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 H2O is 0.38% higher than that of D2O. With the ECP, the H2O 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 H2O is found to be 21% higher than that of D2O, which is in good agreement with the 29.9% higher diffusivity for H2O 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 H2O and D2O 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.