7r-Electronic approximation

The reactivities of isomeric thienothiophenes calculated in n -electron approximation by the PPP method, and those calculated considering all valence electrons, show reasonable agreement. It should be noted, however, that the choice of parameters in PPP calculations is somewhat arbitrary, especially for heavy atoms (e.g., sulfur). This may lead to a discrepancy between theoretical (in 7r-electron approximation) and experimental estimation of reactivities. For example, Clark applied the semiempirical method PPP SCF MO to calculate the reactivities of different positions in thienothiophenes 1—3, thiophene, and naphthalene from the localization energy values and found the following order of decreasing reactivity for electrophilic substitution thieno[3,4-b]-thiophene (3) > thieno[2,3-Z>]thiophene (I) > thieno [3,2-b]thiophene... 

In these integrals the additional superscript it indicates that we are now within the framework of the 7r-electron approximation and that essentially H has been replaced by Ht (see eqn (10-4.1)) and consequently (see eqn (10-3.4)) by... 

The study of the reactivity of the nucleic acid bases utilizes indices based on the knowledge of the molecular electronic structure. There are two possible approaches to the prediction of the chemical properties of a molecule, the isolated and reacting-molecule models (or static and dynamic ones, respectively). Frequently, at least in the older publications, the chemical reactivity indices for heteroaromatic compounds were calculated in the 7r-electron approximation, but in principle there is no difficulty to define similar quantities in the all-valence or allelectron methods. The subject is a very broad one, and we shall here mention only a new approach to chemical reactivity based on non-empirical calculations, namely the so-called molecular isopotential maps. 

The fortunate fact that a number of the biochemical units are conjugated heterocycles has permitted the first theoretical unraveling of problems connected with their electronic structure in the framework of the 7r-electron approximation. However simple the procedures utilized, a careful analysis of the results has allowed the interpretation of a considerable body of experimental facts as well as a number of predictions later confirmed by subsequent experimentation 0. Although these results have survived the test of the successive refinements of the 7r-electron theories and have been complemented by the introduction of a simple representation of the a-framework, the possibilities of treating the a and 7r electrons simultaneously on an equal footing had to be explored in order to establish the theory on a firmer basis and also to gain further insight into some fine features of electronic properties which are otherwise inaccessible. Thus, the first outcome of the penetration of all-valence and all-electrons methods into biochemistry has been to deepen and refine previous studies. 

These a bonds, which may be constructed either from delocalized a AO s or from localized hybrid atomic orbitals, are neglected in a 7r-electron approximation for the delocalized ir system. 

In the forms (l)-(4) the density matrices are expressed in terms of the continuous variables which define the positions of the electrons. But if, as often happens, our wavefunction is compounded out of atomic orbitals (e.g., the LCAO approximation), we may find it instructive to use an AO or an MO base. An example that we shall need later is the MO ground state of butadiene, where, in the 7r-electron approximation, we fill the two mutually... 

It is evident from the chemical structure of the phenyl-based systems, shown in Fig. 1.2 and Fig. 11.3, that the phenyl ring is a key component of the structure. Since at the level of the 7r-electron approximation, phenyl and benzene rings are equivalent, a study of the electronic states of benzene provides useful insight to the electronic states of oligomers and polymers. 

A semiempirical quantum mechanical method to compute the properties of conjugated systems from SCF theory and the 7r-electron approximation. 

---