Hyperpolarizability dipolar molecules

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. 

From the measurement of the intensity of the generated second harmonic for a dipolar molecule and with knowledge of the value of the dipole moment, an experimental value for / can be obtained. The relation of this value to the hyperpolarizability tensor components, in the completely general case... 

From the complementary nature of EFISHG and HRS, application of both techniques to (neutral and dipolar) molecules can lead to the measurement of more tensor components, to the experimental determination of structural parameters [22], or to the independent confirmation of experimentally obtained values for hyperpolarizability tensor components [25]. 

The first common method for molecular first hyperpolarizability determination is the electric field-induced second harmonic generation (EFISH) technique in solution [6-10]. This technique can be applied only to dipolar molecules. Under an applied external electric field, molecules in solution orient approximately in the direction of the field giving rise to second harmonic generation. The measured third-order nonlinear optical susceptibility is given by the following expression ... 

We have discussed previously (5) the possibility that a comparison of the rise time of the Kerr transients would lead to quantitative answers concerning the influence of strong fields on the orientational motion of a dipolar molecule, in the event both the hyperpolarizability (or interactions) and dipole moment con-... 

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. 

For a molecule without symmetry reduction the sum-over-states expression for the hyperpolarizability yean often be modeled within the three level approximation (the ground state (index 0) and two excited states (indices 1,2 - not necessarily indicating the hierarchy of the energy eigenvalues)). If we assume po2 Poll f°r substituted molecules with a centrosymmetric backbone as described above, the number of terms reduces leaving only three terms to consider the negative term N > the dipolar term D , and the two-photon term TP, which includes the second excited state 2Ag. In the static limit one obtains for a one-dimensionally conjugated molecule... 

The vibrationally resonant hyperpolarizability of a molecule can be described with the following expression obtained utilizing perturbation theory [17] (assuming that the only interactions between the electric fields and the media are dipolar interactions). 

For the experimental determination of the second-order first hyperpolarizability, some sort of non-centrosymmetry has to be present in the solution. This can be achieved by applying a static electric field over a solution of neutral molecules with dipolar chromophores. Implicitly, this description limits the applicability of this Electric-field-induced second-harmonic generation (EFISHG) technique ... 

Ever since HRS has been developed as an experimental technique to determine the first hyperpolarizability p of molecules in solution, it has been realized that multiphoton fluorescence is a competing nonlinear process, contributing to the HRS signal [26]. For the classical dipolar and neutral molecules that may exhibit multiphoton fluorescence, electric-field-induced second-harmonic generation (EFISHG) experiments are possible. However, for ionic and non-dipolar compounds, no electric field can be applied over the solution. Hence, no EFISHG measurements are possible. Then it is very tempting to rely on the HRS measurement only. When there is, however, a multi-photon fluorescence (MPF) contribution, an overestimation of the first hyperpolarizability value results [27]. 

The general quantum chemical description of the nonlinear susceptibilities and hyperpolarizabilities in the density matrix formalism was developed by Bloembergen and Shen [36]. A simplification of this model for dipolar organic molecules, by only considering the transition between the ground state and the first excited state, led to the well-known two-state expression for the first hyperpolarizability [37] (Eq. (23)). 

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... 

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