Hyperpolarizability Tensor Components Research Articles

DFT studies on structural stability, vibrational and linear and nonlinear optical properties of low-dimensional zinc sulfide: from the 3D bulk to the 2D monolayer and the 1D zigzag single-walled nanotubes

Through first-principles calculations, we investigate structural stability, vibrational and linear and nonlinear optical properties of the zinc sulfide (ZnS) in different periodic forms ranging from the 3D bulk to the 2D hexagonal monolayer and their corresponding 1D zigzag single-walled nanotubes. To first order, the electronic wave function on the ground state was constructed using linear combinations of Gaussian-type functions at the DFT/B3LYP level. Then, the Raman and IR spectrum is computed by adopting a Coupled-Perturbed-Hartree–Fock/Kohn–Sham (CPHF/KS) approach. Cohesive, relaxation, and rolling energies, elastic and piezoelectric constants, electronic and nuclear contributions to the polarizability tensor, and nonlinear first and second-order hyperpolarizability tensor components are reported. Our study shows that 3D and 2D forms are stable and show semiconducting behavior, good piezoelectric responses, and fascinating linear and nonlinear optical properties. For 1D single-walled nanotubes, dynamic stability is observed only for the smallest (6,0) nanotubes. For n > 6, imaginary mode frequencies in the simulated IR and Raman spectra indicate dynamic instability. A scanning mode procedure along the largest imaginary vibrational mode is applied in order to determine the stable structures of the largest (14,0), (18,0) and (22,0) ZnS nanotubes. After that, no more imaginary phonon frequencies are detected in their vibrational spectra. Their potential energy surface contains two minima between a saddle point corresponding to a slightly distorted nanotube structure. Our study proves that the zinc sulfide nanostructures possess diverse physical properties so useful for potential applications in nanoelectronics and for nanodevices.

Quantum chemical analysis on supramolecular assemblies of guanidinium tetrafluoroborate (GFB) crystal structure: Emission and NLO behavior

The present work explains the experimental and theoretical aspects of guanidinium tetrafluoroborate (GFB) single crystal. The solubility nature of the GFB single crystal was analyzed. The surface of the grown crystal was examined through chemical etching study. Emission properties were characterized using photoluminescence study. CIE colour chromaticity coordinates afford the dominant color emission of the title compound. The optical limiting property of the titular compound was ascertained using z-scan technique. The solid state parameters, such as Plasma energy, Penn gap energy, Fermi energy and electronic polarizabilty were calculated. The intermolecular interactions in the title molecule were studied using Hirshfeld surface analysis. A detailed quantum chemical calculation of the title crystal was performed. Mulliken atomic charge analysis revealed the charge distribution in the molecule. The molecular electrostatic potential (MEP) contour maps were used to study the interactions of guanidinium with fluoroborate ions in the crystal. The charge transfer mechanism was analysed using computed HOMO-LUMO orbitals. The 3D-matrix of hyperpolarizability tensor components was computed to enumerate the NLO activity. The various thermodynamic properties of the GFB molecule were computed. The electronic exchange interaction in the title compound was determined by natural bond orbital (NBO) analysis.

Structural Characterization and Second-Order Nonlinear Optical Behavior of Metal Complexes of Ferrocene Derivative

In this manuscript, a ferrocene-linked vic-dioxime ligand (LH2) and its metal complexes [Ni(LH)2, Cu(LH)2, Co(LH)2(H2O)2, Cd(LH)(H2O)(Cl), and Zn(LH)(H2O)(Cl)] are synthesized, and their structures are studied by spectral methods. Redox behavior of the compounds is studied by cyclic voltammetry (CV). For approaching microscopic second-order nonlinear optical (NLO) behavior of the synthesized ligand and its diamagnetic Cd(II), Zn(II), Ni(II) complexes, the electric dipole moment μ, static dipole polarizability α, and first hyperpolarizability β values are computed using ab-initio quantum chemical procedure [finite field (FF)]. The accumulated data indicate that the compounds exhibit non-zero quadratic hyperpolarizability tensor components, implying microscopic NLO phenomena. The HOMOs, LUMOs and the HOMO—LUMO band gaps for first and second frontier orbitals of LH2 ligand and its Cd(II), Zn(II), Ni(II) complexes are evaluated by means of the Hartree-Fock (HF) method.

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).

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.

New acentric materials constructed from aminopyridines and 4-nitrophenol

Co-crystallization of 4-nitrophenol (I) with five aminopyridines (4-aminopyridine 1, 3,4-diaminopyridine 2, 2,3-diaminopyridine 3, 3-aminopyridine 4, 2-amino-6-methylpyridine 5) and 2,4-diaminopyrimidine 6 resulted in six adducts with the ratio of components 2 : 1 in five and 1 : 1 in one final compounds. Single crystals were grown by slow evaporation technique using ethanol as a solvent. Five adducts with 1–5 crystallize in acentric P21 and Pna21 space groups, and one, 2(I)·6 – in centrosymmetric P21/c space group. Compounds 2(I)·1, 2(I)·2, 2(I)·3 are isomorphous, and demonstrate similar H-bonding patterns despite the differences in aminopyridine molecules. Compound 2(I)·5 is isomorphous to two previously reported compounds. Adducts 2(I)·1, 2(I)·2, 2(I)·3, 2(I)·5, 2(I)·6 represent organic salts composed of pyridinium/pyrimidinium cation, 4-nitrophenolate anion, and 4-nitrophenol neutral molecule. The H-bonded 4-nitrophenol–4-nitrophenolate anionic dimers were found in all compounds with 2 : 1 molar ratio. In adduct I·4 both molecules are in neutral form. The IR spectral data support crystallographic conclusions on salts formation. Plane wave pseudopotential density functional theory calculations were used to predict hyperpolarizability tensor components. Our calculations suggest 2(I)·3 as the best candidate for nonlinear optical materials (14 times more active than urea).

The ‘partial resonance’ of the ring in the NLO crystal melaminium formate: Study using vibrational spectra, DFT, HOMO–LUMO and MESP mapping

The molecular geometry and vibrational spectral investigations of melaminium formate, a potential material known for toxicity and NLO activity, has been performed. The FT IR and FT Raman spectral investigations of melaminium formate is performed aided by the computed spectra of melaminium formate, triazine, melamine, melaminium and formate ion, along with bond orders and PED, computed using the density functional method (B3LYP) with 6-31G(d) basis set and XRD data, to reveal intermolecular interactions of amino groups with neighbor formula units in the crystal, intramolecular H⋯H repulsion of amino group hydrogen with protonating hydrogen, consequent loss of resonance in the melaminium ring, restriction of resonance to N3C1N1 moiety leading to special type resonance of the ring and the resonance structure of CO2 group of formate ion. The 3D matrix of hyperpolarizability tensor components has been computed to quantify NLO activity of melamine, melaminium and melaminium formate and the hyperpolarizability enhancement is analyzed using computed plots of HOMO and LUMO orbitals. A new mechanism of proton transfer responsible for NLO activity has been suggested, based on anomalous IR spectral bands in the high wavenumber region. The computed MEP contour maps have been used to analyze the interaction of melaminium and formate ions in the crystal.

Gas phase hyper-Rayleigh scattering measurements

Measurements of hyper-Rayleigh scattering intensities and polarization ratios are presented for nine small molecules in the gas phase [CH(4), CF(4), CCl(4), N(2)O, NH(3), D(2)O, SO(2), CF(2)Cl(2), and (CH(3))(2)CO]. In four cases [CH(4), CF(4), CCl(4), and N(2)O] all molecular hyperpolarizability tensor components can be determined from the measurements. The results of this experiment are compared with the results of previous ab initio calculations, finding discrepancies up to 60%. Including vibrational contributions decreases the discrepancies for CH(4) and CF(4) and increases them for CCl(4), D(2)O, and NH(3).

The Roles of Molecular Structure and Effective Optical Symmetry in Evolving Dipolar Chromophoric Building Blocks to Potent Octopolar Nonlinear Optical Chromophores

A series of mono-, bis-, tris-, and tetrakis(porphinato)zinc(II) (PZn)-elaborated ruthenium(II) bis(terpyridine) (Ru) complexes have been synthesized in which an ethyne unit connects the macrocycle meso carbon atom to terpyridyl (tpy) 4-, 4'-, and 4''-positions. These supermolecular chromophores, based on the ruthenium(II) [5-(4'-ethynyl-(2,2';6',2''-terpyridinyl))-10,20-bis(2',6'-bis(3,3-dimethyl-1-butyloxy)phenyl)porphinato]zinc(II)-(2,2';6',2''-terpyridine)(2+) bis-hexafluorophosphate (RuPZn) archetype, evince strong mixing of the PZn-based oscillator strength with ruthenium terpyridyl charge resonance bands. Potentiometric and linear absorption spectroscopic data indicate that for structures in which multiple PZn moieties are linked via ethynes to a [Ru(tpy)(2)](2+) core, little electronic coupling is manifest between PZn units, regardless of whether they are located on the same or opposite tpy ligand. Congruent with these experiments, pump-probe transient absorption studies suggest that the individual RuPZn fragments of these structures exhibit, at best, only modest excited-state electronic interactions that derive from factors other than the dipole-dipole interactions of these strong oscillators; this approximate independent character of the component RuPZn oscillators enables fabrication of nonlinear optical (NLO) multipoles with extraordinary hyperpolarizabilities. Dynamic hyperpolarizability (β(λ)) values and depolarization ratios (ρ) were determined from hyper-Rayleigh light scattering (HRS) measurements carried out at an incident irradiation wavelength (λ(inc)) of 1300 nm. The depolarization ratio data provide an experimental measure of chromophore optical symmetry; appropriate coupling of multiple charge-transfer oscillators produces structures having enormous averaged hyperpolarizabilities (β(HRS) values), while evolving the effective chromophore symmetry from purely dipolar (e.g., Ru(tpy)[4-(Zn-porphyrin)ethynyl-tpy](PF(6))(2), β(HRS) = 1280 × 10(-30) esu, ρ = 3.8; Ru(tpy)[4'-(Zn-porphyrin)ethynyl-tpy](PF(6))(2), β(HRS) = 2100 × 10(-30) esu, ρ = 3.8) to octopolar (e.g., Ru[4,4''-bis(Zn-porphyrin)ethynyl-tpy](2)(PF(6))(2), β(HRS) = 1040 × 10(-30) esu, ρ = 1.46) via structural motifs that possess intermediate values of the depolarization ratio. The chromophore design roadmap provided herein gives rise to octopolar supermolecules that feature by far the largest off-diagonal octopolar first hyperpolarizability tensor components ever reported, with the effectively octopolar Ru[4,4''-bis(Zn-porphyrin)ethynyl-tpy](2)(PF(6))(2) possessing a β(HRS) value at 1300 nm more than a factor of 3 larger than that determined for any chromophore having octopolar symmetry examined to date. Because NLO octopoles possess omnidirectional NLO responses while circumventing the electrostatic interactions that drive bulk-phase centrosymmetry for NLO dipoles at high chromophore concentrations, the advent of octopolar NLO chromophores having vastly superior β(HRS) values at technologically important wavelengths will motivate new experimental approaches to achieve acentric order in both bulk-phase and thin film structures.

A Distributed Hyperpolarizability Model for Liquid Water

In a recent work a novel, molecular dynamics (MD) based, theory was presented that provides a direct means to calculate the third order contributions to sum frequency vibrational spectroscopy (SFVS) at charged interfaces.[1] This contribution is described by a time correlation function (TCF) of the system's total hyperpolarizability (β) and dipole. A system's hyperpolarizability[2, 3, 4, 5] is difficult to calculate on the fly – no appropriate non-electronic structure (ES) techniques exist. In this work, such a model is developed for liquid water based on a formalism proposed previously.[1] The model is parametrized from and tested against, ab initio ES calculations. It was found that it is possible to reproduce the hyperpolarizability tensor of a gas phase water molecule and a water dimer accurately. Also, most relevant components of the hyperpolarizability derivative tensor of both the water and water dimer were also accurately fit, however, some elements were not able to be simultaneously reproduced. The model was also tested to assess whether or not it could reproduce the three non-zero condensed phase water hyperpolarizability tensor components. It was found that the model could capture two of the three relevant components.

Time-dependent density functional theory for nonlinear properties of open-shell systems

This paper presents response theory based on a spin-restricted Kohn-Sham formalism for computation of time-dependent and time-independent nonlinear properties of molecules with a high spin ground state. The developed approach is capable to handle arbitrary perturbations and constitutes an efficient procedure for evaluation of electric, magnetic, and mixed properties. Apart from presenting the derivation of the proposed approach, we show results from illustrating calculations of static and dynamic hyperpolarizabilities of small Si(3n+1)H(6n+3) (n=0,1,2) clusters which mimic Si(111) surfaces with dangling bond defects. The results indicate that the first hyperpolarizability tensor components of Si(3n+1)H(6n+3) have an ordering compatible with the measurements of second harmonic generation in SiO2/Si(111) interfaces and, therefore, support the hypothesis that silicon surface defects with dangling bonds are responsible for this phenomenon. The results exhibit a strong dependence on the quality of basis set and exchange-correlation functional, showing that an appropriate set of diffuse functions is required for reliable predictions of the first hyperpolarizability of open-shell compounds.

On the calculated first hyperpolarizability of substituted tri-cyclohexadien-2-yl-amines: Novel targets for experimental research

A new class of molecules, consisting of substituted cyclohexadien-2-yl-amines, is proposed as candidates for new materials with non-linear optical properties. The first hyperpolarizability tensor components for these molecules are calculated at the CPHF/6-31G**++, CPDFT/B3LYP/6-31G**++ and CPDFT/X3LYP/6-31G**++ levels. The results are analyzed in terms of the partition of the tensor into its dipolar and octupolar components. The molecules present calculated β components with values comparable to those of p-nitro-aniline, but with structural features that should result in materials with more than one axis of optical activity, and without the common pitfall of classic push–pull molecules, namely, the tendency to form centro-symmetric crystals. Calculated EFISH values, for future comparison with experimental data, are also presented.

Evolution of the (hyper)polarizability with the size and periodicity of the system. A model investigation from the LiF molecule to the LiF 3D crystal

A finite field (FF) perturbation method, implemented in the CRYSTAL program, is used to investigate the evolution of the response to an applied electric field of systems of increasing size and dimensionality. LiF molecules, chains, slabs and bulk have been considered as model systems. (LiF)$_M$ molecules of increasing length are compared with the periodic infinite linear chain data; systems containing an increasing number of parallel linear chains are compared with the single layer slab, and slabs of increasing thickness are compared with bulk results. The same hamiltonian (Hartree-Fock), Li-F distance and basis set have been used for all systems. Sharp variations are observed in the response properties along the series (from the molecule to the 3D crystal), that are not the same for the parallel and perpendicular components of the tensors. In particular the (hyper)polarizability tensor components can vary by as much as a factor 8.

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.

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.

A novel approach to calculation of the second-order nonlinear optical susceptibilities of organic crystals based on energy-band theory

The second-order nonlinear optical susceptibilities in five organic crystals are studied based on the EHMO band-structure method. The crystals studied included m-aminophenol, urea, m-dinitrobenzene, POM [3-methyl-4-nitropyridine-1-oxide] and m-nitroaniline. The β cell tensor components for a unit cell of crystals are calculated by the sum-over-states method. Results are presented for the density of states and second-order nonlinear optical coefficients d (2)(0), which are compared with other existing calculations and experimental data. The overall agreement of our calculations with available data is quite satisfactory. Moreover, the effect of the interactions between neighboring unit cells on the hyperpolarizability tensor components of β cell is examined and analyzed. The results show that the procedure developed in this work provides a new insight into the second-order susceptibilities of organic molecular crystals, which is important in molecular engineering.

Second-order off-diagonal hyperpolarizability tensor components of substituted carbazoles by hyper-Rayleigh scattering depolarization measurements

The tensor components of the molecular first hyperpolarizability of 3,6-dinitro-9-ethylcarbazole and 3-nitro-9-ethylcarbazole have been analyzed with hyper-Rayleigh scattering and electric-field-induced second-harmonic generation. We show that measurements of the depolarization ratio give information directly about the importance of the off-diagonal molecular tensor components.

Studies of depolarized hyper-Rayleigh scattering of an organic molecule

We study the depolarized hyper-Rayleigh scattering of p-nitroaniline (PNA) using an improved technique. The result indicates that the hyperpolarizability tensor of PNA has essentially the characteristics of a rod-like structure, with a single nonvanishing diagonal component β 333, where the 3-axis corresponds to the polar direction. This is in contrast with previous theoretical calculations, which predicted non-negligible values for some of the off-diagonal components. A plausible explanation of the experimental result is suggested based on a model of the local field correction factors. The result shows that depolarized hyper-Rayleigh scattering may not be very useful in determining the relationship between hyperpolarizability tensor components as previously suggested.

Symmetry Properties of Second Order Hyperpolarizabilities

Abstract Time-reversal symmetry property of a second order nonlinear optical hyperpolarizability is examined in terms of the Manley-Rowe power relation to find relationship to the overall permutation symmetry. An extended symmetry relation is discovered reducing the independent number of the hyperpolarizability tensor components describing the second order nonlinear optical processes. Experimental implications are discussed.