The paper "Determining Internal Coordinate Sets for Optimal Representation of Molecular Vibration" by Kemal Oener, Dennis F. Dinu, and Klaus R. Liedl explores the use of internal coordinates to improve the representation of molecular vibrations. The authors address the limitations of using Cartesian coordinates, which can lead to high coupling between vibrational modes, and propose a systematic approach to selecting optimal internal coordinate sets. They introduce the NOMODECO toolkit, which generates and evaluates internal coordinate sets based on topology and symmetry considerations, aiming to minimize coupling and maximize the clarity of vibrational notations. The toolkit is tested on small to mid-sized molecules, demonstrating its ability to significantly reduce the space of definable internal coordinate sets. The paper also discusses the theoretical foundations of normal mode decomposition, including the transformation between Cartesian and internal coordinates, force constant matrices, and energy distribution matrices. The authors provide detailed examples for linear, planar, and general acyclic molecules, showing how NOMODECO selects the best internal coordinate sets and how these sets can be used to clarify vibrational notations.The paper "Determining Internal Coordinate Sets for Optimal Representation of Molecular Vibration" by Kemal Oener, Dennis F. Dinu, and Klaus R. Liedl explores the use of internal coordinates to improve the representation of molecular vibrations. The authors address the limitations of using Cartesian coordinates, which can lead to high coupling between vibrational modes, and propose a systematic approach to selecting optimal internal coordinate sets. They introduce the NOMODECO toolkit, which generates and evaluates internal coordinate sets based on topology and symmetry considerations, aiming to minimize coupling and maximize the clarity of vibrational notations. The toolkit is tested on small to mid-sized molecules, demonstrating its ability to significantly reduce the space of definable internal coordinate sets. The paper also discusses the theoretical foundations of normal mode decomposition, including the transformation between Cartesian and internal coordinates, force constant matrices, and energy distribution matrices. The authors provide detailed examples for linear, planar, and general acyclic molecules, showing how NOMODECO selects the best internal coordinate sets and how these sets can be used to clarify vibrational notations.