G-RMSD: Root Mean Square Deviation Based Method for Three-Dimensional Molecular Similarity Determination

We present the Generalized Root Mean Square Deviation (G-RMSD) method. G-RMSD is an optimization method to calculate the minimal RMSD value of two atomic structures by optimal superimposition. G-RMSD is not restricted to systems with an equal number of atoms to compare or a unique atom mapping between two molecules. The method can handle any type of chemical structure, including transition states and structures which cannot be explained only with valence bond (VB) theory (non-VB structures). It requires only Cartesian coordinates for the structures. Further information, i.e. atom- and bond types can also be included. Applications of G-RMSD to the classification of α-d-glucose conformers and 3D partial structure search using a dataset containing equilibrium (EQ), dissociation channel (DC), and transition state (TS) structures are demonstrated. We find that G-RMSD allows for a successful classification and mapping for a wide variety of molecular structures.G-RMSD, an optimization method to calculate the minimal RMSD (Root Mean Square Deviation) value of two atomic structures by optimal superimposition, solves a problem of comparing 3D-molecules of different size without a unique atom mapping. It was successfully applied to searching a quantum mechanical based reaction pathway database containing not only equilibrium structures, but also transition state and non-valence structures.