Identification of unavoided crossings in nonadiabatic photoexcited dynamics involving multiple electronic states in polyatomic conjugated molecules

Radiationless transitions between electronic excited states in polyatomic molecules take place through unavoided crossings of the potential energy surfaces with substantial non-adiabatic coupling between the respective adiabatic states. While the extent in time of these couplings are large enough, these transitions can be reasonably well simulated through quantum transitions using trajectory surface hopping-like methods. In addition, complex molecular systems may have multiple "trivial" unavoided crossings between noninteracting states. In these cases, the non-adiabatic couplings are described as sharp peaks strongly localized in time. Therefore, their modeling is commonly subjected to the identification of regions close to the particular instantaneous nuclear configurations for which the energy surfaces actually cross each other. Here, we present a novel procedure to identify and treat these regions of unavoided crossings between non-interacting states using the so-called Min-Cost algorithm. The method differentiates between unavoided crossings between interacting states (simulated by quantum hops), and trivial unavoided crossings between non-interacting states (detected by tracking the states in time with Min-Cost procedure). We discuss its implementation within our recently developed non-adiabatic excited state molecular dynamics framework. Fragments of two- and four-ring linear polyphenylene ethynylene chromophore units at various separations have been used as a representative molecular system to test the algorithm. Our results enable us to distinguish and analyze the main features of these different types of radiationless transitions the molecular system undertakes during internal conversion.