This research article presents a method for determining optimal internal coordinate sets to represent molecular vibrations. The authors propose a normal mode decomposition scheme to select an optimal set of internal coordinates that minimizes coupling between internal coordinates. The NOMODECO toolkit is introduced, which generates internal coordinate sets to find an optimal set for representing molecular vibrations. The resulting contribution tables can be used to clarify vibrational notations. The method is tested on small to mid-sized molecules, showing how the space of definable internal coordinate sets can significantly be reduced. The study highlights the importance of choosing appropriate internal coordinates for accurate vibrational analysis, especially for delocalized vibrations. The method is based on symmetry and topology considerations, and a metric is introduced to evaluate the quality of an internal coordinate set. The results demonstrate that the proposed method effectively reduces the number of possible internal coordinate sets and identifies the optimal set for representing molecular vibrations. The study also shows that the intrinsic frequencies of normal modes can be determined using the proposed method, providing a clearer understanding of molecular vibrations. The results are illustrated with examples of linear, planar, and general acyclic molecules, demonstrating the effectiveness of the method in various molecular systems. The study concludes that the proposed method provides a systematic way to determine optimal internal coordinate sets for molecular vibrations, improving the accuracy and clarity of vibrational analysis.This research article presents a method for determining optimal internal coordinate sets to represent molecular vibrations. The authors propose a normal mode decomposition scheme to select an optimal set of internal coordinates that minimizes coupling between internal coordinates. The NOMODECO toolkit is introduced, which generates internal coordinate sets to find an optimal set for representing molecular vibrations. The resulting contribution tables can be used to clarify vibrational notations. The method is tested on small to mid-sized molecules, showing how the space of definable internal coordinate sets can significantly be reduced. The study highlights the importance of choosing appropriate internal coordinates for accurate vibrational analysis, especially for delocalized vibrations. The method is based on symmetry and topology considerations, and a metric is introduced to evaluate the quality of an internal coordinate set. The results demonstrate that the proposed method effectively reduces the number of possible internal coordinate sets and identifies the optimal set for representing molecular vibrations. The study also shows that the intrinsic frequencies of normal modes can be determined using the proposed method, providing a clearer understanding of molecular vibrations. The results are illustrated with examples of linear, planar, and general acyclic molecules, demonstrating the effectiveness of the method in various molecular systems. The study concludes that the proposed method provides a systematic way to determine optimal internal coordinate sets for molecular vibrations, improving the accuracy and clarity of vibrational analysis.