Graph Theoretical Derivation of Pauling Bond Orders

A method of evaluating Pauling bond orders of conjugated hydrocarbons is outlined. It is based on the reduction of a molecular graph by excising the bond in question and other bonds for which a unique assignment of bond character is possible. The method is general and applicable to alternant and non-alternant systems as well as to cata- and pericondensed hydrocarbons

A Systematic Study of Symmetry Properties of Graphs I. Petersen Graph

Recently (Chem. Phys. Lett. 42 283 (1976) a simple procedure for deriving symmetry properties of graphs has been suggested. It is based on a canonical numbering of the vertices of a graph, and consists in searching for all the acceptable numberings which have a unique adjacency matrix. In the series of papers initiated here we will apply the above procedure and derive all symmetry operations for graphs of interest to chemistry. We start with the Petersen graph which is of interest in discussions of isomerizations of trigonal bipyramidal structures

Hosoya Matrix - A Source of New Molecular Descriptors

We introduce a novel matrix associated with molecular graphs, the construction of which is related to the construction of the Hosoya Z topological index. The new matrix provides a source of novel invariants that may be of interest in structure-property and structure-activity studies. Construction of the novel matrices is outlined and a few novel invariants extracted. A comparison with closely related topological indices is illustrated on regressions with the boiling points in octanes

Hybridization in Planar XY 4 Molecules

Maximum overlap hybriid orbitals for planar XY4 molecules are described assuming various orbitals for ligand and central atoms. Distribution of s and d character in square snp2d2-n hybridization as a tunction of ilnteratomilc distances, and for different relamive effective charges iof bonded atoms .is g.iven. Maximum overlap hybdds, when compared with those based on Pauling\u27s criterion of hybrid 1strength, show a generally smaller contribuition of d z2 orbdtal in the hybnidizati\u27on, especially evident for ~ligand< μm etal, when in SOlffie cases they _ reduce to simple dsp2 hybrids . Calculait:i.ons are based <on tabulated overlap integrals data for Slaiter functions

Enumeration of subtrees of trees

Let $T$ be a weighted tree. The weight of a subtree $T_1$ of $T$ is defined as the product of weights of vertices and edges of $T_1$. We obtain a linear-time algorithm to count the sum of weights of subtrees of $T$. As applications, we characterize the tree with the diameter at least $d$, which has the maximum number of subtrees, and we characterize the tree with the maximum degree at least $\Delta$, which has the minimum number of subtrees.Comment: 20 pages, 11 figure

Hybridization in 1,5,9-Tridehydro(l2)Annulene

The hybridization \u27in l,5,9-tridehydro(12)annulene has been calculated by the method of maximum overlap. The results show that the hybrids describing CC double bonds and CC triple bonds have more s-character than the hybrids of the same carbon atoms involved in single CC bonds. Consequently, CC double and CC triple bonds are strengthened not only by the additional n-type overlap, but also by an increase of cr-type overlap, which accompanies the rise of the s-content. By using available empirical correlations a comparison between calculated and experimental NMR data (spin-spin coupling constant J (C13- H) and chemical shift i;) is made

Hybridization in 1,5,9-Tridehydro(l2)Annulene

The hybridization \u27in l,5,9-tridehydro(12)annulene has been calculated by the method of maximum overlap. The results show that the hybrids describing CC double bonds and CC triple bonds have more s-character than the hybrids of the same carbon atoms involved in single CC bonds. Consequently, CC double and CC triple bonds are strengthened not only by the additional n-type overlap, but also by an increase of cr-type overlap, which accompanies the rise of the s-content. By using available empirical correlations a comparison between calculated and experimental NMR data (spin-spin coupling constant J (C13- H) and chemical shift i;) is made

Hybridization in Highly Strained Small Ring Hydrocarbons. II. Methylene Biscyclopropylidene and Dimethylene Biscyclopropylidenes

The hybridization in methylene biscyclopropylidene, 1,1\u27-dimethylene biscyclopropylidene, and 1,2-dimethylene biscyclopropylidene is considered by applying the method of maximum overlap. The results show variations in hybrids describing exocyclic double bonds: for ring carbons from sp~.ss to sp2-85, and for off-ring carbons from sp1-10 to sp1-41, depending on the immediate surounding. Bond overlaps for C=C consequently vary somewhat, the largest bond overlap being of the central C=C bond connecting two three membered rings. The results of the maximum overlap calculations are compared with available experimental data

Nova nalazišta vrste Euphorbia prostrata Aiton (=Chamaesyce prostrata (Aiton) Small) u Hrvatskoj

The only finding of the American neophyte E. prostrata reported for Croatia so far comes from Mali Lošinj (ČARNI & JOGAN, 1998). This paper reports for the first time finding sites in localities from Škrljevo and Rijeka as well as numerous localities from Dalmatia (Šibenik and surroundings, Zadar, Trogir, Split and Makarska) which indicates that this neophyte has been spreading along the Croatian coast. The findings from Škrljevo and Rijeka in 1981 indicate that E. prostrata existed in Croatia much longer than can be gathered from the data published so far.Jedini dosad objavljeni nalaz amerikanoneofita E. prostrata za Hrvatsku potječe iz Malog Lošinja (ČARNI & JOGAN, 1998). U radu se prvi put navode nalazišta iz Škrljeva i Rijeke te veći broj nalazišta iz Dalmacije (Šibenik i okolica, Zadar, Trogir, Split i Makarska) koji pokazuju da se ovaj neofit širi u obalnom području Hrvatske. Posebno su značajni nalazi iz 1981. godine iz Škrljeva i Rijeke koji pokazuju da je E. prostrata u Hrvatskoj prisutna znatno duže nego što se iz dosad objavljenih podataka moglo zaključiti

Hybridization in 1,3,5-Cycloheptatriene and Some Related Molecules by the Method of Maximum Overlap

The hybridization in 1,3,5-cycloheptatriene, 1,3,5,7-cyclooctatetraene, 1,3-cyclohexadiene, and 1,4-cyclohexadiene has been calculated by the method of maximum overlap. The results show that if the molecules are assumed to be planar, hybrids describing the molecular skeleton deviate from the line joining the neighbouring carbon atoms and are directed towards the ins.ide of the ring. The deviation angles for the above molecules vary between 1.25° and 7 .5°. For non-planar structures the deviation angles are decreased or are equal to zero. The puckering of the molecular skeleton thus considerably reduces the strain