resonance shifts may arise from two causes, the hyperfine contact and pseudocontact interactions. The contact shift arises from the existence of unpaired spin-density at the resonating nucleus and is described by 1 (2) for systems obeying the Curie law. 

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 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. 

It is well-known that the hyperfine interaction for a given nucleus A consists of three contributions (a) the isotropic Fermi contact term, (b) the spin-dipolar interaction, and (c) the spin-orbit correction. One finds for the three parts of the magnetic hyperfine coupling (HFC), the following expressions [3, 9] ... 

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... 

Superhyperfine interactions are not easily observed in dy, because MO s involving the t orbitals cannot include s orbitals from the ligand, and it is the s orbital that contributes the major portion of the superhyperfine interaction. The F19 hyperfine has been detected (42, 45), and it was found that the isotropic contact term was indeed small as expected. Kuska and... 

The observed hyperfine shifts could come from contact coupling or pseudocontact interactions between the electrons and the protons. Contact shifts arise when a finite amount of unpaired electron density is transferred to the observed protons. The contact shifts of the proton resonances for isotropic systems are given by Bloembergen s (9) expression... 

Unlike hyperfine isotropic shifts, which often contain pseudocontact and contact contributions of the same order of magnitude, relaxation rates can often be recognized to be dominated by only one of the possible contributions. In addition, whereas contact and pseudocontact shifts may happen to have different signs, thereby making their separation more uncertain, relaxation contributions are obviously always positive and additive. 

Unpaired electronic density can be delocalized onto the various nuclei of the complex via through-bond scalar hyperfine interactions involving occupied orbitals containing s-character (direct interaction or polarization according to the Fermi mechanism, Wertz and Bolton (1986)). Random electron relaxation thus produces a flip-flop mechanism which affects the nuclear spin and increases nuclear relaxation processes (Bertini and Luchinat, 1996). Since these interactions are isotropic, they do not depend on molecular tumbling and re is the only relevant correlation time for non-exchanging semi-rigid complexes. Moreover, only electronic spin can be delocalized via hyperfine interactions (no orbital contribution) and the contact re-... 

The hyperfine coupling tensor (A) describes the interaction between the electronic spin density and the nuclear magnetic momentum, and can be split into two terms. The first term, usually referred to as Fermi contact interaction, is an isotropic contribution also known as hyperfine coupling constant (HCC), and is related to the spin density at the corresponding nucleus n by [25]... 

This hyperfine coupling is of two kinds An isotropic interaction arises from the possibility that the electronic wave-function, x , be non-zero at the nucleus, N. This is the Fermi contact term and the hyperfine coupling constant is given by ... 

The isotropic hyperfine coupling observed in e.s.r. spectra of radicals arises from the Fermi-contact interaction between the electronic spin angular... 

Chemical Shifts in NMR. The first effect is very useful in chemical analysis The nuclear spin transitions are affected by the "hyperfine" I S coupling between electron spin S (for any single electron in the molecule that has density at the nuclear position) and nuclear spin I this is due to the isotropic Fermi contact term ... 

Energy levels with Overhauser effect (a) Relaxation due to a time-dependent isotropic contact electron-spin-nuclear-spin hyperfine interaction a(t)l S which has a zero time-average, but allows processes X and Y and enhances nuclear spin transitions when the electron populations are made equal by saturation, (b) Relaxation is due to all dipole-dipole interactions, which allow processes X, V, and PNi nuclear spin transitions are forced into emission by the Overhauser effect. In (a) the relative Boltzmann populations before saturation are shown. 

The contact interaction is also referred to as the Fermi contact term. In a given atomic orbital basis -0, the isotropic hyperfine coupling constant (hfcc) for a particular nucleus N,, is given by the expression,... 

Where (3 is the Bohr magneton, H0 is the applied magnetic field, g is the g-tensor, S is the electron spin, I is the nuclear spin, gn and (3n.are the nuclear splitting factor and the nuclear magneton. The hyperfine coupling tensor A consists of an isotropic contact interaction... 

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