Hyperpolarizability Tensor Research Articles

All-optical field-free three-dimensional orientation of asymmetric-top molecules

Orientation and alignment of molecules by ultrashort laser pulses is crucial for a variety of applications and has long been of interest in physics and chemistry, with the special emphasis on stereodynamics in chemical reactions and molecular orbitals imaging. As compared to the laser-induced molecular alignment, which has been extensively studied and demonstrated, achieving molecular orientation is a much more challenging task, especially in the case of asymmetric-top molecules. Here, we report the experimental demonstration of all-optical field-free three-dimensional orientation of asymmetric-top molecules by means of phase-locked cross-polarized two-color laser pulse. This approach is based on nonlinear optical mixing process caused by the off-diagonal elements of the molecular hyperpolarizability tensor. It is demonstrated on SO2 molecules and is applicable to a variety of complex nonlinear molecules.

Quadratic and Cubic Optical Nonlinearities of Y-Shaped and Distorted-H-Shaped Arylalkynylruthenium Complexes.

Straightforward syntheses of bis[bis{1,2-bis(diphenylphosphino)ethane}ruthenium]-functionalized 1,3,5-triethynylbenzene-cored complexes via a methodology employing "steric control" permit facile formation of Y-shaped Sonogashira coupling products and distorted-H-shaped homo-coupled quadrupolar products. Cyclic voltammetric data from these products reveal two reversible metal alkynyl-localized oxidation processes for all complexes. The wavelengths of the linear optical absorption maxima are dominated by the nature of the peripheral alkynyl ligand rather than the substituent at the unique arm of the "Y" or at the quadrupolar complex "core". The quadratic optical nonlinearities of the Y-shaped complexes were assessed by the hyper-Rayleigh scattering technique at 800 nm and employing 100 fs light pulses; introduction of donor NEt2 and/or acceptor NO2 to the wedge periphery resulted in non-zero nonlinearities, with the largest βHRS,800 values being observed for the complexes containing the 4-nitrophenylalkynyl ligands. Depolarization ratios are consistent with substantial off-diagonal first hyperpolarizability tensor components and 2D nonlinear character. Computational studies employing time-dependent density functional theory have been employed to assign the key low-energy transitions in the linear optical spectra and to compute the quadratic nonlinear optical tensorial components. Cubic optical nonlinearities of the quadrupolar complexes were assessed by the Z-scan technique over the range 500-1600 nm and employing 130 fs light pulses; two-photon absorption cross-sections for these distorted-H-shaped complexes are moderate to large in value (up to 5500 GM at 880 nm), while one example displays significant three-photon absorption (1300×10-80 cm6 s2 at 1200 nm).

Molecular dynamics simulations for optical Kerr effect of TIP4P/2005 water in liquid and supercooled states

The optical Kerr effect (OKE) spectroscopy measured with heterodyne detection (HD) is a useful tool to provide information regarding intermolecular vibrations and structural relaxations in liquid water. Recently, the measurements of the OKE spectroscopy have been extended to the supercooled regime of water. Though the measured results can be well described by using a phenomenological model, the time-resolved OKE spectroscopy of liquid and supercooled water still need a comprehensive understanding. In this paper, we investigated the OKE nuclear response functions of this peculiar liquid and their reduced spectral densities by performing molecular dynamics simulations with the TIP4P/2005 water model. The collective polarizability of water was computed via a dipolar induction scheme, which involves the intrinsic polarizability and the first-order hyperpolarizability tensor of water molecule. Our simulation results were qualitatively consistent with the HD-OKE experimental observations for displaying that the polarizability anisotropy relaxation of supercooled water in the high-density liquid phase was fragile-like by following a stretching exponential decay with an exponent βs insensitive to temperature and the temperature dependence of the relaxation time exhibited a power-law divergence at a singular temperature Ts with a critical exponent γs. Indicated by our quantitative results, Ts was predominately determined by the structural arrest, but βs and γs were not only related to the structural relaxation but also influenced by the collective polarizability of the liquid. For all investigations, the effects due to the first-order hyperpolarizability tensor were examined.

NLO properties of a triphenlyguanidine salt: The importance of pseudo-symmetry

Using a combined experimental and computational approach, we were able to trace the quasi-vanishing of the second-order nonlinear optical (NLO) properties of a newly synthesized organic salt, bis(triphenylguanidinium) l-malate, to the pseudo-centrosymmetry of its structure. The employed experimental techniques were single crystal X-ray diffraction to determine the structure, “open-aperture” Z-scan technique to measure the nonlinear absorption, Kurtz and Perry powder method and Maker fringes techniques for second- and third-harmonic generation. The molecular hyperpolarizability tensors (β and γ) were calculated within Density Functional Theory (DFT) and the macroscopic second- and third-order susceptibility tensors were estimated by combining the supermolecule approach with the oriented gas model. The calculations performed with global hybrid GGA and range-separated functionals reproduced the correct order of magnitude of the observed second- and third-order susceptibilities.

What is measured by hyper-Rayleigh scattering from a liquid?

Polarization and angle dependence of hyper-Rayleigh scattering (HRS) measured for liquid acetonitrile and dimethyl sulfoxide (DMSO) is analyzed in terms of contributions from randomly oriented molecules and additional contributions produced during intermolecular collisions and induced by the electric field of dissolved ions. All three contributions show the effect of long-range correlation, and the correlation functions are determined using the HRS observations combined with the results of molecular dynamics simulations. HRS from acetonitrile is polarized transverse to the scattering vector. This is due to long-range molecular orientation correlation produced by the dipole-dipole interaction, and correlation at distances r > 100 nm must be included to account for the HRS observations. Analysis of the HRS measurements for acetonitrile determines the length scale a = 0.185 nm for the long-range longitudinal and transverse orientation correlation functions BL=-2BT=a3/r3. Transverse polarized collision-induced HRS is also observed for acetonitrile, indicating long-range correlation of intermolecular modes. Strong longitudinal HRS is induced by the radial electric field of dissolved ions in acetonitrile. For DMSO, the angle between the molecular dipole and the vector part of the first hyperpolarizability tensor is about 100°. As a result, HRS from the randomly oriented molecules in DMSO is nearly unaffected by dipole correlation, and ion-induced HRS is weak. The strong longitudinal polarized HRS observed for DMSO is due to the collision-induced contribution, indicating long-range correlation of intermolecular modes. The HRS observations require correlation that has r-3 long-range asymptotic form, for molecular orientation and for intermolecular vibration and libration, for both acetonitrile and DMSO.

Nonlinear Optical Properties of the Hula Hoop [n]‐Cycloparaphenylenes and Their Halo Derivatives at Nd:YAG Laser Frequency

AbstractThe present study aims to establish the role of halogen substituents in tuning the nonlinear optical (NLO) properties of cycloparaphenylenes. We employed time dependent density functional theory as our prime investigating tool to estimate the frequency dependent components of first order hyperpolarizability tensors of these systems at neodymium‐doped yttrium aluminium garnet (Nd:YAG) laser frequency. Our results indicate that pristine cycloparaphenylenes have high nonlinear optical properties which corroborates well with reported experimental findings and one can increase this nonlinearity by adding halogen to these species and tuning them as well. This tuning is of great significance as this will allow us to design and synthesize new compounds which have the strong potential to act as NLO materials. Our results also show functional dependence for the NLO tensor components while calculating the NLO properties for molecular systems. The basis set and the solvent effects, however, is not appreciable for the cycloparaphenylenes.

Exact Fundamental Limits of the First and Second Hyperpolarizabilities

Nonlinear optical interactions of light with materials originate in the microscopic response of the molecular constituents to excitation by an optical field, and are expressed by the first (β) and second (γ) hyperpolarizabilities. Upper bounds to these quantities were derived seventeen years ago using approximate, truncated state models that violated completeness and unitarity, and far exceed those achieved by potential optimization of analytical systems. This Letter determines the fundamental limits of the first and second hyperpolarizability tensors using MonteCarlo sampling of energy spectra and transition moments constrained by the diagonal Thomas-Reiche-Kuhn (TRK) sum rules and filtered by the off-diagonal TRK sum rules. The upper bounds of β and γ are determined from these quantities by applying error-refined extrapolation to perfect compliance with the sum rules. The method yields the largest diagonal component of the hyperpolarizabilities for an arbitrary number of interacting electrons in any number of dimensions. The new method provides design insight to the synthetic chemist and nanophysicist for approaching the limits. This analysis also reveals that the special cases which lead to divergent nonlinearities in the many-state catastrophe are not physically realizable.

Solvent fluctuations and nuclear quantum effects modulate the molecular hyperpolarizability of water

Second-Harmonic Scatteringh (SHS) experiments provide a unique approach to probe non-centrosymmetric environments in aqueous media, from bulk solutions to interfaces, living cells and tissue. A central assumption made in analyzing SHS experiments is that the each molecule scatters light according to a constant molecular hyperpolarizability tensor $\boldsymbol{\beta}^{(2)}$. Here, we investigate the dependence of the molecular hyperpolarizability of water on its environment and internal geometric distortions, in order to test the hypothesis of constant $\boldsymbol{\beta}^{(2)}$. We use quantum chemistry calculations of the hyperpolarizability of a molecule embedded in point-charge environments obtained from simulations of bulk water. We demonstrate that both the heterogeneity of the solvent configurations and the quantum mechanical fluctuations of the molecular geometry introduce large variations in the non-linear optical response of water. This finding has the potential to change the way SHS experiments are interpreted: in particular, isotopic differences between H$_2$O and D$_2$O could explain recent second-harmonic scattering observations. Finally, we show that a simple machine-learning framework can predict accurately the fluctuations of the molecular hyperpolarizability. This model accounts for the microscopic inhomogeneity of the solvent and represents a first step towards quantitative modelling of SHS experiments.

Second-order nonlinear optical properties of composite material of an azo-chromophore with a tricyanodiphenyl acceptor in a poly(styrene-co-methyl methacrylate) matrix

The composite material of new synthesized 4-((4-(N,N-n-dibutylamino) phenyl)diazenyl)-biphenyl-2,3,4-tricarbonitrile (GAS dye) in commercial poly(styrene-co-methyl methacrylate) (PSMMA) was prepared, poled and its nonlinear optical properties compared with DR1 dye were studied. High thermal stability of the composite material was revealed, and the maximal concentration of the chromophore was found to reach ∼20 wt%. The dipole moment, polarizability tensor, and first hyperpolarizability tensor of the investigated dyes were calculated by within the framework of the coupled perturbed density functional theory. A nanosecond second-harmonic generation Maker fringes technique was used which is capable of providing the magnitude of the second-order nonlinearity of optical materials at a wavelength of 1064 nm. For the tested GAS–PSMMA composite material, maximal coefficient d33 was found to be 50 pm/V. The nonlinear optical response, which was achieved here, shows possible usefulness of the GAS dye as a component for molecular design of nonlinear-optical materials with advanced characteristics.

Quantum Mechanical Calculations of Vibrational Sum-Frequency-Generation (SFG) Spectra of Cellulose: Dependence of the CH and OH Peak Intensity on the Polarity of Cellulose Chains within the SFG Coherence Domain.

Vibrational sum-frequency-generation (SFG) spectroscopy is capable of selectively detecting crystalline biopolymers interspersed in amorphous polymer matrices. However, the spectral interpretation is difficult due to the lack of knowledge on how spatial arrangements of crystalline segments influence SFG spectra features. Here we report time-dependent density functional theory (TD-DFT) calculations of cellulose crystallites in intimate contact with two different polarities: parallel versus antiparallel. TD-DFT calculations reveal that the CH/OH intensity ratio is very sensitive to the polarity of the crystallite packing. Theoretical calculations of hyperpolarizability tensors (βabc) clearly show the dependence of SFG intensities on the polarity of crystallite packing within the SFG coherence length, which provides the basis for interpretation of the empirically observed SFG features of native cellulose in biological systems.

Spectrally- and polarization-resolved hyper-Rayleigh scattering measurements with polarization-insensitive detection

Determination of the molecular first hyperpolarizability by hyper-Rayleigh scattering (HRS) is usually significantly complicated by a presence of the multiphoton excited fluorescence which has to be separated from HRS to obtain a meaningful values of the hyperpolarizability. We show, by performing a spectrally-resolved measurement, that the intensity and spectral shape of the fluorescence can depend strongly on the fundamental laser wavelength. Consequently, a properly selected excitation wavelength can significantly simplify the process of separation of HRS from the detected signal. We tested the developed experimental setup with a polarization-insensitive detection by measuring HRS generated in water and in aqueous solutions of 2-aminopyrimidine (AMP) and its monocation (HAMP). The effective hyperpolarizability of AMP and HAMP was measured experimentally and compared with that obtained by quantum chemical calculations. The polarization-resolved HRS measurement was performed for AMP and the experimentally obtained depolarization ratio agrees well with that predicted theoretically, which confirms that routine density functional theory computations of static hyperpolarizability tensor components can be considered as a sufficient approach suitable for non-interacting molecules dissolved in water.

General solution to nonlinear optical quantum graphs using Dalgarno–Lewis summation techniques

We develop an algorithm to apply the Dalgarno-Lewis (DL) perturbation theory to quantum graphs with multiple, connected edges. We use it to calculate the nonlinear optical hyperpolarizability tensors for graphs and show that it replicates the sum over states computations, but executes ten to fifty times faster. DL requires only knowledge of the ground state of the graph, eliminating the requirement to determine all possible degeneracies of a complex network. The algorithm is general and may be applied to any quantum graph.

What interactions can distort the orientational distribution of interfacial water molecules as probed by second harmonic and sum frequency generation?

Aqueous interfaces are omnipresent in nature. Nonlinear optical methods such as second harmonic and sum frequency generation (SHG/SFG) are valuable techniques to access molecular level information from these interfaces. In the interpretation of SHG and SFG data for both scattering and reflection mode experiments, the relation between the second-order hyperpolarizability tensor β(2), a molecular property, and the surface second-order susceptibility χ(2), a surface averaged property, plays a central role. To correctly describe the molecular details of the interface, it needs to be determined how molecules are oriented, and what the influence is of interfacial electrostatic fields and H-bonding on the orientational distribution. Here, we revisit the relations between β(2) and χ(2) and show, by means of a Boltzmann average, that significant energy differences are needed to generate measurable changes in the molecular orientational distribution at the interface. In practice, H-bonding and surface pressure such as applied in a Langmuir trough can be strong enough to alter the shape of the orientational distribution function of water. In contrast, electrostatic fields, such as those present in the Stern layer, will not have a significant impact on the shape of the orientational distribution function of water molecules.

L-Histidinium thiocyanurate: Experimental and theoretical studies of a new nonlinear optical material

A new organic compound, l-histidinium thiocyanurate thiocyanuric acid dihydrate, has been synthesized and characterized by single crystal X-ray diffraction, infrared spectroscopy and nonlinear optical measurements. The efficiency of the second-harmonic generation was evaluated with the Kurtz and Perry powder method at a fundamental wavelength of 1064nm. By using the experimental structure, the molecular first hyperpolarizability tensor was determined with Hartree-Fock and density functional theory methods. The second-order susceptibility tensor of the crystal was evaluated using the oriented gas model with the Lorenz-Lorentz and the Wortmann-Bishop local-field corrections.

Structural and nonlinear optical studies of a salt with an octupolar chromophore: Guanidinium cyclopropanecarboxylate

A new organic compound, guanidinium cyclopropanecarboxylate, has been synthesized and characterized by single crystal X-ray diffraction, infrared spectroscopy and nonlinear optical measurements. The infrared spectrum was calculated with density functional theory (DFT). The second-order NLO response was evaluated with the Kurtz and Perry powder method. From the molecular structure, the molecular hyperpolarizability tensor was determined with Hartree-Fock and DFT methods. The second-order susceptibility tensor of the crystal was evaluated by the summation of the effective hyperpolarizability tensors calculated for the asymmetric unit surrounded by ESP-derived charges.

Calculation of the dynamic first electronic hyperpolarizability β(-ω(σ); ω(1), ω(2)) of periodic systems. Theory, validation, and application to multi-layer MoS2.

We describe our implementation of a fully analytical scheme, based on the 2n + 1 rule, for computing the coupled perturbed Hartree Fock and Kohn-Sham dynamic first hyperpolarizability tensor β(-ωσ; ω1, ω2) of periodic 1D (polymer), 2D (slab), and 3D (crystal) systems in the CRYSTAL code [R. Dovesi et al., Int. J. Quantum Chem. 114, 1287 (2014)], which utilizes local Gaussian type basis sets. The dc-Pockels (dc-P) and second harmonic generation (SHG) tensors are included as special cases. It is verified that (i) symmetry requirements are satisfied; (ii) using LiF as an example, the infinite periodic polymer result agrees with extrapolated finite oligomer calculations and, likewise, for the build-up to a 2D slab and a 3D crystal; (iii) the values converge to the static case for low frequencies; and (iv) the Bishop-deKee dispersion formulas relating dc-P, SHG, and general processes are reproduced through quartic terms. Preliminary SHG calculations on multi-layer MoS2 satisfactorily reproduce experimental data.

ChemInform Abstract: Styryl‐Based NLO Chromophores: Synthesis, Spectroscopic Properties, and Theoretical Calculations.

AbstractA series of styryl‐based push‐pull chromophores are synthesized.

Styryl-based NLO chromophores: synthesis, spectroscopic properties, and theoretical calculations

A novel series of styryl-based chromophores is synthesized, the constituents of which are characterized by UV–Vis, NMR, mass spectrometry, and thermal analysis. The chromophores show good solubility in MeOH, THF, and CH2Cl2. They also show good thermal stability for practical applications. Density functional theory calculations are employed in order to ascertain the structural, molecular, and electronic properties of the dyes. Moreover, the second order nonlinear optical (NLO) responses of the dyes are measured by the electric field induced second harmonic (EFISH) generation method. Relatively high scalar products of the vector component of the first hyperpolarizability tensor and the dipole moment vector (μβ) are obtained for some of the compounds.

Aromaticity, response, and nonlinear optical properties of sumanene modified with boron and nitrogen atoms.

We investigated the effects of substitution on the sumanene benzylic CH2 groups with BH and NH groups using density functional theory computations. Our study shows that various properties of sumanene could be finely tuned for the application in the areas closely related to the materials science. Structural properties are significantly altered with such modifications and other properties as well. Charge distributions were evaluated through natural population analysis (NPA), while stability of investigated structures was investigated using quantum molecular descriptors. Using molecular orbital analysis further insight into the effects of substitution was obtained. Potential of sumanene as a candidate for application in the field of organic electronics is assessed through calculations of exciton binding energy. Non-linear optical properties of investigated structures were investigated using the first hyperpolarizability tensor. Special attention was paid to the aromaticity of sumanene. This property was evaluated employing NICS parameter while for detailed study of obtained results we used NBO and NBOdel analysis.

Analytic calculations of hyper-Raman spectra from density functional theory hyperpolarizability gradients

We present the first analytic calculations of the geometrical gradients of the first hyperpolarizability tensors at the density-functional theory (DFT) level. We use the analytically calculated hyperpolarizability gradients to explore the importance of electron correlation effects, as described by DFT, on hyper-Raman spectra. In particular, we calculate the hyper-Raman spectra of the all-trans and 11-cis isomers of retinal at the Hartree-Fock (HF) and density-functional levels of theory, also allowing us to explore the sensitivity of the hyper-Raman spectra on the geometrical characteristics of these structurally related molecules. We show that the HF results, using B3LYP-calculated vibrational frequencies and force fields, reproduce the experimental data for all-trans-retinal well, and that electron correlation effects are of minor importance for the hyper-Raman intensities.