RANGE-X: a gradient-free framework for the discovery of conical intersections and photochemical reaction pathways

Conical intersections (CIs), where two potential energy surfaces, such as those for the ground and first excited states, coincide, are quintessential in photochemistry. Nevertheless, it is usually difficult to find them without substantial chemical intuition and computational cost. As a solution to this problem, we present RANGE-X, a fully automated, gradient-free framework for locating CIs and their energy landscape, including ground- and excited-state minima, transition states, and reaction paths. The workflow is based on the hybrid artificial-bee-colony/genetic-algorithm global optimizer, RANGE (robust adaptive nature-inspired, global explorer), which performs gradient-free sampling with a choice of three cost functions targeting CIs, ground-state minima, and excited-state minima. The output from RANGE is amplified by a machine-learning post-processing layer that combines Gaussian process regression of the cost surface with DBSCAN (density-based spatial clustering of applications with noise) clustering in geometric space, which extracts photochemical-landscape topology, distinct CI clusters, ground-state isomer basins, and approximate transition states from the accumulated data without additional electronic-structure calculations. An optional gradient-based conical-search refinement can be performed to achieve sub-meV accuracy in the CI energy gap. Candidate transition states are validated by a path-interpolation pipeline that distinguishes discrete-well topologies from broad-shoulder topologies that geometry-space clustering alone cannot resolve. The framework is method-agnostic for ground and excited states, as well as for reaction path validation approaches, and can be coupled with any ab initio software on classical or quantum hardware. In the present work, the GAMESS spin-flip time-dependent density functional theory (SF-TDDFT) is used to study the ground and excited states. The reaction path validator is the nudged elastic band (NEB). Both choices are illustrative and can be replaced with other appropriate approaches. The framework is illustrated on eight systems spanning organic, d-block, heterometallic, multi-fragment metal-organic, and f-element chemistry.