Imaging Three-Dimensional Molecular Structure and Dynamics with Multiparticle Covariance and Cumulant Coulomb Explosion Analysis

Coulomb explosion imaging (CEI) has emerged as a powerful approach for imaging molecular structure in the gas phase by leveraging momentum correlations between ionic fragments produced in strong-field or X-ray–driven fragmentation. CEI provides direct access to molecular geometry by correlating fragment ion momenta following breakup of a highly charged molecular ion. Here we demonstrate three-body covariance and four-body cumulant analysis to extract three-dimensional structural information from the X-ray–induced Coulomb explosion of tert-butyl iodide (C₄​H₉​I). Site-selective ionization at the iodine 4d edge using intense femtosecond soft X-ray pulses from the SACLA X-ray Free-Electron Laser (XFEL) initiates rapid charge localization and fragmentation. Correlating ionic fragments in the molecular frame isolates complete dissociation channels and reveals subtle structural signatures, including umbrella-type motion of the branched alkyl group during ionization. The measured fragment correlations show close agreement with point-charge Coulomb explosion simulations, validating the approach. These results establish covariance/cumulant mapping as a general route to 3D structure retrieval in complex polyatomics, and motivate extensions to time-resolved CEI using XFEL and tabletop sources to capture ultrafast structural dynamics.