Orbital angular momentum contribution

The model ESR spectrum, when the magnetic field is parallel to the axis of quantisation, will have a central absorption band surrounded by two lines at 2 D.  

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Copper in aqueous solution, and in proteins, is usually present in the Cu(I) or Cu(II) states. Cu(I) has 10 3d electrons, constituting a filled shell. All the electrons are paired and S = 0. Cu(II) has 9 3d electrons Cu(II) complexes are paramagnetic with S =. Because the 3d orbitals are more than half-filled, orbital angular momentum contributions from the d orbitals cause the average g value to be over 2. The EPR spectra are also affected by hyperfine coupling to the copper nucleus both of the common natural isotopes have I =. ... 

In other S = J iron-nitrosyl complexes, such as the Cys2-Fe(II)-(NO)2 complex, delocalization of the electron in extended molecular orbitals results in reduced orbital angular momentum contributions from the iron d orbitals. In this complex, delocalization apparently reduces the association of the unpaired elec-... 

Two main aspects of the HDW approach are important for the present discussion. One aspect is that the model is valid only in the absence of orbital angular momentum contributions to the system, so that its use has been broadly restricted to (say) binuclear complexes of iron(LLl), octahedral nickel(II), or distorted octahedral copper(II). The other aspect concerns the fact that the parameter is a global parameter of the system sequestering many contributions from various ligands and orbitals and, in this respect, may be compared with how Dq in ligand-field theory represents the net effect of electrostatic and covalent (o and rr) effects in the tjg — eg orbital splitting. Attempts to localize our conception of the exchange phenomenon have been made by various... 

The effect of suUur participation on the orbital g -shifts in the EPR spectra, illustrated in Pig. 20, accounts for the qualitatively different spectra observed for tyrosyl phenoxyl and Tyr-Cys phenoxyl radicals (Gerfen et al., 1996). The rhombicity of the simple tyrosyl radical EPR spectrum is a consequence of the splitting between gx and gy principal g -values. These g -shifts deviate from the free electron g--value ge = 2.00023) as a result of orbital angular momentum contributions. While a nondegenerate electronic state (such as the A" ground state for ere) contains no hrst-order unquenched orbital momentum, second-order spin-orbit mixing between close-lying a and a" functions results... 

Orbital Angular Momentum Contribution - The Free Ion Case... 

In general, when there is a signihcant orbital angular momentum contribution (i.e. for free ions), the value of the magnetic moment is not given by Eq. 8.21. This is a relativistic effect that increases with the atomic number. The result is that the measured magnetic moments of heavy ions are expected to be lower than the spin-only moment. This is because the spin and orbital momenta couple via the spin-orbit interaction ... 

In practice, spin-orbit coupling is small for first-row d-block metal ions, so that equation 7.1 may be applied. Furthermore, the d orbitals of a transition metal ion usually show significant interactions with the ligand orbitals. In such cases, the orbital angular momentum contribution is usually quenched so that gS(S + 1) L(L +1). Where this happens, equation 7.1 can be simplified to the spin-only formula shown in equation 7.2 ... 

The 2-positive ions Co + and Fe2+ are of this type and the good agreement with experiment confirms that orbital angular momentum contributes to the permanent moment. 

ORBITAL ANGULAR MOMENTUM CONTRIBUTION 8.5.1 Magnetic angular momentum... 

The spin Hamiltonian that accounts for the orbital angular momentum contribution is... 

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