Results of new all-electron ab initio calculations and revisit of experimental studies of the interatomic potentials of lower-lying ungerade excited and ground electronic energy states of the Hg_{2} and Cd_{2} van der Waals complexes are used as probes of discrepancies between theory and experiment. From simulations of the previously and presently measured LIF excitation and dispersed emission spectra new analytical representations of the excited- and the ground-state interatomic potentials are proposed. An inverted perturbation approach was also used to improve the studied interatomic potentials. The comparison of the new ab-initio calculated potentials with the results of the analyses illustrates an improve theory-to-experiment agreement for such a demanding system like Hg_{2} or Cd_{2}.