We have investigated M center dot center dot center dot H-C interactions in d(8) square planar Rh and Pt complexes involving different types of C-H bonds, as well as a M center dot center dot center dot H-N hydrogen-bonded complex, using a combination of DFT and "atoms-in-molecules" (AIM) theory. The AIM analysis shows that both M center dot center dot center dot H-C and M center dot center dot center dot H-N interactions in d(8) square planar complexes are of a closed-shell, electrostatic nature, similar to protein backbone hydrogen bonds. However, at the shortest M center dot center dot center dot H distances, both interactions have partial covalence. We find no evidence for the involvement of d(z)(2) orbitals in M center dot center dot center dot H-C interactions but do find evidence for the involvement of d(xz/yz) orbitals in M center dot center dot center dot H-C bonding. The DFT calculations reproduce well the experimental proton NMR chemical shifts, with a theory-versus-experiment correlation coefficient R-2 = 0.985. There are large downfield H-1 NMR chemical shift changes on metal bonding, accompanied by changes in shielding tensor orientations.