LAUSR

Abstract Normal mode analysis has been employed to characterize fundamental phenomena in diverse scientific disciplines, including the identification of molecular vibrations in chemistry and their peak assignments in infrared and Raman spectra. The vibrational modes are traditionally determined from the potential energy surface under the harmonic approximation. Here, we introduce a methodology called Expanded Moment of Inertia Tensor, EMIT, which can extract a complete set of normal coordinates from the molecular geometry at any point in phase space. Its principle lies in the conservative expansion of the angular momentum within the rigidbody framework. This method provides normal modes that resemble those obtained from group theory and show their efficacy by accurately reproducing all characteristic frequencies in the vibrational spectra of NO 2 - and NO 3 - in aqueous solution. Not only this geometry-based method of normal mode determination looks promising in many fields, but it also inspires us to view known molecular quantities in physics differently.