NUMERICAL DETERMINATION OF THE KEKULE STRUCTURE COUNT OF SOME SYMMETRICAL POLYCYCLIC AROMATIC-HYDROCARBONS AND THEIR RELATIONSHIP WITH PI-ELECTRONIC ENERGY (A COMPUTATIONAL APPROACH)

The perfect matching (Kekule structure count) of certain polycyclic ar omatic hydrocarbons (benzenoids, i.e., PAH6) having mirror plane symme try is obtained through a computer program. A computer operation in th e form of an initial approximation (P, Q) is selected such that it ext racts the quadratic factors (QFs) Like (X-2 - A(i)X + B-i) and linear factors (LFs) like (X - a(i)) from the characteristic polynomials (CPs ) of the different components obtained from the mirror plane fragmenta tion technique following an energy scale. The most minimum energy fact or is extracted first, and then the next higher factor is extracted. T his process of gradual extraction of the energy factor concludes after the HOMO level of the fragment is extracted. These factors contain th e positive Huckel eigenvalues which are responsible for the Kekule str ucture count and the x-electron energy (E-pi) of the benzenoid molecul es. A(i), B-i, and a(i) are used to correlate (E-pi) and K-i of the fr agments. A linear relationship between the total pi-electronic energy of benzenoid hydrocarbons on the Kekule structure count is established : E-pi(total) = 2[Sigma(i=1)(n)(X-r)(i) + Sigma(i=1)(n)[1/(X-r)(i)]K-i + Sigma(j=1)(n)K(j)], where K-i and K-j are the parts of the total K obtained through the quadratic and linear operations, respectively, an d X-r are the positive Huckel eigenvalues extracted by the quadratic o perations. Further, n refers to all of the extracted factors, and r ma y be 1 or 2, depicting the first or the second eigenvalue extracted by the QF.