Discrete chemical topology

Discrete Chemical Topology Chemical Bonding and Graph Theory... 

Pantea, C., Gupta, A., Rawlings, J.B., Craciun, G. The QSSA in chemical kinetics as taught and as practiced. In Jonoska, N., Saito, M (eds.) Discrete and Topological Models in Molecular Biology, pp. 419 142. Springer, Berlin (2014)... 

The comparison with results of high level quantum-chemical calculations proves the utility of the simple discrete models of molecular interaction for predicting the most stable topologies of water cycles and PWCs. Based on these discrete models an effective enumerating techniques was developed for hierarchical classification of proton configurations. In spite of the fact that PWCs are very complex systems with complicated interactions, the discrete models of inter-molecular interaction help us to see the wood for the trees (Fig. 3). 

Chemical compounds can be characterized by a wide variety of molecular descriptors" such as physiochemical properties (e.g., their lipophilicity) and topological features (e.g., degree of branching) [5, 61. The term chemical space is commonly used in place of "multi-dimensional descriptor space" it is a region defined by a particular selection of molecular descriptors and the upper and lower values (limits) placed upon them [5,6]. In the context of small-molecule collections, chemical space is generally defined as the total descriptor space that encompasses all small carbon-based molecules that could, in principle, be created [5,6]. Each chemically unique small molecule will have a unique set of molecular properties and thus moleculardescriptorvalues,and will therefore reside at a discrete point in chemical space [5]. 

This article presents uniaxial extension measurements on cis-1,4-polybutadiene networks of known junction functionality. The observed values of the reduced force from uniaxial extension measurements conform to the constrained junction theory of Flory. The reduced force intercept at 1/cX = 0 is fully comprehensible in terms of the cycle rank of the network, and can be calculated from chemical considerations. This holds even though the polybutadiene melt has a high plateau modulus. Therefore, discrete topological entanglements do not contribute perceptibly to the equilibrium modulus of polybutadiene networks. 

Elemental boron exists in a number of allotropic forms of which four (two rhombohedral forms and two tetragonal forms) are well established (Table 5). The structures of all of these allotropic forms of boron are based on various ways of joining B12 icosahedra using the external orbitals on each boron atom. The chemical bonding topology in these B12 icosahedra appears to be exactly analogous to that found in the discrete Bi2Hi2 anion, so that elemental boron provides an example of three-dimensional aromaticity in a refractory material. 

Topology in Chemistry Discrete Mathematics of Molecules Rouvray, D. H., King, R. B., Eds. Horwood series in chemical science Horwood Publishing Ltd. Cambridge (UK), 2002. 

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