Density functional theory-based simulations of sum frequency generation spectra involving methyl stretching vibrations: effect of the molecular model on the deduced molecular orientation and comparison with an analytical approach.

The knowledge of the first hyperpolarizability tensor elements of molecular groups is crucial for a quantitative interpretation of the sum frequency generation (SFG) activity of thin organic films at interfaces. Here, the SFG response of the terminal methyl group of a dodecanethiol (DDT) monolayer has been interpreted on the basis of calculations performed at the density functional theory (DFT) level of approximation. In particular, DFT calculations have been carried out on three classes of models for the aliphatic chains. The first class of models consists of aliphatic chains, containing from 3 to 12 carbon atoms, in which only one methyl group can freely vibrate, while the rest of the chain is frozen by a strong overweight of its C and H atoms. This enables us to localize the probed vibrational modes on the methyl group. In the second class, only one methyl group is frozen, while the entire remaining chain is allowed to vibrate. This enables us to analyse the influence of the aliphatic chain on the methyl stretching vibrations. Finally, the dodecanethiol (DDT) molecule is considered, for which the effects of two dielectrics, i.e. n-hexane and n-dodecane, are investigated. Moreover, DDT calculations are also carried out by using different exchange-correlation (XC) functionals in order to assess the DFT approximations. Using the DFT IR vectors and Raman tensors, the SFG spectrum of DDT has been simulated and the orientation of the methyl group has then been deduced and compared with that obtained using an analytical approach based on a bond additivity model. This analysis shows that when using DFT molecular properties, the predicted orientation of the terminal methyl group tends to converge as a function of the alkyl chain length and that the effects of the chain as well as of the dielectric environment are small. Instead, a more significant difference is observed when comparing the DFT-based results with those obtained from the analytical approach, thus indicating the importance of a quantum chemical description of the hyperpolarizability tensor elements of the methyl group.