Octopolar molecules

Furthermore, Lee et al. used a four-state model to describe the NLO properties of an octopolar molecule such as crystal violet [98]. In addition, they showed that one can use the concept of bond order alternation (BOA) to analyze the NLO structure-property relationship in octopolar molecules. 

Prior to discussing the properties of octopolar molecules, it is instructive to consider first some of the basic properties of tensors. In general, any tensor of rank n can be decomposed in a sum of so-called irreducible tensors that are invariant under three-dimensional rotation [99] ... 

For the hyperpolarizability of purely octopolar molecules, all irreducible tenso-rial components of weight strictly lower than three cancel due to symmetry requirements and P = P [99]. For other molecules, the hyperpolarizability can contain contributions of all irreducible tensor components, depending on the symmetry of the molecule. 

Figure 8. Schematic representation of a) a typical dipolar donor-acceptor molecule with C21, symmetry and b) a purely octopolar molecule with Dj/, symmetry.

One property that makes octopoles interesting is the lack of dipole moment in the ground state. This should increase the probability of non-centrosymmetric crystallization and prevent detrimental dipolar (aggregate) interaction. In addition, the ratio of off-diagonal versus diagonal P tensor components is higher than that for traditional dipolar systems, which opens up the possibility of less stringent polarization schemes for parametric and electro-optic processes [95]. Furthermore, it has been shown that the efficiency-transparency trade-off favors octopolar molecules over traditional dipolar molecules [96]. 

Since octopolar molecules lack a dipole moment, the hyperpolarizability of purely octopolar molecules cannot be determined with the EFISHG technique. Therefore, the experimental determination of these nonpolar molecules remained a problem until the development of the hyper-Rayleigh scattering technique (HRS). As explained in Section 8.2.2, HRS provides a sensitive tool for the determination of the hyperpolarizability of nonpolar molecules in solution. 

Because a strong electric field is required to align the molecules, further restrictions are imposed on the molecules they should have a permanent dipole moment. For instance, EFISHG can not be applied to measure the second-order nonlinear susceptibilities of octopolar molecules, even though at the molecular level, then-molecular hyperpolarizability, is non-zero. Also, EFISHG can not be used with ionic molecules or with a polar solvent. 

For an octopolar molecule with Dy, symmetry only 4 equal tensor components... 

From the directional dependence and the depolarization ratios of the scattered radiation, information may be gained on particular tensor elements of The method has the advantage over EFISH measurements that it is also applicable to noncentro-symmetric molecules that do not posses a permanent dipole moment, in particular to, octopolar molecules of symmetry D3 (such as tricyanomethanide [C(CN)3] ) or of symmetry Tj (such as CCI4). It is to be expected that progress in laser technology and light detection systems will further improve the applicability of the method. 

The dielectric constant is a macroscopic property of the material and arises from collective effects where each part of the ensemble contributes. In terms of a set of molecules it is necessary to consider the microscopic properties such as the polarizability and the dipole moment. A single molecule can be modeled as a distribution of charges in space or as the spatial distribution of a polarization field. This polarization field can be expanded in its moments, which results in the multipole expansion with dipolar, quadrupolar, octopolar and so on terms. In most cases the expansion can be truncated to the first term, which is known as the dipole approximation. Since the dipole moment is an observable, it can be described mathematically as an operator. The dipole moment operator can describe transitions between states (as the transition dipole moment operator and, as such, is important in spectroscopy) or within a state where it represents the associated dipole moment. This operator describes the interaction between a molecule and its environment and, as a result, our understanding of energy transfer. 

The area of molecular nonlinear optics has been rejuvenated by efforts to investigate three-dimensional multipolar systems, functionalized polymers as optoelectronic materials, near infrared optical parametric oscillators and related aspects.71 There have been some advances in chromophore design for second-order nonlinear optical materials 72 these include onedimensional CT molecules, octopolar compounds and organometallics. Some of the polydiacetylenes and poly(/>-phenylenevinylene)s appear to possess the required properties for use as third-order nonlinear optical materials for photonic switching.73... 

However, for most other ratios of P-xxIPzzz octopolar contribution to the nonlinearity is dominant. The dipolar contribution to the hyperpolarizability completely vanishes when P xx/Pzzz = 1 the molecule is purely octopolar. This situation occurs for molecule b with purely octopolar D h symmetry and nonvanishing hyperpolarizability components zzz = -zxx = —xxz = xzx. The hyperpolarizability tensor then reduces to... 

Some examples of intuition-based or modeling-based advances in nonlinear properties, specifically the first hyperpolarizability response p, have been developed in the past three decades. These include the bond-length alternation motif, the idea of octopolar molecular structures, the stronger responses of excited states and the use of purposely twisted -ir-electron molecules to modify the admixture of quinoid and aromatic structures. 

---