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This paper introduces a visualization-based approach to explain condensed-phase spectral line broadening, focusing on conjugated polyene chains. They derive closed-form expressions for electronic motion using a time-dependent H眉ckel Hamiltonian and introduce environmental effects via stochastic fluctuations. The resulting real-space animations and simulated absorption spectra intuitively link microscopic dynamics to macroscopic line shapes, making the topic accessible for undergraduate instruction.
See how stochastic fluctuations in a simple H眉ckel model can bring condensed-phase spectroscopy to life for undergrads.
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.
