Molecular orbital theory Allyl

Self-consistent field (SCF), 230 anti-Sesquinorbornatriene, 248 SHMO, see also Simple Huckel molecular orbital theory allyl, 89... 

The radical is much more stable if both stmctures exist. Quantum mechanical theory implies that the radical exists in both states separated by a small potential. Moreover, both molecular orbital theory and resonance theory show that the allyl carbocation is relatively stable. 

A unified theoretical explanation using molecular orbital theory has been proposed. Grimme [65] investigated the PFR of phenyl acetate as well as the photo-Claisen rearrangement of allyl phenyl ether and the 3-cleavage of para-substituted phenoxyacetones. A unified description of the three reactions has been invoked according to MNDOC-CI and AMl/AMl-HE calculations. No matter what ex-... 

A series of DFT calculations see Molecular Orbital Theory) on Rh() -C3H5)3 indicate that the ground-state structure has no symmetry. Calculated ionization energies agree well with values obtained from photoelectron spectra. The calculated potential-energy surface indicates the presence of three transition states, one of which involves an n] -allyl ligand between the several minima that are found, and variable-temperature NMR measurements appear consistent with there being three distinct fluxional processes see Stability Constants their Determination) ... 

Figure 3.12 shows how the -electrons of the double bond of an allylic cation can move towards the carbon atom bearing the positive charge. This generates an isomeric allylic cation, with the positive charge on the opposite end of the 3-atom system. In free allylic cations, this exchange is so rapid that the two isomers are indistinguishable. In fact, in molecular orbital theory, we consider the system to consist of a single set of orbitals which stretches across all three atoms. Since there is single bond character in each of the bonds, rotation is possible and the three cations, viz. geranyl (3.22), neryl (3.21) and linalyl (3.23), become equivalent. This is often represented as a smear of electrons as shown in structure (3.24) at the foot of Figure 3.12. Therefore in reactions such as those of...

Problem 1.3. Hiickel LCAO-MO theory 1 the allyl radical (See e.g. Lionel Salem, The Molecular Orbital Theory of Conjugated Systems, W. A. Benjamin, Inc. (1974), Chap. 1, or Peter W. Atkins, Physical Chemistry, Wiley-VCH (1988).)... 

An explanation of the stability of the allyl radical can be approached in two ways in terms of molecular orbital theory and in terms of resonance theory (Section 1.8). As we shall see soon, both approaches give us equivalent descriptions of the allyl radical. The molecular orbital approach is easier to visualize, so we shall begin with it. (As preparation for this section, it may help the reader to review the molecular orbital theory given in Sections 1.11 and 1.13.)... 

We can illustrate the picture of the allyl radical given by molecular orbital theory with the following structure ... 

We indicate with dashed lines that both carbon-carbon bonds are partial double bonds. This accommodates one of the things that molecular orbital theory tells us that there is a Tt bond encompassing all three atoms. We also place the symbol y beside the Cl and C3 atoms. This presentation denotes a second thing molecular orbital theory tells us that electron density from the unpaired electron is equal in the vicinity of C1 and C3. Finally, implicit in the molecular orbital picture of the allyl radical is this the two ends of the allyl radical are equivalent. This aspect of the molecular orbital description is also implicit in the formula just given. 

We see, then, that resonance theory gives us exactly the same picture of the allyl radical that we obtained from molecular orbital theory. Structure C describes the carbon-carbon bonds of the allyl radical as partial double bonds. The resonance structures A and B also tell us that the unpaired electron is associated only with the Cl and C3 atoms. We indicate this in structure C by placing a 8 beside Cl and C3. Because resonance structures A and B are equivalent, the electron density from the unpaired electron is shared equally by Cl and C3. 

The lone electron of the allyl radical is associated with the rr-nonbonding MO, which places electron density on carbons 1 and 3 only. This localization is shown clearly in the unpaired electron density map in Figure 8.6. Thus, both the resonance model and molecular orbital theory are consistent in predicting radical character on carbons 1 and 3 of the allyl radical but no radical character on carbon 2, consistent with the experimental observation. Importantly, when there is a difference, the reaction will occur to generate the alkene product that is most stable—in other words, with the more highly substituted double bond. 

Both compounds give allyl carbocations. One of the resonance contributors for the carbocation from (E)-l-chloro-2-butene has its positive charge at a secondary carbon atom. In terms of molecular orbital theory, the methyl group is at the end of an allyl system, where it affects the stability of the MO. The two resonance contributors for the carbocation from 3-chloro-2-methyl-l-propene are both primary. In terms of molecular orbital theory, the methyl group is bonded to the center carbon of an allyl system. There is a node at the C-2 of the Tt MO, and the methyl group cannot stabilize the carbocation. 

Problem 8.28 (a) Apply the MO theory to the allyl system (cf. Problem 8.26). Indicate the relative energies of the molecular orbitals and state if they are bonding, nonbonding, or antibonding, (b) Insert the electrons for the carbocation C,H, the free radical C,H, and the carbanion CjH, and compare the relative energies of these three species. 

The interaction of atomic orbitals giving rise to molecular orbitals is the simplest type of conjugation. Thus in ethylene the two p orbitals can be described as being conjugated with each other to make the n bond. The simplest extension to make longer conjugated systems is to add one p orbital at a time to the n bond to make successively the n components of the allyl system with three carbon atoms, of butadiene with four, of the pentadienyl system with five, and so on. Hiickel theory applies, because in each case we separate completely the n system from the a framework, and we can continue to use the electron-in-the-box model. 

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