However, a more pertinent question is whether a force field model that more accurately captures the QM electrostatic potential also results in more accurate prediction of condensed phase properties. We have therefore trained a series of force field protocols that include virtual sites in the description of the electrostatics (models 5a-5e). Table summarises the accuracy on the training set. As opposed to some of the other design choices, we now see significant accuracy gains for these models, with predictions in liquid densities in the range 0.014-0.021 g/cm 3 and heats of vaporisation between 0.24-0.48 kcal/mol. The lowest density error is observed when virtual sites are used in combination with the B3LYP-D3(BJ)/DZVP QM method (model 5d), and the lowest energy errors when used with rescaled Lennard-Jones interactions (model 5b). Although there is no significant trend in the fit R f ree i parameters on the heavy atoms for these force field protocols (Table ), interestingly there is a consistent shift of the van der Waals radii of the polar hydrogen atoms to higher values (1.27-1.46 Å) when used in combination with virtual sites. This makes intuitive sense since these atoms are likely to be involved in hydrogen bonds with anisotropic polar atoms, like oxygen and nitrogen. The virtual sites will move the centre of electron density closer to the van der Waals surface of the heavy atom, meaning that the Lennard-Jones repulsion should increase to compensate the increase in electrostatic attraction. The improved condensed phase prop-erties seem to indicate that this is a more physically-reasonable balance than the traditional atom-centred point charge approach.