A comparison of density functional methods for the calculation of phosphorus-31 NMR chemical shifts

P-31 NMR chemical shifts for the phosphorus compounds PX3 (X = H, F, Cl, CH3, (C3H7)-C-i and OCH3), OPX3 (X = CH3 and OCH3), Si(PH2)(4), Cr(CO5)(PH3), PX4+ (X = H, CH3), PF6-, P-4 and PN have been calculated with various density functional methods as well as at the Hartree-Fock and MP2 level, using both the IGLO and GIAO variants of introducing distributed gauge origins except for MP2 (only GIAO available) and the new method proposed recently by Wilson, Amos and Handy (WAH, GIAO not available). Except for PCl3 and PN, all density functional approaches achieve comparable accuracy, better than Hartree-Fock and similar to MP2. For PCl3 and PN, the WAH method leads to a substantial improvement. The GIAO and IGLO results are of comparable accuracy. Numerical benchmark values for the absolute magnetic shielding of PN at its experimental equilibrium value are presented and compared with literature data. A theoretical analysis reveals that the approximation used by WAH makes their method lose gauge invariance.