Hyperpolarizability tensor single molecule

The fundamental equation (1) describes the change in dipole moment between the ground state and an excited state jte expressed as a power series of the electric field E which occurs upon interaction of such a field, as in the electric component of electromagnetic radiation, with a single molecule. The coefficient a is the familiar linear polarizability, ft and y are the quadratic and cubic hyperpolarizabilities, respectively. The coefficients for these hyperpolarizabilities are tensor quantities and therefore highly symmetry dependent odd order coefficients are nonvanishing for all molecules but even order coefficients such as J3 (responsible for SHG) are zero for centrosymmetric molecules. Equation (2) is identical with (1) except that it describes a macroscopic polarization, such as that arising from an array of molecules in a crystal (10). 

The HRS technique [25-27] involves the detection of the incoherently scattered second harmonic generated by the molecule in solution under irradiation with a laser of wavelength 2, leading to the mean value of the x tensor product. By analysis of the polarization dependence of the second harmonic signal, which can be evaluated selecting the polarization of the incident and scattered radiation, it is possible to obtain information about the single components of the quadratic hyperpolarizability tensor jS. Unlike EFISH, HRS can also be used for ionic molecular species and for nondipolar molecules such as ocmpolar molecules. In this chapter, the quadratic hyperpolarizability measured with an incident wavelength 2 by the EFISH and HRS techniques will be indicated as /l i(EFISH) and / (HRS), respectively. 

The interaction of long-chain molecules such as polymers is a problem area where the nature of polarization response can be a significant concern on its own. An example is from a study of parallel hexatriene molecules carried out to represent a truncated form of solid-state polyacetylene [192]. This smdy included both ab initio calculations and an electrostatic model using polarizability, a, and second hyperpolarizability, y, tensors distributed to the carbon centers. The ab initio calculations on a single hexatriene molecule were used to find the distributed tensors for the electrical analysis. The objective in this smdy was not the interaction energy, but the effect on each molecule s polarizability and hyperpolarizability due to intermolecular interaction. The ab initio evaluations benchmarked the electrostatic model calculations both for... 

The polarizability of an atom or molecule describes the response of the electron cloud to an external field. The atomic or molecular energy shift KW due to an external electric field E is proportional to i for external fields that are weak compared to the internal electric fields between the nucleus and electron cloud. The electric dipole polarizability a is the constant of proportionality defined by KW = -0(i /2. The induced electric dipole moment is aE. Hyperpolarizabilities, coefficients of higher powers of , are less often required. Technically, the polarizability is a tensor quantity but for spherically symmetric charge distributions reduces to a single number. In any case, an average polarizability is usually adequate in calculations. Frequency-dependent or dynamic polarizabilities are needed for electric fields that vary in time, except for frequencies that are much lower than electron orbital frequencies, where static polarizabilities suffice. 

The study of amphiphile ordering at interfaces is necessary to understand many phenomena, like microemulsions, foams or interfacial reactivity. It is expected that the preferential orientation taken by these compounds at interfaces is entirely determined by their interactions with the two solvants forming the interface and the intermolecular repulsion or attraction within the monolayer. As mentioned above, the SH response at liquid/liquid interfaces is dominated by electric dipole contributions and is therefore surface specific. Neglecting the contribution from the sol-vant molecules, which usually only have a weak nonlinear optical activity, the passage from the macroscopic susceptibility tensor xP to the microscopic molecular hyperpolarizability p of the adsorbate is obtained by merely taking the SHG response of the amphiphile monolayer as the superposition of the contribution from each single moiety. Hence, it yields... 

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