Hückel Theory Applied to Classical, Unbranched, Acyclic Polyenes

Novel approaches to manual computations that provide access to Hückel descriptions for unbranched, acyclic polyenes are introduced and discussed. These approaches include an Aufbau procedure to obtain secular equations, a root miner function to accelerate the determination of secular equation roots, a free-electron model-derived method to establish all possible embeddings for a given unbranched polyene and a relationship between large polyene molecular orbital coefficients and the secular equations of smaller polyenes. This novel material facilitates the creation of Hückel theory courses which introduce some chemical graph theory and illustrate its power.