A Simplified Method of Microscopic Polarizability Tensor Differential of Hyper-Raman Spectroscopy Based on the Bond Additivity Model

Coherent anti-Stokes Raman spectroscopy (CARS) and Ccherent anti-Stokes hyper-Raman spectroscopy (CAHRS), as other high-order nonlinear spectroscopy techniques, are widely exploited in many research fields, such as dynamic processes, gene expression spectrum screening, high-resolution spectroscopy, and nonlinear high-resolution imaging. However, it is difficult to make a quantitative analysis of the spectral signals that involve a large number of high-order micropolarizability tensors. It is reported that the CARS and CAHRS microscopic hyperpolarizability tensor elements can be decomposed into the product of the differentiation of Raman microscopic polarizability tensor α′i′j′ and hyper-Raman microscopic polarizability tensor β′i′j′k′ so that the high-order spectra can be simplified to the analysis of low-order spectra. In this paper, we use the bond additivity model (BAM) combined with experimental corrections to address the carbon dioxide (CO2) molecule and present the simplified scheme for differentiation of hyper-Raman microscopic polarizability tensor elements β′i′j′k′. Taking advantage of this approach, combined with the experimental correction, the differentiation of Hyper-Raman microscopic polarizability tensor elements β′i′j′k′ of the CO2 is obtained and the expressions of β′i′j′k′ for antisymmetric vibrations of CO2 are deduced. Finally, substituting the differentiation of Raman microscopic polarizability tensor elements α′i′j′ reported in the literature into the ratio above can obtain the proportional relationship between the microscopic polarizability tensor elements of CARS and CAHRS of the CO2. This method can provide the basis for the quantitative analysis of high-order nonlinear spectral profiles.