Quantitative vapor-phase IR intensities and DFT computations to predict absolute IR spectra based on molecular structure: I. Alkanes

•Alkane absolute IR absorbance intensity is linearly correlated with molecular size.•IR absorbance correlation is well predicted by the B3LYP theory.•Most MIR absolute absorbance may be predicted easily from alkane structure.

Recently recorded quantitative IR spectra of a variety of gas-phase alkanes are shown to have integrated intensities in both the C3H stretching and C3H bending regions that depend linearly on the molecular size, i.e. the number of C3H bonds. This result is well predicted from CH4 to C15H32 by density functional theory (DFT) computations of IR spectra using Becke's three parameter functional (B3LYP/6-31+G(d,p)). Using the experimental data, a simple model predicting the absolute IR band intensities of alkanes based only on structural formula is proposed: For the C3H stretching band envelope centered near 2930 cm−1 this is given by (km/mol) CH_str=(34±1)×CH−(41±23) where CH is number of C3H bonds in the alkane. The linearity is explained in terms of coordinated motion of methylene groups rather than the summed intensities of autonomous -CH2-units. The effect of alkyl chain length on the intensity of a C3H bending mode is explored and interpreted in terms of conformer distribution. The relative intensity contribution of a methyl mode compared to the total C3H stretch intensity is shown to be linear in the number of methyl groups in the alkane, and can be used to predict quantitative spectra a priori based on structure alone.