Jan V. Knop

Molecular topological index

The molecular topological index (MTI) has been systematically tested for counterexamples (two or more nonisomorphic structures with the same MTI number). The analysis was carried out for alkane trees with up to 16 atoms. The search for counterexamples was positive : the first pair of alkane trees with identical MTI numbers was found in the octane family. The more disturbing finding was that two nonisomorphic alkane trees of different sizes may also possess the same MTI value. An attempt to redefine the MTI in terms of only the distance matrix and the valency matrix was abortive

On the concept of the weighted spanning tree of dualist

The concepts of dual, inner dual and dualist are reviewed. The application of these concepts to polyhexes is briefly described. The concepts of a spanning tree and a weighted spanning tree of dualist are introduced. The uses of the weighted spanning tree of dualist in coding and enumerating polyhex hydrocarbons are outlined.

Theoretical studies of positional isomers obtained by annelation of benzene and 5-membered ring heterocyclics containing nitrogen, oxygen, or sulphur☆

Abstract MO calculations using the Pariser-Parr approach are reported for the “normal” heteroaromatic molecules: indole, benzofuran, and thionaphthene, and for their isoconjugated isomers: isoindole, isobenzofuran, and isothionaphthene. The agreement between the observed and calculated transition energies is satisfactory. The reactive positions towards electrophilic, nucleophilic, and radical attacks are predicted. Recently made benzo[e]isoindole is also studied.

All-electron SCF LCAO MO calculations on various conformations of cis- and trans-stilbene

Ab initio SCF calculations of cis- and trans-stilbene at different conformations were performed using two program systems. Minimal energy is obtained for cis-stilbene when the phenyl rings are rotated by 52 ° out of the molecular plane. The deviation from planarity due to steric hindrance is smaller for the trans isomer yielding a rotational angle of 19 °. The trans isomer is calculated to be more stable by 5.7 kcal/mole than the cis isomer, confirming the experimental estimate according to which the energy of isomerization is about 3 kcal/mole. This is an improvement over semiempirical calculations which predict a lower energy for the trans configuration.

Use of small computers for large computations: Enumerations of polyhex hydrocarbons

The enumeration of polyhex hydrocarbons with up to 16 hexagons is reported. These results are now for the first time available

On irreducible endospectral graphs

The paper considers endospectral trees, a special class of graphs associated with the production of numerous isospectral graphs. Endospectral graphs have been considered in the literature sporadically (the name was suggested very recently [M. Randic, SIAM J. Algebraic Discrete Meth. 6, 145 (1985)]). They are characterized by the presence of a pair of special vertices that, if replaced by any fragment, produce an isospectral pair of graphs. Recently Jiang [Y. Jiang, Sci. Sin. 27, 236 (1984)] and Randic and Kleiner (M. Randic and A. F. Kleiner, ‘‘On the construction of endospectral trees,’’ submitted to Ann. NY Acad. Sci.) considered alternative constructive approaches to endospectral trees and listed numerous such graphs. The listing of all such trees having n=16 or fewer vertices has been undertaken here. It has been found that relatively few endospectral trees have novel structural features and cannot be reduced to some already known endospectral tree. These few have been named ‘‘irreducible endospectral...

Positional and conformational dependence of long-range interactions in 3,16- and 3,17-androstanediones

The 5α- and 5β-conformations of androstane, androstan-3-one, androstan-16-one, androstan-17-one, androstane-3,16-dione and androstane-3,17-dione have been calculated by the SCF MNDO method, using full geometry optimization, in order to assess the dependence of long-range electronic interactions of the carbonyl groups on their location and on the conformation of the steroid ring system.

Electronic structure and long-range interaction in androstanes

Abstract The results of semiempirical MNDO calculations with full geometry optimization are reported for 5α-androstane, 5α-androstan-3-one, 5α-androstan-11-one, 5α-androstan-16-one, 5α-androstan-17-one, 5α-androstane-3,16-dione, 5α-androstane-3,17-dione, 5α-androstane-3,11,17-trione, and five of its unsaturated keto derivatives: androst-5-en-17-one, androst-4-ene-3,16-dione, androst-4-ene-3,17-dione, androst-5-ene-3,17-dione and androsta-1,4-diene-3,17-dione. Emphasis is placed on the long-range effects of carbonyl group(s) located at the biologically important 3-, 11- and/or 17-positions, and on the dependence of these effects on the presence of interpolated localized double bonds. The effects of placing the carbonyl group in the 16- rather than the 17-position were studied and it was found that the former location produced a more efficient mixing of longitudinal and transversal ribbon-like σ-orbitals of the steroidal skeleton and, hence, enhanced the long-range coupling with substituents in the 3-position. Such long-range effects seem to exert considerable influence on conformation and activity, and, particularly, on the fast intramolecular electron transfer that has been observed recently in steroid solutions.

Computer generation of all 1-factors for a class of graphs with all vertices of degree two or three

Abstract An algorithm is proposed for the enumeration and display of all 1-factors for a class of graphs with all vertices of degree two or three.

Note on the application of the reduced graph model in conjunction with search trees to the enumeration ofKekulé structures

The reduced graph model, when used in conjunction with the search trees method, provides a novel combinatorial procedure for the enumeration and generation ofKekulé structures. The procedure is suited for large benzenoid hydrocarbons consisting of cata- and thin peri-condensed parts.ZusammenfassungDas Modell erlaubt mit der im Titel genannten Kombination eine neuartige Methode zur Ermittlung und Generierung vonKekulé-Strukturen. Das Verfahren ist für große benzoide Kohlenwasserstoffe geeignet, die aus cata- und (dünnen) peri-kondensierten Teilstrukturen bestehen.