Interaction orbital hyperfine

Since the g-matrix has only three principal values and there are almost always many potentially interacting molecular orbitals, there is rarely sufficient information to interpret a g-matrix with complete confidence. When a well-resolved and reliably assigned optical spectrum is available, the energy differences, E0—Em, are known and can be used in eqn (4.11) to estimate the contribution of the corresponding MOs to the g-matrix. Extended Hiickel MO (EHMO) calculations can be useful (but do not trust EHMO energies ), but one is most commonly reduced to arguments designed to show that the observed g-matrix is consistent with the interpretation placed on the hyperfine matrix. 

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-... 

We have developed an unified adiabatic approach allowing one to tackle transport problems in traps of different geometry. The magnetic and electrical fields, charge screening, and other factors (a spin-orbit interaction, hyperfine structure, etc) can influence the quantum dot paths within an easily tractable Breit-Wigner-resonance approximation for the electron scattering. The utility... 

Here and H describe radicals A and B of the radical pair and He the interaction of their electrons. The other terms in equation (15) are H g, the spin orbit coupling term, H g and Hgj, representing the interaction of the externally applied magnetic field with the electron spin and nuclear spin, respectively Hgg is the electron spin-spin interaction and Hgi the electron-nuclear hyperfine interaction. 

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] ... 

Each of the eight hyperfine resonances is an unresolved quadmpole doublet, due to the quadmpole interaction of Os in the hexagonal Os metal source. The authors have interpreted the hyperfine fields in terms of core polarization, orbital and spin-dipolar contributions. 

Gardner 45) has observed the spectrum of Cl atoms adsorbed on a silica-gel surface at 77°K. The experimental results indicate that the orbital degeneracy of the 3p atomic orbital has been removed as a result of the electrostatic interaction with the surface. From the occupancy of the atomic orbitals one would predict that gx >011 — 2.00 and indeed the experimental g values are = 2.012 with g = 2.003. The hyperfine coupling indicates that the impaired electron is highly localized in the 3p orbitals. 

The term 11 (0) 2 is the square of the absolute value of the wavefunction for the unpaired electron, evaluated at the nucleus (r = 0). Now it should be recalled that only s orbitals have a finite probability density at the nucleus whereas, p, d, or higher orbitals have nodes at the nucleus. This hyperfine term is isotropic because the s wavefunctions are spherically symmetric, and the interaction is evaluated at a point in space. 

Aniosotropic hyperfine coupling results primarily from dipolar interactions between a magnetic nucleus and an unpaired electron in a p, d, or f orbital. Such interactions give rise to a Hamiltonian... 

An indirect mode of anisotropic hyperfine interaction arises as a result of strong spin-orbit interaction (174)- Nuclear and electron spin magnetic moments are coupled to each other because both are coupled to the orbital magnetic moment. The Hamiltonian is... 

This mode of hyperfine interaction will become important only when the impaired electron is able to partially occupy a low-lying excited state (AE small), and the ground state has orbital angular momentum (L 0). The adsorbed nitric oxide molecule and the superoxide ion with 170 are typical examples where hyperfine coupling via spin-orbit interaction may be observed. 

Electron spin resonance, nuclear magnetic resonance, and neutron diffraction methods allow a quantitative determination of the degree of covalence. The reasonance methods utilize the hyperfine interaction between the spin of the transferred electrons and the nuclear spin of the ligands (Stevens, 1953), whereas the neutron diffraction methods use the reduction of spin of the metallic ion as well as the expansion of the form factor [Hubbard and Marshall, 1965). The Mossbauer isomer shift which depends on the total electron density of the nucleus (Walker et al., 1961 Danon, 1966) can be used in the case of Fe. It will be particularly influenced by transfer to the empty 4 s orbitals, but transfer to 3 d orbitals will indirectly influence the 1 s, 2 s, and 3 s electron density at the nucleus. 

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