Characters from orbits reduce

This picture can qualitatively account for the g tensor anisotropy of nitrosyl complexes in which g = 2.08, gy = 2.01, and g == 2.00. However, gy is often less than 2 and is as small as 1.95 in proteins such as horseradish peroxidase. To explain the reduction in g from the free electron value along the y axis, it is necessary to postulate delocalization of the electron over the molecule. This can best be done by a complete molecular orbital description, but it is instructive to consider the formation of bonding and antibonding orbitals with dy character from the metal orbital and a p orbital from the nitrogen. The filled orbital would then contribute positively to the g value while admixture of the empty orbital would decrease the g value. Thus, the value of gy could be quite variable. The delocalization of the electron into ligand orbitals reduces the occupancy of the metal d/ orbital. This effectively reduces the coefficients of the wavefunction components which account for the g tensor anisotropy hence, the anisotropy is an order of magnitude less than might be expected for a pure ionic d complex in which the unpaired electron resides in the orbital. 

From Table 7-9,2 and using eqn (5-7,2) we can find the diagonal elements of the matrices which represent the 4h point group in the p-orbital basis and in the d-orbital basis. From these elements we get the characters of two reducible representations they are shown in Table 7-9,3, By applying eqn (7-4.2)... 

Here z is the square root of-1. As in equation 12.9,/runs from 0, 1, 2. ... We shall see below, and, very importantly, in the next chapter, that this complex form of the wavefunction is very useful. It is interesting to see where this expression comes from. Group theory provides the answer. The molecular point group of, for example, benzene is However, the group Q is the simplest one we can use which will generate the tt orbitals of the molecule. Table 12.1 shows its character table. The reducible representation for the basis set of six n orbitals is... 

Table 7.10 The reducible representation for the H(ls) orbitals of ethene (D2J. In the application of the reduction formula (lower table) only the nonzero characters from T(H(ls)) need be considered. However, the order of the group (the total number of operations) is b =8, irrespective of zeros in the reducible representation.

Since the most direct evidence for specihc solvation of a carbene would be a spectroscopic signature distinct from that of the free carbene and also from that of a fully formed ylide, TRIR spectroscopy has been used to search for such car-bene-solvent interactions. Chlorophenylcarbene (32) and fluorophenylcarbene (33) were recently examined by TRIR spectroscopy in the absence and presence of tetrahydrofuran (THF) or benzene. These carbenes possess IR bands near 1225 cm that largely involve stretching of the partial double bond between the carbene carbon and the aromatic ring. It was anticipated that electron pair donation from a coordinating solvent such as THF or benzene into the empty carbene p-orbital might reduce the partial double bond character to the carbene center, shifting this vibrational frequency to a lower value. However, such shifts were not observed, perhaps because these halophenylcarbenes are so well stabilized that interactions with solvent are too weak to be observed. The bimolecular rate constant for the reaction of carbenes 32 and 33 with tetramethylethylene (TME) was also unaffected by THF or benzene, consistent with the lack of solvent coordination in these cases. °... 

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