Symmetry matching

In Fig. 6-7, similar procedures are followed for the metal d orbitals. The 42 2orbital-symmetry matches with the in-plane group combination ((Ji-02+molecular orbitals described in Eq. (6-13). 

Figure 6-8. Impossible symmetry matching of ligand a orbitals with metal 4 apply for the xz and yz planes.

Figure 6-10. Symmetry matching of metal t2g orbitals with ligand k functions. Similar diagrams may be drawn in the xz and yz planes.

Fig.6b plots the variation of the energy along a purely a-approach and along the mini-mum-energy approach a considerable barrier is found for the former. The qualitative predictions of orbital symmetry match exactly the outcome of EHT calculations. 

Over the years, a key theme in ATP-dependent proteolysis has been the issue of symmetry-matched vs. symmetry-mismatched complexes. In the light of the... 

Fig. 11.19 Ligand group orbitals (LGOs) and symmetry-matched metal atomic orbitals appropriate for a bonding in an octahedral ML complex.

The nonbonding orbital does not match its symmetry with any available orbital of the adjacent atom (e.g., the 3py of Cl does not have a symmetry match with the Is of H in HC1, where x is the bonding direction and the 2py orbital of H is too high in energy to enter the picture). 

An examination of Table XII shows that in all cases the M-C interaction is a dative bond, i.e., donation of electron charges from the n orbital of olefin to the vacant s orbital of metal and, simultaneously, back-donation of electron charges from the d orbitals of M to the n orbital of olefin (Fig. 12). This can be interpreted in more detail as follows. When the olefin molecule approaches M+, some electronic charge is transferred from the C=C it orbital to the valence s orbital of M+ at the same time, electrons in the filled d orbitals of metal are transferred to the symmetry-matched 7r orbital of olefin. It can be seen from Table XII that upon adsorption, the electron occupancies of the valence s orbitals of Cu and Ag always increase, whereas the total occupancy of their Ad or 5d orbitals always... 

Both combinations of alkyne n orbitals find filled dir orbital symmetry matches in these d4 complexes. Extended Huckel calculations on Mo(HC=CH)2(S2CNH2)2 indicate a large HOMO-LUMO gap of 1.62 eV. These octahedral complexes have proved to be quite robust and resist exchange and substitution reactions in accord with a substantial frontier orbital energy gap (153). 

This expression contains important information regarding the symmetry of the excited states as well. Only those excited states can participate in the reaction whose symmetry matches the symmetry of both the ground state and the reaction coordinate. We already know that Qr belongs to the totally symmetric irreducible representation except at maxima and minima. This implies that only those excited states can participate in the reaction whose symmetry is the same as that of the ground state. This information is instrumental in the construction of correlation diagrams, as will be seen later. 

The local coordination environment at each Mn is approximately tetrahedral. If we had a discrete tetrahedral Mn complex, e.g., Mn(PR3)4, we might expect a qualitative bonding picture such as 45. Four phosphine lone pairs, Zi + t2 in symmetry, interact with their symmetry match, mainly Mn 4s and 4p, but also with the t2 component of the Mn 3d set. Four orbitals, mainly on P, P-Mn o bonding, go down. Four orbitals, mainly on Mn, P-Mn o antibonding, go up. The Mn d block splits in the expected two below three way. 

Figure 8.28 Thermal [4s- -2s]-cycloaddition is symmetry matched for normal electron demand.

Note that for the inverse electron demand, the LUMO of the diene ( T3) and HOMO of the ethene (-tt) are also symmetry matched for supra-supra interaction, the symmetry allowed process (Fig. 8.29). 

Photochemically, the [4s- -2s] process for normal electron demand is symmetry forbidden because the LUMO of dienophile (tt ) does not symmetry matched with the excited state HOMO (i.e. the ground state LUMO) of diene (T s) (Fig. 8.30). 

Eq. 5). The essential feature of a symmetry-allowed reaction is the symmetry-match of occupied molecular orbitals in A with those in B and a similar match of unoccupied A and B orbitals. Thus a band of bonds (oc-... 

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