We present ab initio calculations of the Fermi contact term and experimental correlations of six coupling constants, 3JHNH alpha, 1JC alpha H alpha, 2JC'H alpha, 1JC alpha N, 2JC alpha N and 1JC'N, in a peptide as functions of the backbone dihedral angles, phi and psi. Given estimates of experimental uncertainties, we find semiquantitative experimental correlations for 3JHNH alpha, 1JC alpha N and 2JC alpha N, qualitative correlations for 1JC alpha H alpha and 2JC'H alpha, but no experimental correlations of practical utility for 1JC'N, owing to its complex dependence on at least four dihedral angles. Errors in the estimation of dihedral angles from X-ray crystallographic data for proteins, which result from uncertainties in atom-to-atom distances, place substantial limitations on the quantitative reliability of coupling constant calculations fitted to such data. In the accompanying paper [Edison, A.S. et al., J. Biomol. NMR, 4, 543-551] we apply the results of the coupling constant calculations presented here to the estimation of phi and psi angles in staphylococcal nuclease from experimental coupling constants.