The frequency errors for propanamide in water are generally small, but two modes stand out with high errors, namely modes 23 and 24, with errors of about 20 cm -1 and 45 cm For formaldehyde in water (results presented in Fig. ), the frequency errors are generally small, approximately 1 cm -1 . Similarly, the errors are also small for the normal modes local to the formaldehyde of the formaldehyde-water cluster, i.e., normal modes that have substantial overlap with the normal modes of formaldehyde in water, which is normal Generally, we find that for normal modes consisting of local vibrational motions in the solute and solvent separately, i.e., they are not coupled but have the same frequency, using the PHVA approximation does not have a substantial effect. Conversely, if the normal mode involves collective motions of atoms in the solute and solvent, the PHVA approximation may introduce large errors. This becomes especially apparent in the formaldehyde-water cluster, where the molecular vibrations of the two water molecules are strongly coupled to the water molecules in the solvent. The environmental contribution does not distinguish between the two cases. However, large environmental contributions typically indicate large frequency errors, owing to the lack of coupling between atoms of the solute and solvent in the partial Hessian. However, as in the case of mode 5 for uracil in methanol, the environmental contribution can be small, and there can still be large errors in this case. There are also cases, e.g., normal modes 8 and 9 of propanamide in water, with clear environmental contributions, but the errors are relatively small. The intensity errors, on the other hand, are typically dominated by the truncation of the dipole and polarizability gradients.