Molecular graph potentials

Graph potentials, a new class of atomic invariants defined as the solutions of a system of linear equations, were proposed as an efficient method of atom partitioning. Molecular graph potentials were developed by analogy with an electrical network, where resistors of the network correspond to chemical bonds and the network nodes correspond to atoms, To cause the flow of electrical current in the network, an additional node is introduced and connected with all other nodes of the network by edges containing resistors and current sources. Atom potentials are computed as the roots of the following system of linear equations ... 

The molecular graph potentials of 3-methylhexane (27) are the roots of the system of linear equations (10) ... 

Thorner, D.A., Willett, P., Weight, P.M., and Taylor, R. Similarity searching in files of three-dimensional chemical structures Representation and searching of molecular electrostatic potentials using field-graphs./. Comput.-Aided Mol. Des. 1997, 3 3, 163-174. 

Autocorrelation of Topological Structure Moreau and Broto [24,25] have suggested the autocorrelation vector of a molecular graph as the source for molecular descriptors. This method assumes that each atom i in the graph is uniquely associated with a numeric quantity, qit such as the atomic number, atomic mass, (v)(, (ds), Sv, or electronegativity. The intrinsic atom values of the electrotopological state [26] and the atomic Rd and log Kow parameters [27,28] are other potential atomic descriptors suitable to construct autocorrelation vectors. Generally, the fcth element of the autocorrelation vector is defined as... 

Langlois, M.H., Audry, E., Croizet, F., Dallet, Ph., Carpy, A. and Dubost, J.P. (1993b). Topological Lipophilicity Potential A New Tool for a Fast Evaluation of Lipophilicity Distribution on a Molecular Graph. In Trends in QSAR and Molecular Modelling 92 (Wennuth, C.G., ed.), ESCOM, Leiden (The Netherlands), pp. 354-355. 

Marrn, R.M., Aguirre, N.E. and Daza, E.E. (2008) Graph theoretical similarity approach to compare molecular electrostatic potentials. /. Chem. Inf. Modd., 48, 109-118. 

This case seems to be more promising. Let s consider the DN-model first. As described above, the molecular mechanics model is based on a number of force-field potentials that refer to proper scientific laws. Given the molecular graph the different types of atoms contained in a molecule and their connections and a set of force-field parameters the total strain energy of the molecule can be deduced for every possible atomic arrangement. Is this a DN-explanation The answer is no, and... 

D. A. Thorneg P. Willett, P. M. Wright, and R. Taylor, J. Comput.-Aided Mol. Des., 11,163 (1997). Similarity Searching in Files of Three-Dimensional Chemical Structures Representation and Searching of Molecular Electrostatic Potentials Using Field-Graphs. 

The book is written for the users of such software, as they need to know what is really meant when we speak of the generation of molecular graphs, of substructures, of a goodlist of prescribed substructures, of overlapping substructures, of non-over-lapping substructures, of closed substructures, of substructure counts, of molecular descriptors, and so on. Otherwise, users will not be able to achieve the full potential of the software. It is also meant to provide documentation of the mathematical basics required for the designers of software for computational chemistry or chemoinformatics. 

As pointed out by Matta [20], a threshold of dissimilarity is assumed between the members of a molecular set for the construction of a QSAR model. Similarity is commonly quantified on the basis of amino acid sequence matching [76], mismatching of 2-dimentional chemical graphs [8], on 3-D molecular skeleton superpositions [77], and on point-by-point comparison of electron density—pioneered by Carbo [78-81] or of the molecular electrostatic potential [82-94]. Through relationships (5) and (6) in Ref. [20], a similarity of p r) necessarily leads to the similarity of all other ground-state properties, and hence the most fundamental molecular comparisons are those effected at the electron density level. 

The distribution of the electrostatic potential for two bromine species has further consequences particularly the location of the maxima of EP shows the most probable nucleophilic attacks here. This is why the liner halogen bonds are formed with BrFa while bent ones for the BrFs molecule. Figure 15.8 shows the molecular graph of the BrFa-NCH complex with the reactive surface corresponding to the laplacian of the electron density equal to zero. The straight bond path connecting the bromine atom with the nitrogen Lewis base center of HCN molecule is observed... 

One can enumerate other examples where the molecular graphs inform of the kinds and of the nature of interactions. The complexes of molecular hydrogen may be mentioned here. The dihydrogen possesses Lewis acid and Lewis base characteristics since the positive electrostatic potential is observed at the H-atoms, at edges... 

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