Beyond minimum energy conical intersections: a data-driven reconstruction of the accessible intersection seam.

Minimum energy conical intersections (MECIs) are widely used to rationalize nonadiabatic relaxation pathways, yet it remains unclear to what extent they provide a representative description of the intersection seam effectively explored during dynamics. In this work, we combine large ensembles of seam points from nonadiabatic simulations with dimensionality reduction and density-based analysis to systematically investigate the structure of the accessed seam regions and its relationship to MECIs. We first establish a robust, physically-meaningful protocol for representing seam morphology across systems. After accounting for rigid-body alignment and permutation symmetry, Cartesian coordinates are found to best preserve structural relationships, while densMAP provides an optimal low-dimensional embedding that captures both geometric variation and sampling density. Applying this framework to ethylene, butadiene, and benzene, reveals that the intersection seam is organized into dynamically accessible basins that are not uniformly represented by discrete MECIs. While MECIs associated with highly populated basins are located near density maxima and capture the dominant relaxation pathways, many other MECIs correspond to peripheral or weakly sampled regions. Moreover, neither geometric proximity nor energetic accessibility alone reliably predicts dynamical relevance: geometrically closest MECIs do not always correspond to optimization outcomes, and low-energy MECIs may remain largely unvisited. These results demonstrate that MECIs should be viewed as discrete markers within a broader, continuous, and dynamically weighted seam landscape. A comprehensive understanding of photochemical relaxation therefore requires not only the identification of MECIs, but also an explicit characterization of the regions of the seam that are actually sampled and the pathways connecting them.