A Computational Exercise Illustrating Molecular Vibrations and Normal Modes

Abstract

Molecular vibration plays an important role in chemistry, both in chemical reactions and in the characterization and measurement of molecular structure and bonding. Normal modes provide the conceptual framework for understanding molecular vibrations. For example, the analysis of infrared spectra, an important tool for chemists, relies heavily on the concept of normal modes; yet, undergraduate students, even chemistry majors, seldom gain a thorough understanding of normal modes through the traditional chemistry curriculum. In fact, the most commonly used physical chemistry textbooks give only a cursory introduction to this concept, leaving out the substantive development. This occurs presumably because normal modes emerge from a multistepped mathematical analysis of the molecular dynamics. While the mathematical skill needed for each step typically has been covered in an introductory calculus course, the full development is a lengthy process and skipped in the texts. Thus, students have little opportunity to develop a sound conceptual understanding of ‘vibrational modes’ and ‘fundamental vibrational frequencies,’ even though they inevitably encounter these terms in their future work.