In the classical molecular dynamics for a complicated system the trajectory remains relatively close to any arbitrarily chosen starting configuration of the nuclei. This is because of a prohibitively large volume of the configurational space as well as of energy barriers between numerous potential energy basins. In the present paper the molecular dynamics is performed on a deformed potential energy hypersurface. The deformation is tunable, and when increased, the barriers become lower or even disappear; therefore, the system is able to explore much larger regions of the configurational space. The deformation is slowly released, and finally the molecular dynamics is continued on the undeformed potential energy hypersurface. As a result of such a procedure, some low-energy structures may be found in a more effective way. The method has been applied to the clusters of the N Lennard-Jones atoms, N = 5,..., 66, which is the most extensive systematic study of the clusters published till now. The energies of the clusters are lower than those obtained by the classical molecular dynamics (at the same numerical effort) for the starting points being far away from the lowest energy region. Contrary to the molecular dynamics, they are independent of the starting point to a significant degree. The size of the most stable cluster turned out to be a stepwise increasing function of N, which reflects building of new atomic shells. However, for N = 38 some qualitative change of the structure to the one characteristic for the infinite crystal occurs and the cluster size becomes abnormally low when compared to the clusters with N < 38 and N > 38.y