相干反斯托克斯拉曼及相干反斯托克斯超拉曼光谱微观极化率张量元的简化方案-C3v对称性

doi:10.3964/j.issn.1000-0593(2020)05-1382-06

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Abstract Coherent Anti-Stokes Raman Spectroscopy (CARS) and Coherent Anti-Stokes Hyper-Raman Spectroscopy (CAHRS) recently have been widely used in the study of the spectral properties of molecules, the structure of tumor cells and the dynamics of molecular reactions. However, the main difficulty in quantitative analysis CARS and CAHRS is that the number of molecular, microscopic hyperpolarizability tensors in the high order nonlinear optical process are large and the relationships are complex. Our previous work has reported the simplification schemefor CARS and CAHRS microscopic hyperpolarizability tensor elementsbased on the C_∞v molecular symmetry. In this paper, we present the simplified scheme for microscopic hyperpolarizability tensor elements of CARS and CAHRS belonging to the C_3v symmetry. First, the tensor elements β_{i′j′k′l′} of the CARS microscopic hyperpolarizability are expressed as the product of the differentiation of Raman microscopic polarizability tensor α′_i′j′. The CAHRS microscopic hyperpolarizability tensor elements β_{i′j′k′l′m′} are expressed as the product of the differentiation of Raman microscopic polarizability tensor α′_i′j′ and the differentiation of hyper Raman microscopic polarizability tensor β′_i′j′k′. The ratio between β_{i′j′k′l′} and β_{i′j′k′l′m′} can be simplified by using the ratio between α′_i′j′ and β′_i′j′k′. For the symmetric vibrational mode A1 of C_3v symmetric type molecular groups, 9 non-zero and 3 independent CARS microscopic hyperpolarizability tensors can be described by a ratio between R^R_SS and α′_i′j′, and 21 non-zero and 6 independent CAHRS microscopic hyperpolarizability tensors can be described by three ratios of R^R_SS, R^HR_{SS, 1} and R^HR_{SS, 2} between α′_i′j′ and β′_i′j′k′. Then, the Bond Additivity Model method is used to calculate the coupling between every single bond in the C_3v symmetric molecular group, from which the ratio of hyper Raman microscopic polarizability tensor differential β′_i′j′k′ for the symmetric vibrational mode A1 of C_3v symmetric type molecular groups is obtained. Combined with the ratio of the Raman microscopic polarizability tensor differential α′_i′j′ component given in the literature, the relationship between the CARS and CAHRS microscopic hyperpolarizability tensors of C_3v symmetry molecular group is further simplified. These relationships between the microscopic hyperpolarizability tensor elements of CARS and CAHRS obtained in this paper are ready to be used for simplifying the expression of CARS and CAHRS signals and generalized oriented functional R_IJK(θ), whichcan obtain the variation of R_IJK(θ) with the orientation angle θ of the interface molecule group. Furthermore, the expressions of intensity factor d_IJK, generalized oriented functional R_IJK(θ) and generalized orientation parameters c₂ and c₄ are obtained. This work provides a theoretical basis for quantitative analysis of interface molecular orientation information.

Key words：Coherent anti-stokes Raman spectroscopy; Coherent anti-stokes hyper-Raman spectroscopy; Microscopic hyperpolarizability; Bond additivity model; Molecular orientation; Quantitative analysis; C_3v symmetry

Received: 2018-12-05 Accepted: 2019-04-22

ZTFLH:

O657.37

Corresponding Authors: ZHANG Zhen E-mail: zhangz@iccas.ac.cn

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https://www.gpxygpfx.com/EN/10.3964/j.issn.1000-0593(2020)05-1382-06 OR https://www.gpxygpfx.com/EN/Y2020/V40/I05/1382