Reaction yield oscillates over reaction time in first-order chemical reactions

The yield of a first-order chemical reaction normally has a unimodal trend over reaction time. In other words, once the population of a product decreases, it will normally never increase again by elongating the reaction time. However, in analyzing the full reaction path network of the Strecker reaction, we encountered a nontraditional behavior, where the population of an intermediate increased again after decreasing, even in a first-order reaction. Furthermore, simulations on model reaction path networks suggested that the reaction yield can oscillate multiple times over the reaction time. We mathematically prove that the number of reaction yield oscillations is at most N _EQ/2, where N _EQ denotes the number of equilibrium structures in the reaction path network. We also show that this upper bound is tight by constructing a model network that exhibits the maximum number of yield oscillations. This study provides new theoretical insight into reaction optimization strategies aimed at controlling product yields.