Ab initio calculations of hydrogen NMR chemical shielding have been ca
rried out at the correlation-including GIAO MP2 level on nine small mo
lecules whose gas phase isotropic shieldings are well known. A range o
f basis sets from very small to rather large has been studied. While c
orrelation effects at this level of theory are small, basis set and ro
vibrational effects are large. Large basis sets and the inclusion of r
ovibrational effects are necessary to calculate hydrogen shieldings we
ll on an absolute basis (chemical shieldings), while the constraints a
re less demanding for calculations on a relative scale (chemical shift
s) where agreement with experiment for the set of molecules studied as
measured by the standard error is 0.11 ppm.