Second-order molecular hyperpolarizability

Stark effect measurements for determination of molecular orientation and second-order molecular hyperpolarizability... 

Evaluation of second-order molecular hyperpolarizability using the quadratic Stark effect... 

On the two level model [3], second-order molecular hyperpolarizability p is given by... 

Effective second harmonic generation is attained in materials which have both high second-order molecular hyperpolarizability, p, and high second-order bulk susceptability, x - Molecular polarization is described by the field dependent molecular dipole moment, p (eq 1), expanded as a function of the applied field strength, E, which may be electric or optical (that is, electromagnetic) in nature. The field strength E is a vector, and Pq is the intrinsic dipole... 

Suzuki, H., Photophysical evaluation of second-order molecular hyperpolarizabilities of organic nonlinear materials. Application of the three-level model to systems with low energy double transitions. Mol. Cryst. Liq. Cryst., 182, 33 (1990). 

Despite these shortcomings it will become clear that in the one-dimensional NLO-phores treated in this section, which display a wide range of seemingly disparate chemical structures, the crude model works surprisingly well. Thus, as a consequence of the validity of the two-state model, their second-order polarizabilities in principle reduce to p-nitroaniline . The reader may even gain the impression that the efforts to improve on the hyperpolarizabilities of even the simplest and most easily accessible -n systems (like p-nitroaniline) have been futile. It is true that an efficiency-transparency trade-off exists At a given wavelength of absorption (related to A ) a maximum value for the second-order molecular polarizability per volume element exists which is not tremendously different from that of very basic unoptimized rr systems. However, for applications like the electro-optical effect, a bathochromic shift of the UV-visible absorption is tolerable so that to strive for maximum hyperpolarizabilities is a viable quest. Furthermore, molecular structures with the same intrinsic second-order polarizabilities may differ substantially in their chemical stabilities and their abilities to be incorporated into ordered bulk structures. 

N- and N, (9-heterocycles as second-order nonlinear optical chromophores with both large first-order molecular hyperpolarizability and good transparency 03MI108. 

Quantum mechanical expressions of the molecular polarizability can be derived from Eq. (1.163) which describe the hyperpolarizability of scattering phenomena, discussed in Chapter 1. The second-order molecular polarizability is given by the following equations ... 

In order to obtain a useful material possessing a large second order nonlinear susceptibility tensor % 2) one needs to use molecules with a large microscopic second order nonlinear hyperpolarizability tensor B organised in such a way that the resulting system has no centre of symmetry and an optimized constructive additivity of the molecular hyperpolarizabilities. In addition, the ordered structure thus obtained must not loose its nonlinear optical properties with time. The nonlinear optical (NLO) active moieties which have been synthesized so far are derived from the donor-rc system-acceptor molecular concept (Figure 1). 

The SFG technique probes the second-order nonhnear hyperpolarizability tensor this tensor includes the Raman and IR susceptibihty, which requires that the molecular vibrational modes are both Raman and IR active. Since Raman- and IR-dipole moment transition selection rules for molecules with a center of symmetry indicate that a vibrational mode is either Raman or IR active but not both, only molecules in a non-centrosymmetric environment on the surface interact with the electric fields molecules in the isotropic bulk phase show inversion symmetry where the third rank hyperpolarizability tensor goes to zero [25-27]. 

First, let us turn our attention to the issue of optimizing chromophore hyperpolarizability. An obviously important and necessary aspect of the process is the characterization of hyperpolarizabilities. The two most popular methods for characterizing chromophore second-order molecular optical nonlinearity are electric field-induced second harmonic generation (EFISH) [3,10,21-24] and hyper-... 

A computer program for the theoretical determination of electric polarizabilities and hyperpolarizabilitieshas been implemented at the ab initio level using a computational scheme based on CHF perturbation theory [7-11]. Zero-order SCF, and first-and second-order CHF equations are solved to obtain the corresponding perturbed wavefunctions and density matrices, exploiting the entire molecular symmetry to reduce the number of matrix element which are to be stored in, and processed by, computer. Then a /j, and iap-iS tensors are evaluated. This method has been applied to evaluate the second hyperpolarizability of benzene using extended basis sets of Gaussian functions, see Sec. VI. 

The large molecular hyperpolarizability of the merocyanine chromophore (4,5) and the highly polar environment of the quasicrystals has prompted studies of the second order nonlinear optical properties of these materials (6). 

For obtaining the information on fabrication of noncentrosymmetric LB films with highly efficient second-order optical nonlinearity, six azobenzene-linked amphiphiles were synthesized as a model compound, and their molecular hyperpolarizabilities (3, monolayer-formation at the air-water interface, and molecular orientation and second-order susceptibilities of the azobenzene-linked amphiphiles LB films were evaluated. The molecular structures of the azobenzene-linked amphiphiles are shown in Fig.2. 

We have considered scalar, vector, and matrix molecular properties. A scalar is a zero-dimensional array a vector is a one-dimensional array a matrix is a two-dimensional array. In general, an 5-dimensional array is called a tensor of rank (or order) s a tensor of order s has ns components, where n is the number of dimensions of the coordinate system (usually 3). Thus the dipole moment is a first-order tensor with 31 = 3 components the polarizability is a second-order tensor with 32 = 9 components. The molecular first hyperpolarizability (which we will not define) is a third-order tensor. 

This paper is a tutorial overview of the techniques used to characterize the nonlinear optical properties of bulk materials and molecules. Methods that are commonly used for characterization of second- and third-order nonlinear optical properties are covered. Several techniques are described briefly and then followed by a more detailed discussion of the determination of molecular hyperpolarizabilities using third harmonic generation. 

As mentioned above, the powder SHG method is a useful technique for the screening of second-order nonlinear materials. However, because of the sensitivity of the SHG coefficients of crystalline materials to the orientational aspects of the molecular packing and because the measurement is performed on an essentially random distribution of microcrystalline particles, the powder SHG method is not generally useful for obtaining information about molecular hyperpolarizabilities. 

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. 

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