Additive Model for the Second Harmonic Generation Hyperpolarizability Applied to a Collagen-Mimicking Peptide (Pro-Pro-Gly)10

Second harmonic generation (SHG) spectrometry has been recently applied to investigate the structure of proteins and sugars (collagen, myosin, starch, etc.). The interpretation of experimental data at the molecular length-scale remains often qualitative because of the difficulty to model the SHG signal of such large molecules. Simpson and co-workers proposed to estimate the hyperpolarizability of the peptide backbone as the sum of the individual hyperpolarizabilities of the peptide bonds.(49) This article discusses the hyperpolarizabilities obtained using such an additive model for a peptide (Pro-Pro-Gly)(10) modeling collagen, for which experimental hyperpolarizabilities have been measured and modeled recently.(46) To investigate possible parameters for the model, we performed time-dependent density functional theory (TDDFT) calculations of the hyperpolarizability of a few molecules containing one peptide bond. In a second step, the additive model is applied. The results produced using different input parameters are compared to each other and to experimental data. For the chosen peptide, the additive model using N-methylacetamide as a building block agrees qualitatively with hyper-Rayleigh scattering data. The results emphasize the need for more reference data to test the additivity hypothesis and the transferability of the parameters to other secondary structure of proteins.