Hyperpolarizabilities for the one-dimensional infinite single-electron periodic systems. II. Dipole-dipole versus current-current correlations

Based on Takayama-Lin-Liu-Maki model, analytical expressions for the third-harmonic generation, dc Kerr effect, dc-induced second-harmonic optical Kerr effect, optical Kerr effect or intensity-dependent index of refraction, and dc-electric-field-induced optical rectification are derived under the static current-current (J0J0) correlation for one-dimensional infinite chains. The results of hyperpolarizabilities under J0J0 correlation are then compared with those obtained using the dipole-dipole correlation. The comparison shows that the conventional J0J0 correlation, albeit quite successful for the linear case, is incorrect for studying the nonlinear optical properties of periodic systems.     

The calculation of frequency-dependent hyperpolarizabilities including electron correlation effects

The theory for the calculation of the frequency-dependent hyperpolarizabilities β(?2ω; 0, ω), β(?ω; 0, ω), and β(0; ω, ?ω) is discussed. New relations between these tensors are derived for those wave functions that obey the time-dependent Hellmann–Feynman theorem (e.g., the self-consistent field [SCF] or the exact wave function). Using second-order Møller–Plesset perturbation theory (MP2), expressions are obtained for the hyperpolarizabilities in terms of derivatives of appropriately defined linear polarizability tensors with respect to a static electric field. Results are presented for ammonia and formaldehyde for the optical Kerr effect and for secondharmonic generation. These results indicate that it is desirable to determine the frequency-dependent contribution to the hyperopolarizability at the MP2 rather than the SCF level of theory, in cases where the static hyperpolarizability has a large contribution from electron correlation and/or where the frequency-dependent contribution may be more significant, such as for secondharmonic generation.     

Computer simulation of the linear and nonlinear optical susceptibilities of p-nitroaniline in cyclohexane, 1,4-dioxane, and tetrahydrofuran in quadrupolar approximation. I. Molecular polarizabilities and hyperpolarizabilities

This is the first part of a study of the local field effects on (non)linear optical susceptibilities of solutions of para-nitroaniline (pNA) in three different solvents, cyclohexane (CH), 1,4-dioxane (DI), and tetrahydrofuran (THF), using a discrete molecular representation of the condensed phase. To account for dipolar and quadrupolar effects, the latter of which are especially important for DI solution, all the electric properties necessary to compute the local fields and local field gradients in quadrupolar approximation as well as the dipolar hyperpolarizabilities for the four molecules are computed, including frequency dispersion and vibrational contributions to the dipolar properties. The convergence of the perturbation treatment for the pure vibrational (PV) contributions is examined by comparison of the values obtained at the lowest order with those of partially computed second order in mechanical and electrical anharmonicity. For pNA, for which previous computations of the hyperpolarizabilities have generally found poor agreement with experimental results, a thorough investigation of the effects of solvent-induced geometry changes, dynamic and static correlation, frequency dispersion, and classical thermal averaging over the torsional modes of the substituent groups and the inversion mode of the amino group on the dipolar properties is carried out. Computations using self-consistent continuum reaction field models show that the amino group is substantially less pyramidalized in polar solvents than in the gas phase. With all the effects taken into account, reasonable agreement with the experimental electric-field induced second harmonic generation (EFISH) result on pNA vapor of Kaatz, Donley, and Shelton is obtained.     

Electrical and dynamooptical properties of Frechet dendron-modified polystyrene molecules in solutions

The electrooptical, dynamic, and dielectric characteristics of polystyrene modified by the Frechet dendrons of 1–4 generations have been studied in benzene, chloroform, and THF solutions. It has been shown that the Kerr constant and the shear optical coefficient for all the studied polymers coincide in sign and their absolute values increase with the dendron generation number. The intrinsic optical anisotropy of the repeating unit of dendronized polystyrene molecules is negative in sign, and its absolute value tends to grow with an increase in the generation number of dendrons. The frequency dispersions of the Kerr constand and of the dielectric polarization have been discovered for solutions of the modified polymer. The ratio between the times of relaxation characterizing the dispersion of dielectric permittivity and of the Kerr constant of solutions and the times of a rise and decay of electric birefringence measured on the onset and termination of the rectangular-pulsed field does not obey the longitudinal relaxation theory for polar macromolecules. The relaxation times of dielectric polarization and of electric birefringence tend to increase with the dendron generation number.     

Ultralarge hyperpolarizability twisted pi-electron system electro-optic chromophores: synthesis, solid-state and solution-phase structural characteristics, electronic structures, linear and nonlinear optical properties, and computational studies

This contribution details the synthesis and chemical/physical characterization of a series of unconventional twisted pi-electron system electro-optic (EO) chromophores. Crystallographic analysis of these chromophores reveals large ring-ring dihedral twist angles (80-89 degrees) and a highly charge-separated zwitterionic structure dominating the ground state. NOE NMR measurements of the twist angle in solution confirm that the solid-state twisting persists essentially unchanged in solution. Optical, IR, and NMR spectroscopic studies in both the solution phase and solid state further substantiate that the solid-state structural characteristics persist in solution. The aggregation of these highly polar zwitterions is investigated using several experimental techniques, including concentration-dependent optical and fluorescence spectroscopy and pulsed field gradient spin-echo (PGSE) NMR spectroscopy in combination with solid-state data. These studies reveal clear evidence of the formation of centrosymmetric aggregates in concentrated solutions and in the solid state and provide quantitative information on the extent of aggregation. Solution-phase DC electric-field-induced second-harmonic generation (EFISH) measurements reveal unprecedented hyperpolarizabilities (nonresonant mubeta as high as -488,000 x 10(-48) esu at 1907 nm). Incorporation of these chromophores into guest-host poled polyvinylphenol films provides very large electro-optic coefficients (r(33)) of approximately 330 pm/V at 1310 nm. The aggregation and structure-property effects on the observed linear/nonlinear optical properties are discussed. High-level computations based on state-averaged complete active space self-consistent field (SA-CASSCF) methods provide a new rationale for these exceptional hyperpolarizabilities and demonstrate significant solvation effects on hyperpolarizabilities, in good agreement with experiment. As such, this work suggests new paradigms for molecular hyperpolarizabilities and electro-optics.     

TTF+1-π共轭桥-6-氧四联氮阳离子双自由基NLO性质的理论研究

采用量子化学UPBE1PBE结合有限场(FF)方法,对系列TTF+?-π共轭桥-6-氧四联氮阳离子双自由基体系的稳定性,极化率αs和第一超极化率βtot进行研究.结果表明,TTF+?-6-氧四联氮阳离子双自由基引入共轭桥后,随体系共轭性增强,αs和βtot值均增大(体系2S的βtot值除外).自旋多重度和构象对双自由基体系的极化率和第一超极化率都有影响,双自由基体系由单重态转变为三重态时,极化率减小,而第一超极化率明显增大.以体系2为例,在单重态时αs和βtot值随构象变化较小,而三重态时αs和βtot值随二面角θ1和θ2的增加而减小.     

Semiempirical prediction of the hyperpolarizabilities for cyanovinyl-substituted donor-acceptor molecules

We present here a systematically theoretical study on the nonlinearities and their structure-property relationship of cyanovinyl-substituted donor-acceptor molecules by virtue of semiem-pirical PM3/AM1-FF approach.Good consistency between measured and calculated hyperpolarizabil-ities is obtained.Results show that conformation has a significant effect on hyperpolarizabilities.The torsion angle change between two conjugated parts of the molecular systems can substantially alter the nonlinearities.The total amount of charge transfer difference from donor to acceptor has been introduced to understand the microscopic nature of the nonlinear optical properties for the title molecules.General guidelines may be sought out in the search of molecules with large values of β Some molecules with large molecular hyperpolarizabilities can be predicted by the optimization for the longer π-electron systems with both acceptor and donor groups.     

Calculations of the structure and electronic properties of extended polar hydrocarbons

The structure and nonlinear optical potential of a series of polar unsaturated hydrocarbons containing the electron-donating heptafulvene ring and electron-attracting pentafulvene ring have been explored in terms of their first hyperpolarizabilities using a semiempirical sum-over-states and time-dependent coupled Hartree-Fock approach. Both methods predict that the hyperpolarizabilities of these simple hydrocarbons are substantial and exceed those found for many extended conventional donor-acceptor systems. © 1997 John Wiley & Sons, Inc.     

Rearrangement correction to higher polarizabilities of two-electron systems

In this paper we include the rearrangement correction (discussed in the preceding paper) in a coupled Hartree–Fock (CHF) calculation of atomic hyperpolarizabilities and other related properties. We have studied the effect of these corrections on properties like electric dipole hyperpolarizabilities, uniform electric field quadrupole polarizabilities and shielding factors in two-electron ions and have noticed significant changes in the computed values over the CHF results.     

Anomalous Kerr effect relaxation in an alternating field

Perturbation theory is used to derive the complex harmonic components (stationary regime) arising in Kerr effect relaxation for an assembly of nonelectrically interacting, polar, and polarizable symmetric-top molecules acted on by a strong dc bias electric field superimposed on a weak ac electric field. The approach starts from a fractional kinetic equation written in configuration space and represents an extension of the Smoluchowski equation to fractional dynamics. This equation is solved in the context of a subdiffusive process characterized by an anomalous exponent alpha ranging from 0 to 1, the Brownian limit. By using a perturbation procedure restricted to the second order in the ac field strength, analytic expressions for the electric birefringence spectra representing the frequency dependence of the first (in omega) and the second (in 2omega) harmonic components are obtained. Various Cole-Cole-like diagrams are presented in order to illustrate the results so obtained and to emphasize the role played by the fractal parameter alpha in the anomalous diffusion collision process. A comparison of our theoretical model with experimental measurements of the ac Kerr effect response of a dilute polymer solution [poly(3-hexylthiophene)] appears to be quite satisfactory.     

Electric field effect on the nematic-isotropic phase transition

Pulsed electric fields are used to study the influence of a strong field on the nematic-isotropic phase transition for cyanobiphenyl and stilbene-type liquid crystals. Deviation of the electric field-induced optical anisotropy from the Kerr law is observed and it is shown that such electric fields can shift the transition temperature substantially. The induced birefringence and the shift of the transition temperature are measured as a function of the electric field strength. The results are explained qualitatively in the context of the Landau-De Gennes theory with two order parameters. The coefficients of the phenomenological theory are calculated using the simple density functional theory of polar nematics developed in this paper and the results for the shift of the transition temperature are compared with experiment results.     

Nonlinear response theory with relaxation: the first-order hyperpolarizability

Based on the Ehrenfest theorem, an equation of motion that takes relaxation into account has been presented in wave-function theory, and the resulting response functions are nondivergent in the off-resonant as well as the resonant regions of optical frequencies. The derivation includes single- and multideterminant reference states. When applied to electric dipole properties, the response functions correspond to the phenomenological sum-over-states expressions of Orr and Ward [Mol. Phys. 20, 513 (1971)] for polarizabilities and hyperpolarizabilities of an isolated system. A universal dispersion formula is derived for the complex second-order response function. Response theory calculations are performed on lithium hydride and para-nitroaniline for off-resonant and resonant frequencies in the electro-optical Kerr effect and second-harmonic generation.     

有机及金属有机苯乙炔树状分子体系的非线性光学性质的理论研究

应用密度泛函理论研究了一系列有机及金属有机苯乙炔树状分子的激发态性质和非线性光学性质。计算的电子吸收光谱显示这些树状分子均在低能区域有一个最强的吸收;此外,金属有机体系的吸收光谱和有机体系相比发生了明显的红移。响应性质的计算结果表明共轭体系的扩展和金属有机基团的引入都使得苯乙炔树状分子的非线性光学极化率显著增加,尤其是含Ru体系,其β和γ值呈数量级增长。对于有机体系和含Pd体系,发生在共轭体系内部的π→π*电荷跃迁是产生分子一阶和二阶超极化率的主要原因。而含Ru体系相当大的非线性响应则主要起源于Ru的轨道到共轭体系的π*的跃迁,同时与Ru相邻的C≡C到共轭体系的π→π*跃迁起着辅助贡献。     

Problems in the comparison of theoretical and experimental hyperpolarizabilities revisited

The relationship between nonlinear susceptibilities and hyperpolarizabilities defined using different conventions is reexamined. In previous work [Willetts et al., J. Chem. Phys. 97, 7590 (1992)], relations between different conventions for microscopic hyperpolarizabilities have been derived, but the application of the corresponding conversion factors led to several inconsistencies. It is shown that different conventions for macroscopic susceptibilities have to be taken into account, too, in order to arrive at consistently comparable values. The complete set of conversion factors between several conventions are given for second harmonic generation, electric field induced second harmonic (EFISH) generation, and third harmonic generation. As an illustration, experimental EFISH and hyper-Rayleigh scattering results of p-nitroaniline are compared with each other and with recent results of ab initio computations including solvation effects. Several problems in the comparison of computational and experimental values are also discussed.     

The magnitude and temperature dependence of the Kerr constant in liquid crystal blue phases and the dark conglomerate phase

A new method of evaluating the Kerr constant in liquid crystals (LCs) is used to determine the temperature dependence of the Kerr effect in blue phases I and II (BPI and BPII) and to investigate the Kerr constant of the isotropic dark conglomerate (DC) phase. This method employs relatively small driving voltages and a vertical field switching (VFS) device geometry. An unusually large Kerr constant, K, is determined in the BPs of a non-polymer-stabilised material, ～3×10^?9 mV^?2 (BPI). The large value of K is attributed to significant pre-transitional values of the dielectric anisotropy and birefringence. K follows an inverse dependence on temperature and we consequently suggest that BPI demonstrates properties best suited to electro-optic devices. The new methodology has the advantage of revealing the dispersion of K in a single measurement. It is also possible to deconvolute the influence of the Kerr effect from measurements of electrostriction of the BP lattice. Finally, the Kerr effect has been measured for the first time in the DC phase of an oxadiazole bent-core liquid crystalline material, and is found to take rather low values, ～1×10^?11 mV^?2, which can be understood in the context of the physical properties of the material.     

不同溶剂中硝基苯胺分子非线性光学性质的研究

The solvent effects on the nonlinear optical properties of para-nitroaniline (pNA) molecule are studied on the base of time dependent density functional theory. The polarized continuum model is used to simulate the influence of the solvent environment of the solute molecule. In the first place, the geometrical structures of pNA molecule in each solvent are optimized by use of density functional theory and the influence of solvent on the geometry of pNA molecule is thus illustrated. Then, the energies and dipole moments of the excited states with pNA molecule in different solvents are computed on the base of time dependent density functional theory. The dispersion relations of the first-order nonlinear hyperpolarizabilities in second harmonic generation process for pNA molecule in different solvents are given by using two-state model for the first time. It is shown that polar solvents have much influence on the nonlinear optical properties. At low frequency radiation field, the theoretical results of the dispersion relation agree well with the experimental results. While at higher frequency radiation field, other methods need to be developed to compute the dispersion relation of the first order nonlinear hyperpolarizability. At last, possible explanations are given for the results and the validity of the two-state model is discussed.     

Anomalous nonlinear dielectric and Kerr effect relaxation steady state responses in superimposed ac and dc electric fields

It is shown how the rotational diffusion model of polar molecules (which may be described in microscopic fashion as the diffusion limit of a discrete time random walk on the surface of the unit sphere) may be extended to anomalous nonlinear dielectric relaxation and the dynamic Kerr effect by using a fractional kinetic equation. This fractional kinetic equation (obtained via a generalization of the noninertial kinetic equation of conventional rotational diffusion to fractional kinetics to include anomalous relaxation) is solved using matrix continued fractions yielding the complex nonlinear dielectric susceptibility and the Kerr function of an assembly of rigid dipolar particles acted on by external superimposed dc E0 and ac E1(t)=E1 cos omegat electric fields of arbitrary strengths. In the weak field limit, analytic equations for nonlinear response functions are also derived.     

Incorporation of solvent effects into density functional predictions of molecular polarizabilities and hyperpolarizabilities

A study of the effect of the field, the basis set, the functional, and the cavity size on molecular polarizabilities and hyperpolarizabilities of substituted benzenes in liquid or solution is reported. The calculations have been performed using the density functional theory (DFT) within the conductor‐like screening model (COSMO). The optimized computational parameters are adopted to calculate molecular polarizabilities and hyperpolarizabilities of substituted benzenes in liquid or solution. The results show good agreement with the experimental values. From comparison of the different theoretical results, it is found that at the same theoretical level, the selection of the different solvation models may play an important role in the calculations of molecular solvation polarizability, and using the same solvation model, the effects of the different theoretical methods are relatively small. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Frequency-dependent hyperpolarizabilities of the Ne, Ar, and Kr atoms using the approximate coupled cluster triples model CC3

The frequency-dependent electric field-induced second harmonic generation (ESHG) second hyperpolarizabilities gamma of neon, argon, and krypton are calculated using the approximate coupled cluster triples model CC3. Systematic basis set investigations are carried out to establish basis set limits, and scalar relativistic effects are accounted for by direct perturbation theory. To estimate higher-order correlation effects, full configuration-interaction results are used to benchmark the accuracy of CC3. The best theoretical estimates obtained thereby for the static second hyperpolarizabilities gamma(0) are 107.4, 1159, and 2589 a.u. for neon, argon, and krypton, respectively. These values as well as the results for the dispersion curve of the parallel component gamma( parallel) agree well with the latest experimental values from electric field-induced second harmonic generation. In addition, the dispersion of the perpendicular component gamma( perpendicular) and the hyperpolarizability ratios gamma( parallel)gamma( perpendicular) has been studied for the first time on a consistently correlated ab initio level. The analysis of the results indicates that, in particular for neon and krypton, the presently available experimental values are flawed.     

Kerr Effect of Xanthan/DTAB Aqueous Solutions

The Kerr effect of the Xanthan (charged polyelectrolyte; 113 ppm)/DTAB (surfactant) mixture in aqueous solution was studied. The static Kerr constant (B) and mean relaxation times (τ) values as a function of surfactant concentration (C_DTAB ) were determined. The observed birefringence (Δn) is not a linear function of the electric applied field (E ²). For small E values Δn grows with E ² and at a certain field value the birefringence tends to saturate. The addition of small quantities of DTAB lowers B values with respect to the Kerr constant of Xanthan (113 ppm) aqueous solution. The relaxation time of the mixtures is linearly dependent on the applied field and it decreases when DTAB concentration increases. The importance of the equivalent point is signalled. It is supposed that the initial rigidity of the polyelectrolite decreases because of the surfactant addition. Conductivity (σ) values as a function of surfactant concentration are presented.