The strengths and limitations of effective centroid force models explored by studying isotopic effects in liquid water.

The development of effective centroid potentials (ECPs) is explored with both the constrained-centroid and quasi-adiabatic force matching using liquid water as a test system. A trajectory integrated with the ECP is free of statistical noises that would be introduced when the centroid potential is approximated on the fly with a finite number of beads. With the reduced cost of ECP, challenging experimental properties can be studied in the spirit of centroid molecular dynamics. The experimental number density of H2 O is 0.38% higher than that of D2 O. With the ECP, the H2 O number density is predicted to be 0.42% higher, when the dispersion term is not refit. After correction of finite size effects, the diffusion constant of H2 O is found to be 21% higher than that of D2 O, which is in good agreement with the 29.9% higher diffusivity for H2 O observed experimentally. Although the ECP is also able to capture the redshifts of both the OH and OD stretching modes in liquid water, there are a number of properties that a classical simulation with the ECP will not be able to recover. For example, the heat capacities of H2 O and D2 O are predicted to be almost identical and higher than the experimental values. Such a failure is simply a result of not properly treating quantized vibrational energy levels when the trajectory is propagated with classical mechanics. Several limitations of the ECP based approach without bead population reconstruction are discussed.