Alternant hydrocarbons first order

A satisfactory feature of (116) is that the first-order term, which describes the interaction between the external charge and the unperturbed molecule, continues to disappear if the electron distribution is highly uniform as in an alternant hydrocarbon in such cases the propensities for reaction are still dominated by the polarization term, but this now has a less simple form, depending upon all atom-atom polarizabilities and on the position of the attacking ion with respect to all conjugated centres. 

A rigorous theoretical treatment of the non-alternant and heterocyclic indolizine is extremely difficult and, even for the related isoconjugate hydrocarbon, far from conclusive. Many questions, however, in which experimentalists are interested may be answered in a satisfactory way on the basis of a perturbational treatment. This approach has been used for a discussion of the electronic spectra of indolizine and some azaindolizines (63JCS3999). Following first-order PMO theory the 7r-stabilization which follows from aza substitution at the different positions of the model molecule depends on the ir-electron density qt as well as the change in electronegativity Sat (B-75MI30801). The perturbations caused by aza substitution of the indenyl anion are depicted in Scheme 1. 

In hydrocarbon solvents, /3-diketones are predominantly (> 90%) enolized and these solutions have been subjected to flash photolysis, which causes photoisomerization to the diketo form9). Reversion of the diketone to the more stable cis enol was then followed by UV spectroscopy and pseudo first order rate constants at room temperature were in the range 14-68 x 10-3 s-1 (e.g. AA = 23 x 10-3 s 1) with half-lives of several hours. The same research also reveals an alternative transformation on irradiation. In this the cis enol form is converted by rotation about a C-C or C=C bond into one of the possible trans enol isomers. These may then go on to the diketo form but mainly they revert very rapidly to the cis enol with rate constants of 0.1 to 70 s 1 (e.g. AA = 0.27 s-l)9). 

First-order perturbation theory within the simple MO method derives the following generalizations for changes in spectra by substituting a nitrogen for a carbon atom in an alternant hydrocarbon. 

Figure 1.6. Schematic representation of first-order configuration interaction for alternant hydrocarbons. Within the PPP approximation, conHgurations corresponding to electronic excitation from MO 4>i into and from MO., into are degenerate. The two highest occupied MOs (i =, k = 2) and the two lowest unoccupied MOs (f = r and k = 2 ) are shown. Depending on the magnitude of the interaction, the HOMO- LUMO transition

First-order Cl, which for alternant hydrocarbons gives rise to the distinction between plus and minus states (cf. Section 1.2.4). 

Figure 2.23. Odd alternant hydrocarbon radicals a) Schematic representation of the frontier orbital energy levels and of the various configurations that are obtained by single excitations from the ground configuration o. (It should be remembered that spin eigenstates cannot be represented correctly in these diagrams.) b) Energies of these configurations and effect of first-order configuration interaction.

For alternant hydrocarbons cj, = cj,. for all p, and there is no first-order energy change for the HOMO LUMO transition, as is apparent from Figure 2.26. This result is remarkably well confirmed by the absorption spectra of naphthalene, quinoline, and isoquinoline shown in Figure 2.27. 

While first-order effects of purely inductive substituents on excitation energies of alternant hydrocarbons vanish, higher-order perturbation theory gives nonzero contributions. Thus, Murrell (1963), using second-order perturbation theory, derived the relation... 

Alternant hydrocarbons, 33, 86, 97, 112, 127. 167, 441. jT bond order, 441 excited stales. 17 first order Cl, 17, 54, 70 longest-wavelength transition. 74-75... 

If the transition considered is the HOMO LUMO transition of an alternant hydrocarbon, then first-order theory predicts that inductive perturbation will have no effect at all, because for = fo as a consequence of the pairing theorem. Small red shifts are in fact observed that can be attributed to hyper conjugation with the pseudo-7t MO of the saturated alkyl chain.290 On the other hand, alkyl substitution gives rise to large shifts in the absorption spectra of radical ions of alternant hydrocarbons whose charge distribution is equal to the square of the coefficients of the MO from which an electron was removed (radical cations) or to which an electron was added (radical anions), and these shifts are accurately predicted by HMO theory.291... 

The mechanism governing the early stages of initiation in aliphatic solvents is still unknown. The concentration of the active, monomeric RLi might be exceedingly low in those solvents because the dissociation in aliphatic hydrocarbons is not facilitated by solvation. Hence, the rate of dissociation could be the rate determining step, or a slow, direct reaction of the aggregate with the monomer could start the process. In either case the rate of the early initiation would be proportional to the first power of the initiator concentration, as seems to be the case. The dependence on monomer concentration differentiates between the two alternatives discussed above. Apparently, the rate is first order in monomer164,175) and this observation favors the second alternative. The... 

Figure 1.6. Schematic representation of first-order configuration interaction for alternant hydrocarbons. Within the PPP approximation, configurations corresponding to electronic excitation from MO into and from into are degenerate.

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