Walk counts, labyrinthicity, and complexity of acyclic and cyclic graphs and molecules

It is demonstrated how the complexity of a (molecular) graph can be quantified in terms of the walk counts, extremely easily obtained graph invariants that depend on size, branching, cyclicity, and edge and vertex weights (unsaturation, heteroatoms). The influence of symmetry is easily accounted for. The term labyrinthicity is proposed for what is measured by walk counts alone, neglecting symmetry. The total walk count and recently advanced measures of labyrinthicity or complexity are compared with respect to the ordering of structures and to the computational effort required to obtain numerical values.     

Estimations of subgraph positions in molecular graphs and their common subgraph peculiarities

Some questions emerged from electronic data processing of molecular structures (graphs) and its fragments have been considered in this work. Quantitative estimations of subgraph positions in molecular graphs are presented and some properties of their maximal common subgraphs are described.     

Design, synthesis, and operation of small molecules that walk along tracks

The synthesis and system dynamics of a series of small-molecule walker-track conjugates, 3,4-C(n) (n = 2, 3, 4, 5, and 8), based on dynamic covalent linkages between the "feet" of the walkers and the "footholds" of the track, is described. Each walker has one acyl hydrazide and one sulfur-based foot separated by a spacer chain of "n" methylene groups, while the track consists of four footholds of alternating complementary functionalities (aldehydes and masked thiols). Upon repeatedly switching between acid and base, the walker moiety can be exchanged between the footholds on the track, primarily through a "passing-leg gait" mechanism, until a steady state, minimum energy, distribution is reached. The introduction of a kinetically controlled step in the reaction sequence (redox-mediated breaking and reforming of the disulfide linkages) can cause a directional bias in the distribution of the walker on the track. The different length walker molecules exhibit very different walking behaviors: Systems n = 2 and 3 cannot actually "walk" along the track because their stride lengths are too short to bridge the internal footholds. The walkers with longer spacers (n = 4, 5, and 8) do step up and down the track repeatedly, but a directional bias under the acid-redox conditions is only achieved for the C(4) and C(5) systems, interestingly in opposite directions (the C(8) walker has insufficient ring strain with the track). Although they are extremely rudimentary systems, the C(4) and C(5) walker-track conjugates exhibit four of the essential characteristics of linear molecular motor dynamics: processive, directional, repetitive, and progressive migration of a molecular unit up and down a molecular track.     

Global molecular identification from graphs. Neutral and ionized main-group diatomic molecules

Diophantine equations and inequalities are presented for main-group closed-shell diatomic molecules. Specifying various bond types (covalent, dative, ionic, van der Waals) and multiplicities, it becomes possible to identify all possible molecules. While many of the identified species are probably unstable under normal conditions, they are interesting and present a challenge for computational or experimental analysis. Ionized molecules with net charges of -1, 1, and 2 are also identified. The analysis applies to molecules with atoms from periods 2 and 3 but can be generalized by substituting isovalent atoms. When closed-shell neutral diatomics are positioned in the chemical space (with axes enumerating the numbers of valence electrons of the free atoms), it is seen that they lie on a few parallel isoelectronic series.     

MOLGEN-CID--A canonizer for molecules and graphs accessible through the Internet

The MOLGEN Chemical Identifier MOLGEN-CID is a software module freely accessible via the Internet. For a molecule or graph entered in molfile format (2D) it produces, by a canonical renumbering procedure, a canonical molfile and a unique character string that is easily compared by computer to a similar string. The mode of operation of MOLGEN-CID is detailed and visualized with examples.     

Dyad algebra and multiplication of graphs. II. Undirected graphs

In paper I abstract vectors |e>, their adjoints <e|, dyads such as |e><e|, and abstract linear operators were related to graphs which are in general directed. With an Hermitian operator one gets equivalence classes of undirected graphs with or without loops and multi-lines. The present paper II gives rules for the multiplication of such graphs based on their underlying dyad algebra. The results may be used in the evaluation of the outcome of successive applications of operators for observables as in the case of the powers of a one-electron Hamiltonian in the method of moments, or in using projection operators, electron density, and the like.     

Dyad algebra and multiplication of graphs. I. Directed graphs

The ket-bra algebra for quantum mechanics and for the quantum chemistry.in valence shells was made by this author fully covariant recently. The resulting principle of linear covariance allowed diverse approaches such as molecular orbital, valence bond, localized orbital theories to come out as special cases in particular basis frames not necessarily orthonormal. The principal also led to the pictorial VIF (valency interaction formula) methods for deducing qualitative quantum chemistry directly from the structural formulas of molecules. The present set of two papers (II on undirected graphs) develops graphs and graph rules for abstract linear vector spaces, bras, kets, and abstract operators as ket-bra dyads. Multiplications of such operators are carried out with graphs of two kinds of lines and two kinds of vertices. The theorems are demonstrated on some examples and are useful, e.g., with the recent method of moments and in deriving Lie algebras pertinent to quantum chemistry.     

Synthetic receptors as sensor coatings for molecules and living cells.

Non-covalent molecularly imprinted polymers are applied as sensitive coatings to planar waveguides and mass-sensitive devices for the selective detection of various groups of analytes in the gaseous and aqueous phases. Cavity imprinting in the bulk of the sensor material as well as surface imprinting techniques are used to enrich analytes ranging from sub-nanometres to micrometres in analyte size. The coated devices provide sensitivity to e.g. polycyclic aromatic hydrocarbons, xanthine derivatives, complex coffee samples and whole microorganisms.     

Computer generation of characteristic polynomials of edge-weighted graphs,heterographs, and directed graphs

The computer code developed previously (K. Balasubramanian, J. Computational Chem., 5 , 387 (1984)) for the characteristic polynomials of ordinary (nonweighted) graphs is extended in this investigation to edge-weighted graphs, heterographs (vertex-weighted), graphs with loops, directed graphs, and signed graphs. This extension leads to a number of important applications of this code to several areas such as chemical kinetics, statistical mechanics, quantum chemistry of polymers, and unsaturated systems containing heteroatoms which include bond alternation. The characteristic polynomials of several edgeweighted graphs which may represent conjugated systems with bond alternations, heterographs (molecules with heteroatoms), directed graphs (chemical reaction network), and signed graphs and lattices are obtained for the first time.     

On-line storage and retrieval of chemical information. II. Substructure and biological activity searching

An improved interactive system for searching substructure and biological activity data has been developed. Features of the system include a two-level substructure search (fragment screen and atom by atom) and an expanded biological activity data base. The system operates on a file of about 150 000 compounds.     

Two-dimensional arrays in the analysis of trends in series of molecules: strongly subspectral molecular graphs, formula periodic tables, and number of resonance structures

Two-dimensional arrays consisting of strongly subspectral molecular graphs and formula periodic tables for polycyclic aromatic hydrocarbons are briefly reviewed. New two-dimensional arrays for free-radical benzenoid hydrocarbons are presented with general analytical expressions for counting their number of resonance structures (SC). The structural origin of the coefficients to these analytical expressions is discussed.     

Design,Synthesis and Herbicidal Activity of Novel Sulfonylureas Containing Tetrahydrophthalimide Substructure

To develop novel sulfonylurea herbicides, a series of chlorsulfuron derivatives was designed and synthesized through introducing tetrahydrophthalimide substructure taken from protoporphyrinogen IX oxidase(PPO) inhibitors onto the critical 5-position of the classical benzene ring. The structures of title compounds were confirmed by infrared spectroscopy, ultraviolet spectroscopy, ¹H and ¹³C NMR spectrometry, mass spectrometry and elemental analysis. In addition, the crystal structure of compound II-5 was further determined by X-ray diffraction analysis. Bioassay results showed that individual compounds exhibited good herbicidal activities, especially compound II-8, which displayed 100% inhibition rate against Echinochloa crusgalli at 150 g/ha(1 ha=10⁴ m²) with the method of foliage spray in the pot experiment.     

19F Magic angle spinning NMR reporter molecules: empirical measures of surface shielding, polarisability and H-bonding

Magic Angle Spinning (MAS) (19)F NMR spectra have been obtained and chemical shifts measured for 37 molecules in the gas phase and adsorbed on the surfaces of six common materials: octadecyl- and octyl-functionalised chromatography silicas, Kieselgel 100 silica, Brockmann neutral alumina, Norit activated charcoal and 3-(1-piperidino)propyl functionalised silica. From these six surfaces, octadecyl-silica is selected as a non-polar reference to which the others are compared. The change in chemical shift of a fluorine nucleus within a molecule on adsorption to a surface from the gas phase, Deltadelta(gas)(surface), is described by the empirical relationship: Deltadelta(gas)(surface) = delta(s) + (alpha(s)+pi(s))/alpha(r) (Deltadelta(gas)(reference) - delta(r)) + delta(HBA) + delta(HBD), where delta(s) and delta(r) are constants that describe the chemical shift induced by the electromagnetic field of the surface under investigation and reference surface, alpha(s) and alpha(r) are the relative surface polarisability for the surface and reference, pi(s) is an additional contribution to the surface polarisabilities due to its ability to interact with aromatic molecules, and delta(HBA) and delta(HBD) are measurements of the hydrogen acceptor and donor properties of the surface. These empirical parameters are measured for the surfaces under study. Silica and alumina are found to undergo specific interactions with aromatic reporter molecules and both accept and donate H-bonds. Activated charcoal was found to have an extreme effect on shielding but no specific interactions with the adsorbed molecules. 3-(1-Piperidino)propyl functionalised silica exhibits H-bond acceptor ability, but does not donate H-bonds.     

Ionization,atomization, and bond energies as functions of distances in inorganic molecules and crystals

The ionization potentials and dissociation energies of diatomic molecules are determined as functions of bond length, and the atomization energies of metals and crystalline compounds are determined as E = a/d ⁿ functions. In most cases, n ≥ 1; but for a number of metals and compounds, n < 1, as distinct from all known types of interatomic interactions. It is shown that the ratios of the bond energies and bond lengths of Group 1A and 1B metals to the respective molecular parameters have similar values, proving the identical valence states of the atoms of these metals in crystal structures.     

Molecular clips with extended aromatic sidewalls as receptors for electron-acceptor molecules. Synthesis and NMR, photophysical, and electrochemical properties

We have synthesized molecular clips 1 comprising (i) two benzo[k]fluoranthene sidewalls and (ii) a dimethylene-connected benzene bridge that carries two acetoxy (1a), hydroxy (1b), or methoxy (1c) substituents in the para position. Their NMR spectra, single-crystal structures, and photophysical (fluorescence intensity, lifetime, depolarization) and electrochemical properties are discussed. For the purpose of comparison, similar compounds (2 and 3) containing only one benzo[k]fluoranthene unit have been prepared and studied. The strongly fluorescent clips 1 form stable complexes with electron-acceptor guests because of a highly negative electrostatic potential on the inner van der Waals surface of their cavity. The complexation constants in chloroform solution for a variety of guests, determined by NMR and fluorescence titration, are much larger than those of the corresponding anthracene and naphthalene clips (4 and 5), particularly in the case of extended aromatic guests. The effect of the substituents in the para position of the benzene spacer unit of clips 1 is discussed on the basis of the host-guest complex structures obtained by X-ray analysis and molecular mechanics simulations. In the case of 9-dicyanomethylene-2,4,7-trinitrofluorene (TNF) guest, complex formation with clip 1a causes dramatic changes in the photophysical and electrochemical properties: (i) a new charge-transfer band at 600 nm arises, (ii) a very efficient quenching of the strong benzo[k]fluoranthene fluorescence takes place, (iii) shifts of both the first oxidation (clip-centered) and reduction (TNF-centered) potentials are observed, and (iv) reversible disassembling of the complex can be obtained by electrochemical stimulation.     

Combinatorial enumeration of ethane derivatives as three-dimensional chemical structures,not as graphs. A systematic approach for enumerating and characterizing stereoisomers of tartaric acids and related compounds

Fujita’s proligand method is applied to the enumeration of ethane derivatives, where the counting of stereoisomers of tartaric acids is examined in detail as a probe for testing the versatility of the method. The cycle index with chirality fittingness (CI-CF) for enumerating ethane derivatives is obtained by Fujita’s proligand method and compared with the CI-CF derived alternatively by the direct calculation of permutations of substitution positions. The two CI-CFs are identical with each other so that the methodology underlying in Fujita’s method is demonstrated in a concrete fashion. The enumeration results are compared with those derived by Pólya’s corona. Fujita’s proligand method is shown to be capable of enumerating stereoisomers, whereas Pólya’s corona is concluded to enumerate graphs, but not stereoisomers. The conceptually change from graphs to three-dimensional (3D) chemical structures is discussed, where the superiority of Fujita’s proligand method is demonstrated.