Atomic Ring Invariant and Modified CANON Extended Connectivity Algorithm for Symmetry Perception in Molecular Graphs and Rigorous Canonicalization of SMILES

Abstract

We propose new invariant (the product of the corresponding primes for the ring size of each bond of an atom) as a simple unambiguous ring invariant of an atom that allows distinguishing symmetry classes in the highly symmetrical molecular graphs using traditional local and distance atom invariants. Also, we propose modifications of Weininger’s CANON algorithm to avoid its ambiguities (swapping and leveling ranks, incorrect determination of symmetry classes in non-aromatic annulenes, arbitrary selection of atom for breaking ties). The atomic ring invariant and the Modified CANON algorithm allow us to create a rigorous procedure for the generation of canonical SMILES which can be used for accurate and fast structural searching in large chemical databases.

SELFIES and the future of molecular string representations

“…These are then assigned numerical values such as atomic number, number of unshared electrons, and bond order, which are considered invariants of the graph, as they do not depend on the labeling scheme of the nodes (atoms). 118 Most approaches allow all edges to connect just two nodes, in line with the standard 2c-2e bonds that dominate most of organic chemistry.…”

“…However, the approach of Dietz, Ugi, and Stein is based on groups of nodes and edges, which are additionally characterized by the number of unshared VEs and delocalized electrons. 118 This approach tries to exactly capture the electronic structure but leads to complicated nested sets of brackets that may be hard to comprehend. Furthermore, a clear assignment of VEs is often not possible in transition-metal chemistry due to extensive delocalization.…”

TUCAN: A molecular identifier and descriptor applicable to the whole periodic table from hydrogen to oganesson

“…Many popular canonicalization procedures in chemistry are variants of the classical Morgan algorithm [21], which however uses the bond type of edges as an initial atom invariant and therefore is not domain-independent. Furthermore, non-equivalent atoms can still be assigned identical extended connectivity values, in particular in highly symmetrical molecules [23,36], a problem that is particularly relevant to inorganic cluster chemistry. In contrast, TUCAN only relies on the atomic number as a chemistry-specific invariant.…”

TUCAN: A molecular identifier and descriptor applicable to the whole periodic table from hydrogen to oganesson

“…Comparison with other software Many popular canonicalization procedures are variants of the classical Morgan algorithm, [32] which however use the bond type of edges as an initial atom invariant and therefore is not domain-independent. Furthermore, non-equivalent atoms can still be assigned identical extended connectivity values, in particular in highly symmetrical molecules, [35,44] a problem that is particularly relevant to inorganic cluster chemistry. In contrast, the algorithm introduced by TUCAN only relies on the atomic number as a chemistry-speci c invariant and greatly simpli es the handling of complex clusters by identi cation and enumeration of "fundamental" (chordless) cycles as part of its invariant code.…”