Hyperpolarizability electric field-induced second harmonic

The CCSD model gives for static and frequency-dependent hyperpolarizabilities usually results close to the experimental values, provided that the effects of vibrational averaging and the pure vibrational contributions have been accounted for. Zero point vibrational corrections for the static and the electric field induced second harmonic generation (ESHG) hyperpolarizability of methane have recently been calculated by Bishop and Sauer using SCF and MCSCF wavefunctions [51]. 

Experimental and theoretical results are presented for four nonlinear electrooptic and dielectric effects, as they pertain to flexible polymers. They are the Kerr effect, electric field induced light scattering, dielectric saturation and electric field induced second harmonic generation. We show the relationship between the dipole moment, polarizability, hyperpolarizability, the conformation of the polymer and these electrooptic and dielectric effects. We find that these effects are very sensitive to the details of polymer structure such as the rotational isomeric states, tacticity, and in the case of a copolymer, the comonomer composition. 

Electric arcs, in metal vapor synthesis, 1, 224 Electric-field-induced second harmonic generation Group 8 metallocenes, 12, 109 for hyperpolarizability measurement, 12, 107 Electrochemical cell assembly, in cyclic voltammetry, 1, 283 Electrochemical irreversibility, in cyclic voltammetry, 1, 282 Electrochemical oxidation, arene chromium carbonyls, 5, 258 Electrochemical properties, polyferrocenylsilanes, 12, 332 Electrochemical reduction, bis-Cp Zr(III) and (IV) compounds, 4, 745 Electrochemical sensors biomolecule—ferrocene conjugates... 

TDDFT methods have also been applied successfully to the description of the linear and nonlinear optical properties of heteroleptic sandwich complexes. The optical spectrum and the hyperpolarizability of Zr(OEP)(OEPz,) for which large first hyperpolarizabilities, /JSHG (SHG=second-harmonic generation) were measured in an electric field induced second-harmonic generation (EFISH) experiment [182], have been investigated by TDDFT methods [134]. The excitation energies and oscillator strengths calculated... 

While the above discussion clearly highlights the importance of including solvent effects in the calculations, the calculated properties cannot be compared directly with experimental results. This is mainly caused by the many different conventions used for representing hyperpolarizabilities and susceptibilities. However, the calculated properties can be combined with appropriate, calculated Lorentz/Onsager local field factors to obtain macroscopic susceptibilities that can be compared with experimental results. For water, we used this to calculate the refractive index and the third harmonic generation (THG) and the electric field-induced second harmonic (EFISH) non-linear susceptibilities. The results are collected in Table 3-11. 

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]. 

Experimental Hyperpolarizabilities for Gas and Liquid. The usual sources of hyperpolarizability data are EFISH (Electric Field Induced Second Harmonic), the static and optical Kerr effect (KE and OKE) and hyper-Rayleigh scattering (HRS). The extraction of molecular hyperpolarizabilities from the EFISH signal requires careful analysis of the second harmonic output signal... 

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 ... 

The Electric-Field-Induced Second-Harmonic Generation (EFISHG) technique makes it possible to measure the molecular hyperpolarizability, p, on liquids or molecular solutions. The centrosymmetry of tire solution is broken by applying a DC electric field to induce an average orientation of the molecules due to interactions of the permanent dipoles of the molecules and the electric field. The energy of a dipole with a permanent dipole fi in an electric field E is given by ... 

The theoretical framework developed above is valid in the electric dipole approximation. In this context, it is assumed that the nonlinear polarization PfL(2 >) is reduced to the electric dipole contribution as given in Eq. (1). This assumption is only valid if the surface susceptibility tensor x (2 > >, a>) is large enough to dwarf the contribution from higher orders of the multipole expansion like the electric quadrupole contribution and is therefore the simplest approximation for the nonlinear polarization. At pure solvent interfaces, this may not be the case, since the nonlinear optical activity of solvent molecules like water, 1,2-dichloroethane (DCE), alcohols, or alkanes is rather low. The magnitude of the molecular hyperpolarizability of water, measured by DC electric field induced second harmonic... 

Suslick et al. measured the first hyperpolarizabilities ()S) of porphyrins having electron-donor (amino) and -acceptor (nitro) groups in the para-position of 5,10,15,20-substituted tetraphenylporphyrins (Figure 25) using electric field induced second harmonic generation (EFISH) technique at 1.19 pm with chloroform solutions. The dipole moment (p) and P values were affected by the position of donor and acceptor groups. A P value of 30 x 10 esu and dipole moment of 7 x 10 esu were measured for the porphyrin having R = R = NO2, R = R = NH2 and the porphyrin... 

Experimentally, mainly two techniques - the electric field induced second harmonic generation (EFISH) and hyper-Rayleigh scattering (HRS, also termed harmonic light scattering method) - are used in order to determine in solution the experimental value of the quadratic hyperpolarizability of molecular NLO chromophores. 

First, let us turn our attention to the issue of optimizing chromophore hyperpolarizability. An obviously important and necessary aspect of the process is the characterization of hyperpolarizabilities. The two most popular methods for characterizing chromophore second-order molecular optical nonlinearity are electric field-induced second harmonic generation (EFISH) [3,10,21-24] and hyper-... 

The static and dynamic linear responses, a(0 0) and a( co co), correspond to the so-called static and dynamic polarizabilities, respectively. At second order in the fields, the responses are named first hyperpolarizabilities whereas second hyperpolarizabilities correspond to the third-order responses. Different phenomena can be distinguished as a function of the combination of optical frequencies. So, p(0 0,0), p(—co co,0), p(0 o), — ea), and p(— 2co co,co) are associated with the static, dc-Pockels (dc-P), optical rectification (OR), and second harmonic generation (SHG) processes whereas y(0 0,0,0), y(- ( ( ,0,0), y( 2co co,( ,0), y( co co, — ca, ), and y(— 3 , , ) describe the static, dc-Kerr, electric-field-induced second harmonic generation (EFISHG), degenerate four-wave mixing (DFWM),... 

By combining classical samplings with quantum chemistry semiempirical TDHF calculations the impact of dynamic fluctuations on the first hyperpolarizability of helical strands has been evidenced . In particular, these fluctuations are responsible for relative variations of 20% in the hyper-Rayleigh responses in both pyridine-pyrimidine (py-pym) and hydrazone-pyrimidine (hy-pym) strands. Dynamical disorder has an even more important impact on the electric field-induced second harmonic generation responses, whose variations can reach 2 (py-pym) or 5 (hy-pym) times their mean value. These results demonstrate that geometrical fluctuations have to be taken into account for a reliable description of the second-order NLO properties in flexible structures such as helical strands. This work has also highlighted the relationships between the nature of the unit cell and the helical conformation of foldamers and their second-order NLO responses. In particular, the value of the hyper-Rayleigh depolarization ratio, which is characteristics of octupolar symmetry, is related to the helix periodicity, of three unit cells per turn in both compounds. 

Assuming that arises from the third-order hyperpolarizability, elements of give information about the degree of orientational order. Measurements of electric-field-induced second-harmonic generation (EFISH) have been carried out [88] on 5CB, showing the expected temperature dependence. In liquid crystals, may originate from order or flexoelectric effects, or other mechanisms resulting in electric polarization. 

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