Symmetry calculation for molecules and transition states

Abstract

The symmetry of molecules and transition states of elementary reactions is an essential property with important implications for computational chemistry. The automated identification of symmetry by computers is a very useful tool for many applications, but often relies on the availability of three-dimensional coordinates of the atoms in the molecule and hence becomes less useful when these coordinates are a priori unavailable. This article presents a new algorithm that identifies symmetry of molecules and transition states based on an augmented graph representation of the corresponding structures, in which both topology and the presence of stereocenters are accounted for. The automorphism group order of the graph associated with the molecule or transition state is used as a starting point. A novel concept of label-stereoisomers, that is, stereoisomers that arise after labeling homomorph substituents in the original molecule so that they become distinguishable, is introduced and used to obtain the symmetry number. The algorithm is characterized by its generic nature and avoids the use of heuristic rules that would limit the applicability. The calculated symmetry numbers are in agreement with expected values for a large and diverse set of structures, ranging from asymmetric, small molecules such as fluorochlorobromomethane to highly symmetric structures found in drug discovery assays. The new algorithm opens up new possibilities for the fast screening of the degree of symmetry of large sets of molecules.

Understanding the reactivity of unsaturated alcohols: Experimental and kinetic modeling study of the pyrolysis and oxidation of 3-methyl-2-butenol and 3-methyl-3-butenol

“…The latter program produces a CHEMKIN readable input file based on a set of initial molecules, thermochemical databases, and a set of reaction families. Symmetry numbers of molecules and transition states are assigned using the computer code SIGMA [42]. The use of Genesys for the construction of kinetic models has been discussed by Van de Vijver et al [43].…”

Implementation of Stereochemistry in Automatic Kinetic Model Generation

“…For this, a combination of group contribution methods is used such as Benson group additivity and the Hydrogen Bond Increment method of Lay et al , as described in previous work . Symmetry numbers are automatically calculated based on graph theoretical algorithms . The current study does not contain a large number of species; nevertheless, group contribution was chosen to illustrate the strategy.…”

“…without considering the bond lengths and dihedral angles in the “real” molecule. The determination of topological symmetry is solely based on the atom connectivity and can entail both external as well as internal symmetry, which is discussed in previous work .…”

“…Atom permutations that preserve the connectivity between the atoms of the original molecule belong to a permutation group called the automorphism group. It has been shown that the automorphism group order is an upper limit for the topological symmetry in chemical structures . The newly developed tool uses an existing algorithm to obtain the automorphism group and determine the symmetry of a chemical graph.…”

Accurate Thermochemistry with Small Data Sets: A Bond Additivity Correction and Transfer Learning Approach

“…In fact, training a machine learning model to predict entropies that are symmetry-corrected is a more difficult task because the model has to implicitly learn symmetry numbers, which instead could easily be applied after training a model that does not include symmetry. Of course, correct computational determination of symmetry numbers, whether by estimating point groups from three-dimensional molecular geometries or from a computation based on a molecular graph representation, is a complex task in itself already discussed in the literature − and is outside the scope of this study.…”