The Quantum Mechanical Particle-in-a-Box Experiment–A Revisit Using NMR Spectroscopy

The particle-in-a-box experiment is a well-known method used to teach quantum mechanics concepts in physical chemistry laboratories for undergraduates. The investigation involves measuring the wavelength at maximum absorbance (λmax) of electronic transitions in the UV–vis spectrum and linking it to the box length. As the electronic configurations directly influence the nuclear shielding, a computational approach to estimate the nuclear magnetic resonance (NMR) chemical shifts is shown to relate to the box length. This work revisits what Flewwelling and Laidlaw suggested over 50 years ago: NMR chemical shifts can indirectly be related to the box’s length via electron density calculations. For a series of molecules (polyenylic ions) of increasing carbon chain length, the activity allows the students to develop a broader understanding of how Schrödinger’s equation for a particle in a box model, electron density calculations, and NMR spectroscopy are all connected at the atomic level. Additionally, the open-ended computational procedure leverages easily accessible tools to estimate NMR chemical shifts, and this approach is suitable as a viable remote learning exercise that supplements traditional UV–vis experiments.