Applications of the molecular orbital graph theory (XI)——The molecular moment's method of evaluating π-bond grade and judging relative reactivity of even AH

The tree graph method of evaluating the local molecular moment is proposed. By applying this method and the molecular moment formula of π-electron energy in the molecular orbital graph theory, a topological method of using the molecular moment to judge the relatively reactive point of even AH is achieved.     

Evaluation of molecular moments by three methods

The three evaluative methods of the moment by means of the coefficient a_k of the HMO characteristic polynomial, the tree graph, and walk graph have been studied. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 78: 237–244, 2000     

Characterization of molecular complexity

We put forward a novel index of molecular complexity, ξ, taking into account the symmetry of a molecular graph and the specificity of structural components considered. The ξ index is defined as the sum of augmented valences of all mutually nonequivalent vertices in a molecular graph. The augmented valence of a vertex in a graph is the sum of its valence and valences of all neighboring vertices with the weight 1/2^d depending on their distance, d, from the vertex. The ξ index is examined on the set of octane isomers and some special classes of graphs. It is also compared with a certain number of alternative complexity measures considered in the literature. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

Fast construction of assembly trees for molecular graphs

A number of modeling and simulation algorithms using internal coordinates rely on hierarchical representations of molecular systems. Given the potentially complex topologies of molecular systems, though, automatically generating such hierarchical decompositions may be difficult. In this article, we present a fast general algorithm for the complete construction of a hierarchical representation of a molecular system. This two-step algorithm treats the input molecular system as a graph in which vertices represent atoms or pseudo-atoms, and edges represent covalent bonds. The first step contracts all cycles in the input graph. The second step builds an assembly tree from the reduced graph. We analyze the complexity of this algorithm and show that the first step is linear in the number of edges in the input graph, whereas the second one is linear in the number of edges in the graph without cycles, but dependent on the branching factor of the molecular graph. We demonstrate the performance of our algorithm on a set of specifically tailored difficult cases as well as on a large subset of molecular graphs extracted from the protein data bank. In particular, we experimentally show that both steps behave linearly in the number of edges in the input graph (the branching factor is fixed for the second step). Finally, we demonstrate an application of our hierarchy construction algorithm to adaptive torsion-angle molecular mechanics.     

Novel Indices for the Topological Complexity of Molecules

Abstract

The development of molecular complexity measures is reviewed. Two novel sets of indices termed topological complexities are introduced proceeding from the idea that topological complexity increases with the overall connectivity of the molecular graph. The latter is assessed as the connectivity of all connected subgraphs in the molecular graph, including the graph itself. First-order, second-order, third-order, etc., topological complexities ⁱ TC are defined as the sum of the vertex degrees in the connected subgraphs with one, two, three, etc., edges, respectively. Zero-order complexity is also specified for the simplest subgraphs–the graph vertices. The overall topological complexity TC is then defined as the sum of the complexities of all orders. These new indices mirror the increase in complexity with the increase in the number of atoms and, at a constant number of atoms, with the increase in molecular branching and cyclicity. Topological complexities compare favorably to molecular connectivities of Kier and Hall, as demonstrated in detail for the classical QSPR test-the boiling points of alkanes. Related to the wide application of molecular connectivities to QSAR studies, a similar importance of the new indices is anticipated.     

Molecular graph fingerprint: a new molecular structural characterization method for the modelling and prediction of chromatographic retention behaviour of several persistent organic pollutants

How to extract and characterize information on molecular microstructures is deemed to be the key task to accurately simulate and predict molecular properties. In terms of atomic attributes, atoms in a molecule are divided into three levels. Based upon that, inter-atomic correlations are mapped to certain reasonable spatial coordinates in virtue of radial distribution function, generating the novel molecular graph fingerprint (MoGF), which essentially provides insight into molecular inner structures. MoGF, committing itself to transformation of molecular structures into characteristic graph curves, shows valuable advantages such as easy calculation, experimental parameters-free, rich information content, and structural significance and intuitive expressions. QSRR studies were performed for 115 polychlorinated dibenzofurans (PCDFs), 41 polychlorinated dibenzo-p-dioxins (PCDDs), 62 polychlorinated naphthalenes (PCNs), and 210 polychlorinated biphenyls (PCBs including the biphenyl)) tested for their retention behaviours on gas chromatographic column DB-5. The resulting PLS models showed good performances with correlation coefficients for both training and test sets above 0.97.     

Graph theory and molecular orbitals—VI : A discussion of non-alternant hydrocarbons

Non-alternant hydrocarbons (NAH's) have been studied using a graph-theoretical approach. A number of general rules are given which enable one to predict several topology-dependent molecular properties (redox behaviour, charge distribution, dipole moment orientation and its approximate magnitude) only by inspection of the molecular graph. The obtained results are in agreement with experimental facts.     

分子拓扑学方法估算多环芳香烃类化合物的电离能

It was found that the ionization potentials (Ip) is related with the polarizability effect index (PEI) for the fragments CH, CH2, and CH3 of polycyclic aromatic hydrocarbon. Therefore a kind of adjacent matrix of molecular graph was constructed, in which the characteristics of the diagonal elements were expressed with the PEI of the fragments C, CH, CH2, and CH3 in molecular graph. The research result shows that there is a good correlation between the eigenvalue of the matrix and the ionization potential for the title compounds: Ipi=4.756+2.870OMOi, R=0.9853, s=0.1765, n=446. This new calculation method has only one parameter for calculating ionization potentials of polycyclic aromatic hydrocarbon. The obtained result shows that the topologic molecular method is convenient and reliable.     

Complete graph conjecture for inner-core electrons: homogeneous index case

The complete graph conjecture that encodes the inner-core electrons of atoms with principal quantum number n >or= 2 with complete graphs, and especially with odd complete graphs, is discussed. This conjecture is used to derive new values for the molecular connectivity and pseudoconnectivity basis indices of hydrogen-suppressed chemical pseudographs. For atoms with n = 2 the new values derived with this conjecture are coincident with the old ones. The modeling ability of the new homogeneous basis indices, and of the higher-order terms, is tested and compared with previous modeling studies, which are centered on basis indices that are either based on quantum concepts or partially based on this new conjecture for the inner-core electrons. Two similar algorithms have been proposed with this conjecture, and they parallel the two "quantum" algorithms put forward by molecular connectivity for atoms with n > 2. Nine properties of five classes of compounds have been tested: the molecular polarizabilities of a class of organic compounds, the dipole moment, molar refraction, boiling points, ionization energies, and parachor of a series of halomethanes, the lattice enthalpy of metal halides, the rates of hydrogen abstraction of chlorofluorocarbons, and the pED(50) of phenylalkylamines. The two tested algorithms based on the odd complete graph conjecture give rise to a highly interesting model of the nine properties, and three of them can even be modeled by the same set of basis indices. Interesting is the role of some basis indices all along the model.     

Molecular relaxation of components of LC mixture 2f- 3333 (ROLIC) for dual- frequency electrooptic shutters

ABSTRACT

Dual-frequency liquid crystal materials are used in fast response electrooptic modulators in different devices for digital information displaying and processing. In an NLC mixture 2f-3333 (ROLIC, Switzerland) there are components with lateral dipole moment. Their molecular relaxation is investigated by a method of dielectric spectroscopy. Values of relaxation time and its activation energy, molecular friction coefficient, rotational diffusion are obtained. They are compared with data obtained by other methods like LC viscosimetry.     

Critical evaluation of search algorithms for automated molecular docking and database screening

The DOCK program explores possible orientations of a molecule within a macromolecular active site by superimposing atoms onto precomputed site points. Here we compare a number of different search methods, including an exhaustive matching algorithm based on a single docking graph. We evaluate the performance of each method by screening a small database of molecules to a variety of macromolecular targets. By varying the amount of sampling, we can monitor the time convergence of scores and rankings. We not only show that the site point–directed search is tenfold faster than a random search, but that the single graph matching algorithm boosts the speed of database screening up to 60-fold. The new algorithm, in fact, outperforms the bipartite graph matching algorithm currently used in DOCK. The results indicate that a critical issue for rapid database screening is the extent to which a search method biases run time toward the highest-ranking molecules. The single docking graph matching algorithm will be incorporated into DOCK version 4.0. © 1997 John Wiley & Sons, Inc. J Comput Chem 18: 1175–1189     

A Central Partition of Molecular Conformational Space. III. Combinatorial Determination of the Volume Spanned by a Molecular System

In the first work of this series (Gabarro-Arpa, Comp. Biol. Chem. 27 (2003) 153–159) it was shown that the conformational space of a molecule could be described to a fair degree of accuracy by means of a central hyperplane arrangement. The hyperplanes divide the space into a hierarchical set of cells that can be encoded by the face lattice poset of the arrangement. The model however, lacked explicit rotational symmetry, which made impossible to distinguish rotated structures in conformational space. This problem was solved in a second work (Gabarro-Arpa, Proc. 26th Ann. Int. Conf. of the IEEE EMBS (San Franciso, 2004) 3007–3010) by sorting the elementary 3-dimensional components of the molecular system into a set of morphological classes that can be properly oriented in a standard 3-D reference frame. This also made possible to find a solution to the problem that is being addressed in the present work: for a molecular system immersed in a heat bath we want to enumerate the subset of cells in conformational space that are visited by the molecule in its thermal wandering. If each visited cell is a vertex on a graph with edges to the adjacent cells, here it is explained how such graph can be built.     

Conjugated chemical trees with minimal energy and prescribed diameter

The energy of a molecular graph G is defined as the sum of the absolute values of the eigenvalues of A(G), where A(G) is the adjacency matrix of this graph. This article characterizes conjugated chemical trees with prescribed diameter and minimal energies and presents explicit expressions of their Hosoya indices. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Dielectric Study of Charge-transfer Complexes in Binary and Ternary Systems at 35°C

Abstract

The measurements of dielectric constant of a number of binary and ternary mixtures of butyl acetate, butyl alcohol, quinoline, pyridine and o-cresol in carbon tetrachloride and benzene have been made at 35°C. Molecular interaction of these aromatic compounds have been studied in terms of variations in parameters; ‘dipole moment’ (μ), ‘interaction dielectric constant’ (δ?), ‘molecular polarisation’ (P) and ‘excess polarisation’ (P_E ). The dipole moment has been calculated using Hysken's method, the interaction dielectric constant utilizing the equation of ideal mole fraction law and excess polarisation using the theory of Erap and Glasstone. The positive values of δ?₁₂ for binary mixtures of quinoline and butyl acetate in carbon tetrachloride and benzene have been attributed to the formation of charge transfer complexes. The negative values of δ?₁₂ and δ?₁₂₃ with pyridine suggest that charge transfer interaction is weakened by pyridine in its binary and ternary mixtures. The plot between the excess polarisation value and the product of mole fractions yielded a straight line passing through the origin showing the formation of charge transfer complexes.     

Core electrons and hydrogen atoms in chemical graph theory

General and complete graphs have recently been used to free chemical graph theory, and especially molecular connectivity theory, from spurious concepts, which belonged to quantum chemistry with no direct counterpart in graph theory. Both types of graph concepts allow the encoding of multiple bonds, non-bonding electrons, and core electrons. Furthermore, they allow the encoding of the bonded hydrogen atoms, which are normally suppressed in chemical graphs. This suppression could sometimes have nasty consequences, like the impossibility to differentiate between compounds, whose hydrogen-suppressed chemical graphs are completely equivalent, like for the CH₂F₂ and BHF₂ compounds. At the computational level the new graph concepts do not introduce any dramatic changes relatively to previous QSPR/QSAR studies. These concepts can nevertheless help in encoding the many electronic features of a molecule, achieving, as a bonus, an improved quality of the modeled properties, as it is here exemplified with a set of properties of different classes of compounds.