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

Abstract

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 gradient-corrected 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 high-exponent 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.

The role of the exchange-correlation response kernel and scaling corrections in relativistic density functional nuclear magnetic shielding calculations with the zeroth-order regular approximation

“…For the present work, an implementation of the response kernel f XC for functionals of the local density approximation (LDA) and generalised gradient approximation (GGA) types in the ADF J-coupling module [20,21,43] has been adapted for the ZORA NMR shielding module. A brief description follows.…”

“…Details regarding the numerical evaluation of the XC kernel, in particular of the spin-density gradient terms, can be found in [43] where a corresponding implementation in the J-coupling module of ADF has been documented. All ZORA NMR calculations employed the quadruple-ζ quadruply polarised all-electron STO basis QZ4P in the version as included in the ADF basis set library.…”

Measurement of Δ1J(199Hg, 31P) in [HgPCy3(OAc)2]2 and relativistic ZORA DFT investigations of mercury–phosphorus coupling tensors

“…The CPL module was used to calculate indirect nuclear spin-spin coupling tensors [28,29]. The VWN local density approximation [46] and the PBE generalized gradient approximation functional and corresponding exchange correlation kernel [47,48] were used. An all-electron basis set for mercury was obtained from J. Autschbach.…”

Static and dynamic second hyperpolarizability calculated by time-dependent density functional cubic response theory with local contribution and natural bond orbital analysis

“…27,34 In previous work based on our response methodology as interfaced with the ADF package, we have adopted a nonhybrid Kohn-Sham potential along with the local density approximation ͑LDA͒ for the adiabatic f XC ͑i.e., we have applied the adiabatic LDA f XC response kernel 26,[40][41][42] and its functional derivatives͒. In some cases, 33,43 we have also applied gradient corrections to f XC based on the Perdew-BurkeErnzerhof ͑PBE͒ generalized gradient approximation ͑GGA͒ functional. [44][45][46] In addition to nonhybrid DFT functionals, for the present work we have now also implemented the calculation of Hartree-Fock ͑HF͒ exchange contributions to f XC .…”