Uncovering individual hydrogen bonds in rotaxanes by frequency shifts

We present a theoretical investigation of amide pseudorotaxane IR spectra in the harmonic approximation. In particular, we focus on the effect of axle substitution on the hydrogen bonds that are formed between axle and wheel. Two types of pseudorotaxanes are studied: one with the substituent affecting mostly the axle's carbonyl group and one with the effect influencing primarily the amide NH group. Sizeable red shifts are predicted for the carbonyl stretching frequencies, and large red shifts for the NH stretching frequencies. For the wheel amide groups involved in hydrogen bonding merely with their NH hydrogens, a small shift is observed for the carbonyl stretch mode. A clear relation is observed between the NH stretch shifts and individual hydrogen bond energies. This is confirmed by correlations of the shared electron number with the NH stretch shift showing that this quantity can be taken as an indicator for individual hydrogen bond energies. Axle substitution influences the strengths of the individual hydrogen bonds which is again reflected in the NH stretch frequency shifts. A linear relationship of Hammett's substituent parameters with the NH frequency shifts can be established.