Quantum mechanical calculations are presented that predict that one-bond deuterium isotope effects on the 15N chemical shift of backbone amides of proteins, 1Δ15N(D), are sensitive to backbone conformation and hydrogen bonding. A quantitative empirical model for 1Δ15N(D) including the backbone dihedral angles, Φ and Ψ, and the hydrogen bonding geometry is presented for glycine and amino acid residues with aliphatic side chains. The effect of hydrogen bonding is rationalized in part as an electric-field effect on the first derivative of the nuclear shielding with respect to N–H bond length. Another contributing factor is the effect of increased anharmonicity of the N–H stretching vibrational state upon hydrogen bonding, which results in an altered N–H/N–D equilibrium bond length ratio. The N–H stretching anharmonicity contribution falls off with the cosine of the N–H···O bond angle. For residues with uncharged side chains a very good prediction of isotope effects can be made. Thus, for proteins with known secondary structures, 1Δ15N(D) can provide insights into hydrogen bonding geometries.
