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

Abstract

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.