We present dissociative adsorption probabilities of H-2 on Pd(111) computed with the classical trajectory method. We perform both classical (C) and quasiclassical (QC) calculations, the latter including, by contrast with the former, the initial zero point energy (ZPE) of H-2. We analyze in detail the role played by the ZPE and demonstrate the strong and weak points of both C and QC calculations. We show that ZPE is crucial in accelerating the molecules toward the surface through vibrational softening. However, at low energies, dynamic trapping is quenched in QC calculations by processes of vibration to rotation energy transfer that would be associated with closed channels in a quantum approach. In this study we use a new representation of the H-2/Pd(111) potential energy surface (obtained by interpolation of ab initio data) with a significantly better accuracy in the entrance channel region which plays a decisive role in the dissociation dynamics.