Orbits delocalized

Ferrocene (Figure 2-61a) has already been mentioned as a prime example of multi-haptic bonds, i.c, the electrons tlrat coordinate tire cyclopcntadicnyl rings with the iron atom are contained in a molecular orbital delocalized over all 11 atom centers [811, for w hich representation by a connection table having bonds between the iron atom and the five carbon atoms of cither cyclopcntadicnyl ring is totally inadequate. 

Consider now the rr-system in benzene. The MO approach will generate linear combinations of the atomic p-orbitals, producing six rr-orbitals delocalized over the whole molecule with four different orbital energies (two sets of degenerate orbitals). Figure 7.3. The stability of benzene can be attributed to the large gap between the HOMO and LUMO orbitals. 

There have also been computational studies of several three-membered rings related to the above doubly reduced cyclotrigaUenes [65]. These concern species of formula o- (GaH)(CH)2, M[c- GaH)2(CH) ], [c- (GaH)2(CH) ]" c- (GaH)(SiH)2l, M[c- (GaH)(SiH)2 ] (M = Li, Na or K) and [c- (GaH) (SiH)2 ]. It was concluded that all these hypothetical compounds were also aromatic with a 27r-electron orbital delocalized over the three-membered ring. 

Optical Properties. The double-decker complexes of porphyrazines have characteristic electronic absorption spectra (Table V). The intense Soret bands of the double-decker complexes are blue shifted with respect to the single pz ligand as a consequence of the strong n-n interactions. Another characteristic of sandwich compounds is the additional appearance of absorption bands shifted to the red (termed Q ) and to the blue (termed Q") of the normal g-band region. These new transitions are thought to result from orbitals delocalized over the two macrocyclic ligands (33, 82). 

In the case of the sulfur analogues thioesters and thioacids, this delocalization is much less favourable. In the oxygen series, delocalization involves overlap between the oxygen sp orbital and the n system of the carbonyl, which is composed of 2p orbitals. Delocalization in the sulfur series would require... 

The next peak, at approximately 5.6 eV from the LUMO minimum, arises from a TT-type orbital delocalized over all the molecule but originating from the highest TT-type orbital of CeHe (i>2g)- Superposed to this contribution there is a second one, of a-type and also localized on the CeHe moiety, whose main character is ctc-h antibonding. Thus, the first and fourth peaks are considerably more concentrated in the benzene ring whereas all other peaks are strongly based on orbitals. This is clear from the comparison of the C and N PDOS in Fig. 6.5(d). 

How can the MO and VB methods be improved The answer depends on what one wants— more accurate calculations or better qualitative understanding. To improve VB calculations we need orbitals that allow the electrons to spread out over more than one atom. The GVB orbitals discussed in Section 6-6 suit this purpose and give an energy curve only slightly above the exact curve of Figure 21-11. In the GVB treatment the orbitals delocalize less as / increases. 

Estimations [21] give / [ 3.7 eV and /i2 2.8 eV. In view of these estimations according to expression (10) the difference AEX— AE reaches value 0.1 eV at decrease of the polymer chain length (IV- - oo) down to value N0A equal, 40 dimer units or 80 bonds C-C. At the same time, experimental data for polyenes give the value A0.i 20 bonds C-C [22]. Thus, the model of noninteracting molecular orbitals delocalized along the whole chain overestimates increase AE with reduction of length of a chain. 

The description of the bonding of ethene to transition metals is known as the Dewar-Chatt-Duncanson model. This builds on the previous descriptions for CO and CH2 with the exception that we must now consider the frontier orbitals of the ligand to be molecular orbitals delocalized over the two (or more) donor atoms. The basic features are presented for ethene however, the bonding scheme applies in principle to the side-on coordination of any multiple bond to a transition metal. 

Theoretical Calculations. According to the McConnell relation, Eq. (9), the proton hyperfine sphtting constants are proportional to p , the unpaired tt electron density of the carbon atom bonded to the proton. Using quantum mechanics p can be calculated at different levels of approximation. The approach outlined here is one of the simplest, the Hiickel molecular orbital (HMO) method. This model assumes that a tt molecular orbital, delocalized over n atoms, can be written as a hnear combination of n atomic orbitals (z is perpendicular to the molecular plane). 

Within the framework of current transport theories, the task of the chemist is to prepare donor molecules in which the molecule has the appropriate oxidation potential, orbital delocalization, and solubility. Further, the effects of dipolar disorder and intermolecular dimer sites must be minimized. Finally, the physical and chemical interactions of the transport and generation materials (whether in a single or dual-layer configuration) must promote efficient charge generation and injection. The systematic integration of all of these characteristics is indeed formidable. 

Conjugation stabilizes the allyl carbocation because overlap of three adjacent p orbitals delocalizes the electron density of the n bond over three atoms. 

Oo) ]. A third class of interaction dependent on the dihedral angle 4> between four bonded atoms is the torsional potential K [l + cos( -S)] used to account for orbital delocalization and to compensate for other deficiencies in the force field. A harmonic term [V2K ( - is often introduced for dihedral angles 5 that are relatively fixed, such as those in aromatic rings. Coulomb s law [qiqJiATreQe ij)] is the simplest approach to the contribution of electrostatics to the potential V ... 

CIDNP effects observed for norcarene [147, 178] supported a radical cation, 87 +, which spin and charge are delocalized between the olefinic group and the Walsh orbital of the (more highly substituted) internal cyclopropane bond. The bicyclo-heptene system, 87 +, appears to be more flexible than 86 + either the internal or the lateral cyclopropane bond can align with the alkene p-orbitals. Delocalization of spin and charge into the more highly substituted bond is preferred. 

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