## Abstract

The perfect matching (Kekulé structure count) of certain polycyclic aromatic hydrocarbons (benzenoids, i.e., PAH6) having mirror plane symmetry is obtained through a computer program. A computer operation in the form of an initial approximation (P, Q) is selected such that it extracts 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 fragmentation technique following an energy scale. The most minimum energy factor is extracted first, and then the next higher factor is extracted. This process of gradual extraction of the energy factor concludes after the HOMO level of the fragment is extracted. These factors contain the positive Hückel eigenvalues which are responsible for the Kekulé structure count and the π-electron energy (E_{π}) of the benzenoid molecules. A_{i}, B_{i}, and a_{i} are used to correlate (E_{π})_{i} and K_{i} of the fragments. A linear relationship between the total π-electronic energy of benzenoid hydrocarbons on the Kekulé structure count is established: E_{π}(total) = 2[Σ_{i=1} ^{n}(X_{r})_{i} + Σ_{i=1} ^{n}[1/(X_{r})_{i}]K_{i} + Σ_{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, and X_{r} are the positive Hückel eigenvalues extracted by the quadratic operations. Further, n refers to all of the extracted factors, and r may be 1 or 2, depicting the first or the second eigenvalue extracted by the QF.

Original language | English (US) |
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Pages (from-to) | 113-124 |

Number of pages | 12 |

Journal | Journal of Chemical Information and Computer Sciences |

Volume | 38 |

Issue number | 2 |

State | Published - Mar 1 1998 |

## ASJC Scopus subject areas

- Chemistry(all)
- Information Systems
- Computer Science Applications
- Computational Theory and Mathematics