Second-order molecular polarizability

TTiis review attempts to survey second-order molecular polarizabilities of organic molecules. Emphasis will primarily be given to the underlying physical principles of non-linear optics (e.g. molecular topology), and to the establishment of structure-property relationships. We will largely remain paradigmatic and will not attempt an exhaustive compilation of data because several good review articles and books exist that incorporate tabulations of numerous... 

The Cartesian indices refer to an arbitrarily chosen laboratory frame. For certain NLO processes intrinsic permutation symmetry can be used to reduce further the number of independent components. In the case of the Kerr susceptibility, (-w w,0,0), intrinsic permutation symmetry in the last two indices holds, xltJ zx X xx- The most general Kerr susceptibility of an isotropic medium therefore has only two independent components, x9 zz and x9 xx Likewise, the EFISHG susceptibility (-2w w, w,0), important for the evaluation of second-order molecular polarizabilities in solution (see pp. 158 and 162), has only two independent components, x zz and x9]txz, because of intrinsic permutation symmetry in the second and third indices. 

The equations derived for two- and three-level contributions to the second-order polarizability can be used to derive design strategies for the optimization of second-order molecular polarizabilities. As shown in the section above, the NLO response of molecules is controlled by three molecular parameters transition dipoles between ground and excited states, yu. and ju. ", dipole differences between ground and excited states, AjU,, and transition energies between ground and excited states, hoj/g and Here we concentrate on TT-conjugated systems and the analysis of the transition dipoles and dipole differences associated with tttt transitions. 

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. 

Paul. F.. Costuas, K., Ledoux, I., Deveau, S.. Zyss, J., Halet, J.-F., Lapinte. C. Redox-switchable second-order molecular polarizabilities with electron-rich iron cr-aryl acetyhdes. Organometalhcs 21, 5229-5235 (2002)... 

Where uM is the induced dipole moment due to the mesomeric effect ( , = /iJA). The second-order molecular polarizability, P, is given by Eq. (5.25). 

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 practical systems, the second-order molecular polarizability can be approximated by the fourth term of Eq. (5.27). Assuming here a two-level system where the permanent and transient dipole moments have the same direction (the x-axis), then the second-order molecular polarizability is expressed by Eq. (5.28),... 

The second-order molecular polarizability, /, and the third-order nonlinear susceptibility, have been measured for many compounds (see Table 5.7). Note that the f value of nitroaniline, where the centrosymmetric benzene ring carries an electron withdrawing nitro-group and an electron-donating amino-group, is larger than that of monosubstituted benzenes. 

Here we discuss a joint theoretical and experimental study of the influence of solvent polarity on the second-order molecular polarizability p of p-nitroaniline and the push-pull polyene l,l-dicyano-6-dibutylamine-hexa-triene [144]. The calculations are carried out at the Har-tree-Fock ab initio level on the basis of an expanded self-consistent reaction field approach and are compared to hyper-Rayleigh scattering measurements performed in solvents with a wide range of dielectric constants. 

In the nonlinear cases the surface nonlinear susceptibility (SNS) arising from a monolayer of adsorbates is linearly proportional to the surface density of the molecules and the second order molecular polarizability (SMP) averaged over the molecular orientational distribution. Since the SH output in the reflected direction is proportional to the square of SNS the intensity is proportional to the square of Ns. Furthermore, with input and output beam polarizations and geometry properly chosen, the various elements of SNS can be selectively measured by the SH. Consequently in the case that SMP is dominated by a single component along a molecular axis one can then determine the orientation of this axis. 7 Furthermore, for a constant orientational distribution, the SH output can be nulled by properly chosen optical polarization and geometry. 

Optical second harmonic generation (SHG), which stems from the conversion of two photons of frequency to to a single photon of frequency 2(o, is an inherently surface-sensitive technique. Whereas no optical second harmonic wave is generated in the centrosymmetric bulk of a liquid, molecules participating in the asymmetry of the interface between two liquids (noncentrosymmetric environ-ment) contribute to SHG. Since the square root of SHG signal intensity, is proportional to the number N (per unit area), the molecular orientation (I) and the second order nonlinear polarizability of the SHG active species at the interface... 

The polarizability a is an important second-order molecular property. Its variation with internuclear separation has been investigated for H2 and Hs by Zeroka,58 using the method of Das and Bersohn. Spectroscopic constants calculated from the BO and adiabatic KW functions for H2 were also studied by Wu and Beckel.59... 

Let us now consider the second-order molecular properties. The static electric dipole-polarizability tensor is given by the expression... 

In the present paper, we have discussed the ab-initio evaluation of the static polarizabilities and magnetizabilities of molecular systems, with emphasis on the principles underlying such calculations. With the recent widespread availability of powerful computers, these second-order molecular properties may nowadays be calculated a priori for large molecular systems, allowing us to explore, for instance, the relationship between the properties and molecular structure. Such calculations complement the experimental work in the area and may help in reassessing and improving on the empirical schemes... 

This paper reviews experimental work done on the NLO properties of photochromes other than azo derivatives, which have been described in the preceding chapters of this book. In the first part, the molecular second-order NLO polarizabilities will be given the NLO properties of the materials will indeed depend on these values. In the second part, photoassisted poling of different photochromes in polymer matrices will be described. The photo-switching of second-order NLO properties of poled polymers or crystals will then be described in the third section. Both second and third parts will end with some applications of these optical phenomena. We will conclude with the prospectives of these materials in NLO. 

Other Work on Water-Related Systems. Sonoda et al.61 have simulated a time-resolved optical Kerr effect experiment. In this model, which uses molecular dynamics to represent the behaviour of the extended medium, the principle intermolecular effects are generated by the dipole-induced-dipole (DID) mechanism, but the effect of the second order molecular response is also include through terms involving the static molecular / tensor, calculated by an MP2 method. Weber et al.6S have applied ab initio linear scaling response theory to water clusters. Skaf and Vechi69 have used MP2/6-311 ++ G(d,p) calculation of the a and y tensors of water and dimethylsulfoxide (DMSO) to carry out a molecular dynamics simulation of DMSO/Water mixtures. Frediani et al.70 have used a new development of the polarizable continuum model to study the polarizability of halides at the water/air interface. 

The surface SHG allows us to measure directly an averaged molecular orientation. The basic principle is as follows. The second-order surface nonlinear susceptibility 2) g layer is related to the second-order nonlinear polarizability "o ) Qf he molecules by... 

Since is a vector described by three Cartesian components Ej, Ej, Ei ), a, p, and Y are tensors of second, third, and fourth ranks, respectively a = a,y, p = Py, , and y= jijkh are, respectively, linear, second-order, and third-order molecular polarizabilities. The induced electric polarization P, defined as the dipole moment per unit volume, is therefore of the form... 

Second order molecular electronic polarizabilities are obtained by solving for Substituting Equation (10.22) for p t) in the right-hand side of Equation... 

Several methods have beeu developed for calculating these molecular nonlinear polarizabilities. These methods have proven to be fairly reliable for predicting the second- and third-order molecular polarizabilities of organic molecules and polymers in general and liquid crystalline molecules in particular. For treating the ordered phases of liquid crystals, oue has to account for molecular correlations and ordering by introducing an orientational distribution function. ... 

Electrostatic terms other than the simple charge interactions above are commonly included in molecular mechanics calculations. particularly dipole-dipole interactions. More recently, second-order electrostatic interactions like those describing polarizability have been added to some force fields. 

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