Hyperpolarizability coefficients

The non-linear optical properties of a material are evaluated by measuring (using techniques from the field of physics) its molecular hyperpolarizability coefficient (3. 

This paper summarizes the theoretical analysis of some new molecules with methylsulfonyl group as the electron acceptor group, describes the syntheses of new stilbene and azobenzene systems, and presents the measurements of their optical spectra, ground-state dipole-moments, and molecular hyperpolarizability coefficients, p. We compare theoretical and experimental results and comment on the potential usefulness of these chromophores as components for NLO materials. The incorporation of sulfonyl-containing chromophores into polymers, and the NLO properties of the resulting materials, will be discussed in our forthcoming paper (9). 

If we compare AX values (AX - XDMSO - Xj0iuene) for the four dyes under study we get 35 nm (1428 cm 1), and 27 nm (1269 cm 1), for the nitro, and methylsulfonyl azobenzene derivatives, respectively, and 22 nm (1077 cm 1), and 7 nm (457 cm1), for the nitro, and methylsulfonyl stilbene derivatives, respectively. Further examination reveals that the difference in AX between the two stilbene derivatives is 15 nm (620 cm 1), while that in the case of the azobenzene derivatives is 8 nm (159 cm1). Thus, two interesting conclusions can be drawn from this data a) the bathochromic shift is not only a function of the donor and acceptor groups, but also of the intermediate -system between them and (b) while the measured hyperpolarizability coefficients for the stilbene and azobenzene sulfonyl derivatives are very similar (see below), their solvatochromism behavior is different, and therefore solvatochromism is not an accurate prediction of p. 

In this study we have described theoretical calculations, syntheses, optical spectra, ground-state dipole moment measurements, and measurements of molecular second-order hyperpolarizability coefficients (/J) for new stilbene and azobenzene derivatives containing a methylsulfonyl group as the electron acceptor. We have shown that theoretical calculations can be used to predict the ratio of molecular hyperpolarizabilities between similar compounds, and that these gas phase calculations underestimate /J, probably as a result of the valence basis set used in the calculations. 

Theoretical calculations have been made on stilbene which are relevant to photoisomerization dynamics. MNDO calculations of stilbene potential energy properties shows no evidence of a doubly excited "phantom" state but a singly excited state with adiabatic rotation around the central ethylene bond has only a small barrier on this path23T Calculations of dipole moments, optical spectra, and second order hyperpolarizability coefficients of some mono- and disubstituted stilbene molecules allows the design of useful nonlinear optical molecules 38. 

The hyperpolarizability coefficients of these model compounds, determined by the HRS method, are given in Table 10.3. 

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 third order hyperpolarizability coefficients x have been determined under double resonance conditions for thin films of PcGaCl and PcAlF [187a]. Depending on the deposition conditions, the films consist, in variable ratios, of cofacially stacked (triclinic) and slipstacked (monoclinic) small crystallites. The samples were irradiated at 1064 nm, a frequency where the compounds are... 

Theoretical expressions of hyperpolarizability coefficients can be obtained by quantum mechanical methods (time dependent perturbation theory). In fact, the oscillating electric field of the incident electromagnetic wave, Eq cos cot, (Eq is the amplitude and co the frequency) can be considered as a time dependent perturbation acting on the molecule. Using second order perturbation theory, the following expression is obtained for Pyk (SHG effect is considered) [6]... 

In 1992, they published the results of EFISH measurements of these compounds. The measured hyperpolarizability coefficients for BNB and BNA are quite high P is 42 x 1(H and 72 x IQ- esu, respectively (Lequan et al., 1992a). The experimental studies confirmed the calculations made by Kanis et al. in 1991 the dimesitylborane group has an electron-accepting strength comparable to a nitro group. 

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