Coronoids, patches and generalised altans Bašić, Nino; Fowler, Patrick W.; Pisanski, Tomaž
Journal of mathematical chemistry,
04/2016, Letnik:
54, Številka:
4
Journal Article
Recenzirano
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In this paper we revisit coronoids, in particular multiple coronoids. We consider a mathematical formalisation of the theory of coronoid hydrocarbons that is solely based on incidence between ...hexagons of the infinite hexagonal grid in the plane. In parallel, we consider perforated patches, which generalise coronoids: in addition to hexagons, other polygons may also be present. Just as coronoids may be considered as benzenoids with holes, perforated patches are patches with holes. Both cases, coronoids and perforated patches, admit a generalisation of the altan operation that can be performed at several holes simultaneously. A formula for the number of Kekulé structures of a generalised altan can be derived easily if the number of Kekulé structures is known for the original graph. Pauling Bond Orders for generalised altans are also easy to derive from those of the original graph.
Limitations of Pauling Bond Order Concept Vukičević, Damir; Đurđević, Jelena; Gutman, Ivan
Polycyclic aromatic compounds,
20/1/1/, Letnik:
32, Številka:
1
Journal Article
Recenzirano
It is shown that Kekulé structures do not realistically predict the behavior of π-electron properties of those polycyclic hydrocarbons that have many fixed double bonds. This is caused by the fact ...that such molecules would be destabilized by delocalization. We analyze a group of polycyclic hydrocarbons with a large number of fixed bonds, whose geometry was determined by means of an unrestricted symmetry-broken UB3LYP/6-311G(d,p) DFT method. We put forward a new concept, the unpaired bond order, and show that it is well correlated with bond lengths, but poorly correlated with Pauling bond orders. Hence, in this way we provide a simple test of the validity of the Pauling-bond-order concept for the molecule being considered.
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The Pauling bond order can be viewed as a measure of the π-electron content of the respective carbon-carbon bond. In benzenoid hydrocarbons its values lie between 0 (in the case of essential single ...bonds) and 1 (in the case of essential double bonds). If the benzenoid molecule does not possess essential single and double bonds, then the Pauling bond orders are greater than 0 and less than 1, but may assume values arbitrarily close to 0 and 1. The π-electron content of a ring is equal to the sum of the π-electron contents of the carbon-carbon bonds forming this ring. We show that in benzenoid hydrocarbons the π-electron content of any (six-membered) ring lies between 0 and 5.5. If the molecule does not possess essential single and double bonds, then the π-electron content of any ring is greater than 0 and less than 5.5, but may assume values arbitrarily close to 0 and 5.5.
The ‘quantum-mechanically derived reaction coordinates’ (QMRC) for the proton transfer in hydrogen bonds involving fluorine, oxygen and chlorine have been derived from earlier
calculations of ...potential energy surfaces. A comparison is made between QMRC and the corresponding reaction coordinates (BORC) derived by applying the Pauling bond order concept together with the principle of conservation of bond order. Theoretical calculations have shown that the sum of the bond orders remains close to constant along the reaction coordinate in agreement with the Pauling postulate. The BORC correlation curves agree very well with theoretical results. The results indicate that the BORC curve gives a good representation of the reaction coordinates (proton transfer path) for any X-H---Y aggregate.
The relation between Pauling and Coulson bond orders in benzenoid hydrocarbons is examined. The carbon-carbon bonds of benzenoid hydrocarbons have to be classified into three classes, depending on ...the number of attached hydrogen atoms. Within each class the correlation between the bond orders is linear. The results can be used to rationalize the recently discovered correlation between the energy and electron contents of rings. An approximate expression for the total π-electron energy is also deduced.
In analogy to the recently introduced concept of π-electron content of a ring (EC), that is calculated from the Pauling bond orders, we define the π-electron energy content of the ring (ec), ...calculated in an analogous manner from the Coulson bond orders. The relations between EC and ec are analyzed for the rings of catacondensed benzenoid hydrocarbons.
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A new program has been developed for the efficient calculation of the total number of the Kekulé Structures and Pauling Bond Orders for large-scale conjugated hydrocarbons. The basic idea of the ...program is that the molecule is divided into three parts and the calculations of Kekulé Structures and Pauling Bond Orders are carried out for the divided parts. After these calculations, the results are unified to obtain Kekulé Structures and Pauling Bond Orders for the original system. The results obtained by the present method are the same as those obtained by other methods. The computational time by this method is less than those given by conventional methods.
The concept of fully benzenoid hydrocarbons (molecular graphs; FBHs) is generalized. Each full-hexagon unit (aromatic sextet) in a FBH is replaced with a larger "hexagon-shaped" unit (subgraph; e.g., ...naphthalene, pyrene, coronene, or ovalene units). Such a molecular species may be called a "fully hexagonoid" hydrocarbon (FHHs). The Pauling bond order calculation suggests that a bond (edge) which interlinks one hexagon-shaped unit with another in the bottom of bays of FHH is quasi-single, if the two units are connected by more than two bonds. As a consequence, the hexagon-shaped units are delocalized locally in the hexagonoidal (graph-theoretical) partitioning.
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This note first defines a class of cylindrical polyarenes polycyclic aromatic hydrocarbons (PAHs) C
2(m+ 1)n
H
2n
, for which the periphery is acenic. From this class the leapfrog algorithm derives ...the second class of cylindrical PAHs C
6nm
H
4n
, where the periphery is phenacenic. One further application of this algorithm to the second class leads to the third class of cylindrical PAHs C
12nm
H
8n
, where the less regular periphery has 2n capes (i.e., hexagons exposed on four adjacent sides to the external "sea" of space). Each molecule in the second and third classes is totally covered by aromatic sextets, that is, appears related to a fully benzenoid hydrocarbon (FBH). The Pauling bond order, and several new indices derived from the Pauling bond order and Clar sextet counts are calculated for the three classes with increasing numbers of carbons. This calculation suggests that a typical cylindrical PAH becomes more graphite-like than a typical flat FBH.
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