Analytical calculation of nuclear magnetic resonance indirect spin-spin coupling constants at the generalized gradient approximation and hybrid levels of density-functional theory

A fully analytical implementation of the nuclear magnetic resonance (NMR) indirect nuclear spin-spin coupling constants at the density-functional theory (DFT) level is presented. The implementation involves all four contributions of the nonrelativistic Ramsey theory: The dia- and para-magnetic spin-orbit contributions as well as the paramagnetic Fermi-contact and spin-dipole contributions. Three different exchange-correlation functionals-LDA (local density approximation), BLYP (Becke-Lee-Yang-Parr), and B3LYP (hybrid BLYP)-are tested by comparison with experiment and high-level ab initio calculations for a series of molecules containing first-row elements. All three levels of theory represent a significant improvement on restrictred Hartree-Fock (RHF) theory in the sense that the RHF instability problems are absent in DFT. Also, there is a steady improvement in the quality of the calculated spin-spin couplings in the sequence LDA, BLYP, and B3LYP. For the first-row molecules investigated by us, the hybrid B3LYP functional performs particularly well, with errors similar to those observed at the best ab initio levels of theory. (C) 2000 American Institute of Physics. [S0021-07-7(90)31545-3].