Directed toward the Development of a Unified Structure Theory of Polycyclic Conjugated Hydrocarbons: The Aufbau Principle in Structure/Similarity Studies

SUMMARY By the unique coupling of the aufbau principle andstrongly subspectral relationship, a new tool for similarityevaluation of ð -electronic molecular systems has been de-veloped. End effects of some types of ð -electronic polymerstrips have been interpreted, and examples of infinite polymerstrips that are complementary 2 have been presented. REFERENCES AND NOTES (1) Hall, G. G. The Bond Orders of Some Conjugated Molecules.Trans. Faraday Soc. 1957, 53, 573-581; Eigenvalues of MolecularGraphs. Bull. Inst. Math Appl. 1981, 17,70-72; Eigenvalue Dis-tributions in Alternant Hydrocarbons. J. Math. Chem. 1993, 13, 191-203.(2) McClelland, B. J. Graphical Method for Factorizing Secular Deter-minants of Huckel Molecular Orbital Theory. J. Chem. Soc., FaradayTrans. 2 1974, 70, 1453-1456; Eigenvalues of the Topological Matrix.J. Chem. Soc., Faraday Trans. 2 1982, 78, 911-916; On the GraphicalFactorization of Huckel Characteristic Equations. Mol. Phys. 1982,45, 189-190. Dias, J. R. Properties and Relationships of Right-HandMirror-Plane Fragments and Their Eigenvectors: the Concept ofComplementarity of Molecular Graphs. Mol. Phys. 1996, 88, 407-417.(3) Dias, J. R. Molecular Orbital Calculations Using Chemical GraphTheory; Springer: Berlin, 1993.(4) Trinajstic´, N.Chemical Graph Theory; CRC Press: Boca Raton, FL,1992.(5) Dias, J. R. A Formula Periodic Table for Benzenoid Hydrocarbonsand the Aufbau and Excised Internal Structure Concepts in BenzenoidEnumeration. Z. Naturforsch. 1989, 44a, 765-771; J. Math. Chem.1990, 4,17-29.(6) Dias, J. R. Benzenoids to Fullerenes and the Circumscribing Algorithm.Chem. Phys. Lett. 1993, 209, 439-444; Algorithm for GeneratingFullerenes by Circumscribing. J. Chem. Inf. Comput. Sci. 1994, 34,248-251.(7) Dias, J. R. The Characteristic Polynomial and 1-Factorable and2-Factorable Graph Structures Associated with Benzenoid Hydrocar-bons. NouV. J. Chim. 1985, 9, 125-134.(8) Dias, J. R. Almost-Isospectral Conjugated Polyene Molecules.Chem.Phys. Lett. 1996, 253, 305-312; Dias, J. R. Techniques in FacileCalculation of Molecular Orbital Parameters and Related Conceptu-alizations. J. Mol. Struct. (THEOCHEM) 1997, 417,49-67.(9) Dias, J. R. Strongly Subspectral Conjugated Molecular Systems. FromSmall Molecules to Infinitely Large Electronic Networks. J. Phys.Chem. A 1997, 101, 7167-175.(10) Morales, D. A. On the Calculation of a Limit for Infinite Systemsfrom Data on Finite Systems. Theor. Chem. Acc. 1997, 98,65-67.Randic´, M.; Klein, D. J.; Zhu, H.-Y.; Trinajstic´, N.; Zivkovic, T.Comparative Study of Large Molecules. Highly Accurate Calculationof a Limit for Infinite Systems from Data on Finite Systems. Theor.Chim. Acta 1995, 90,1-19.(11) Koenig, T.; Wielesek, R.; Snell, W.; Balle, T. Helium(I) PhotoelectronSpectrum of p-Quinodimethane.J. Am. Chem. Soc. 1975, 97, 3225-3226.(12) Skattebol, L.; Charlton, J. L.; deMayo, P. Tetravinylethylene. Tetra-hedron Lett. 1966, 2257-2260.(13) Chakrabarti, A.; Anusooya, Y.; Ramasesha, S. Properties of theCorrelated Electronic States of Pyrene and Hydrogenated Pyrene. Mol.Phys. 1996, 89, 1019-1032.(14) Dias, J. R. Dias Isomer Enumeration and Topological Characteris-tics of Benzenoid Quinones. J. Chem. Inf. Comput. Sci. 1990, 30,53-61.