Estimating the carbonyl anharmonic vibrational frequency from affordable harmonic frequency calculations.

A linear correlation between harmonic and anharmonic frequencies of water calculated at B3LYP level of theory was observed with a number of basis sets. Similar relationships were found in both the gas phase and solution for several small molecules. The best correlation was found for C = O stretch mode in formaldehyde, formamide and N-methylacetamide. The average difference between B3LYP harmonic and anharmonic ν(C = O) frequencies calculated with several basis sets in these molecules was 30 cm(-1). The ad hoc correction of -30 cm(-1), added to harmonic frequencies of two different carbonyl groups present in a structure of a larger molecule was tested as a fast way of predicting anharmonic frequencies without elaborated calculations. The proposed approach was tested successfully on a larger molecule of E and Z isomers of N-acetyl-α,β-dehydrophenylalanine N',N'-dimethylamide [Ac-(E/Z)-ΔPhe-NMe(2)] and the estimated anharmonic ν(C = O) frequencies were close to directly calculated results.