Calculation of 3- and 4-bond proton-proton coupling constants in compounds modeling the peptide structure

Abstract

The two angles φ and Ψ of a peptide residue determine the secondary structure of polypeptides. These two angles also determine the dihedral relation between protons separated by three and four bonds, respectively. These 3- and separated by three and four bonds, respectively. These 3-and 4-bond proton-proton coupling constants have been calculated, as a function of dihedral angle, for N-methylformamide and acetamide which model the peptide structure. The finite perturbation procedure was used and calculations were done with both CNDO and INDO (which includes σ−π spin polarization) wavefunctions in an effort to analyze π-contributions to the coupling. The vicinal or 3-bond coupling, as a function of dihedral dihedral angle, obeys theusual Karplus-type relation with the coupling being very small at 90° and large and positive when the protons are in a cis- or trans-relationship. The vicinal calculations, while in qualitative agreement with experiment, appear to overemphasize the difference between the coupling for protons cis- or trans-to each other, when compared with available empirical evidence. The 3-bond coupling is predicted to be the same whether it occurs in a cis- or trans-peptide. In cis-peptides, the 4-bond coupling is predicted to be as large as +2 Hz when the protons are in a W conformation, whereas, in trans-peptides the 4-bond coupling is predicted to be always less than ±.5 Hz. The predicted conformational dependence of the 4-bond proton-proton coupling in both cis- and trans-peptides has also been least-squares fit to a relation of the form 4 J = A cos 2 θ + B cos θ + C. Calculations on ethane, propene, and methylimide are compared with those on the amides.