For the formaldehyde-water cluster in water, the projection affects a significantly larger number of normal modes beyond the six lowest-frequency modes. The majority of pseudotranslational and pseudo-rotational contributions are concentrated in the 13 lowest-frequency modes, each of which shows contributions of at least 10 %. However, up to the 18 lowestfrequency modes exhibit at least 1 % pseudo-translational and pseudo-rotational contributions. On most of the 18 lowest-frequency modes, the projection has a considerable impact on frequencies and intensities. Specifically, modes 19-24 exhibit substantial frequency errors ranging from 55 to 85 cm -1 , all corresponding to intermolecular stretching or bending modes in the formaldehyde-water cluster. Interestingly, the normal modes in the formaldehydewater cluster that have the greatest overlap with the normal modes in formaldehyde in water are among the 13 highest-frequency modes, which exhibit similarly low errors as those in formaldehyde in water. Therefore, the increase in pseudo-translational and pseudo-rotational contributions and the associated errors seen in the formaldehyde-water cluster likely stem from the inclusion of the two solvent water molecules to the QM subsystem.