The calculation of nuclear spin coupling constants from LCAO–SCF–Xα wavefunctions

Investigation of the NMR Spin−Spin Coupling Constants across the Hydrogen Bonds in Ubiquitin: The Nature of the Hydrogen Bond as Reflected by the Coupling Mechanism

The indirect scalar NMR spin-spin coupling constants across the H-bonds of the protein ubiquitin were calculated, including the Fermi contact, the diamagnetic spin-orbit, the paramagnetic spin-orbit, and the spin dipole term, employing coupled perturbed density functional theory in combination with the B3LYP functional and different basis sets: (9s,5p,1d/5s,1p)[6s,4p,1d/3s,1p] and (11s,7p,2d/5s,1p)[7s,6p,2d/4s,2p]. Four different models based on either the crystal or the aqueous solution structure of ubiquitin were used to describe H-bonding for selected residue pairs of ubiquitin. Calculated and measured 3hJ(NC') coupling constants differ depending on the model used, which is due to the fact that the geometry of ubiquitin is different in the solid state and in aqueous solution. Also, conformational averaging leads to a decrease of the magnitude of the measured 3hJ(NC') constants, which varies locally (larger for -sheets, smaller for -helix). Two different spin-spin coupling mechanisms were identified. While mechanism I transmits spin polarization via an electric field effect, mechanism II involves also electron delocalization from the lone pair of the carbonyl oxygen to the antibonding orbital of the N-H bond. Mechanism I is more important in the crystal structure of ubiquitin, while in aqueous solution, mechanism II plays a larger role. It is possible to set up simple relationships between the spin-spin coupling constants associated with the H bond in proteins and the geometrical features of these bonds. The importance of the 3hJ(NC') and 1J(N-H) constants as descriptors for the H-bond is emphasized.