We investigate the accuracy of the recently proposed centroid molecular dynamics (CMD) method [J. Cao and G. A. Voth, J. Chem. Phys. 100, 5106 (1994)] in the presence of highly anharmonic steep short range repulsive potentials. Such potentials are often present in condensed phases and govern collisions between solvent particles. We compare the results of CMD simulations with exact quantum results for several model one- and two-dimensional nondissipative systems and a one-dimensional system under isobaric conditions. We show that, for nondissipative systems, CMD is accurate only for very short times, and is unable to reproduce the effects of quantum coherences, which play an important role in these few-dimensional systems. CMD gives much better results under isobaric conditions. The correlation functions and the general lineshape of the absorption cross-section in the dipole limit are well reproduced. This is primarily due to dephasing of quantum coherences through inhomogeneous broadening.