ViPA: A computer program for vector projection analysis of normal vibrational modes of molecules Original Research Article

We describe a program designed to give a quantitative comparison of the normal vibrational modes of similar molecules by using calculated force constant matrices. The program uses the normal modes of one molecule to form a basis set to describe the normal modes of a second, similar molecule. Vibrational projection analysis, a specific application of vector projection analysis, is thus used to determine a percentage similarity by calculating the dot product between each of the 3N normal modes of one molecule and the 3N′ normal modes of the other and virtually automates the assignment of normal mode descriptions for one molecule to another, structurally similar molecule. The ViPA program for Vibrational Projection Analysis can accomodate molecules with different numbers of atoms and different orientations, and it can calculate vibrational frequencies and modes of isotopically substituted molecules. The program has been used to compare normal modes of molecules which differ by perturbations of their masses (e.g., isotopic substitutions), their force constants (e.g., different oxidation states, electronic states, or non-covalent contacts) or both (e.g., chemical substitution), as well as to compare the results of calculations using different quantum chemical methods and/or basis sets. Although the program currently uses force constant matrices from the quantum chemistry program Gaussian94, potential applications of the method include analyzing normal modes from molecular mechanics or molecular dynamics calculations, comparing modes calculated by different methods, and perhaps calculating Franck-Condon factors. Thus, the vibrational projection analysis concept is not limited to small molecules, but will prove useful for ordered periodic solids as well as proteins, and perhaps disordered polymers and liquids too.