A Simplified Method of Microscopic Hyperpolarizability of Coherent Anti-Stokes Raman Spectroscopy and Coherent Anti-Stokes Hyper-Raman Spectroscopy-C3v Symmetry
WANG Yuan1, ZHANG Zhen2*, GUO Yuan2, 3
1. Institute of Technology, University of Sanya, Sanya 572022, China
2. Beijing National Laboratory for Molecular Sciences (BNLMS), Institute of Chemistry, Chinese Academy of Sciences, Beijing 100010, China
3. University of Chinese Academy of Sciences, Beijing 100049, China
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 C3v symmetry. First, the tensor elements βi′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 βi′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 βi′j′k′l′ and βi′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 C3v symmetric type molecular groups, 9 non-zero and 3 independent CARS microscopic hyperpolarizability tensors can be described by a ratio between RRSS and α′i′j′, and 21 non-zero and 6 independent CAHRS microscopic hyperpolarizability tensors can be described by three ratios of RRSS, RHRSS, 1 and RHRSS, 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 C3v 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 C3v 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 C3v 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 RIJK(θ), whichcan obtain the variation of RIJK(θ) with the orientation angle θ of the interface molecule group. Furthermore, the expressions of intensity factor dIJK, generalized oriented functional RIJK(θ) and generalized orientation parameters c2 and c4 are obtained. This work provides a theoretical basis for quantitative analysis of interface molecular orientation information.
