We have performed a fully converged calculation for electronic structure of vertically coupled double quantum dots (DQDs) using linear combination of atomic orbitals. We find that to reach high accuracy of results and get a quick convergence, a special attention in choice of basis functions has to be paid, specially for small quantum dots. We also find the character of electronic states of DQDs evolves from atomic-like to molecular characteristic (bounding and anti-bounding) states as interdot distance decreases. We show that the electronic structure of DQDs can be engineered through properly DQD design. It is in sharp contrast to the natural molecules in which the geometric positions of composed atoms are fixed. (C) 2010 Elsevier B. V. All rights reserved.