Oriented gas model

In solution, although solute contributions can generally be singled out, difficulties arise sometimes solvent-solute interactions may induce a shift of the solute absorption and consequently of its susceptibility or hydrogen bonded molecular complexes may modify the liquid structure. This situation has been studied both theoretically and experimentally by Zyss and Berthier (10) and by Ledoux and Zyss (13) in the case of urea derivatives in various solvents and in crystal showing the importance of environment considerations and thus the limitations of an oriented gas model for crystals. 

Interpretable Polarization. Since C02 is a linear molecule, the IR polarization of its asymmetric stretching mode is particularly easy to interpret. In the absence of resonant interactions with modes of neighboring molecules (see below), it is safe to assume that the oriented gas model holds, and that the absorption of polarized light is maximum in the direction of the long axis [52]. The polarization of the bending mode can also be interpreted, although we have not used it as much. 

In the EFISH method, the molecule of interest is dissolved in an appropriate solvent and put into a cell of the type shown in Figure 9. Electrodes above and below the cell provide the means for a D.C. electric field, which orients the solute (and solvent) molecules through its interaction with the molecular dipoles. Similar to the poled polymer approach, the average molecular orientation is increased along the field direction and an oriented gas model used to extract p. 

In the limit of the oriented gas model with a one-dimensional dipolar molecule and a two state model for the polarizability (30). the second order susceptibility X33(2) of a polymer film poled with field E is given by Equation 4 where N/V is the number density of dye molecules, the fs are the appropriate local field factors, i is the dipole moment, p is the molecular second order hyperpolarizability, and L3 is the third-order Langevin function describing the electric field induced polar order at poling temperature Tp - Tg. 

Since the dipoles of chromophore molecules are randomly distributed in an inert organic matrix in amorphous PR materials, the material is centrosymmet-ric and no second-order optical nonlinearity can be observed. However, in the presence of a dc external field, the dipole molecules tend to be aligned along the direction of the field and the bulk properties become asymmetric. Under the assumption that the interaction between the molecular dipoles is negligible compared to the interaction between the dipoles and the external poling field (oriented gas model), the linear anisotropy induced by the external field along Z axis at weak poling field limit (pE/ksT <[Pg.276]

The usual way of treating the optical properties of systems containing organic molecules is in terms of the oriented gas model, that is, the macroscopic property is treated as the sum of molecular contributions, allowing... 

When free molecules are incorporated in a lattice, their axes are first oriented, i.e., v h the angle between the u and the a axis is 6 = 63.6 °. This is one aspect of the oriented gas model . However, as Fig. 2.7-9a shows, the molecules are not exactly planar the hydrogen atoms are directed toward the neighboring S atoms. The symmetry plane (j uv) of the free molecule is thus lost, the new point group of the molecule is determined by the symmetry of the lattice site, Q. According to the site symmetry model, the a and b species are therefore combined to afford a species a, while the U2 and hj species afford a , see Table 2.7-3 and Fig. 2.7-8. 

The existence of two polymorphic structures of the dichloro derivative of 6-XXXV (R = Cl) (Bernstein and Izak 1976) provided an opportunity for the direct examination of the relationship between the molecular structure and the electronic spectrum. The two structures are conformational polymorphs, with the metastable very pale yellow triclinic needle form exhibiting a planar molecular conformation a = fi = 0°) (Bernstein and Schmidt 1972) and the stable yellow orthorhombic form (with chunky rhombic crystals) exhibiting a non-planar conformation (a = 25° fi = —25°) (Bernstein and Izak 1976). Assuming that the two crystal structures merely serve to hold the molecule in the two different conformations (i.e. the oriented gas model), the absorption spectra should reflect the difference in conformation that measured on the triclinic structure, with a planar conformation, should closely resemble the spectra of 6-XXXVI and 6-XXXVII, while that for the orthorhombic structure, with the nonplanar molecular conformation, should retain the characteristics of 6-XXXV (R = H) in solution. 

At the opposite extreme from the oriented gas model for molecular crystals, the neighbouring molecules do interact with each other resulting in spectral properties of the bulk that differ considerably from those of the individual molecule. Interacting molecules of this type often tend to form aggregates even in solution, a phenomenon that has been exploited by the photographic industry for the tuning of the spectral response of silver halide emulsions (Herz 1974 Smith 1974 Nassau 1983). Aggregate formation can lead to the development of new, and often quite intense absorption bands... 

Schnepp. J. Chem. Phys. 23, 234-7 (1955). IR dichroism oriented gas model tested, naphthalene. 

The well-known NLO molecular crystal POM (3-methyl-4-nitropyridine-1-oxide) is simulated through cluster calculations by Guillaume et al.216 Semi-empirical and MP2 ab initio results are considered and comparisons of the NLO response with those obtained from the usual oriented gas model are made. POM is also selected by Hamzaoui et al 11 as an example of an NLO molecular crystal on which to test their procedure for relating the polarizabilities to the multipolar components of the ground state charge distribution determined by X-ray diffraction methods. 

The applications were extended to mixed molecular crystals such as tetracene contained as a dilute impurity in anthracene. Choudhury and Ganguly [213] had measured the absorption spectmm of tetracene at 480 nm and interpreted it with the assumption, later confirmed by crystal packing calculations, that the molecules are held in the anthracene lattice in almost the same position and orientation as the molecules they replace. They made the remarkable discovery that the intensity ratio for absorption along the b and a crystal axes was not 7.7 1 expected on the oriented gas model, but around 2 1. We later refined the measurements [84] to give values close to 3 1. 

By this time Thuraiappah Thirunamachandran had come to me as a PhD student, with study leave from his staff position in the University of Ceylon. He showed [74] that the experimental results in this and some other cases were very well accounted for by the transfer of intensity from strong to weaker transitions under the dipole-dipole coupling (3.3). It had become clear that the oriented-gas model was not a satisfactory approximation. 

To understand and optimize the electro-optic properties of polymers by the use of molecular engineering, it is of primary importance to be able to relate their macroscopic properties to the individual molecular properties. Such a task is the subject of intensive research. However, simple descriptions based on the oriented gas model exist [ 20,21 ] and have proven to be in many cases a good approximation for the description of poled electro-optic polymers [22]. The oriented gas model provides a simple way to relate the macroscopic nonlinear optical properties such as the second-order susceptibility tensor elements expressed in the orthogonal laboratory frame X,Y,Z, and the microscopic hyperpolarizability tensor elements that are given in the orthogonal molecular frame x,y,z (see Fig. 9). 

Because of its simplicity, the oriented gas model relies on a large number of simplifications and approximations (i) at the poling temperature the chromophores are assumed free to rotate under the influence of the applied field and any coupling... 

In tune with the above introductory remarks, we have arranged this review in the following way Section II deals with the oriented gas model that employs simple local field factors to relate the microscopic to the macroscopic nonlinear optical responses. The supermolecule and cluster methods are presented in Section III as a means of incorporating the various types of specific interactions between the entities forming the crystals. The field-induced and permanent mutual (hyper)polarization of the different entities then account for the differences between the macroscopic and local fields as well as for part of the effects of the surroundings. Other methods for their inclusion into the nonlinear susceptibility calculations are reviewed in Section IV. In Section V, the specifics of successive generations of crystal orbital approaches for determining the nonlinear responses of periodic infinite systems are presented. Finally,... 

The oriented gas model was first employed by Chemla et al. [4] to extract molecular second-order nonlinear optical (NLO) properties from crystal data and was based on earlier work by Bloembergen [5]. In this model, molecular hyperpolarizabilities are assumed to be additive and the macroscopic crystal susceptibilities are obtained by performing a tensor sum of the microscopic hyperpolarizabilities of the molecules that constitute the unit cell. The effects of the surroundings are approximated by using simple local field factors. The second-order nonlinear response, for example, is given by... 

Chemla et al. [4] used the oriented gas model in combination with knowledge of the crystal symmetry and orientation of the molecules in the unit... 

Among the few determinations of of molecular crystals, the CPHF/ INDO smdy of Yamada et al. [25] is unique because, on the one hand, it concerns an open-shell molecule, the p-nitrophenyl-nitronyl-nitroxide radical (p-NPNN) and, on the other hand, it combines in a hybrid way the oriented gas model and the supermolecule approach. Another smdy is due to Luo et al. [26], who calculated the third-order nonlinear susceptibility of amorphous thinmultilayered films of fullerenes by combining the self-consistent reaction field (SCRF) theory with cavity field factors. The amorphous namre of the system justifies the choice of the SCRF method, the removal of the sums in Eq. (3), and the use of the average second hyperpolarizability. They emphasized the differences between the Lorentz Lorenz local field factors and the more general Onsager Bbttcher ones. For Ceo the results differ by 25% but are in similar... 

Table II provides a survey of representative calculations of p and 7 of molecular aggregates with an eye toward determining the bulk susceptibilities or, at least, toward addressing the effect that crystal packing has on the NLO responses. Initial studies focused on the first hyperpolarizability, and this was a consequence of the earlier work by Chemla, Zyss, and collaborators and of the necessity to improve the oriented gas model (see Section II). Dirk et al. [47] studied dimers of urea and of (A)-(5-nitropyrid i)-2(i.)-prolinol (PNP) by adopting a Pariser Parr Pople (PPP) Hamiltonian. They showed the limits of...

Since the concepts of atoms and bonds are central to chemical understanding, approaches based on atom-additivity and bond-additivity are very appealing. Due to their simplicity, they were used in the early days for actual calculations, but nowadays they continue to be employed for interpretative purposes. Needless to say, their accuracy can be surpassed by methods based on quantum mechanics. As with field-free isolated molecules, early models used to estimate second- and third-order macroscopic nonlinear responses considered such simple schemes. In the following, we describe methods that treat either chemical bonds or atoms as the central quantities for evaluating the bulk NLO responses. The philosophy consists in incorporating in the description of these central constructs the effects of the surroundings. In this way the connection with more elaborate methods, such as the oriented gas model that focuses on one molecule with local field factor corrections, or with the crystalline orbital approach that reduces the system to its unit cell, is more obvious. In what follows, a selection of such schemes is analyzed and listed in Table VII. 

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