¹⁴N NQR spectroscopy reveals the proton position in N-HN bonds: a case study with proton sponges

The position of protons in hydrogen bonds is often uncertain to some degree, as the technique most often used for structure determination, X-ray diffraction, is sensitive to electron density, which is not particularly abundant around protons. In hydrogen bonds, protons introduce an additional problem: the potential for proton motion is inherently anharmonic and thus requires the consideration of nuclear quantum effects (NQEs). Here, we demonstrate that 14N NQR spectroscopy is able to rather accurately determine proton positions in N-HN bonds, in certain cases with an accuracy comparable to that of X-ray and neutron diffraction at room temperature. We first derive, using ab initio calculations considering also the NQEs, a relation between the proton distance from the bond midpoint and the difference between the quadrupole coupling constants for the two nitrogen sites. The found relation is linear with a proportionality constant of 0.108 Å MHz-1 for tertiary amine nitrogens. Then, we validate our theoretical calculations experimentally, using several 1,8-bis(dimethylamino)naphthalene (DMAN) complexes.