Automated handling of complex chemical structures in Z ‐matrix coordinates—The chemcoord library

In this work, we present a fully automated method for the construction of chemically meaningful sets of hierarchical nonredundant internal coordinates (ICs; also commonly denoted as Z-matrices) from the Cartesian coordinates of a molecular system. Particular focus is placed on avoiding ill-definitions of angles and dihedrals due to linear arrangements of atoms, to consistently guarantee a well-defined transformation to Cartesian coordinates, even after structural changes. The representations thus obtained are particularly well suited for pathway construction in double-ended methods for transition state search and optimizations with nonlinear constraints. Analytical gradients for the transformation between the coordinate systems were derived for analytical geometry optimizations purely in Z-matrix coordinates. The geometry optimization was coupled with a Symbolic Algebra package to support arbitrary nonlinear constraints in Z-matrix coordinates, while retaining analytical energy gradient conversion. The difference to the commonly used nonhierarchical IC transformations is discussed. Sample applications are provided for a number of common chemical reactions and illustrative examples.