Counterexamples in Chemical Ring Perception

Abstract

Abstract. Ring information is a large part of the structural topology used to identify and characterize molecular structures. It is hence of crucial importance to obtain this information for a variety of tasks in computational chemistry. Many different approaches for "ring perception", i.e., the extraction of cycles from a molecular graph, have been described. The chemistry literature on this topic, however, reports a surprisingly large number of incorrect statements about the properties of chemically relevant ring sets and, in particular, about the mutual relationships of different sets of cycles in a graph. In part these problems seem to have arisen from a sometimes rather idiosyncratic terminology for notions that are fairly standard in graph theory. In this contribution we translate the definitions of concepts such as the Smallest Set of Smallest Rings, Essential Set of Essential Rings, Extended Set of Smallest Rings, Set of Smallest Cycles at Edges, Set of Elementary Rings, K-rings, and β-rings into a more widely-used mathematical language. We then outline the basic properties of different cycle sets and provide numerous counterexamples to incorrect claims in the published literature. These counterexamples may have a serious practical impact because at least some of them are molecular graphs of well-known molecules. As a consequence, we propose a catalogue of desirable properties for chemically useful sets of rings.

Technical Note: Development of chemoinformatic tools to enumerate functional groups in molecules for organic aerosol characterization

“…b Miloslav et al (2015). (Berger et al, 2004;May and Steinbeck, 2014). In this work, we use the smallest set of smallest rings (SSSR) (Downs et al, 1989) as defined by OpenBabel and many chemoinformatic software packages to enumerate the number of aromatic rings in this work.…”

A robust method for searching the smallest set of smallest rings with a path-included distance matrix

“…A set of graphs tested by Berger et al was used to test the robustness of RP-Path in finding SSSR (10). Fig.…”

“…Some theoretical aspects are summarized by Downs et al (9). Although various methods to find SSSRs have been developed using algorithms based on both methods, none are robust (10).…”

Minimum path bases and relevant paths

“…We use the same symbol H for a subgraph of G, its edge set, and the corresponding incidence vector. It is customary to consider H as a vector over GF (2). Hence vector addition, C ⊕ D, corresponds to the symmetric difference of the edge sets of subgraphs C and D of G.…”

“…They have direct applications in diverse areas of science and engineering, such as the static analysis of rigid framework structure [16], chemical structure storage and retrieval systems [2,9], and electric circuit theory [8]. Flux Analysis in chemical reaction networks [10,20] considers stationary fluxes as kernel vectors of the stoichiometric matrix, which in the case of a network of isomerization reactions reduces to the incidence matrix of a directed graph.…”