Energy alternant hydrocarbons

The calculation of localization energies in heteroaromatic systems derived from alternant hydrocarbons has been simplified by Dewar and Maitlis (57JCS2521). This approach has had considerable success the results provide a somewhat empirical index of reactivity. 

FIGURE 2.7 Energy levels in odd- and even-alternant hydrocarbons. The arrows represent electrons. The orbitals are shown as having different energies, but some may be degenerate. 

In the HMO or extended Hiickel approach, the individual ionization potentials should be set equal to orbital energies. The inadequacy of the HMO treatment is apparent with odd alternant hydrocarbons (e.g., allyl, benzyl), where a constant value is obtained, in disagreement with the experiment. Streitwieser and Nair (105) showed, however, that reasonable results can be obtained with the co technique. 

Gutman, I., Trinajstic, N. Graph theory and molecular orhitals. Total tc-electron energy of alternant hydrocarbons. Chem. Phys. Lett. 1972, 17, 535-538. 

The energy levels of an alternant hydrocarbon (AH), equal in number to the number of conjugated carbon atoms, are arranged symmetrically about ao (Fig. 9)... 

Fig. 9. Change of energy levels AH of alternant hydrocarbon with limiting levels coincide with the levels RM of the residual molecule.

The existence of these inequalities is less surprising when it is remembered that the early stages of the localization process described above correspond precisely to polarization of the isolated molecule, and that the subsequent changes in levels and orbitals, as discussed in Section III, follow essentially by an analytic continuation. It follows that predictions of the sequence of active centres, in an even alternant hydrocarbon, based on localization energies must agree with those based on polarizabilities. This... 

Equally interesting is the situation in the second class of compounds studied (analogues of non-alternant hydrocarbons), which is best divided into two sub-groups analogues of the tropylium ion and analogues of azulene. The empirical correlation of experimental and theoretical excitation energies studied requires a further subdivision into compounds with one heteroatom (e.g. thiopyrylium ion) and two heteroatoms, either adjacent (e.g., 1,2-dithiolium ion) or non-adjacent (e.g., 1,3-dithiolium ion). Experimental and theoretical data are presented in Table VII. Table VIII summarizes data for the derivatives of dithiolia. Figure 15 shows the absorption curves of 1-benzo-... 

Benzene is an example of an alternant hydrocarbon, which is a planar conjugated hydrocarbon in which the carbons can be divided into two sets, starred and unstarred, with each starred carbon bonded only to unstarred carbons, and vice versa. For alternant hydrocarbons, the HMO pi energies are symmetrically disposed above and below a, and the HMO coefficients in the MO with energy a xft can be found simply by changing the signs of the unstarred-atom AO coefficients in the paired MO with energy a + xft. 

Which of these two states has the lowest energy and what is the transition intensity to the two states. These simple properties of excited states of alternant hydrocarbons remain approximately valid in more accurate theories, at least for the lower excited states. 

Based on a Huckel model for the anthracene fragments of BA (which is an even alternant hydrocarbon) one can show that the delocalized LE state and the CT states should all have the same 7t bond order. This in turn implies that the vibrational modes and frequencies should be similar for LE, CT, and CT. Thus the vibrations of bianthryl can be ignored in the energy dependence on z (even for highly polar solvents). 

The energy levels in an alternant hydrocarbon are symmetrical with respect to a. Therefore, any orbital Fp having an energy a + xp / has a corresponding orbital WLp of energy a — xp ft. The coefficients of the starred atoms are identical in Fp and for the non-starred atoms, they are equal but opposite in sign. 

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