New Keys for Old Keywords: Hybridization and Aromaticity, Graphs and Topology

  • Marilena FerbinteanuEmail author
  • Fanica Cimpoesu
  • Mihai V. Putz


Heuristic concepts of structural chemistry, like hybridization and aromaticity, that ensure the communication with chemists specialized in experimental branches, are revisited with state-of-the-art methodologies, from an original perspective. We find that the celebrated hybrids made of s and p orbitals have not fallen into caducity, as too simple for applied structural chemistry, good only for the kindergarten of elementary chemical training. Looking beyond the sp, sp2, and sp3 standard hybridization formats, exploring the meaning of s u p v differential degrees of hybridization, obtainable by means of post-computational tools of Natural Bond Orbitals (NBO) theories, meaningful lines of discussion can be drawn. Besides, the differential hybrids s u p v can be obtained in advance of calculation, on grounds of simple geometry analysis. If hybridization exists as real force (driven by the local character of electronic correlation), then the bond angles around central atoms with low site-symmetries can be interrelated. An interesting series of this sort is presented as proof of hybridization, as a non-superfluous concept. Checking the validity of hybrids made of s, p, and d functions, one finds that these cannot be invoked in Wernerian transition metal complexes (as is the case of d2sp3 octahedral hybridization), but gain relevance in organometallic systems. Here, the isolobality qualitative model, based intrinsically on the isomorphism of hybrid orbital sets from metal versus non-metal moieties, is a valuable rationalization clue for series of compounds. The concept of aromaticity is thoroughly debated, from different perspectives with various models, paying tribute to the importance of this issue and to the extremely diversified panoply of existing interpretations. With advanced multi-configuration calculations, Complete Active Space Self-Consistent Field (CASSCF) and Valence Bond (VB), followed by subsequent modeling by the Heisenberg spin Hamiltonian, that follows consistently the VB phenomenology, we dig into the causal factors of molecular geometry for the C6H6 and C4H4, taken as prototypes of aromatic and anti-aromatic behavior. It is seen then that, if only the π electrons existed, the systems would go to anti-aromatic type of bond alternating distortion, the aromaticity of benzene being secretly sustained by the strength of its σ skeleton. We present a detective story that deserves to be closely followed. Inorganic and organometallic clusters, generalizing the covering area of the aromaticity paradigm, are illustrated, with an interesting example where the theoretical prediction helps to identify specific reactivity features. The NBO frame is illustrated, by its Natural Resonance Theory (NRT) branch and specific tools of energy components analysis, as a surrogate to the VB calculations. Although the nominal meaning of resonance structures differs in the NBO versus VB computation frames (density component vs. wave function), the interpretation tempts similar heuristics. Another series of original considerations on aromaticity is constructed with reactivity criteria and on the grounds of graph theory, decorating the topological determination with meaningful parameters. It appears that aromaticity may be a tool of chemical structure and reactivity characterization while assuming for it a viable quantum definition, i.e. differently counting at molecular orbital and atoms-in-molecule chemical bonding level. Yet further insight is obtained when also the molecular topology by special adjacency in bonding is considered, within the so-called “colored” chemical reactivity by chemical topology.


Hybridization Bond angles Natural bond orbitals Isolobality Aromaticity Anti-aromaticity Valence bond Resonance structures Resonance energy Spin hamiltonian Natural resonance theory Analytical modeling Orbital deletion analysis Graph theory Chemical reactivity 


  1. Aihara J (1976) A new definition of Dewar-type resonance energies. J Am Chem Soc 98:2750–2758CrossRefGoogle Scholar
  2. Aihara J (1977) Resonance energies of benzenoid hydrocarbons. J Am Chem Soc 99:2048–2053CrossRefGoogle Scholar
  3. Aihara J, Kanno H (2005) Aromaticity of C32 fullerene isomers and the 2(N + 1)2 rule. J Mol Structure: THEOCHEM 722:111–115CrossRefGoogle Scholar
  4. Aihara J, Kanno H, Ishida T (2005) Aromaticity of planar boron clusters confirmed. J Am Chem Soc 127:13324–13330CrossRefGoogle Scholar
  5. Al-Fahemi JHA, Cooper DL, Allan NL (2009) Predictions of toxicity to Chlorella vulgaris and the use of momentum-space descriptors. Croat Chem Acta 82:311–316Google Scholar
  6. Ashrafi AR, Doslic T, Saheli M (2011) The eccentric connectivity index of TUC4C8(R) nanotubes. MATCH Commun Math Comput Chem 65:221–230Google Scholar
  7. Bader RFW (1985) Atoms in molecules. Acc Chem Res 18:9–15CrossRefGoogle Scholar
  8. Bader RFW (1990) Atoms in molecules: a quantum theory. Oxford University Press, OxfordGoogle Scholar
  9. Barbier C, Berthier G (2000) Half a century of hybridization. Adv Quant Chem 36:1–25CrossRefGoogle Scholar
  10. Barford W, Bursill RJ (2006) Effect of quantum lattice fluctuations on the Peierls broken-symmetry ground state. Phys Rev B 73:045106CrossRefGoogle Scholar
  11. Becke AD, Edgecombe KE (1990) A simple measure of electron localization in atomic and molecular systems. J Chem Phys 92:5397–5403CrossRefGoogle Scholar
  12. Beernaert H (1979) Gas chromatographic analysis of polyclylic aromatic hydrocarbons. J Chromatogr 173:109–118CrossRefGoogle Scholar
  13. Berkowitz M (1987) Density functional approach to frontier controlled reactions. J Am Chem Soc 109:4823–4825CrossRefGoogle Scholar
  14. Bersuker IB (1984) The Jahn–Teller effect and vibronic interactions in modern chemistry. Plenum Press, New YorkCrossRefGoogle Scholar
  15. Bersuker IB (2001) Modern aspects of the Jahn–Teller effect theory and applications to molecular problems. Chem Rev 101:1067–1114CrossRefGoogle Scholar
  16. Besalú E, Carbó R, Mestres J, Solà M (1995) Foundations and recent developments on molecular quantum similarity. Top Curr Chem 173:31–62CrossRefGoogle Scholar
  17. Biegler-König F, Schönbohm J, Bayles D (2001) AIM2000—A Program to Analyze and Visualize Atoms in Molecules. J Comp Chem 22:545-559Google Scholar
  18. Boldyrev AI, Wang LS (2005) All-metal aromaticity and antiaromaticity. Chem Rev 105:3716–3757CrossRefGoogle Scholar
  19. Boldyrev AI, Simons J (1998) Tetracoordinated planar carbon in penta atomic molecules. J Am Chem Soc 120:7967–7972CrossRefGoogle Scholar
  20. Bratsch SG (1985) A group electronegativity method with Pauling units. J Chem Educ 62:101–103CrossRefGoogle Scholar
  21. Bühl M, Hirsch A (2001) Spherical aromaticity of fullerenes. Chem Rev 101:1153–1184CrossRefGoogle Scholar
  22. Bultinck P, Ponec R, Gallegos A, Fias S, Van Damme S, Carbo-Dorca R (2006) Generalized Polansky Index as an aromaticity measure in polycyclic aromatic hydrocarbons. Croat Chem Acta 79:363–371Google Scholar
  23. Bultinck P, Ponec R, van Damme S (2005) Multicenter bond indices as a new measure of aromaticity in polycyclic aromatic hydrocarbons. J Phys Org Chem 18:706–718CrossRefGoogle Scholar
  24. Capponi S, Guihery N, Malrieu JP, Miguel B, Poilblanc D (1996) Bond alternation of polyacetylene as a spin-peierls distortion. Chem Phys Lett 255:238–243CrossRefGoogle Scholar
  25. Carbó R, Arnau M, Leyda L (1980) How similar is a molecule to another? An electron density measure of similarity between two molecular structures. Int J Quantum Chem 17:1185–1189CrossRefGoogle Scholar
  26. Cataldo F, Ori O, Graovac A (2011a) Graphene topological modifications. Int J Chem Model 3:45–63Google Scholar
  27. Cataldo F, Ori O, Iglesias-Groth S (2010) Topological lattice descriptors of graphene sheets with fullerene-like nanostructures. Mol Simul 36:341–353CrossRefGoogle Scholar
  28. Cataldo F, Ori O, Vukicevic D, Graovac A (2011b) Topological determination of 13C-NMR spectra of C66 fullerenes. In: Cataldo F, Graovac A, Ori O (eds) The mathematics and topology of fullerenes. Springer, Dordrecht, pp 205–216CrossRefGoogle Scholar
  29. Chattaraj PK, Sarkar U, Roy DR (2007) Electronic structure principles and aromaticity. J Chem Edu 84:354–358CrossRefGoogle Scholar
  30. Chemical Book (2011) []
  31. Chen Z, Wannere CS, Corminboeuf C, Puchta R, Schleyer PVR (2005) Nucleus-independent chemical shifts (NICS) as an aromaticity criterion. Chem Rev 105:3842–3888CrossRefGoogle Scholar
  32. Ciesielski A, Krygowski TM, Cyranski MK, Dobrowolski MA, Balaban AT (2009) Are thermodynamic and kinetic stabilities correlated? A topological index of reactivity toward electrophiles used as a criterion of aromaticity of polycyclic benzenoid hydrocarbons. J Chem Inf Model 49:369–376CrossRefGoogle Scholar
  33. Cimpoesu F, Chihaia V, Stanica N, Hirao K (2003) The spin Hamiltonian effective approach to the vibronic effects-selected cases. Adv Quantum Chem 44:273–288CrossRefGoogle Scholar
  34. Cimpoesu F, Hirao K, Ferbinteanu M, Fukuda Y, Linert W (2005) New keys for old keywords: case studies within the updated paradigms of the hybridization and aromaticity. Monatsh Chem 136:1071–1185CrossRefGoogle Scholar
  35. Cioslowski J, Matito E, Solà M (2007) Properties of aromaticity indices based on the one-electron density matrix. J Phys Chem A 111:6521–6525CrossRefGoogle Scholar
  36. Clar E (1964) Polycyclic Hydrocarbons. Academic Press, LondonCrossRefGoogle Scholar
  37. Coulson CA, O’Leary B, Mallion RB (1978) Hückel theory for organic chemists. Academic Press, LondonGoogle Scholar
  38. Coulson CA, Moffitt WE (1949) The properties of certain strained hydrocarbons. Philos Mag 40:1–35CrossRefGoogle Scholar
  39. Dapprich S, Frenking G (1995) Investigation of donor-acceptor interactions: a charge decomposition analysis using fragment molecular orbitals. J Phys Chem 99:9352–9362CrossRefGoogle Scholar
  40. Dauben HJ Jr, Wilson JD, Laity JL (1968) Diamagnetic susceptibility exaltation as a criterion of aromaticity. J Am Chem Soc 90:811–813CrossRefGoogle Scholar
  41. Dewar MSJ, de Llano C (1969) Ground states of conjugated molecules. XI. Improved treatment of hydrocarbons. J Am Chem Soc 91:789–795CrossRefGoogle Scholar
  42. Doering WV, Detert F (1951) Cycloheptatrienylium oxide. J Am Chem Soc 73:876–877CrossRefGoogle Scholar
  43. Doslic T, Graovac A, Ori O (2011) Eccentric connectivity index of hexagonal belts and chains. MATCH Commun Math Comput Chem 65:745–752Google Scholar
  44. Doslic T, Saheli M, Vukicevic D (2010) Eccentric connectivity index: extremal graphs and values. Iranian J Math Chem 1:45–55Google Scholar
  45. Duchowicz PR, Bucknum MJ, Castro EA (2007) New molecular descriptors based upon the Euler equations for chemical graphs. J Math Chem 41:193–208CrossRefGoogle Scholar
  46. Dureja H, Madan AK (2007) Superaugmented eccentric connectivity indices: new-generation highly discriminating topological descriptors for QSAR/QSPR modelling. Med Chem Res 16:331–341CrossRefGoogle Scholar
  47. Elian M, Chen MML, Mingos DMP, Hoffmann R (1976) Comparative bonding study of conical fragments. Inorg Chem 15:1148–1155CrossRefGoogle Scholar
  48. Elian M, Hoffmann R (1975) Bonding capabilities of transition metal carbonyl fragments. Inorg Chem 14:1058–1076CrossRefGoogle Scholar
  49. Engel E, Ratel J (2007) Correction of the data generated by mass spectrometry analyses of biological tissues: application to food authentication. J Chromatogr A 1154:331–341CrossRefGoogle Scholar
  50. Erlenmeyer E (1866) Studien über die s. g. aromatischen Säuren. Liebigs Ann Chem 137:327–359CrossRefGoogle Scholar
  51. Feixas F, Matito E, Poater J, Solà M (2008) On the performance of some aromaticity indices: a critical assessment using a test set. J Comput Chem 29:1543–1554CrossRefGoogle Scholar
  52. Ferbinteanu M, Roesky HW, Cimpoesu F, Atanasov M, Kopke S, Herbst-Irmer R (2001) New synthetic and structural aspects in the chemistry of alkylaluminum fluorides: the mutual influence of hard and soft ligands and the hybridization as rigorous structural criterion. Inorg Chem 40:4947–4955CrossRefGoogle Scholar
  53. Fradera X, Solà M (2002) Electron localization and delocalization in open-shell molecules. J Comput Chem 23:1347–1356CrossRefGoogle Scholar
  54. Fuchs JN, Lederer P (2007) Spontaneous parity breaking of graphene in the quantum hall regime. Phys Rev Lett 98:016803CrossRefGoogle Scholar
  55. Garciabach MA, Blaise P, Malrieu JP (1992) Dimerization of polyacetylene treated as a spin-Peierls distortion of the Heisenberg Hamiltonian. Phys Rev B: Condens Matter 46:15645–15651CrossRefGoogle Scholar
  56. Geerts Y, Klärner G, Müllen K (1998) Hydrocarbon oligomers. In: Müllen K, Wagner G (eds) Electronic materials: the oligomer approach. Wiley-VCH, Weinheim, pp 1–103Google Scholar
  57. Giambiagi M, de Giambiagi MS, dos Santos CD, de Figueiredo AP (2000) Multicenter bond indices as a measure of aromaticity. Phys Chem Chem Phys 2:3381–3392CrossRefGoogle Scholar
  58. Glendening ED, Badenhoop JK, Weinhold F (1998) Natural resonance theory: III. Chemical applications. J Comput Chem 19:628–646CrossRefGoogle Scholar
  59. Glendening ED, Reed AE, Carpenter JE, Weinhold F. The NBO3.0 program, University of Wisconsin, Copyright 1996–2001Google Scholar
  60. Glendening ED, Weinhold F (1998a) Natural resonance theory: I. General formalism. J Comput Chem 19:593–609CrossRefGoogle Scholar
  61. Glendening ED, Weinhold F (1998b) Natural resonance theory: II. Natural bond order and valency. J Comput Chem 19:610–627CrossRefGoogle Scholar
  62. Graovac A, Gutman I, Randi M, Trinajsti N (1973) Kekulé index for valence bond structures of conjugated polycyclic systems. J Am Chem Soc 95:6267–6273CrossRefGoogle Scholar
  63. Guihery N, Benamor N, Maynau D, Malrieu JP (1996) Approximate size-consistent treatments of Heisenberg Hamiltonians for large systems. J Chem Phys 104:3701–3708CrossRefGoogle Scholar
  64. Gutman I, Milun M, Trinajstic N (1977) Graph theory and molecular orbitals. 19. Nonparametric resonance energies of arbitrary conjugated systems. J Am Chem Soc 99:1692–1704CrossRefGoogle Scholar
  65. Hess BA, Schaad LJ (1971) Hückel molecular orbital π; resonance energies: benzenoid hydrocarbons. J Am Chem Soc 93:2413–2416CrossRefGoogle Scholar
  66. Hirsch A, Chen Z, Jiao H (2001a) Spherical aromaticity of inorganic cage molecules. Angew Chem Int Ed 40:2834–2838CrossRefGoogle Scholar
  67. Hirsch A, Chen Z, Jiao H (2001b) Spherical aromaticity of inorganic cage molecules. Angew Chem 113:2916–2920CrossRefGoogle Scholar
  68. Hoffman R (1982) Building bridges between inorganic and organic chemistry (Nobel Lecture). Angew Chem Int Ed 21:711–724CrossRefGoogle Scholar
  69. Hollas B, Gutman I, Trinajstić N (2005) On reducing correlations between topological indices. Croat Chem Acta 78:489–492Google Scholar
  70. Hückel E (1931a) Quantentheoretische beiträge zum benzolproblem. I. Die elektronenkonfiguration des benzols und verwandter verbindungen. Z Physik 70:204–286CrossRefGoogle Scholar
  71. Hückel E (1931b) Quanstentheoretische beiträge zum benzolproblem. II. Quantentheorie der induzierten polaritäten. Z Physik 72:310–337Google Scholar
  72. Hückel E (1932) Quantentheoretische beiträge zum Problem der aromatischen und ungesättigten Verbindungen. III. Z Physik 76:628–648CrossRefGoogle Scholar
  73. Hypercube (2002) Program Package, HyperChem 7.01; Hypercube Inc., Gainesville, FLGoogle Scholar
  74. Iranmanesh A, Ashrafi AR, Graovac A, Cataldo F, Ori O (2012) Wiener index role in topological modeling of hexagonal systems: from fullerenes to grapheme. In: Gutman I, Furtula B (eds) Distance in molecular graphs. University of Kragujevac and Faculty of Science, Kragujevac, pp 135–155Google Scholar
  75. Jemmis ED, Balakrishnarajan MM, Rabcharatna D (2002) Electronic requirements for macropolyhedral boranes. Chem Rev 102:93–114CrossRefGoogle Scholar
  76. Julg A, Françoise P (1967) Recherches sur la géométrie de quelques hydrocarbures non-alternants: son influence sur les énergies de transition, une nouvelle définition de l’aromaticité. Theor Chem Acta 8:249–259CrossRefGoogle Scholar
  77. Katritzky AR, Jug K, Oniciu DC (2001) Quantitative measures of aromaticity for mono-, bi-, and tricyclic penta- and hexaatomic heteroaromatic ring systems and their interrelationships. Chem Rev 101:1421–1450CrossRefGoogle Scholar
  78. Katritzky AR, Topson RD (1971) The σ- and π- inductive effects. J Chem Edu 48:427–431CrossRefGoogle Scholar
  79. Kekulé A (1865) Sur la constitution des substances aromatiques. Bull Soc Chim Fr 3:98–110Google Scholar
  80. King RB (2001) Three-dimensional aromaticity in polyhedral boranes and related molecules. Chem Rev 101:1119–1152CrossRefGoogle Scholar
  81. King RB (2003) Metal cluster topology. 21. Sigma aromaticity in triangular metal carbonyl clusters. Inorg Chim Acta 350:126–130CrossRefGoogle Scholar
  82. Koch W, Holthausen MC (2001) A chemist’s guide to density functional theory. Wiley-VCH, WeinheimCrossRefGoogle Scholar
  83. Komninos Y, Nicolaides CA (1999) Molecular shape, shape of the geometrically active atomic states, and hybridization. Int J Quant Chem 71:25–34CrossRefGoogle Scholar
  84. Kruszewski J, Krygowski TM (1972) Definition of aromaticity basing on the harmonic oscillator model. Tetrahedron Lett 13:3839–3842CrossRefGoogle Scholar
  85. Krygowski TM (1993) Crystallographic studies of inter- and intramolecular interactions reflected in aromatic character of π-electron systems. J Chem Inf Comput Sci (actually J Chem Inf Model) 33:70–78CrossRefGoogle Scholar
  86. Krygowski TM, Cyranski MK, Czarnocki Z, Häfelinger G, Katritzky AR (2000) Aromaticity: a theoretical concept of immense practical importance. Tetrahedron 56:1783–1796CrossRefGoogle Scholar
  87. Kumar V, Sardana S, Madan AK (2004) Predicting anti-Hiv activity of 2,3-Diaryl-1,3-Thiazolidin-4-Ones: computational approach using reformed eccentric connectivity index. J Mol Model 10:399–407CrossRefGoogle Scholar
  88. Landis CR, Cleveland T, Firman TK (1995) Making sense of the shapes of simple metal hydrides. J Am Chem Soc 117:1859–1860CrossRefGoogle Scholar
  89. Langenbach HJ, Keller E, Vahrenkamp H (1980) Reaktivität von metall—metall-bindungen. Vierkernkomplexe mit kettenförmiger anordnung von metall- und brükenatomen. J Organomet Chem 191:95–106CrossRefGoogle Scholar
  90. Li X, Kuznetsov AE, Zhang HF, Boldyrev AI, Wang LS (2001) Observation of all-metal aromatic molecule. Science 291:859–861CrossRefGoogle Scholar
  91. Mallion RB (2008) Topological ring-currents in condensed benzenoid hydrocarbons. Croat Chem Acta 81:227–246Google Scholar
  92. Maretti L, Ferbinteanu M, Cimpoesu F, Islam SM, Ohba Y, Kajiwara T, Yamashita M, Yamauchi S (2007) Spin coupling in the supramolecular structure of a new tetra(quinoline TEMPO)yttrium(III) complex. Inorg Chem 46:660–669CrossRefGoogle Scholar
  93. Matito E, Duran M, Solà M (2005a) The aromatic fluctuation index (FLU): a new aromaticity index based on electron delocalization. J Chem Phys 122:014109CrossRefGoogle Scholar
  94. Matito E, Poater J, Duran M, Solà M (2005b) An analysis of the changes in aromaticity and planarity along the reaction path of the simplest Diels-Alder reaction: exploring the validity of different indicators of aromaticity. J Mol Struc: THEOCHEM 727:165–171CrossRefGoogle Scholar
  95. Matito E, Salvador P, Duran M, Solà M (2006) Aromaticity measures from fuzzy-atom bond orders (FBO): the aromatic fluctuation (FLU) and the para-delocalization (PDI) indexes. J Phys Chem A 110:5108–5113CrossRefGoogle Scholar
  96. McKee ML, Wang ZX, PvR Schleyer (2000) Ab initio study of the hypercloso boron hydrides BnHn and BnHn-: exceptional stability of neutral B13H13. J Am Chem Soc 122:4781–4793CrossRefGoogle Scholar
  97. McWeeny R (1979) Coulson’s valence. Oxford University Press, OxfordGoogle Scholar
  98. Mingos DMP (1984) Polyhedral skeletal electron pair approach. Acc Chem Res 17:311–319CrossRefGoogle Scholar
  99. Minkin VI, Glukhovtsev MN, Simkin BY (1994) Aromaticity and antiaromaticity. Wiley, New YorkGoogle Scholar
  100. Moran D, Simmonett AC, Leach FE III, Allen WD, PvR Schleyer, Schaefer HF III (2006) Popular theoretical methods predict benzene and arenes to be nonplanar. J Am Chem Soc 128:9342–9343CrossRefGoogle Scholar
  101. Mulliken RS (1965) Molecular scientists and molecular science: some reminiscences. J Chem Phys 43:S2–S11CrossRefGoogle Scholar
  102. Nalewajski RF (1998) Kohn-Sham description of equilibria and charge transfer in reactive systems. Int J Quantum Chem 69:591–605CrossRefGoogle Scholar
  103. Nicolaides CA, Komninos Y (1998) Geometrically active atomic states and the formation of molecules in their normal shapes. Int J Quant Chem 67:321–328CrossRefGoogle Scholar
  104. Nikolic S, Milicevic A, Trinajstic N (2006) QSPR study of polarographic half-wave reduction potentials of benzenoid hydrocarbons. Croat Chem Acta 79:155–159Google Scholar
  105. Oda J, Yasuhara A, Matsunaga K, Saito Y (1998) Identification of polycyclic aromatic hydrocarbons of the particulate accumulated in the tunnel duct of freeway and generation of their oxygenated derivatives. Jpn J Toxicol Environ Health 44:334–351CrossRefGoogle Scholar
  106. Ori O, D’Mello M (1992) A topological study of the structure of the C76 fullerene. Chem Phys Lett 197:49–54CrossRefGoogle Scholar
  107. Ori O, D’Mello M (1993) Analysis of the structure of the C78 fullerene: a topological approach. Appl Phys A Solids Surf 56:35–39CrossRefGoogle Scholar
  108. Parr RG, Yang W (1984) Density functional approach to the frontier electron theory of chemical reactivity. J Am Chem Soc 106:4049–4050CrossRefGoogle Scholar
  109. Pauling L, Sherman J (1933) The nature of the chemical bond. VI. The calculation from thermochemical data of the energy of resonance of molecules among several electronic structures. J Chem Phys 1:606–618CrossRefGoogle Scholar
  110. Pauling L, Wheland GW (1933) The nature of the chemical bond. V. The quantum-mechanical calculation of the resonance energy of benzene and naphthalene and the hydrocarbon free radicals. J Chem Phys 1:362–375CrossRefGoogle Scholar
  111. Poater J, Duran M, Solà M (2001) Parametrization of the Becke3-LYP hybrid functional for a series of small molecules using quantum molecular similarity techniques. J Comput Chem 22:1666–1678CrossRefGoogle Scholar
  112. Poater J, Fradera X, Duran M, Solà M (2003) An insight into the local aromaticities of polycyclic aromatic hydrocarbons and fullerenes. Chem Eur J 9:1113–1122CrossRefGoogle Scholar
  113. Putz MV (2006) Systematic formulation for electronegativity and hardness and their atomic scales within density functional softness theory. Int J Quantum Chem 106:361–386CrossRefGoogle Scholar
  114. Putz MV (2008) Absolute and chemical electronegativity and hardness. NOVA Publishers, New YorkGoogle Scholar
  115. Putz MV (2010a) On absolute aromaticity within electronegativity and chemical hardness reactivity pictures. MATCH Commun Math Comput Chem 64:391–418Google Scholar
  116. Putz MV (2010b) Compactness aromaticity of atoms in molecules. Int J Mol Sci 11:1269–1310CrossRefGoogle Scholar
  117. Putz MV (2011a) Electronegativity and chemical hardness: different patterns in quantum chemistry. Curr Phys Chem 1:111–139CrossRefGoogle Scholar
  118. Putz MV (2011b) Quantum parabolic effects of electronegativity and chemical hardness on carbon π-systems. In: Putz MV (ed) Carbon bonding and structures: advances in physics and chemistry. Springer, London, pp 1–32CrossRefGoogle Scholar
  119. Putz MV (2012) Chemical orthogonal spaces. Mathematical Chemistry Monographs 14. University of Kragujevac and Faculty of Science, KragujevacGoogle Scholar
  120. Putz MV (2016a) Quantum nanochemistry: a fully integrated approach. Vol. II: quantum atoms and periodicity. Apple Academic Press & CRC Press, TorontoGoogle Scholar
  121. Putz MV (2016b) Quantum nanochemistry: a fully integrated approach. Vol. III: quantum molecules and reactivity. Apple Academic Press & CRC Press, TorontoGoogle Scholar
  122. Putz MV, Ori O, Cataldo F, Putz AM (2013a) Parabolic reactivity “coloring” molecular topology: application to carcinogenic PAHs. Curr Org Chem 17:2816–2830CrossRefGoogle Scholar
  123. Putz MV, Ori O, De Corato M, Putz AM, Benedek G, Cataldo F, Graovac A (2013b) Introducing “colored” molecular topology by reactivity indices of electronegativity and chemical hardness. In: Cataldo F, Iranmanesh A, Ori O (eds) Topological modeling of nanostructures and extended systems, AR. Springer, Dordrecht, pp 265–286CrossRefGoogle Scholar
  124. Putz MV, Russo N, Sicilia E (2003) Atomic radii scale and related size properties from density functional electronegativity formulation. J Phys Chem A 107:5461–5465CrossRefGoogle Scholar
  125. Putz MV, Russo N, Sicilia E (2004) On the application of the HSAB principle through the use of improved computational schemes for chemical hardness evaluation. J Comp Chem 25:994–1003CrossRefGoogle Scholar
  126. Putz MV, Tudoran MA, Putz AM (2013c) Structure properties and chemical-bio/ecological of PAH interactions: from synthesis to cosmic spectral lines, nanochemistry, and lipophilicity-driven reactivity. Curr Org Chem 17:2845–2871CrossRefGoogle Scholar
  127. Randić M (1977) Aromaticity and conjugation. J Am Chem Soc 99:444–450CrossRefGoogle Scholar
  128. Reed AE, Curtiss LA, Weinhold F (1988) Intermolecular interactions from a natural bond orbital, donor-acceptor viewpoint. Chem Rev 88:899–926CrossRefGoogle Scholar
  129. Root DM, Landis CR, Cleveland T (1993) Valence bond concepts applied to the molecular mechanics description of molecular shapes. 1. Application to nonhypervalent molecules of the P-block. J Am Chem Soc 115:4201–4209CrossRefGoogle Scholar
  130. Rouvray DH (1975) The chemical application of graph theory. MATCH Commun Math Comput Chem 1:61–70Google Scholar
  131. Rubin SG, Khosla PK (1977) Polynomial interpolation methods for viscous flow calculations. J Comp Phys 24:217–244CrossRefGoogle Scholar
  132. Ruedenberg KJ (1954) Free-electron network model for conjugated systems. V. Theoretical equivalence with the LCAO MO model. Chem Phys 22:1878–1895Google Scholar
  133. Rzepa HS (2007) The aromaticity of pericyclic reaction transition states. J Chem Edu 84:1535–1540CrossRefGoogle Scholar
  134. Saebo S, Pulay P (1993) Local treatment of electron correlation. Ann Rev Phys Chem 44:213–236CrossRefGoogle Scholar
  135. Said M, Maynau D, Malrieu JP (1984) Excited-state properties of linear polyenes studied through a nonempirical Heisenberg Hamiltonian. J Am Chem Soc 106:580–587CrossRefGoogle Scholar
  136. Salem L (1966) The molecular orbital theory of conjugated systems. Benjamin, New YorkGoogle Scholar
  137. Santos JC, Andres JL, Aizman A, Fuentealba P (2005) An aromaticity scale based on the topological analysis of the electron localization function including σ and π contributions. J Chem Theor Comput 1:83–86CrossRefGoogle Scholar
  138. Savin A, Nesper R, Wengert S, Fässler TF (1997) ELF: the electron localization function. Angew Chem Int Ed 36:1808–1832CrossRefGoogle Scholar
  139. PvR Schleyer, Jiao H (1996) What is aromaticity? Pure Appl Chem 68:209–218CrossRefGoogle Scholar
  140. PvR Schleyer, Maerker C, Dransfeld A, Jiao H, Eikema Hommes NJRV (1996) Nucleus-independent chemical shifts: a simple and efficient aromaticity probe. J Am Chem Soc 118:6317–6318CrossRefGoogle Scholar
  141. PvR Schleyer, Najafian K (1994) Are polyhedral boranes, carboranes, and carbocatins aromatic? In: Casanova J (ed) The borane, carborane, carbocation continuum. Wiley, New York, pp 169–190Google Scholar
  142. PvR Schleyer, Najafian K (1998) Stability and three-dimensional aromaticity of closo-monocarbaborane anions, CB(n)()(-)(1)H(n)(-), and closo-Dicarboranes, C(2)B(n)()(-)(2)H(n)(). Inorg Chem 37:3454–3470CrossRefGoogle Scholar
  143. Schutz M, Hetzer G, Werner HJ (1999) Low-order scaling local electron correlation methods. I. Linear scaling local MP2. J Chem Phys 111:5691–5705CrossRefGoogle Scholar
  144. Shaik S, Shurki A, Danovich D, Hiberty PC (2001) A different story of π-delocalization: the distortivity of π-electrons and its chemical manifestations. Chem Rev 101:1501–1540CrossRefGoogle Scholar
  145. Sharma V, Goswami R, Madan AK (1997) Eccentric connectivity index: a novel highly discriminating topological descriptor for structure property and structure activity studies. J Chem Inf Comput Sci 37:273–282CrossRefGoogle Scholar
  146. Shuai Z, Bredas JL (2000) Coupled-cluster approach for studying the electronic and nonlinear optical properties of conjugated molecules. Phys Rev B 62:15452–15460CrossRefGoogle Scholar
  147. Silvi B, Savin A (1994) Classification of chemical bonds based on topological analysis of electron localization functions. Nature 371:683–686CrossRefGoogle Scholar
  148. Solà M, Mestres J, Carbó R, Duran M (1994) Use of ab initio quantum molecular similarities as an interpretative tool for the study of chemical reactions. J Am Chem Soc 116:5909–5915CrossRefGoogle Scholar
  149. Song C, Lai W-C, Madhusudan Reddy K, Wei B (2003) Temperature-programmed retention indices for GC and GC-MS of hydrocarbon fuels and simulated distillation GC of heavy oils. In: Hsu CS (ed) Analytical advances for hydrocarbon research. Kluwer Academic/Plenum Publishers, New York, pp 147–193CrossRefGoogle Scholar
  150. Stasch A, Ferbinteanu M, Prust J, Zheng W, Cimpoesu F, Roesky HW, Magull J, Schmidt HG, Noltemeyer M (2002) Syntheses, structures, and surface aromaticity of the new carbaalane [(AlH)6(AlNMe3)2(CCH2R)6] (R = Ph, CH2SiMe3) and a stepwise functionalization of the inner and outer sphere of the cluster. J Am Chem Soc 124:5441–5448CrossRefGoogle Scholar
  151. Stephens FG (1974) Crystal and molecular structure of di-µ-carbonyl-dicarbonyl(triethyl-phosphine)cobalt(π-cyclopentadienylnickel). J Chem Soc, Dalton Trans 10:1067–1070CrossRefGoogle Scholar
  152. Summer GG, Klug HP, Alexander LE (1964) The crystal structure of dicobalt octacarbonyl. Acta Crystallogr 17:732–742CrossRefGoogle Scholar
  153. Tanaka H, Neukermans S, Janssens E, Silverans RE, Lievens P (2003) Aromaticity of the bimetallic Au5Zn + cluster. J Am Chem Soc 125:2862–2863CrossRefGoogle Scholar
  154. Tarko L (2008) Aromatic molecular zones and fragments. ARKIVOC 11:24–45Google Scholar
  155. Tarko L, Putz MV (2010) On electronegativity and chemical hardness relationships with aromaticity. J Math Chem 47:487–495CrossRefGoogle Scholar
  156. Thomson JJ (1921) On the structure of the molecule and chemical combination. Philos Mag 41:510–538CrossRefGoogle Scholar
  157. Todeschini R, Consonni V (2000) Handbook of molecular descriptors. Wiley-VCH, WeinheimCrossRefGoogle Scholar
  158. Trauzettel B, Bulaev DV, Loss D, Burkard G (2007) Spin qubits in graphene quantum dots. Nat Phys 3:192–196CrossRefGoogle Scholar
  159. Trinajstić N, Gutman I (1975) Some aspects of graph spectral theory of conjugated molecules. MATCH Commun Math Comput Chem 1:71–82Google Scholar
  160. Tudoran MA, Putz MV (2015) Molecular graph theory: from adjacency information to colored topology by chemical reactivity. Curr Org Chem 19:358–385CrossRefGoogle Scholar
  161. Vukicevic D, Lukovits I, Trinajstic N (2006) Counting Kekulé structures of benzenoid parallelograms containing one additional benzene ring. Croat Chem Acta 79:509–512Google Scholar
  162. Wade K (1971) The structural significance of the number of skeletal bonding electron-pairs in carboranes, the higher boranes and borane anions, and various transition-metal carbonyl cluster compounds. J Chem Soc D Chem Commun 15:792–793CrossRefGoogle Scholar
  163. Wade K (1976) Structural and bonding patterns in cluster chemistry. Adv Inorg Chem Radiochem 18:1–66CrossRefGoogle Scholar
  164. Weinhold F, Landis CR (2005) valency and bonding: a natural bond orbital donor-acceptor perspective. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  165. Wheland GW (1944) The theory of resonance and its application to organic chemistry. Wiley, New YorkGoogle Scholar
  166. Wiener H (1947) Structural determination of paraffin boiling points. J Am Chem Soc 69:17–20CrossRefGoogle Scholar
  167. Yang W, Parr RG (1985) Hardness, softness, and the Fukui function in the electronic theory of metals and catalysis. Proc Natl Acad Sci USA 82:6723–6726CrossRefGoogle Scholar
  168. Yang W, Parr RG, Pucci R (1984) Electron density, Kohn-Sham frontier orbitals, and Fukui functions. J Chem Phys 81:2862–2863CrossRefGoogle Scholar
  169. Zeng Y-X, Zhao C-X, Liang Y-Z, Yang H, Fang H-Z, Yi L-Z, Zeng Z-D (2007) Comparative analysis of volatile components from Clematis species growing in China. Ann. Chim Acta 595:328–339CrossRefGoogle Scholar
  170. Zhou B, Trinajstic N (2008) Bounds on the Balaban Index. Croat Chem Acta 81:319–323Google Scholar
  171. Zhou B, Trinajstic N (2010) Mathematical properties of molecular descriptors based on distances. Croat Chem Acta 83:227–242Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Marilena Ferbinteanu
    • 1
    Email author
  • Fanica Cimpoesu
    • 2
  • Mihai V. Putz
    • 3
  1. 1.Department of Inorganic ChemistryUniversity of BucharestBucharestRomania
  2. 2.Institute of Physical Chemistry “Ilie Murgulescu”BucharestRomania
  3. 3.West University of Timişoara & National Institute of Research and Development for Electrochemistry and Condensed Matter Timişoara (INCEMC)TimişoaraRomania

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