Analysis of the Cartesian Tensor Transfer Method for Calculating Vibrational Spectra of Polypeptides

The Cartesian Tensor Transfer Method (CTTM) was proposed as an efficient way to calculate infrared, Raman, and Raman Optical Activity (ROA) spectra for large molecules from the Hessian matrix and property tensor derivatives calculated for smaller molecular fragments. Although this approach has been widely used, its reliability has not been analyzed in depth yet. Especially for ROA spectra, such an analysis became only recently possible because of methodological advances that allow for the calculation of full ROA spectra of fairly large molecules with large basis sets. In this work, we investigate an α-helical polypeptide of 20 alanine amino acids, for which we reported the full ROA spectra earlier, in order to study the CTTM for protein subunits. By comparing the full first-principles calculation of the vibrational spectra with spectra reconstructed with the CTTM from different fragment sizes, we find that infrared and Raman spectra are mostly well reproduced. However, this is not the case for the ROA spectrum. This might have implications for peptide and protein CTTM ROA spectra that have already been published in the literature.