Quartet spin state

The above treatment of a three-eleetron ease shows how to generate quartet (spin states are named in terms of their spin degeneraeies 2S+1) and doublet states for a eonfiguration of the form... 

The two sets of coefficients result in two sets of Fock matrices (and their associated density matrices), and ultimately to a solution producing two sets of orbitals. These separate orbitals produce proper dissociation to separate atoms, correct delocalized orbitals for resonant systems, and other attributes characteristic of open shell systems. However, the eigenfunctions are not pure spin states, but contain some amount of spin contamination from higher states (for example, doublets are contaminated to some degree by functions corresponding to quartets and higher states). 

The amount of spin contamination is given by the expectation value of die operator, (S ). The theoretical value for a pure spin state is S S + 1), i.e. 0 for a singlet (Sz = 0), 0.75 for a doublet (S = 1/2), 2.00 for a triplet (S = 1) etc. A UHF singlet wave function will contain some amounts of triplet, quintet etc. states, increasing the (S ) value from its theoretical value of zero for a pure spin state. Similarly, a UHF doublet wave function will contain some amounts of quartet, sextet etc. states. Usually the contribution from the next higher spin state from the desired is... 

Photoionization can also access excited electronic states of the ion that are difficult to study by optical methods. The photoionization yield of FeO increases dramatically 0.36 eV above the ionzation energy. This result corresponds to the threshold for producing low spin quartet states of FeO. These states had not been previously observed, as transitions to them are spin forbidden and occur at inconveniently low energy. Because the FeO + CH4 reaction occurs via low spin intermediates, accurately predicting the energies of high and low spin states is critical. 

Table 3 Unrestricted Hartree-Fock energies (Hartrees) for Ceo and C70 and their muon adducts, muon in atomic units (and MHz) after quartet spin state annihilation. The value of the total spin operator, < >, is also given after quartet spin state...

Let us now turn to the description of the reaction pathways. Figure 13-5 schematically depicts the shapes of the corresponding potential energy curves for the sextet and quartet spin-states and Table 13-11 contains the thermochemical information obtained at different levels of theory. 

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 comparison of Fe(III) spin transition systems with those of other metal ions reveals the greater variety of chromophores for which spin crossover is observed in iron(III). This is reflected in a generally more diverse coordination environment as well as a far broader range of donor atom sets. For six-coordinate systems the spin crossover generally involves an S=l/2<->S=5/2 change, whereas for five-coordinate materials an intermediate (quartet) spin state is involved in S=l/2<->S=3/2 transitions. There is just one report of such a transition in a six-coordinate system and that is considerably distorted [126]. 

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