Visualization-Based Approach to Condensed-Phase Line Broadening Using Polyene Chains

TL;DR

This paper introduces a visualization-based method combining analytic and numerical techniques to help undergraduates understand spectral line broadening in conjugated molecules through simulations and animations.

Contribution

It presents an accessible educational approach using MATLAB to illustrate how molecular orbital structure and environmental interactions influence spectral line shapes.

Findings

Closed-form expressions for electronic motion in polyene chains

Visualization of environmental effects disrupting coherence

Simulated spectra linking microscopic dynamics to observed line shapes

Abstract

Condensed-phase spectral line shapes encode the strength and timescale of interactions between molecules and their environments, yet these ideas are often difficult to introduce at the undergraduate level due to their reliance on formal theoretical treatments. We present a visualization-based approach that combines analytic results with numerical simulations to illustrate the physical origins of spectral line broadening in conjugated molecular systems. Using a time-dependent H\"uckel Hamiltonian, we derive closed-form expressions for coherent electronic motion in finite polyene chains and show how these results provide direct insight into the role of molecular orbital structure in light absorption. Environmental effects are introduced through stochastic fluctuations of the Hamiltonian matrix elements, allowing students to observe how system--environment interactions disrupt coherent motion and produce scattering-like features in electronic trajectories. Real-space animations and simulated absorption spectra provide an intuitive link between microscopic dynamics and measured line shapes. The MATLAB code provided with this work offers an accessible platform for integrating computation and visualization into undergraduate instruction while introducing key concepts in condensed-phase spectroscopy.