Fermi contact term evaluation

The first-order contribution of these hyperfine interactions to the effective electronic Hamiltonian involves the diagonal matrix elements of the individual operator terms over the electronic wave function, see equation (7.43). As before, we factorise out those terms which involve the electronic spin and spatial coordinates. For example, for the Fermi contact term we need to evaluate matrix elements of the type ... 

Linear scaled coupling constants evaluated using the Fermi contact term only, averaged over the five different basis sets. 

The occurrence of hyperfine coupling for a particular isotope indicates non-zero spin density at that nucleus in accordance with the Fermi contact term (which includes the electron wave function evaluated at the nucleus) [1]. The analysis in terms of spin density then requires at least a comparison with the (calculated [5]) isotropic hyperfine splitting constant ao, ideally, results from increasingly available open-shell quantum-chemical calculation procedures [64] are employed. 

The isotropic component of the hyperfine tensor (Aiso - Fermi contact term) was evaluated in open-shell KSCED calculations as ... 

One of the simplest van der Waals complexes is the helium dimer. The small size of the system has made it possible to evaluate the He- He spin-spin coupling constant in an accurate manner, at the full configuration interaction level The Fermi-contact term has been found to have non-negligible value of 1.3 Hz at R=5.6 a.u. (dose to the energy minimum), while the other contributions are practically zero. The coupling decreases very fast, in an exponential manner, with the intemuclear distance R. For R equal to 4 a.u. it is over 22 Hz, while for R over 7 a.u. it falls below... 

Detailed theoretical studies, based on EPR experimental data, on both trapped electron centres and on electron transfer toward adsorbed molecules on MgO have also appeared. In the latter paper, beside further investigation of the Fs +/N2 system, a detailed analysis of the Fs +/02" complex was reported with particular emphasis on the whole hyperfine structure of adsorbed O2 . The Fermi contact term was evaluated as = —20.3 G and the resulting dipolar tensor was = — 56 G, Byy = -1-27.5 G, B = +28.6 G. An experimental paper appeared some months later reporting a fully resolved hyperfine structure of adsorbed 2. The powder spectrum contained a large number of lines and was further comphcated by the presence of several off-axis extra features. The simulation of such a complex pattern of fines gave Uiso = 4.8 G and a dipolar tensor (J) with a value remarkably close to the theoretically calculated value. This vahdates the quahty of the model but also the capabihty of modern theoretical approaches in forecasting EPR hyperfine parameters. 

As this component depends on the value of the unpaired spin density evaluated at the position of the nucleus only, p -P(0), it is often referred to as a contact interaction, or Fermi contact term. This does not have a classical analog, but is a consequence of the quantum nature of the particles. The remainder of the hyperfine part of the spin Hamiltonian is a traceless tensor that describes the deviation from spherical... 

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