The investigation of the chemical reactivity of complex systems such as transition metal clusters is a very complicated task because often the structures of the corresponding transition states are far from being intuitive. Bimetallic transition metal clusters represent a particular class of complex systems. In this work, density functional theory (DFT) is applied to study the isomerization reactions of the Cu15V+ cluster. Full geometry optimizations of dozens of initial structures taken along Born-Oppenheimer molecular dynamics (BOMD) trajectories were performed using a quasi-Newton method in a reduced space Cartesian coordinate system that works considering the internal degrees of freedom. Harmonic frequencies calculations were performed at the optimized structures. To study the isomerization reactions between the obtained stable isomers, a hierarchical transition state algorithm has been applied to locate the transition states of this cluster. The found transition states were than connected with the corresponding minimum structures by calculating the intrinsic reaction coordinates. This work demonstrates the capability of the applied method to study non-intuitive rearrangement mechanisms in complex finite systems and to create networks between minima and transition state structures on their potential energy surface.