Vibrational projection analysis: New tool for quantitatively comparing vibrational normal modes of similar molecules

A new method for quantitatively comparing calculated vibrational modes is described that relies on projecting the vectors describing the normal modes of one molecule onto those of a basis molecule. The procedure virtually automates the assignment of vibrational modes from one molecule to a second, structurally similar one. We illustrate the concept by using the classical Wilson modes of benzene as a basis for describing normal modes of the monosubstituted benzene derivatives phenol, phenol‐ d 5, and phenol radical cation. These examples demonstrate the method's power for accurately assigning and comparing the normal modes of molecules perturbed by chemical substitution, isotopic substitution, or oxidation state. The vibrational projection analysis method—a special case of vector projection analysis—is compared and contrasted with total energy distribution analysis, perhaps the most commonly used technique for quantitatively comparing vibrational modes, and is found superior in each case when comparing normal modes. Vibrational projection analysis need not be limited to single molecules and quantum calculations, because normal modes may be obtained for much larger systems using molecular mechanics or molecular dynamics techniques. The method should therefore prove useful for interpreting the normal modes of ordered periodic solids and structures perturbed by noncovalent contacts, including proteins and polymers. The method may also prove useful in evaluating new computational methods by allowing direct, quantitative comparison of the vibrational modes obtained from different techniques. The power of this technique will make vibrational projection analysis a valuable tool for computational chemists as well as those using calculations to complement vibrational spectroscopic measurements. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1663–1674, 1998