The most stable forms of E(5)Li(7)(+) (E = Ge, Sn, and Pb) have been explored by means of a stochastic search of their potential-energy surfaces by using the gradient embedded genetic algorithm (GEGA). The preferred isomer of the Ge(5)Li(7)(+) ion is a slightly distorted analogue of the D(5h) three-dimensional seven-pointed starlike structure adopted by the lighter C(5)Li(7)(+) and Si(5)Li(7)(+) clusters. In contrast, the preferred structures for Sn(5)Li(7)(+) and Pb(5)Li(7)(+) are quite different. By starting from the starlike arrangement, corresponding lowest-energy structures are generated by migration of one of the E atoms out of the plane with the a corresponding rearrangement of the Li atoms. To understand these structural preferences, we propose a new energy decomposition analysis based on isomerizations (isomerization energy decomposition analysis (IEDA)), which enable us to extract energetic information from isomerization between structures, mainly from highly charged fragments.