Quantitative Vapor-phase IR Intensities and DFT Computations to Predict Absolute IR Spectra based on Molecular Structure: I. Alkanes
Williams SD, TJ Johnson, SW Sharpe, V Yavelak, RP Oats, and CS Brauer. 2013. "Quantitative Vapor-phase IR Intensities and DFT Computations to Predict Absolute IR Spectra based on Molecular Structure: I. Alkanes." Journal of Quantitative Spectroscopy and Radiative Transfer 129:298-307. doi:10.1016/j.jqsrt.2013.07.005
Recently recorded quantitative IR spectra of a variety of gas-phase alkanes are shown to have integrated intensities in both the C-H stretching and C-H bending regions that depend linearly on the molecular size, i.e. the number of C-H bonds. This result is well predicted from CH4 to C15H32 by DFT computations of IR spectra at the B3LYP/6-31+G(d,p) level of DFT theory. A simple model predicting the absolute IR band intensities of alkanes based only on structural formula is proposed: For the C-H stretching band near 2930 cm-1 this is given by (in km/mol): CH¬_str = (34±3)*CH – (41±60) where CH is number of C-H 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 C-H bending mode is explored and interpreted in terms of conformer distribution. The relative intensity contribution of a methyl mode compared to the total C-H stretch intensity is shown to be linear in the number of terminal methyl groups in the alkane, and can be used to predict quantitative spectra a priori based on structure alone.