The trans hydrogen bond (3h)J(NC') coupling observed between peptide groups in proteins is shown to be mediated by a closed shell. noncovalent interaction between the donor hydrogen atom and the acceptor oxygen atom. The magnitude of (3h)J(NC') is shown to be an exponential function of the mutual penetration of the nonbonding van der Waals shells of the isolated donor and acceptor fragments. Our results also show that the magnitude of J(FF), the through-space coupling between two nonbonded fluorine nuclei in organic molecules and in a protein, exhibits a similar exponential dependence upon penetration of nonbonding monomer charge densities. These results support the idea that the existence of electron-coupled nuclear spin-spin coupling requires neither a covalent bond nor an attractive electrostatic bond between the coupled nuclei. By relating the results of calculations using Bader's theory of Atoms in Molecules, (Bader, R. F. W. Atoms in Molecules-A Quantum Theory; Clarendon Press: Oxford, 1990) to these couplings and to H-1 chemical shifts in proteins and model systems, a simple chemical description of protein backbone hydrogen bonds, the short, strong hydrogen bonds implicated in enzyme catalysis, as well as low-barrier hydrogen bonds, is obtained. Unlike protein backbone hydrogen bonds, the short, strong hydrogen bonds in enzymes have partial covalent character, which is shown to increase exponentially as the H-1 nucleus becomes more deshielded. Between ca. 20 and 21 ppm, the chemical shift region of experimentally observed low-barrier hydrogen bonds, the hydrogen bond becomes a fully covalent, shared-electron interaction.