Density functional study of H-D coupling constants in heavy metal dihydrogen and dihydride complexes: The role of geometry, spin-orbit coupling, and gradient corrections in the exchange-correlation kernel

The H-D nuclear spin-spin coupling constants J(H-D) of 14 heavy transition-metal dihydrogen and dihydride complexes were calculated with density functional theory using the "zeroth-order regular approximation" (ZORA) for the one-electron operators. The applied gradientcorrected density functional was able to achieve an average agreement with experimental data that is almost comparable to what has been obtained recently with hybrid functionals [J. Am. Chem. Soc. 2004, 126, 14249]. However, a systematic overestimation of J(H-D) for complexes with short H-D distances was obtained, which could be traced back to problems of the gradient functional to describe the H-D coupling in free dihydrogen well. We implemented gradient corrections for the exchange-correlation (XC) kernel and employed a basis sets with highexponent 1s function for the coupled hydrogens. The gradient terms in the XC kernel turned out to be very important in order to achieve reasonable agreement with experimental coupling constants. On the other hand, our study reveals that spin-orbit relativistic corrections on the H-D coupling constants are comparatively small and need not to be considered at the accuracy level of currently available "standard" density functionals. The discussion of the results highlights the strong dependence of the coupling constants on the H-D distance and the possibility of large vibrational contributions to them. We also discuss the coupling constant for the hydrogen molecule in detail because of its relevance to the coupling in dihydrogen and dihydride complexes.