Molecular mechanics force fields are widely used in computer-aided drug design for the study of drug-like molecules alone or interacting with biological systems. In simulations involving biological macromolecules, the biological part is typically represented by a specialized biomolecular force field, while the drug is represented by a matching general (organic) force field. In order to apply these general force fields to an arbitrary drug-like molecule, functionality for assignment of atom types, parameters, and charges is required. In the present article, which is part I of a series of two, we present the algorithms for bond perception and atom typing for the CHARMM General Force Field (CGenFF). The CGenFF atom typer first associates attributes to the atoms and bonds in a molecule, such as valence, bond order, and ring membership among others. Of note are a number of features that are specifically required for CGenFF. This information is then used by the atom typing routine to assign CGenFF atom types ba...

Automation of the CHARMM General Force Field (CGenFF) I: bond perception and atom typing.

Aromaticity as a cornerstone of heterocyclic chemistry.

A history of graph entropy measures

Novel molecular descriptors based on a leverage matrix similar to that defined in statistics and usually used for regression diagnostics are presented. This leverage matrix, called Molecular Influence Matrix (MIM), is here proposed as a new molecular representation easily calculated from the spatial coordinates of the molecule atoms in a chosen conformation. The proposed molecular descriptors are called GETAWAY (GEometry, Topology, and Atom-Weights AssemblY) as they try to match 3D-molecular geometry provided by the molecular influence matrix and atom relatedness by molecular topology, with chemical information by using different atomic weightings (atomic mass, polarizability, van der Waals volume, and electronegativity, together with unit weights). A first set of molecular descriptors, called H-GETAWAY, is derived by using only the information provided by the molecular influence matrix, while a second set, called R-GETAWAY, combines this information with geometric interatomic distances in the molecule. The prediction ability in structure-property correlations of the new descriptors was tested by analyzing regressions of these descriptors for selected properties of octanes.

Structure/Response Correlations and Similarity/Diversity Analysis by GETAWAY Descriptors. 1. Theory of the Novel 3D Molecular Descriptors

The Wiener index W is the sum of distances between all pairs of vertices of a (connected) graph. Hexagonal systems (HS's) are a special type of plane graphs in which all faces are bounded by hexagons. These provide a graph representation of benzenoid hydrocarbons and thus find applications in chemistry. The paper outlines the results known for W of the HS: method for computation of W, expressions relating W with the structure of the respective HS, results on HS's extremal w.r.t. W, and on integers that cannot be the W-values of HS's. A few open problems are mentioned. The chemical applications of the results presented are explained in detail.

https://www.fmf.uni-lj.si/~klavzar/preprints/Wiener-survey.pdf

Wiener Index of Hexagonal Systems

A new molecular graph matrix, the reciprocal distance (RD) matrix, is defined. Its nondiagonal elements are equal to the reciprocals of the topological distances between the corresponding vertices, while the diagonal elements are all equal to zero. Based on the RD matrix, a real-number local vertex invariant, RDS was proposed, and three topological indices, namely RDSUM, RDSQ, and RDCHI, were defined. Their degeneracy was investigated and proved to be lower than that of the topological index W based on the distance matrix. The correlational ability of the new molecular descriptors was tested against van der Waals molecular surfaces and boiling points of alkanes, showing a satisfactory monoparametric dependence.

Design of topological indices. Part 4. Reciprocal distance matrix, related local vertex invariants and topological indices

A new approach is presented for obtaining graph invariants which have very high discriminating ability for different vertices within a graph. These invariants are obtained as the solution set (local invariant set, LOIS) of a system of linear equationsQ · X = R, whereQ is a topological matrix derived from the adjacency matrix of the graph, andR is a column vector which encodes either a topological property (vertex degree, number of vertices in the graph, distance sum) or a chemical property (atomic number). Twenty examples of LOOIs are given and their degeneracy and ordering ability of vertices is discussed. Interestingly, in some cases the ordering of vertices obtained by means of these invariants parallels closely the ordering from an entirely different procedure based on Hierarchically Ordered Extended Connectivities which was recently reported. New topological indices are easily constructed from LOISs. Excellent correlations are obtained for the boiling points and vaporization enthalpies of alkanesversus the topological index representing the sum of local vertex invariants. Les spectacular correlations with NMR chemical shifts, liquid phase density, partial molal volumes, motor octane numbers of alkanes or cavity surface areas of alcohols emphasize, however, the potential of this approach, which remains to be developed in the near future.

A new approach for devising local graph invariants: Derived topological indices with low degeneracy and good correlation ability

By applying information theory to the set of topological distances from one vertex to all other graph vertices, one obtains four new types of vertex invariants (ui,vi,xi,Yi) which are real numbers (as opposed to integers). They may be combined in many ways to afford new topological indices. One such type leads to indicesU, V, X andY which show no degeneracy for alkanes with up to 15 vertices.

New vertex invariants and topological indices of chemical graphs based on information on distances

Recently, four new types of vertex invariants, namelyu, v, x, andy, were defined on the basis of information on graph distances. They were combined to give four highly selective topological indices:U, V, X, andY. The degeneracy, i.e. equal values for nonisomorphic graphs, of the four topological indices is investigated. A structural condition and a graphical method which gives pairs of molecular graphs with identicalU, V, X, andY topological indices are introduced. The smallest pair of 4-trees representing alkanes having degeneratedU, V, X, andY values consists of trees with eighteen vertices.

T. S. Balaban

Papers

Design of topological indices. Part 4. Reciprocal distance matrix, related local vertex invariants and topological indices

A new approach for devising local graph invariants: Derived topological indices with low degeneracy and good correlation ability

New vertex invariants and topological indices of chemical graphs based on information on distances

Chemical graphs with degenerate topological indices based on information on distances

Δ3-Dihydropyrans and tetrahydropyrans by reduction of pyrylium salts with sodium borohydride in acetic acid☆