Alternant conjugated hydrocarbons

In this calculation, we confirm the fact that the ionization potential / and the electron affinity A of alternant conjugated hydrocarbon molecules have the relationship ... 

The effects of various structural factors of the molecular graph on the HOMO-LUMO separation, Ahl, of alternant conjugated hydrocarbons were investigated and some graph-theoretic formulas were obtained for Ahl- As can be derived from equation (77), when computed at the Hiickel level, the absolute hardness r] equals half the HOMO-LUMO separation Ahl as an important consequence of this fact, all theoretical relationships derived for Ahl are also valid for r). An approximation to Ahl for benzenoid hydrocarbons was derived by Cioslowski as a function of simple graph invariants, namely N, M, and KSC ... 

Hence, naphthalene, phenanthrene, pyrene, and biphenylene are alternant hydrocarbons, while azu-lene, pyracylene, and its isomers are non-alternant conjugated hydrocarbons. The idea of classification of hydrocarbons as alternant and non-alternant goes back to Coulson and Longuet-Higgins and the early days of HMO theory. An important property of alternant hydrocarbons, as opposed to non-alternant, is that for alternant systems all HMO eigenvalues come in pairs Xu while this is not the case for nonalternant systems. It is interesting to mention that this particular mathematical property of alternant... 

An important distinction for conjugated hydrocarbons is the classification into alternant and non-alternant hydrocarbons. Alternant hydrocarbons are those like ethene, hexatriene, benzene and naphthalene where we can divide the carbon atoms into two sets called starred and unstarred , such that no member of one set is directly bonded to another member (Figure 7.4). 

Recently, a nonempirical rr-electron SCF approach was reported and applied to interpretations of spectra of various conjugated hydrocarbon radicals (147). The greatest attention, however, has been paid to radical ions derived from even alternant hydrocarbons (10, 58-60, 63, 125, 135, 148-153). Here, numerous experimental material suitable for systematic testing of the MO methods has been accumulated. In particular, the following sources of experimental data should be mentioned Hamill and collaborators (24) prepared... 

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. 

A conjugated hydrocarbon is alternant if its carbon atoms can be divided into two classes starred and non-starred. No two atoms belonging to the same class can be linked directly. 

SAD Spin-alternant determinant. The VB determinant with one electron per site and with alternating spins. Other terms describing the same determinant are the quasiclassical (QC) state, and the antiferromagnetic (AF) state. In nonalternant hydrocarbons, where compete spin alternation is impossible, the determinant is called MS AD, namely, the maximum spin-alternating determinant. The SAD MSAD are the leading terms in the wave function of molecules with one electron per site, for example, conjugated hydrocarbons. In radicals (e.g., allyl radical) the SAD is the root cause of spin polarization (i.e., negative spin densities flanked by positive ones). See Chapters 7 and 8. 

Polyacetylene is a physical realization of such a system and it is known-that it does present bond alternation [46,47]. Since a parameterization to a model spin Hamiltonian is available [18] for conjugated hydrocarbons, this system is a good test for the NSBA and RVB ansatze. Therefore, in Ref. 34 the geometry of polyacetylene has been computed using this sort of ansatze. 

This uniformity is generally observed for the so-called alternate hydrocarbons which are the conjugated hydrocarbons whose C atoms in the classical structural formula can be labelled alternately by a star, no star, a star, no star, and so on, such that no two starred or unstarred atoms are neighbours when the labelling is complete. This is the case, for example, for benzene... 

Conjugated hydrocarbons that do not contain an odd-membered ring are called alternant hydrocarbons (AHs). The distinction between alternant and non-alternant hydrocarbons (NAHs) provides a very important classification of conjugated hydrocarbons, especially with regard to excited states. In AHs, the unsaturated C atoms can be assigned to two sets, the starred ( ) and the unstarred (o) set, such that no atoms of the same set are bound to each other. This is not possible for NAHs (Figure 4.18). 

The left-hand part of both Structures 5.3 and 5.4 will contribute more to the resonance hybrid than the others. Benzene is thus a delocalized hydrocarbon whereas buta-1,3-diene with its alternating carbon-carbon bond lengths is a conjugated hydrocarbon. 

We introduce here for the conjugated hydrocarbon radicals the same classification which we used for the closed-shell hydrocarbons 55). We divide the hydrocarbons into two large groups alternant and nonalternant. Further classification concerns the even and odd systems, and the presence of cycles in the skeleton. The phenyl substituents are... 

Scheme 13.1 Part of a conjugated hydrocarbon molecule, in which carbon atoms are hnked alternately by single and double bonds. Note C, carbon H, hydrogen bonds connecting the atoms are shown as lines...

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