Hyperpolarizabilities interaction

The perturbation V = H-H appropriate to the particular property is identified. For dipole moments ( i), polarizabilities (a), and hyperpolarizabilities (P), V is the interaction of the nuclei and electrons with the external electric field... 

The fundamental equation (1) describes the change in dipole moment between the ground state and an excited state jte expressed as a power series of the electric field E which occurs upon interaction of such a field, as in the electric component of electromagnetic radiation, with a single molecule. The coefficient a is the familiar linear polarizability, ft and y are the quadratic and cubic hyperpolarizabilities, respectively. The coefficients for these hyperpolarizabilities are tensor quantities and therefore highly symmetry dependent odd order coefficients are nonvanishing for all molecules but even order coefficients such as J3 (responsible for SHG) are zero for centrosymmetric molecules. Equation (2) is identical with (1) except that it describes a macroscopic polarization, such as that arising from an array of molecules in a crystal (10). 

Based on the fundamental dipole moment concepts of mesomeric moment and interaction moment, models to explain the enhanced optical nonlinearities of polarized conjugated molecules have been devised. The equivalent internal field (EIF) model of Oudar and Chemla relates the j8 of a molecule to an equivalent electric field ER due to substituent R which biases the hyperpolarizabilities (28). In the case of donor-acceptor systems anomalously large nonlinearities result as a consequence of contributions from intramolecular charge-transfer interaction (related to /xjnt) and expressions to quantify this contribution have been obtained (29). Related treatments dealing with this problem have appeared one due to Levine and Bethea bearing directly on the EIF model (30), another due to Levine using spectroscopically derived substituent perturbations rather than dipole moment based data (31.) and yet another more empirical treatment by Dulcic and Sauteret involving reinforcement of substituent effects (32). 

In order to measure molecular hyperpolarizabilities the now standard D-C induced SHG experiment is used (12). Although it would be more suitable to work in the gas phase to minimize molecular interactions, high molecular weights (low vapour pressure) and chemical decomposition processes make it hardly feasible for the molecules of interest. 

The ethynyl-linked complexes 105 were prepared and explored as potential building blocks for nonlinear optical (NLO) materials.129 Spectroscopic and cyclic voltammetry data indicate a small but real interaction between the ferrocenyl donor group and the borabenzene unit, increasing in the order RuHyper-Rayleigh scattering revealed small values for the first hyperpolarizability / , which increases in the same order. 

K. L. C. Hunt. Long-range dipoles, quadrupoles, and hyperpolarizabilities of interacting inert-gas atoms. Chem. Phys. Lett., 70 336, 1980. 

In the above equation a is the linear polarizability. The terms 3 and Y, called first and second hyperpolarizabilities, describe the2 nonlinear optical interactions and are microscopic analogues of x and x... 

Characterization of Molecular Hyperpolarizabilities Using Third Harmonic Generation. Third harmonic generation (THG) is the generation of light at frequency 3co by the nonlinear interaction of a material and a fundamental laser field at frequency co. The process involves the third-order susceptibility x 3K-3 , , ) where —3 represents an output photon at 3 and the three s stand for the three input photons at . Since x(3) is a fourth (even) rank tensor property it can be nonzero for all material symmetry classes including isotropic media. This is easy to see since the components of x(3) transform like products of four spatial coordinates, e.g. x4 or x2y2. There are 21 components that are even under an inversion operation and thus can be nonzero in an isotropic medium. Since some of the terms are interrelated there are only four independent terms for the isotropic case. 

Our calculations predict only minor differences between the ground state dipole moments for molecules containing nitro electron acceptors versus those possessing methylsulfonyl. In contrast, the hyperpolarizabilities behave much differently, in that calculated J3Z for the aminonitrostilbenes is about twice that of the aminosulfonylstilbenes and the nitroanilines are more than 5 times more nonlinear than the sulfonylanilines. The hyperpolarizabilities appear to be very sensitive to the details of the electron donors-acceptor interaction and hence accentuate the differences in the a values for nitro and methylsulfonyl. 

The use of salt formation to expand the number of crystals which contain a single molecular type was first applied by Meredith (26), and more recently by Marder et. al. (22). In the latter work, ionic interactions are used to offset dipolar interactions among achiral molecules, which enhances the probability that the resulting crystal will be noncentrosymmetric. In our case, of course, noncentrosymmetry is ensured by the chirality of the molecules involved. It is important to note that, within the picture we have presented, neither the assurance of noncentrosymmetry, nor the enhanced hyperpolarizability of the chiral molecule guarantees that the nonlinearity of any particular chiral organic salt crystal will be large. These properties simply ensure that each crystal so formed has an equal opportunity to express the molecular hyperpolarizability in an optimized way. 

Our present focus is on correlated electronic structure methods for describing molecular systems interacting with a structured environment where the electronic wavefunction for the molecule is given by a multiconfigurational self-consistent field wavefunction. Using the MCSCF structured environment response method it is possible to determine molecular properties such as (i) frequency-dependent polarizabilities, (ii) excitation and deexcitation energies, (iii) transition moments, (iv) two-photon matrix elements, (v) frequency-dependent first hyperpolarizability tensors, (vi) frequency-dependent polarizabilities of excited states, (vii) frequency-dependent second hyperpolarizabilities (y), (viii) three-photon absorptions, and (ix) two-photon absorption between excited states. 

In case of the frequency-dependent first hyperpolarizability, we note that the average value of the hyperpolarizability changes sign as a water molecule is transferred from vacuum to the condensed phase. This observation has also been observed experimentally. Furthermore, the effects of the polarization terms in the structured environment are important since the quadratic response calculation within the MCSCF/CM approach without the polarization interactions leads to much smaller values for the average hyperpolarizability. 

Similar to the average hyperpolarizability, the two-photon absorption cross-sections are also affected by the interactions with the structured environment. For forbidden transitions we have observed that the structured environment perturbs these transitions significantly. Generally, the results from the MCSCF/CM model including polarization contributions compare very well with the available experimental data on two-photon cross-sections of liquid water. 

G. Maroulis, Static hyperpolarizability of the water dimer and the interaction hyperpolarizability of two water molecules. J. Chem. Phys. 113, 1813-1820 (2000)... 

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