Hückel theory is a simple and powerful method for predicting the molecular orbital and the energy of conjugated molecules. However, the presence of nitrogen atoms in aza aromatic molecules alters the Coulomb and resonance integrals owing to the difference in electronegativity between nitrogen and carbon atoms. In this study, we focus on acridine and phenazine. Further correction is implemented based on the ring current model, thus revealing the change in resonance integral for the carbon-carbon bond along the bridge of the molecule. The Hamiltonian of the π-electron system in the Hückel method is solved using the HuLiS software. Various geometry-based aromaticity indices are used to obtain the aromaticity indices of the two non-equivalent rings. For further evaluation, the results for bond lengths are used to calculate the associated bond energy. Considering the carbon-hydrogen (CH) bonds, the total molecular energy is compared with the experimental heats of formation for a number of benzenoid hydrocarbons and aza aromatics, in addition to the two studied molecules. Finally, the correlation between the nitrogen atom on the aromaticity index and the ring energy content is evaluated to determine to which extent the Hückel model agrees with previous experimental and advanced computational studies. However study phenazine carboncarbon molecule πelectron π electron software geometrybased geometry nonequivalent non equivalent rings evaluation carbonhydrogen hydrogen CH (CH bonds aromatics Finally studies

Excessive degeneracy in the ground state of the π-electron energy levels of anthracene was removed using the Hückel method by correcting the Coulomb integral of the four central carbon atoms. A further correction to the resonance integral was proposed based on the ring-current model, which describes the π-ring current flow along the molecule’s perimeter, by introducing a new parameter for the bridge carbon atoms expressed as a fraction of the resonance energy. The solution to the Hamiltonian was obtained based on the symmetry group theory, which provides the advantage of solving the determinant matrix or secular equations in a particular irreducible representation with a relatively small matrix dimension. The results were further analyzed to determine the bond order and bond length. The values of the harmonic oscillator model of aromaticity, GEO, and EN indices of aromaticity and their ratio for the central and outer rings of benzene were used to evaluate the validity of the correction. Applying the same method to phenanthrene as a topological analog of anthracene allows for an interesting comparison of the stabilities of the two molecules.

In this study, we investigate the effects of nitrogen and boron dopants on the properties of phenalene/phenalenyl systems based on the Hückel theory by using the Hueckel Molecular Orbital software. The dopants configurations are graphitic, pyridinic, and pyrrolic. The electronic configuration of bare phenalene confirms the delocalization of π electrons and the radical properties of the molecule, which is in good agreement with the results of previous studies. Dopant types and positions strongly affect the number of π electrons in the system, molecular orbital energy, total energy, average π-electron energy, and gap energy. The molecular energy level degeneracy strongly depends on the rotational symmetry of the system, in the order of graphitic, pyridinic, and pyrrolic. A preserved radical behavior and the number of π electrons are found for the pyridinic dopant type, while closed electronic configuration is observed for graphitic and pyrrolic types. A lower gap energy is typically found for B-doped phenalene compared to that for N-doped phenalene; this opens the possibility for the enhancement of photoluminescence intensity. This study, although qualitative, confirms the effects of dopants on the chemical and physical properties of phenalene/phenalenyl systems.