Adjacent p-orbitals

The syn isomer can achieve a conjugated system with angles of up to 35° between adjacent p orbitals. The anti isomer is much more twisted. An X-ray crystal structure of the syn isomer shows C—C bond lengths between 1.368 and 1.418 A for the conjugated system (Fig. 9.3). ° The spectroscopic properties of the syn isomer are consistent with considering it to be a delocalized annulene. B3LYP calculations indicate that both the syn and anti structures are stabilized by delocalization, the syn (17.6kcal/mol) more so than the anti (8.1 kcal). ... 

The electronic and photoelectron spectra of these types of molecules can only be rationalized in terms of appreciable transannular interactions. The transannular resonance integral has been estimated to be about 40% of that between adjacent p orbitals in benzene. It would seem, therefore, that [130] is more correctly referred to as homonaphthalene and [131] as homoanthracene , etc. It is of interest to note that our probes for homoaromaticity correctly discern the importance of homoconjugation in [130] (Williams et al., 1988). Similar significant transannular interactions are also evident in homoazulene [133] (see Scott et al., 1985 Scott, 1986). 

The relaxed nonvertical excited state is referred to as the p-state as it has adjacent p-orbitals which are orthogonal due to a 90° angle of twist from the geometry of the vertical excited state. Figure 8.1 shows that the same p-state is produced from both geometrical isomers, and similarly, rapid radiationless decay of this p-state can produce either the cis or the trans isomer. 

Overlapping could, of course, take place, 1,2 3,4 5,6 or 1,6 5,4 3,2, leading to formulations corresponding to the Kekule structures 4a and 46) but, as an alternative, all six adjacent p orbitals could overlap, as with conjugated dienes (p. 12), resulting in the formation of six molecular orbitals, three bonding 3) and three anti-bonding... 

Formation of a sigma bond (o) from two s orbitals and formation of a pi bond (n) from two adjacent p orbitals. 

In a linear jr system the relative energies of the molecular orbitals are determined by the pairwise overlaps of adjacent p orbitals along the chain. An excess of bonding interactions, -l- with -i- or - with -, denotes a bonding MO an excess of antibonding interactions, + with -, denotes an antibonding MO. ... 

Figure 10.7. Activation of a C—H bond toward electrophilic attack by a neighboring substituent (a) X substituent (b) C substituent (only the adjacent p orbital is shown).

Qualitatively, the resonance picture is often used to describe the structure of molecules, but quantitative valence-bond calculations become much more difficult as the structures become more complicated (e.g., naphthalene, pyridine, etc.). Therefore the molecular-orbital method is used much more often for the solution of wave equations.5 If we look at benzene by this method (qualitatively), we see that each carbon atom, being connected to three other atoms, uses sp1 orbitals to form a bonds, so that all 12 atoms are in one plane. Each carbon has a p orbital (containing one electron) remaining and each of these can overlap equally with the two adjacent p orbitals. This overlap of six orbitals (see Figure 2.1) produces six new orbitals, three of which (shown) are bonding. These three (called it orbitals) all occupy approximately the same space.6 One of the three is of lower energy than... 

Thus, if there were no 7r bonding in ethene and no repulsion between the electrons, the energy of the two electrons (one in each of the two adjacent p orbitals of the carbons) would be twice the Coulomb energy, or 2a. This would be the situation for two carbons such as 3 that are widely separated. 

Ethylene, the first member of the series, is already familiar. Two adjacent p orbitals interacting will yield a bonding orbital, symmetric with respect to reflection in the mirror plane lying midway between the two carbons and perpendicular to the C—C axis, and an antibonding orbital antisymmetric with respect to that mirror plane. Figure 10.18 illustrates the interaction and the resulting orbitals. 

For MCAT proposes, two conditions must exist for resonance to occur 1) a species must contain an atom either with a p orbital or an unshared pair of electrons 2) that atom must be single bonded to an atom that possesses a double or triple bond. Such species are called conjugated u use hi rated systems. The adjacent p orbital in a conjugated system may contain zero, one, or two electrons (as in another Jt-bond - The p orbital allows the adjacent ji-bund to extend and encompass more than two nuclei. 

As we saw for the formate ion in Figure 3.15, resonance structures are just different ways of arranging pi bonds and electrons among a series of adjacent p orbitals that form a conjugated system. 

The lowest-energy molecular orbital is entirely bonding, with constructive overlap between all pairs of adjacent p orbitals. There are no vertical nodes in this lowest-lying MO. 

The all-antibonding tt% has three nodal planes. Each pair of adjacent p orbitals is out of phase and interacts destructively. 

In addition to the sp hybrids, each carbon atom has two half-occupied p orbitals, oriented at right angles to each other, and to the interatomic axis. These are two sets of parallel and adjacent p orbitals, and they can thus merge into two sets of n orbitals. 

In order to calculate the energy, the simple Hiickel theory for tt systems is used. That is, only the tt interactions between adjacent p orbitals are considered the overlap integrals are neglected. Equation 5.21 then becomes equal to ... 

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

The overiap of adjacent p orbitals increases I the electron density in the C-C o bond. 

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