Molecular first hyperpolarizability

We have considered scalar, vector, and matrix molecular properties. A scalar is a zero-dimensional array a vector is a one-dimensional array a matrix is a two-dimensional array. In general, an 5-dimensional array is called a tensor of rank (or order) s a tensor of order s has ns components, where n is the number of dimensions of the coordinate system (usually 3). Thus the dipole moment is a first-order tensor with 31 = 3 components the polarizability is a second-order tensor with 32 = 9 components. The molecular first hyperpolarizability (which we will not define) is a third-order tensor. 

Second, the effect of applied electric field changing the mixing of neutral and charge-separated forms of the charge-transfer chromophores will define the magnitude of electric field required to achieve a given phase shift. Molecular first hyperpolarizability (3 can be understood within the framework of the parameters of this two-state charge-transfer process, as shown in Eq. (5) (see also the Appendix) ... 

Fig-8. EO coefficient data, as a function of chromophore number density, for FTC (circles) and FTC-2H (diamonds) chromophores in PMMA. Also shown is the theoretical curve computed for FTC. Note that for FTC-2H, the two butyl groups (attached to the thiophene ring) are replaced by protons. The more ellipsoidal FTC-2H exhibits a smaller maximum electrooptic activity and the position of the maximum is shifted to lower number density. Consistent with EFISH, HRS, and other measurements, the dipole moments and molecular first hyperpolarizabilities of these two chromophores are comparable (The values for FTC-2H may be slightly larger)... 

Fig-9. EO coefficient data, as a function of chromophore number density, for CLD-type chromophores with (solid circles) and without (open triangles) isophorone protection of the polyene bridge. The maximum achievable electro-optic activity is smaller for the naked polyene bridge structure and the maximum of the curve is shifted to lower number density. The dipole moment and molecular first hyperpolarizability values are comparable (The unprotected polyene bridge variation may exhibit slightly higher values of p(3)... 

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 ... 

Schmalzlin et al. [90] have used the HRS technique to determine the molecular first hyperpolarizabilities (3 values of retinal Schiff base in its protonated and unprotonated form. Results of their HRS measurements performed at 1064,1300 and ISOOnm were reported. The derived hyperpolarizabilities are self-consistent with the two-state model for all three wavelengths, but they are an order of magnitude lower than those reported by Hendrickx et al. 

Although EFISHG is used to indirectly compute and the molecular first hyperpolarizability, for centrosymmetric structures, when /jl = O and jS = 0, EFISHG will measure only contributions from the third-order molecular polarizability. 

Coe, B.J., Houbrechts, S., Asselberghs. I.. Persoons. A. Efficient, reversible redox-switching of molecular first hyperpolarizabilities in ruthenium(II) complexes possessing large quadratic optical nonlinearities. Angew. Chem. Int. Ed. 38. 366-369 (1999)... 

In formula (34), /u, (f) = (0 /Ai(f) 0 ) is the ground state, permanent, electric dipole moment of species f, while ) is the molecular first hyperpolarizability tensor defined by... 

Oudar and Chemla proposed a simple two-state quantum mechanical model as a powerful tool to predict the molecular first hyperpolarizability [1 in the design of the second-order NLO chromophores [29] ... 

XXII. The factor of four to seven between these two sets of results emphasizes the importance of taking into account, even in a simple way, the influence of environment on the macroscopic suscqitibilities. In this case, the estimated value for x (-2 d 0,(O) is now in rather good agreement with experiment. The agreement gets even better if using the Paaa( 2(D (D,0f)) values corrected for electron correlation effects X ( 2g) (0,(0) = 1.3 x 212 padV - 276 pmA. These values can also be compared to the oriented gas estimate of Ref 19 which amounts to 558 120 pmA. The latter was evaluated using the EFISH-extracted molecular first hyperpolarizabilities. 

Molecular first hyperpolarizability increases significantly with increasing length of the ir-electron bridge but in general, structure—function relationships for j8 are not simple and optimization of j8 requires guidance fi om carefiiUy evaluated quantum mechanical calculations (see Section 6.2). 

Theoretically Inspired Optimization of Molecular First Hyperpolarizability... 

FIGURE 6.3 Molecular first hyperpolarizability, p, values calculated by semi-empirical INDO methods are shown as a function of twist angle for a twisted chromophore (see upper part of the figure). The maximum predicted... 

If the ground state of a chromophore is dominated by the neutral form, the molecular first hyperpolarizability will be of positive sign whereas it will be negative if the chromophore ground state is dominated by the zwitterionic contribution. Obviously, solvatochromic shifts will be of opposite signs for these two cases. 

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