The atom assignment problem in automated de novo drug design. 2. A method for molecular graph and fragment perception

Summary If atom assignment onto 3D molecular graphs is to be optimized, an efficient scheme for placement must be developed. The strategy adopted in this paper is to analyze the molecular graphs in terms of cyclical and non-cyclical nodes; the latter are further divided into terminal and non-terminal nodes. Molecular fragments, from a fragments database, are described in a similar way. A canonical numbering scheme for the fragments and the local subgraph of the molecular graph enables fragments to be placed efficiently onto the molecular graph. Further optimization is achieved by placing similar fragments into bins using a hashing scheme based on the canonical numbering. The graph perception algorithm is illustrated in detail.     

Some results on energy of unicyclic graphs with n vertices

A unicyclic graph is a connected graph whose number of edges is equal to the number of vertices. Hou (J Math Chem 29:163–168, 2001) first considered the minimal energy for general unicyclic graphs. In this paper, we determine the unicyclic graphs with the minimal energy in U_n^l{\mathcal {U}_n^l} and the unicyclic graphs with the first forth smallest energy in U_n (n 3 13){\mathcal {U}_n\,(n\geq 13)} vertices.     

On walks in molecular graphs.

Walks in molecular graphs and their counts for a long time have found applications in theoretical chemistry. These are based on the fact that the (i, j)-entry of the kth power of the adjacency matrix is equal to the number of walks starting at vertex i, ending at vertex j, and having length k. In recent papers (refs 13, 18, 19) the numbers of all walks of length k, called molecular walk counts, mwc(k), and their sum from k = 1 to k = n - 1, called total walk count, twc, were proposed as quantities suitable for QSPR studies and capable of measuring the complexity of organic molecules. We now establish a few general properties of mwc's and twc among which are the linear dependence between the mwc's and linear correlations between the mwc's and twc, the spectral decomposition of mwc's, and various connections between the walk counts and the eigenvalues and eigenvectors of the molecular graph. We also characterize the graphs possessing minimal and maximal walk counts.     

Intracule functional models. V. Recurrence relations for two-electron integrals in position and momentum space

The approach used by Ahlrichs [Phys. Chem. Chem. Phys., 2006, 8, 3072] to derive the Obara-Saika recurrence relation (RR) for two-electron integrals over Gaussian basis functions, is used to derive an 18-term RR for six-dimensional integrals in phase space and 8-term RRs for three-dimensional integrals in position or momentum space. The 18-term RR reduces to a 5-term RR in the special cases of Dot and Posmom intracule integrals in Fourier space. We use these RRs to show explicitly how to construct Position, Momentum, Omega, Dot and Posmom intracule integrals recursively.     

Two metrics for a graph-theoretical model of organic chemistry

A graph-theoretical model of organic chemistry is proposed. The main idea behind this model is a molecular graph in the form of a multigraph with loops; its vertices are evaluated by vertex labels (atomic symbols). The chemical distance between two graphs from the same family of isomeric graphs is based on the maximal common subgraph. The produced reaction graph is composed of the minimal number of edges and/or loops. The reaction distance assigned to the chemical transformationG ₁ G ₂ is equal to the minimal number of the so-called elementary transformations that are necessary for the transformation ofG ₁ intoG ₂ Because these metrics are not isometric, the resulting reaction graphs may depend on the metric used.Dedicated to the memory of Professor Milan Sekanina     

Graphic rules for reducing the order of the Hückel determinant

McClelland's rules are generalized to construct characteristic polynomials of molecular graphs with a symmetry plane. A new graphic representation of the adjacency matrix is suggested. Diagonal matrix elements are assigned to graph nodes with directed loops; the number of edges connecting the adjacent nodes is equal to the product of the symmetric off-diagonal elements. Graphic rules for reducing the order of the Hückel determinant are suggested. The rules can be used in Hückel, vibration, and perturbation theories. Institute of Chemical Kinetics and Combustion, Siberian Branch, Russian Academy of Sciences. Translated fromZhurnal Struktumoi Khimii, Vol. 35, No. 6, pp. 13–22, November–December, 1994. Translated by O. Kharlamova     

Structural and pathway complexity of beta-strand reorganization within aggregates of human transthyretin(105-115) peptide

Interstrand conformational rearrangements of human transthyretin peptide (TTR(105-115)) within dimeric aggregates were simulated by means of molecular dynamics (MD) with implicit solvation model for a total length of 48 micros. The conformations sampled in the MD simulations were clustered to identify free energy minima without any projections of free energy surface. A connected graph was constructed with nodes (=clusters) and edges corresponding to free energy minima and transitions between nodes, respectively. This connected graph which reflects the complexity of the free energy surface was used to extract the transition disconnectivity graph, which reflects the overall free energy barriers between pairs of free energy minima but does not contain information on transition paths. The routes of transitions between important free energy minima were obtained by further processing the original graph and the MD data. We have found that both parallel and antiparallel aggregates are populated. The parallel aggregates with different alignment patterns are separated by nonnegligible free energy barriers. Multiroutes exist in the interstrand conformational reorganization. Most visited routes do not dominant the kinetics, while less visited routes contribute a little each but they are numerous and their total contributions are actually dominant. There are various kinds of reptation motions, including those through a beta-bulge, side-chain aided reptation, and flipping or rotation of a hairpin formed by one strand.     

A representation of the McClelland method of graph splitting. Stack graphs

McClelland's rules on graph splitting can be represented using the generalized graph notation. Generalized graphs are edge- and vertex-weighted graphs, which are becoming important to chemical problems. By this the McClelland method of graph splitting has a wider range of applications. “Stack graphs” are constructed from identical “base graphs” by connecting corresponding vertices from one base to another. Their eigenvalues are related to the eigenvalues of the base graph. Two- and even three-layered graphs may be used as a simple model for the inter-ring interaction in a cyclophane.     

Graphs of unbranched hexagonal systems with equal values of the wiener index and different numbers of rings

Graphs of unbranched hexagonal systems consist of hexagonal rings connected with each other. Molecular graphs of unbranched polycyclic aromatic hydrocarbons serve as an example of graphs of this class. The Wiener index (or the Wiener number) of a graph is defined as the sum of distances between all pairs of its vertices. Necessary conditions for the existence of graphs with different numbers of hexagonal rings and equal values of the Wiener index are formulated, and examples of such graphs are presented.     

Common vertex matrix: A novel characterization of molecular graphs by counting

We present a novel matrix representation of graphs based on the count of equal‐distance common vertices to each pair of vertices in a graph. The element (i, j) of this matrix is defined as the number of vertices at the same distance from vertices (i, j). As illustrated on smaller alkanes, these novel matrices are very sensitive to molecular branching and the distribution of vertices in a graph. In particular, we show that ordered row sums of these novel matrices can facilitate solving graph isomorphism for acyclic graphs. This has been illustrated on all undecane isomers C₁₁H₂₄ having the same path counts (total of 25 molecules), on pair of graphs on 18 vertices having the same distance degree sequences (Slater's graphs), as well as two graphs on 21 vertices having identical several topological indices derived from information on distances between vertices. © 2013 Wiley Periodicals, Inc.     

计算机自动结构解析专家系统研究──一个新的拓扑等价性识别算法

介绍了一个正确识别化合物结构或结构片断中各原子的拓扑等价性问题的新算法。算法中引入了节点矩阵Ｎ和键矩阵Ｂ，并由这两个新矩阵来计算化合物结构图中的各节点的特征值，以此来表征节点的环境特征，从而识别节点的拓扑等价性，以保证结构解析专家系统结构产生器的穷举和非冗余性。     

S5 graphs as model systems for icosahedral Jahn–Teller problems

The degeneracy of the eigenvalues of the adjacency matrix of graphs may be broken by non-uniform changes of the edge weights. This symmetry breaking is the graph-theoretical equivalent of the molecular Jahn–Teller effect (Ceulemans et al. in Proc Roy Soc 468:971–989, 2012). It is investigated for three representative graphs, which all have the symmetric group on 5 elements, S ₅ , as automorphism group: the complete graph K₅, with 5 nodes, the Petersen graph, with 10 nodes, and an extended K₅ graph with 20 nodes. The spectra of these graphs contain fourfold, fivefold, and sixfold degenerate manifolds, respectively, and provide model systems for the study of the Jahn–Teller effect in icosahedral molecules. The S ₅ symmetries of the distortion modes of the quintuplet in the Petersen graph yield a resolution of the product multiplicity in the corresponding $ H \otimes \left( {g + 2h} \right) $ icosahedral Jahn–Teller problem. In the extended Petersen graph with 20 nodes, a selection rule prevents the Jahn–Teller splitting of the sextuplet into two conjugate icosahedral triplets.     

Hückel and Möbius cyclic conjugated molecules

Generalized graphs represent Hückel-type and Möbius-type polycyclic conjugated systems. We show that the number of generalized graphs with different spectra for a given parent graph is not larger than 2 ^N(R) and is equal to 2 ^N(R) if no two rings are equivalent,N(R) being the number of rings (fundamental circuits) in the parent graph. We demonstrate that the rule for the stability of generalized graphs, proved in a previuos paper, and the information on the relative magnitudes of the effects of individual circuits enable one to predict the stabilities of generalized graphs without performing numerical calculations.     

Multiparametric curve fitting--X: a structural classification of programs for analysing multicomponent spectra and their use in equilibrium-model determination

A functional structure-classification of programs for analysis of spectra elucidates their efficiency for determination of the stoichiometric indices, stability constants and molar absorptivities of complex species. SQUAD (84) introduces new functional units for (i) determination of the number of light-absorbing species, (ii) a rigorous fitness test, (iii) plotting three-dimensional graphs of a paraboloid minimum response-surface as a function of two selected parameters, and a graph of the fitted absorbance response-plane, (iv) simultaneous estimation of stoichiometric indices and stability constants, (v) simulation of an absorbance matrix data by loading with random errors related to the instrumental variance of the absorbance. A guide to experimental procedure and computational strategy for chemical model determination is given and nine diagnostic tools useful in finding the number of species present and their stoichiometry and stability constants by regression analysis of spectra are tested, by use of literature data.     

多金属氧酸盐材料在二氧化碳电催化还原领域中的研究进展

随着工业发展和全球人口的持续增长,人类对化石燃料的消耗日益增加,从而导致大气中二氧化碳含量的显著增加以及与之相伴的一系列环境问题.电化学还原二氧化碳制备高附加值的燃料和化学品具有稳定的效率和较高的经济可行性等特点,目前已成为一种有前景的策略来缓解当前全球面临的能源短缺和气候变暖问题.然而,电催化二氧化碳还原过程存在反应...