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

Abstract

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 (λ max ) 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 Schrodinger'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.

Using Particle-on-a-Ring to Predict Carbon–Carbon Bond Length of Synthesized Porphyrins

“…A year-long physical chemistry sequence is often split into a macroscopic semester and a microscopic semester. The macroscopic material tends to lend itself better to traditional wet experiments while the microscopic material has recently seen an abundance of theoretical or computational experiments become utilized, with a focus on helping students engage with introductory quantum principles. − While this abundance of quantum focused experiments is excellent, there is not as diverse a pool of wet experiments involving synthesis that help students explore some of the basic tenets of quantum theory. One commonly utilized wet experiment is the UV–vis spectroscopy of a number of cyano dyes to model the energy levels of the 1-D particle in a box system .…”