Approaches for constraining uncertainty and degeneracy in geometry reconstruction of molecules from simulated Coulomb explosion data

Abstract

Coulomb explosion imaging (CEI) data, consisting of atomic ion momenta, resulting from a rapid (few fs) ionization event, is typically recorded as a first step in the generation of a single molecule geometry measurement or the production of a ‘molecular movie’ that watches the evolution of an excited state geometry in time. Deriving a reliable geometry from this data is a crucial and challenging step, as unique solutions may not exist. In this work, we start by simulating the geometries of a molecule, which is out of equilibrium, the asymmetric carbonyl sulfide (OCS) molecule. We generate momentum data resulting from six-fold ionization and investigate two methods to reconstruct geometries. The first method is a look-up table, which is simple in principle but shows limitations in terms of accuracy and ability to identify multiple ‘degenerate’ solutions. The second is a new method using nonlinear constrained optimization, which shows potential for scalability to higher dimension. We investigate the possibility of identifying problematic geometry regions where different degenerate geometries can not be distinguished.