Zero-point vibrationally averaged (r(g)(0)) structures were computed at the PBE0/SDD/6-31G* level for the [pt(35)Cl(n)(37)Cl(5-n)((H2O)-O-18)](-) (n = 0-5), cis-(PtClnCl4-n)-Cl-35-Cl-37 ((H2O)-O-18)((H2O)-O-16) (n = 0-4), fac-[(PtCnCl3-n)-C-35-Cl-37((H2O)-O-18)((H2O)-O-16)(2)](+) (n = 0-3), [(PtClnCl5-n)-Cl-35-Cl-37((OH)-O-16/18)](2-) (n = 0-5), cis-[(PtClnCl4-n)-Cl-35-Cl-37((OH)-O-16/18)(2)](2-) (n = 0-4), fac-[(PtClnCln37)-Cl-35-Cl-35 Cl3-n ((OH)-O-16/18)(3)](2-) (n = 0-3), cis-[(PtClnO2-n)-Cl-35-O-37 ((OH)-O-16/18)(4)](2-) (n = 0-2), [(PtClnCln37Cl1-n)-Cl-35-Cl-37((OH)-O-16/18)(5)](2-) (n = 0-1), [(RhClnCl5-n)-Cl-35-Cl-37 (H2O)](2-) (n = 0-5), cis[(RhClnCl4-n)-Cl-35-Cl-37(H2O)(2)](-) (n = 0-4), and fac-(RhCnCl3-n)-C-35-Cl-37 (H2O)(3) (n = 0-3) isotopologues and isotopomers. Magnetic shielding constants, computed at the ZORA-SO/PW91/QZ4P/TZ2P level, were used to evaluate the corresponding Cl-35/37 isotope shifts on the Pt-195 and Rh-103 NAIR spectra, which are known experimentally. While the observed effects are reproduced reasonably well computationally in terms of qualitative trends and the overall order of magnitude (ca. 1 ppm), quantitative agreement with experiment is not yet achieved. Only small changes in M-Cl and M-O bonds upon isotopic substitution, on the order of femtometers, are necessary to produce the observed isotope shifts.