The hypothesis that nuclear motion can be described classically has been tested for several critical systems. We investigate the inversion of ammonia and the heat capacities of water and hydrogen. We use conventional ab initio molecular dynamics, which describes nuclear motion classically and the electron cloud using density functional theory. Ammonia inversion is described perfectly by the tunneling of the p orbital through the molecular plane. Nuclear tunneling is not needed to describe this phenomenon. While the investigation of heat capacities is hampered by the brief simulation times and limited system sizes, we can nevertheless make some qualitative statements. Indeed, the heat capacity can be frozen out in molecular dynamics simulations of solids, and hence, a quantized description is not required. © 2019 The Authors. International Journal of Quantum Chemistry published by Wiley Periodicals, Inc.