We present applications to molecular problems of a recently developed quantum Monte Carlo algorithm [Phys. Rev. E 55, 3664 (1997)] for the calculation of excited state energies of multi-dimensional quantum systems, employing a projection operator imaginary time spectral evolution (POITSE). The extraction of vibrational energies is demonstrated on a double well potential and on two coupled harmonic oscillators, and on excited rotational states of a rotating harmonic oscillator. All energies extracted by the quantum Monte Carlo algorithm are in good agreement with exact results, showing that the new method is very promising for the calculation of tunneling splittings, and of vibrational and rotational excitations in real multi-dimensional molecular systems. (C) 1997 American Institute of Physics.