Nuclear Scalar Spin−Spin Couplings and Geometries of Hydrogen Bonds

Ab initio calculations of the scalar coupling constants 1J15N-1H ≡ JNH and 2J15N···15N ≡ JNN of the N−H···N hydrogen bonds in the anion [C⋮15N···L···15N⋮C]- (1), L = H, D, and of the cyclic hydrogen-bonded formamidine dimer (HCNHNH2)2 (2) have been performed using the density functional formalism as a function of the hydrogen bond and molecular geometries. The coupling constants are discussed in comparison with the experimental and calculated constants 1J19F-1H ≡ JFH and 2J19F-19F ≡ JFF reported previously as first set of examples of scalar couplings across hydrogen bonds for the hydrogen-bonded clusters of [F(HF)n]-, n = 1−4 by Shenderovich, I. G.; Smirnov, S. N.; Denisov, G. S.; Gindin, V. A.; Golubev, N. S.; Dunger, A.; Reibke, R.; Kirpekar, S.; Malkina, O. L.; Limbach, H. H. Ber. Bunsen-Ges. Phys. Chem. 1998, 102, 422. Using the valence bond order model, which has been successfully applied previously to explain hydrogen bond correlations in crystallography and solid-state NMR of hydrogen-bonded systems, the coupling constants are related to the hydrogen bond geometries and NMR chemical shifts. In terms of this model, there is no principal difference between FHF- and NHN hydrogen-bonded systems. Whereas the coupling constant values calculated using the DFT method for the fluorine case only reproduce the experimental trends, the agreement between theory and experiment is much better in the nitrogen cases, which allows one to determine the hydrogen bond geometries including the hydrogen bond angle from a full set of experimental coupling constants. It is found that the coupling constants JAB in A−H···B are proportional to the product of valence bond orders (pAHpHB)m, where m is an empirical parameter equal to 2 in the case of fluorine bridge atoms and close to 1 in the case of nitrogen bridge atoms. The coupling constants JAH depend on two terms, a positive term proportional to pAH and a negative term proportional to pAH(pHB)2 leading to vanishing or even negative values of JAH at larger A···H distances; in this region the constants JAB are larger than the absolute values of JAH. As a consequence, vanishing couplings between a hydrogen-bonded proton to a heavy nucleus across the hydrogen bond cannot be taken as an indication for a noncovalent character of this hydrogen bond. The existence of JAB is taken as a strong evidence for the covalent character of the hydrogen bonds studied. This is corroborated by a analysis of the molecular orbitals of (1) and their individual contributions to the coupling constants