Approximate spin-projection (AP) method, which eliminates a spin contamination error from the broken-symmetry (BS) state, is extended to calculations of vibrational frequencies and optimizations of transition state structure. In the case of methylene, the BS solution overestimates the biradical character and gives worse results than the symmetry-adapted solution. The AP method gives proper corrections on the geometry and vibrational frequencies. As for the [2 + 2] reaction of singlet oxygen ((1)Delta(g)) with ethylene, the spin contamination error on transition state structures is corrected, and the new method can provide more accurate stationary points for the reactions. (C) 2009 Elsevier B. V. All rights reserved.