Helping Students Understand the Role of Symmetry in Chemistry Using the Particle-in-a-Box Model

Abstract

In a course on chemical applications of symmetry and group theory, students learn to use several useful tools (like character tables, projection operators, and correlation tables), but in the process of learning the mathematical details, they often miss the conceptual big picture about “why” and “how” symmetry leads to the quite dramatic consequences that it does. This pedagogical gap is addressed in this paper by using one of the simplest chemical model systems, the particle in a box, along with a simple symmetry operator, parity, to get a clear understanding of the consequences of symmetry. The analysis of the particle-in-a-box model is extended by analogy to molecules, and connections are made to chemically important concepts like symmetry labels of molecular states, spectroscopic selection rules, and symmetry adapted linear combinations of orbitals.

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

“…Moreover, this model can be applied to a physical chemistry experiment called the particle-in-a-box experiment, which uses the absorption spectra of polymethine dyes to determine the length of a one-dimensional box. , The apparent box length estimated in this exercise allows the students to relate the basics of the system’s wavefunction, and the energy levels (eigenvalues) truly represent the boundary conditions of the Schrödinger equation. This topic has garnered much interest in this Journal , with over 25 manuscripts discussing the particle-in-a-box model, including the system’s symmetry and degeneracy, − improved selection of molecules, − and expanded applications of the model. − …”