Hyperpolarizability Tensor Research Articles

Optimization of Nonlinear Optical Properties by Substituent Position, Geometry and Symmetry of the Molecule: An ab Initio Study

Static polarizability and first- and second-order hyperpolarizability tensors are computed at the correlated level for a series of para-nitroaniline derivatives. The importance of including electron correlation effects in the determination of equilibrium structure and the molecular properties is investigated. A qualitative description of the substitution effects, planarity, and symmetric effect of the molecule on the molecular susceptibility is discussed.

Hyper-Rayleigh spectral intensities of gaseous Kr–Xe mixture

Binary collision-induced hyper-Rayleigh (CIHR) spectra of Kr-Xe gaseous system are computed quantum mechanically and classically within the frequency range up to 380 cm(-1). The intensities are expressed in absolute units. The details of the theory developed for the CIHR spectra are given and the properties of the profiles as well as the depolarization ratio frequency dependence are discussed. The contributions to the spectra related to the vector b10(r) and the septor b30(r) components of the hyperpolarizability tensor are evaluated.

Quantitative spectral and orientational analysis in surface sum frequency generation vibrational spectroscopy (SFG-VS)

Sum frequency generation vibrational spectroscopy (SFG-VS) has been proven to be a uniquely effective spectroscopic technique in the investigation of molecular structure and conformations, as well as the dynamics of molecular interfaces. However, the ability to apply SFG-VS to complex molecular interfaces has been limited by the ability to abstract quantitative information from SFG-VS experiments. In this review, we try to make assessments of the limitations, issues and techniques as well as methodologies in quantitative orientational and spectral analysis with SFG-VS. Based on these assessments, we also try to summarize recent developments in methodologies on quantitative orientational and spectral analysis in SFG-VS, and their applications to detailed analysis of SFG-VS data of various vapour/neat liquid interfaces. A rigorous formulation of the polarization null angle (PNA) method is given for accurate determination of the orientational parameter D = ⟨cos θ ⟩/⟨cos3 θ⟩, and comparison between the PNA method with the commonly used polarization intensity ratio (PIR) method is discussed. The polarization and incident angle dependencies of the SFG-VS intensity are also reviewed, in the light of how experimental arrangements can be optimized to effectively abstract crucial information from the SFG-VS experiments. The values and models of the local field factors in the molecular layers are discussed. In order to examine the validity and limitations of the bond polarizability derivative model, the general expressions for molecular hyperpolarizability tensors and their expression with the bond polarizability derivative model for C 3 v , C 2 v and C ∞ v molecular groups are given in the two appendixes. We show that the bond polarizability derivative model can quantitatively describe many aspects of the intensities observed in the SFG-VS spectrum of the vapour/neat liquid interfaces in different polarizations. Using the polarization analysis in SFG-VS, polarization selection rules or guidelines are developed for assignment of the SFG-VS spectrum. Using the selection rules, SFG-VS spectra of vapour/diol, and vapour/n-normal alcohol (n∼ 1–8) interfaces are assigned, and some of the ambiguity and confusion, as well as their implications in previous IR and Raman assignment, are duly discussed. The ability to assign a SFG-VS spectrum using the polarization selection rules makes SFG-VS not only an effective and useful vibrational spectroscopy technique for interface studies, but also a complementary vibrational spectroscopy method in general condensed phase studies. These developments will put quantitative orientational and spectral analysis in SFG-VS on a more solid foundation. The formulations, concepts and issues discussed in this review are expected to find broad applications for investigations on molecular interfaces in the future.

Second-harmonic generation optical activity of a polypeptide α-helix at the air∕water interface

Quantitative measurements of second-harmonic generation optical activity (SHG-OA) have been performed for alpha-helical polypeptides poly-(gamma-benzyl-L-glutamate) and poly-(gamma-ethyl-L-glutamate) adsorbed at the airwater interface, with the fundamental frequency variant Planck's over 2piomega = 2.96 eV (lambda = 417 nm). The chiral component of the nonlinear susceptibility chi(XYZ) ((2)) is small for both polymers, being comparable in magnitude with the susceptibility chi(XXZ) ((2)) of the clean airwater interface. The microscopic origin of the nonlinear response has been investigated by using semiempirical ZINDOS calculations in conjunction with standard time-dependent perturbation theory to evaluate the molecular hyperpolarizability tensor of a model alpha-helix composed of glycine residues. Calculated nonlinear susceptibilities (per monomer unit) are in good agreement with experimental measurements for both the chiral and achiral response. The computational results indicate that charge transfer transitions of the alpha-helix have a large influence on the achiral components of the hyperpolarizability tensor, and produce characteristic features in the response under suitable experimental conditions. The dominant origin of SHG-OA for the model alpha-helix is a structural effect due to the tilt of the plane of each amide group of the helix relative to the helical axis. SHG-OA is associated with the orientational distribution of isolated, achiral chromophores, and is present in the absence of electronic coupling between the amide subunits of the polypeptide alpha-helix.

First hyperpolarizabilities of dipolar, bis-dipolar, and octupolar molecules

A series of dipolar ( 1), bis-dipolar ( 2), and octupolar molecules ( 3) containing 1, 2, and 6 dipolar units within a molecule has been synthesized and their hyperpolarizabilities were analyzed. The β HRS increases in the order, 1 < 2 < 3. The ‘monomeric’ β zzz increases by approximately twofold from 1 to 2, whereas β zzz of 2 and β xxx of 3 are similar. Noteworthy is the parallel increase in the hyperpolarizability tensor with the λ max.

A simulation study of the optical Kerr effect in liquid water

A molecular dynamics simulation study is presented for the dynamics of the polarizability anisotropy of liquid water using the SPC/E model and a dipolar induction scheme that involves the intrinsic polarizability and first hyperpolarizability tensors obtained from ab initio quantum chemical calculations at the MP2/6-311++G(d,p) level. The time-correlation functions for the collective polarizability anisotropy, the optical Kerr effect response, and the frequency spectra are analyzed in terms of the intrinsic and induced polarizability contributions. At short times, the simulated Kerr nuclear response exhibits maxima near 15, 50 and 180 fs, followed by a diffusive tail which has been fitted by a bi-exponential with time constants ca. 0.4 and 2.5 ps. The short time features are in good agreement with available simulation and experimental results. The agreement with experiments is less satisfactory for the diffusive components. The main features of the frequency spectrum include a rotational-diffusion peak centered around 3 cm(-1), a collision-induced (hindered translations) band near 200 cm(-1), and a broad librational band at 450 cm(-1). The simulation results are in good agreement with experimental frequency spectra obtained from Kerr effect and related spectroscopies, but fail to reproduce the experimental band near 60 cm(-1).

Electric dipole polarizability and hyperpolarizability of NCCN, NCCP, and PCCP

Components of the static electric dipole polarizabilty (α), and second hyperpolarizability (γ); tensors have been determined by accurate ab initio calculations for three molecules containing two conjugated carbon - nitrogen and/or carbon - phosphorus triple bonds. For the NCCP molecule the dipole moment (μ) and non-vanishing components of the first hyperpolarizability (β) tensor have also been calculated. Electron correlation effects have been taken into account by the second-order Many Body Perturbation Theory (MBPT(2)), and coupled cluster (CCSD and CCSD(T)) calculations. The basis set developed by Sadlej (Pol) and designed to be used in electric properties calculations together with its extension (HyPol) have been applied and compared to the results obtained with the standard aug-cc-PVTZ sets of Dunning.

Hyperpolarizability Components for α- and ω-Helical Polypeptides in Polar Crystals Determined from Second-Harmonic Generation Measurements

Second-harmonic generation (SHG) properties of α-helical and ω-helical polypeptides have been investigated by using crystalline films prepared by casting lyotropic liquid crystal solutions of poly(γ-phenylpropyl L-glutamate) (3PLG) and poly(β-benzyl L-aspartate) (PBLA) under a high electric field. The crystalline films generated SH light upon irradiation of the Nd:YAG laser, which ensures that the films have a polar structure. The in-plane anisotropy of the polarized SH light intensity is well explained by theoretical descriptions under the C6 and C4 symmetries for 3PLG and PBLA, respectively. On the basis of the SHG results, the hyperpolarizability tensor components of the individual polypeptide helical molecules are characterized as βZXX/βZZZ=1.2, βXZX/βZZZ=3.8, and 2βZXX/βXZX=0.7 for the α-helix 3PLG, and βZXX/βZZZ=3.8, βXZX/βZZZ=5.0, and 2βZXX/βXZX=1.5 for the ω-helix PBLA, where the z-axis is set as the helical axis. Quantum chemical calculation is successfully performed to reveal the general character of the polypeptide helix, βZXX>βZZZ.

Relaxational diffusion in guest–host polyphosphazene thin films: Temperature dependence

The relaxation of poled guest–host polyphosphazene (PPZ) films containing the 4-[(4′-nitrophenyl)azo]phenoxy (NPAP) azo-dye chromophore (Tg=144 °C) has been investigated by measuring the time decay of the nonlinear optical susceptibility tensor in the 80–120 °C temperature range. The kinetic data have been analyzed on the basis of the Legendre polynomial decomposition of the orientational distribution function. In the measuring time range, two components (fast and slow) of the decay have been found together with a constant component that disappears at temperatures close to Tg. This component accounts for the nonreorientable fraction of the molecules at each temperature. The temperature dependence of the two lifetimes has been determined and fitted to an Adam–Gibbs law. At a high temperature, (120 °C) the ratio of lifetimes closely follows the predictions of the orientational diffusion equation. This allows one to determine the two nonlinear components βzzz=−88.10−30 esu and βzxx=71.10−30 esu of the quadratic hyperpolarizability tensor in our rodlike (C∞v symmetry) molecules, showing the non-negligible contribution of the nondiagonal components.

Determination of Hyperpolarizability Tensor Ratios in the Absence of Kleinman Symmetry by Depolarized Hyper-Rayleigh Scattering

Determination of Hyperpolarizability Tensor Ratios in the Absence of Kleinman Symmetry by Depolarized Hyper-Rayleigh Scattering

Polarizability anisotropy relaxation in pure and aqueous dimethylsulfoxide

A molecular dynamics simulation study is presented for the relaxation of the polarizability anisotropy of liquid dimethylsulfoxide (DMSO) and DMSO–water mixtures of DMSO mole fractions xD=0.05, 0.10, 0.25, 0.50, and 0.75. The system’s collective polarizability is computed through a dipolar induction mechanism involving the intrinsic polarizability and first hyperpolarizability tensors for water and DMSO, obtained from ab initio quantum chemical calculations at the MP2/6-311++G(d,p) level. The rotational-diffusion components of the anisotropy relaxation of the pure liquids increase upon mixing to a maximum near 25% DMSO, showing consistency with other dynamical properties of these mixtures. Features of the optical Kerr effect (OKE) nuclear response of liquid water, previously ascribed to hydrogen bonding distortions, show significant enhancement upon addition of DMSO due to the formation of strong DMSO–water H-bonds. The OKE spectrum for DMSO is in close agreement with experimental measurements, but there are discrepancies for pure water in the vicinity of 60 cm−1, pointing to the existence of inaccuracies in our description of OKE sensitive polarizability fluctuations of water. The mixtures OKE spectra feature an enhancement in the high frequency water librational band.

Effects of Trifluoromethyl and Alkoxycarbonyl Groups on the Structure and Reactivity of Acrylates

Ab initio calculations with full geometry optimization have been performed for β-CF3-substituted cis- and trans-methyl crotonates, methyl-β,β-bis(trifluoromethyl) acrylate, and dimethylhexafluoroisopropylidene malonate using the restricted Hartree-Fock (RHF) method (6-31G* basis set). The effects of substituents at the multiple bond on the geometrical and electronic structure, dipole moments, polarizability and first molecular hyperpolarizability tensors, normal vibration frequencies, one-electron levels, electrostatic potentials, and local electron density at the C=C bond have been studied. Two substituents in the acrylic system prevent the conjugation of C=C and C=O bonds. The major effect on the structure and properties of the title compounds is produced by π-π interactions of the CF3 group with the multiple bond and by incoherent exchange interactions of substituents at the C=C bond.

The hyper-Rayleigh light scattering spectrum of gaseous Ne–Ar mixture

Hyper-Rayleigh binary collisional spectra for a Ne–Ar gaseous system are computed within the frequency range up to 500 cm−1 with four new ab initio hyperpolarizability models used. The properties of the profiles as well as the depolarization ratio frequency dependence are discussed. The contributions to the spectra given by the dipolar b1(r) and the octopolar b3(r) components of the hyperpolarizability tensor and the multipolar model HR spectrum are compared.

A theoretical study on the second-order nonlinear optical susceptibilities of lithium formate monohydrate crystal, HCOOLi·H2O

Abstract Ab initio calculations of the first hyperpolarizabilities of (HCOOLi·H 2 O) 2 n supermolecules, as the building-blocks of lithium formate monohydrate (LFM) crystal with extended system, were performed for the first time. The dependence of the static β ijk 0 values on chain length was explored, and the frequency dependence of β ijk (−2 ω ; ω , ω ) was measured, and the influences of electron correlation and basis set on β ijk 0 were evaluated. Finally, we predicted the second-order nonlinear optical coefficients of LFM crystal. The β ijk 0 value of (HCOOLi·H 2 O) 2 n is linearly dependent on the chain length of supermolecule, which is quite unusual for an extended system connected by the O–Li bonds with ionic characters. Although the static component of β zzz 0 tensor is the static largest in these three components under study, the absolute value of frequency-dependent β zyy (−2 ω ; ω , ω ) element, transforming the smallest into the largest, is the most sensitive to frequency. After the fundamental wavelength is smaller than 500 nm, it is found that the β ijk (−2 ω ; ω , ω ) value is resonantly enhanced to a great extent due to the double frequency lies in the region of resonance. In addition, the β zxx 0 value goes from negative to positive with changes of electron correlation and basis set. Obviously, it is very necessary to take into account the effect of electron correlation, if the hyperpolarizability tensor components must be accurately calculated. Moreover, it is also very important whether it is adopted a complete basis set with diffuse and polarization functions. The calculated nonlinear coefficients at high level suggest that the scaled set reported by Robert seem more reasonable.

Polar structure in a ferroelectric bent-core mesogen as studied by second-harmonic generation.

Second-harmonic generation (SHG) measurements have been conducted in the ferroelectric liquid crystalline phase of a chiral bent-core molecule, P-8-OPIMB6*. Well-aligned cells were obtained by applying an electric field parallel to the substrate surfaces. In-plane anisotropy of the SHG signal observed at normal incidence of light shows two- or four-leaf patterns depending on polarization conditions, indicating a ferroelectric uniform structure. The detailed analysis of the data by taking account of optical anisotropy in the SHG active bulk leads to the determination of nonlinear susceptibility tensor components, d(333)=14.4 pm/V and d(311)=49.2 pm/V. Using the d coefficients thus determined, the hyperpolarizability tensor components of the molecule are also determined as beta(zzz)=14.5 x 10(-30) esu and beta(zxx)=67.6 x 10(-30) esu. These values well agree with those of the achiral homolog P-12-OPIMB previously determined by hyper-Rayleigh scattering.

Quadratic nonlinear optical coefficients of organic-inorganic crystal: 2-amino-5-nitropyridinium chloride

The quadratic nonlinear optical efficiency of the 2-amino-5-nitropyridinium dihydrogen chloride crystal is studied. The quadratic coefficients are determined by second-harmonic generation as d11=9 pm/V and d12=8 pm/V. The effective coefficients are obtained as deff=5.1 pm/V for type I and deff=9.7 pm/V for type II. Following the gas-oriented model, the dimensions of the hyperpolarizability tensor bIJK of the 2-amino-5-nitropyridinium are examined. Considering the arrangement of the organic and inorganic entities in the unit cell, the failure of the two-dimensional model can be due to the local electric field induced by the Cl- anions.

Unique determination of the hyperpolarizability tensor ratio through depolarized hyper-Rayleigh scattering under an external electric field

We have analyzed the depolarized hyper-Rayleigh scattering from a molecular system with partial macroscopic polar ordering. It is shown that the hyperpolarizability tensor ratio and the molecular dipole moment can be determined simultaneously by the measurement of depolarization as a function of external field strength. As an experimental example, we performed a quantitative analysis of the electric-field-dependent depolarized hyper-Rayleigh signal from a poly-γ-benzyl-l-glutamate solution, obtaining the dipole moment and the ratio of hyperpolarizability components as 4.0 D and β311/β333=-0.81, respectively.

Cubic nonlinear optical response of a molecule in an inhomogeneous solvation environment: A response theory formalism

A method for determining cubic response molecular properties of heterogeneously solvated molecules is presented. The molecule is either located at the surface of a metal or solvated alongside the surface of a metal. We represent the metal as a perfect conductor and the solvent as a dielectric medium. The electronic structure of the molecular systems is described both at the uncorrelated and correlated electronic structure levels. The latter is given by the multiconfigurational self-consistent field method. From this method it is possible to calculate fourth order molecular properties such as frequency-dependent second-order hyperpolarizabilities (γ), three-photon absorptions, two-photon absorption between excited states, and frequency-dependent polarizabilities of excited states. From the frequency-dependent second-order hyperpolarizabilities one can calculate for heterogeneously solvated molecules the third harmonic generation, the static electric field-induced second harmonic generation, the static electric field induced Kerr effect. Calculations of the frequency dependent second-order hyperpolarizability tensor for heterogeneously solvated CO are presented. The calculations show that the second-order hyperpolarizability tensor elements depend strongly on the heterogeneous solvent configuration.

Efficient methods to calculate dynamic hyperpolarizability tensors by time-dependent density-functional theory

A derivation of density-functional response theory is presented which is based directly on the Runge–Gross theorem and does not invoke the action formalism and thus does not violate causality requirements in time. Working equations to treat linear and nonlinear response properties of electronic systems by time-dependent density-functional theory in the frequency domain are given. Efficient noniterative methods to calculate dynamic hyperpolarizability tensors of molecules for arbitrary frequency combinations are presented. With the introduced methods, hyperpolarizabilities of benzene and stilbene derivatives are investigated. The results show that the influence of substituents on the frequency-dependent hyperpolarizability is well described by time-dependent density-functional theory at the adiabatic local density level. Inspection of the linear and nonlinear response of the electron density shows the importance of screening effects for the response properties of larger molecules on electric fields and electromagnetic radiation.

Multipolar engineering of molecules and materials for quadratic nonlinear optics

The first generation of molecular engineering studies whereby a one-dimensional bipolar donor–acceptor conjugated system had served, since the early 1970s, as a quasi-exclusive template, had failed to take into account the tensorial dimension attached to the β quadratic hyperpolarizability tensor. We review here the outgoing second generation of molecular design studies based on three-dimensional multipolar charge transfer which reflects on enhanced values for all β ijk coefficients, then opening-up the possibility of polarization-independent nonlinear interactions. This can be ensured by more isotropic crystalline lattices or statistical polymer-based orientational distribution out of reach for the cruder one-dimensional systems. A particular challenge which has in fact triggered this domain in the early 1990s to this day has been set by octupolar systems whereby the symmetry-imposed cancellation of the dipole moment precludes the utilization of an electric field coupling scheme to orient molecules into a noncentrosymmetric order. We will review this new domain, encompassing both physical and chemical considerations, all the way from new molecular engineering techniques, with associated quantum modeling, to advanced characterization methods and macroscopic ordering schemes jointly aiming at promoting and exploiting the so far largely ignored tensorial dimension of nonlinear light–matter coupling schemes in molecules. To cite this article: I. Ledoux, J. Zyss, C. R. Physique 3 (2002) 407–427.