Carbon disulfide dimers (CS2)2 are doubly ionized by an intense 40-fs laser pulse leading to fragmentation into a pair of CS2+ cations. Unlike previous studies on atomic dimers, their kinetic energy, gained by mutual electrostatic repulsion, deviates strongly from the value determined by applying the Coulomb interaction approximation to the (CS2)22+ ion. An ab initio calculation shows that inclusion of non-Coulombic interactions in (CS2)22+ is crucial to account for the observed kinetic energy. These interactions result in 16 (CS2)22+ electronic microstates, which obstructs accurate determination of intermolecular bond distances in (CS2)2 from the fragments' kinetic energy. The situation will be similar for most other weakly bonded atomic and molecular complexes.