State, spin admixed

6 OTHER INTERACTIONS IN MONONUCLEAR SYSTEMS 8.6.1 Spin-admixed states 

In Section 8.5.13 we have seen that the matrix elements of the spin-orbit coupling can interconnect certain atomic terms. In real metal complexes, however, the matrix elements of the spin-orbit coupling operator have to be evaluated between the strong-field kets. In the crystal field of cubic (Oh) symmetry the following reduction applies 

The coupling coefficients (.r1yl.r2y2. ry) are introduced as members of the unitary matrix that transforms the uncoupled kets 11 )ft) and r2y2), belonging to the y,th component of the irreducible representation F to the kets / ) hence 

The last condition is necessary for the non-vanishing coupling coefficient, i.e. r should be contained in the direct product of Fj and F2. 

The coupling coefficients are closely related to the Griffith V-coefficients [48] 

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Table 27 Formulae for the spin admixed states of d5 configuration...

At the edge of the intermediate-field scale the high-spin and low-spin patterns strongly interfere, and the appropriate model should take into account spin-admixed states (this is instantaneously covered by the calculation in the complete d7 basis of 120 functions). 

A relatively high contribution of the S=3/2 spin state in the spin-admixed state of the studied highly n atively charged iron(III) porphyrins is nicely reflected in the kinetic behavior of the latter complexes concerning... 

Magnetic measurements revealed anomalous magnetic behavior with intermediate magnetic moment values between quartet and doublet states. From MO theory, the larger a molecule is and more metal atoms it contains and the lower the energy gap between the HOMO and LUMO. Consequently, the higher spin state is more accessible. The C07 chain has spin admixed state from S = 1/2 to S = 7/2. 

An interesting example of a spin-admixed nonheme iron(lll) complex with S - (3/2, 5/2) ground state is the organometallic anion [Fe CeCls) which has four pentachloro phenyl ligands in tetrahedrally distorted planar symmetry [122]. 

An intermediate spin state (a quartet 4A2) similarly is feasible for five-coordinate iron(III) though, as pointed out by Kahn [118], the situation may be more complex. If the states are close in energy then they can interact through spin-orbit coupling to give a so-called spin-admixed ground state. 

The magnetic properties of the iron porphyrins may be considered in terms of their tetragonal symmetry, which results in the existence of three possible spin states. For the ds Fe111 centre these are the low-spin S = 3 state, the intermediate-spin S = state and the high-spin S = state. Examples of each type are given in Table 15, with information on bond lengths. The S = state can couple to a nearby S = f state to give a new admixed intermediate state (S = , ), which must not be viewed as a spin equilibrium. 

The six-coordinate species is spin-admixed (S = 3/2,5/2) while the predominantly five-coordinate species (1-OH) is high spin (S = 5/2). The spin states have significance, it will be shown in interpreting some of the kinetics results. Reversible binding of NO to 1-H20 leads to formation of the linearly bonded diamagnetic porphyrin nitrosyl, (TMPS)Fen(NO + )(H20), (1-NO). The product of reaction of 1-OH with NO has a noticeably different UV/visible spectrum from that of 1-NO, and this was ascribed to the species (TMPS)Fen(NO + )(OH). 

Figure 2 Possible oxidation and spin states of iron porphyrins and the d orbital configurations expected in each case. AU of these states (excluding high-spin d, which is not included in the figure) have been observed for iron porphyrins, and are discussed in this article. In addition, the spin-admixed 5 = 3/2,5/2 state of Fe " and the alternative orbital configuration for low-spin Fe , with dxy higher in energy than dxi,dyz are also discussed...

These angular variations are responsible for the different g values found in the FPR spectrum (i.e. qualitatively they depend on the symmetry of the electronic wave function). However these deviations from ge actually arise from the admixture of orbital angular momentum into the spin ground state via spin orbit coupling. The extent of this admixing depends on which orbital contributes to the spin ground state (p, d or f). The real components of the g matrix are then given by ... 

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