Comparability graphs and electronic spectra of condensed benzenoid hydrocarbons

A systematic topological approach to the search for regularities in molecular properties has been proposed on the basis of the so-called comparability graphs of isomeric classes of molecules. It is shown that the ordering of the isomeric benzenoid hydrocarbons in the comparability graphs coincides with that of the longest wavelenght in the p band of their electronic spectra.     

Topological hamiltonian spectra of polycyclic benzenoid hydrocarbons

A general theory which points out the relations between Hückel-electron energy, the number of Kekulé structures and the HOMO-LUMO separation is presented. Some normalized topological invariants are derived from the concept of the spectral density function. A reasonably simple (three parameters) model spectral density function leads to universal relations between topological invariants that, although valid for any alternant molecule, were tested numerically for polycyclic benzenoid hydrocarbons. Some general conclusions concerning a distribution of the adjacency matrix eigenvalues are drawn.     

On the number of benzenoid hydrocarbons

We present a new algorithm which allows a radical increase in the computer enumeration of benzenoids b(h) with h hexagons. We obtain b(h) up to h = 35. We prove that b(h) approximately const.kappa(h), prove the rigorous bounds 4.789 < or = kappa < or = 5.905, and estimate that kappa = 5.16193016(8). Finally, we provide strong numerical evidence that the generating function summation operator b(h)z(h) approximately A(z) log(1 - kappa z), estimate A(1/kappa) and predict the subleading asymptotic behavior. We also provide compelling arguments that the mean-square radius of gyration (h) of benzenoids of size h grows as h(2 nu), with nu = 0.64115(5).     

The electronic spectra of unsaturated hydrocarbons a VESCF-CI treatment

A modified Pariser-Parr method, which allows for the inductive effect of alkyl groups by a VESCF method, has been applied to the calculation of the electronic spectra of a number of hydrocarbons. All singly- and doubly-excited configurations are included in the configuration interaction treatment, except for large molecules for which the configuration interaction matrices are truncated to an order of 110. The red shifts which result from methylation of the polyenes are well calculated. For azulene, the shift to either the red or the blue, depending on the location of the substituent, is also well calculated. The largest deviation between the calculated and experimental transition energies for all of the compounds studied was 1.1 eV, while the standard deviation of all observed transitions for planar compounds was 0.24 eV. The ionization potentials and the singlet-triplet transitions of these compounds were also studied.

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Zusammenfassung Die Spektren einer Reihe von Kohlenwasserstoffen wurden nach einer modifizierten Pariser-Parr-Methode, bei der der induktive Effekt von Alkylgruppen mittels eines VESCF-Verfahrens berücksichtigt wird, berechnet, wobei alle ein- und zweifach angeregten Konfigurationen eingeschlossen wurden außer bei sehr großen Molekülen, wo deren Zahl auf 110 begrenzt wurde. Dabei ergeben sich in schöner Weise die Rotverschiebungen, die bei Methylierung von Polyenen beobachtet werden, desgleichen die Rot- und Violettverschiebungen je nach Ort des Substituenten bei Azulen. Die größten Abweichungen zwischen berechneten und beobachteten Übergangsenergien ist 1,1 eV, die Standardabweichung bei planaren Verbindungen 0,24 eV. Ferner wurden Ionisationspotentiale sowie Sigulett-Triplett-Übergänge der behandelten Verbindungen untersucht.

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Résumé Une méthode Pariser-Parr modifieé, qui tient compte de l'effet inductif des groupes alkyles dans le cadre VESCF, a été employeé pour calculer les spectres électroniques de quelques hydrocarbures. Toutes les configurations mono- et di-excitées sont comprises dans le traitement d'interaction de configurations, excepté pour les grosses molécules; pour ces dernières, l'ordre des matrices d'interaction de configuration a été réduit à 110. Les déplacements versle rouge, après methylation de polyènes, sont bien calculés. Pour l'azulène, les déplacements vers le rouge ou le bleu, suivant le lieu de substitution, sont également bien calculés. La plus grande déviation entre les énergies de transition calculée et expérimentale était de 1.1 eV pour tous les produits étudiés, alors que la déviation standard de toutes les transitions observeés était de 0,24 eV dans les composés planaires. Le potential d'ionisation et les transitions singulet-triplet ont aussi été étudiés.

     

On the electronic influence of alkyl groups in alkylferrocenes

The ¹³C NMR signals of α- and β-carbons in methyl-, ethyl-, isopropyl- and t-butyl-ferrocenes were assigned using deuterium labelling. The electronic influence of alkyl groups in alkylferrocenes is discussed.     

On dioxo derivatives of benzenoid hydrocarbons

Extending a problem occurring in connection with the stability order of the tautomers of hypericin, we examine the topological factors influencing the stability of the isomeric dioxo derivatives of benzenoid hydrocarbons, in particular the rules determining the number of Kekulé structures in them. Depending on the position of the oxo groups, the pattern of cyclic conjugation varies significantly, as does the Kekulé structure count. Some general regularities along these lines are established.     

The significance of benzenoid rings for the stability of aromatic hydrocarbons

The hitherto unknown tribenzotetracene(V) was synthesized and fitted into the series: heptacene(I), benzohexacene(II), the dibenzopentacenes III and IV, tribenzotetracene(V) and tetrabenzanthracene (VI). It is obvious that in the series I → VI the stability increases and the absorption bands shift to shorter wavelength with the number of benzenoid rings (marked with circles). In contrast to this the absorption spectra of the benzotetracenes show little change in the annellation series VII → V → VIII because the benzenoid rings were fused to double bond which are already localized.     

Enumeration and classification of benzenoid hydrocarbons

The enumeration of benzenoids is studied with the aid of different modifications of a computer program. Known values for the number of cata-condensed and of all benzenoids with h (number of hexagons) up to eight are reproduced. These benzenoids are classified into (a) unbranched of different symmetries and branched cata-condensed, and (b) normal, essentially disconnected and non-Kekuléan peri-condensed. Within the normal benzenoids a more detailed classification is performed: basic benzenoids, fused, or annelated. For h = 9 an almost complete classification along the same lines was achieved.     

Perimeter topology of benzenoid polycyclic hydrocarbons

The equivalence of the perimeter topological equations derived by Dias and the 13 possible modes of hexagon adjacency in fused benzenoid systems subsequently presented by Cyvin, Gutman, and collaborators is shown. The aufbau principle for generation of all fused total resonant sextet (TRS) benzenoid hydrocarbons is proved. The precise distinction and topological properties between fused, nonfused, strain-free, strained, helical, and nonhelical benzenoid hydrocarbons are carefully delineated. The TRS benzenoid isomers have the maximum number of bay regions, and expressions for the number of bay regions that any given TRS benzenoid will have are given.     

The electronic spectra of the alkyl,fluorine and chlorine substituted derivatives of silane

The main characteristics of the ultraviolet absorption spectra of simple alkyl, fluorine and chlorine derivatives of silane are described. The interpretation of these spectra is discussed in relation to the respective photoelectron spectra, the Rydberg-valence-shell distinction and involvement of 3d atomic orbitals.Dedicated to Professor Dr. Hermann Hartmann on the occasion of his 65th birthday.     

The effect of electronegative substituents on the electronic spectra of porphyrins

The Hückel approximation MO method is used to calculate -electron levels of energy and forces of dipole transitions, giving rise to a Soret absorption band in the spectra of porphyrins with carbethoxyl substituents. Comparison with experimental data shows that the theory correctly represents changes in electronic absorption spectra with changes in structure.     

The conjugated-circuit model: The optimum parameters for benzenoid hydrocarbons

A search for the optimum set of parameters for the conjugated-circuit computations on benzenoid hydrocarbons in reported. The SCFπ-MO resonance energies (REs) of Dewar and de Llano were used as standards for the determination ofR _n (n= l,2,3) parameters, which correspond to 4n + 2 conjugated circuits. The following set of parameters:R ₁ = 0.827 eV.R ₂ = 0.317 andR ₃ = 0.111 eV produced the best agreement between the REs calculated by the conjugated-circuit model and the REs calculated using the SCF π-MO model.     

The electronic structures and spectra of nonbenzenoid aromatic hydrocarbons containing the cyclopropenyl ring

The ground-state electronic properties and electronic spectra of triafulvene, I, triafulvalene, II, calicene, III, heptatriafulvalene, IV, benzocalicene, V, and dibenzocalicene, VI, have been studied by the semiempirical SCF CI LCAO--MO method which allows for bond order-bond length correlation at each iteration. The dependence of the resonance integral on bond length is scrutinized by trying to reproduce the properties of the ground and excited states in a series of reference compounds. For the bonds in the cyclopropenyl ring a new bond order-bond length relationship is proposed which allows for the fact that their components are bent. The calculated dipole moment and bond lengths of III and the predicted electronic spectra of III, V, and VI are in good agreement with the available experimental data.

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Zusammenfassung Grundzustand und Elektronenspektren von Triafulven, Triafulvalen, Calicen, Heptatriafulvalen, Benzocalicen und Dibenzocalicen wurden mittels eines semiempirischen SCF-Verfahrens mit Korrelation zwischen Bindungsordnung und -länge untersucht. Die Abhängigkeit des Resonanzintegrals von der Bindungslänge wurde bestimmt, indem Grund- und angeregte Zustände einer Reihe von Bezugssubstanzen zur Justierung herangezogen wurden. Für die Bindungen im Cyclopropylenring wird eine neue Beziehung zwischen Bindungsordnung und -länge vorgeschlagen, die den verzerrten -Komponenten Rechnung trägt. Die berechneten Dipolmomente und Bindungslängen von Calicen und die Spektren aller drei Calicene stimmen befriedigend mit dem Experiment überein.

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Résumé La méthode SCF-CI-LCAO--MO avec variation de la longueur de liaison en fonction de l'indice de liaison à chaque itération, a été utilisée pour l'étude des propriétés électroniques de l'état fondamental et du spectre des composés suivants: I triafulvène, II triafulvalène, III calicène, IV heptatriafulvalène, V benzocalicène, VI dibenzocalicène. La dépendance à la longueur de liaison de l'intégrale de résonance est sondée par ajustement à l'expérience de propriétés moléculaires. Pour le cyclopropylène une nouvelle relation entre longueur et indice de liaison est proposée pour tenir compte de ce que les composantes sont courbes. Le moment dipolaire et les longueurs de liaison de III et les spectres électroniques de III, V et VI sont prévus en bon accord avec les données expérimentales disponibles.

     

Additivity of resonance energy in benzenoid hydrocarbons

A simple method is described for the calculation of resonance energies (RE ) of linear acenes based on their number of Kekulé structures. The values obtained for the first five linear acenes are used to graph–theoretically calculate RES of a wide variety of benzenoid hydrocarbons. Excellent linear relationships are found between RES and each of A-II, graph-theoretical (GT ), Hess–Schaad (HS ), and Dewar resonance energies (SCF ). These relations apply to 42 hydrocarbons and lead to the following equations: A-II = 0.084RE + 0.080 (0.9999); GT = 0.072RE + 0. 135 (0.9832); HS = 0. 106RE + 0. 169 (0.9889); and SCF = 0.316RE + 0. 166 (0.9899). Correlation coefficients are shown in parentheses. A linear relation also exists between RES and the square roots of the wavelengths of the UV spectra of hydrocarbons of the linear acenes and phene series. Least-squares analysis of the data leads to the following equation: RE = 0.412(λ)^½ ?15.479, with a correlation coefficient equal to 0.9903, in which λ is the wavelength of the β band of the UV spectra of these hydrocarbons. The method predicts no resonance energies for both open chain polyenes and the radialenes.     

A unified theory of the stability of benzenoid hydrocarbons

The spectral density operator technique is proved to be a convenient tool for derivation of approximate topological formulae for total pi-electron energy (E_pi) of benzenoid hydrocarbons (BH s). Developed mathematical formalism points out a common origin of three different measures for the stability of BH s, namely: resonance energy (RE), number of Kekule structures (K) and HOMO -LUMO separation (X_HL). In turn, a novel topological invariant corresponding to “normalized” RE is derived. Numerical calculations for a representative set of BH s demonstrate effectiveness of the present approach. Various approaches to an estimation of BH stabilities are discussed.     

Resonance energy of very large benzenoid hydrocarbons

The resonance energy of conjugated benzenoid systems is expressed as contributions arising from independent conjugated circuits. The scheme has been applied to numerous very large conjugated systems. In many cases, it was possible to find regularities in the increments for the resonance energy within a family of benzenoid systems as the number of benzene rings is increased.     

A novel compact nomenclature of the condensed benzenoid hydrocarbons

Rules of a simplified nomenclature are formulated for condensed benzenoid hydrocarbons. They refer to all the hydrocarbons which could be treated as plane. In naming the hydrocarbon use is made of the numerator determining the number of rings and of the numeric code describing their immediate positional relationship. The proposed nomenclature enables quick and simple assignment of the name to the hydrocarbon and also provides a useful method for deriving the hydrocarbon structural formula from its name.     

CNDO,INDO and RCNDO-CI calculations on the electronic spectra of saturated hydrocarbons

CNDO, INDO and RCNDO (CNDO including higher (Rydberg) atomic orbitals in the basis) calculations completed by first order configuration interaction were performed on straight chain and branched chain paraffins.The results interpret reasonably the main characteristics of the observed electronic spectra. The importance of outer atomic orbitals is stressed and it is found that the first singlet-singlet transition of highly branched paraffins leads to an excited state with considerable Rydberg character.

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Zusammenfassung Rechnungen vom Typ CNDO, INDO und RCNDO (CNDO mit höheren (Rydberg) Atomorbitalen in der Basis) unter Einschluß von Konfigurationswechselwirkung 1. Ordnung wurden für unverzweigte und verzweigte gesättigte Kohlenwasserstoffe durchgeführt.Die Resultate lassen eine Deutung der Hauptcharakteristika der beobachteten Elektronen-spektren zu. Die Wichtigkeit der äußeren Atomorbitale ist zu betonen. Die ersten Singulett-Singulett-Übergänge der stark verzweigten Paraffine führen zu angeregten Zuständen mit beträchtlichem Rydbergcharakter.

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Résumé Des calculs CNDO, INDO et RCNDO (ayant des orbitales atomiques supérieures dans la base) ont été effectués sur les paraffines normales et ramifiées tenant compte de l'intéraction de configuration de premier ordre jusqu'à 30 configurations.Les résultats interprêtent d'une manière raisonnable les spectres électroniques mesurés. L'importance des orbitales atomiques supérieures apparaît clairement. La première bande observée des hydrocarbures hautement ramifiés comme le néopentane ou l'isobutane est attribuée à une transition dont l'état excité possède un fort caractère Rydberg.

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The research for this paper was supported in part by the Defense Research Board of Canada; Grant Number 9530-63.