Dynamic Hyperpolarizabilities Research Articles

Experimental and theoretical investigation of the first-order hyperpolarizability of a class of triarylamine derivatives.

This paper reports on the static and dynamic first-order hyperpolarizabilities of a class of push-pull octupolar triarylamine derivatives dissolved in toluene. We have combined hyper-Rayleigh scattering experiment and the coupled perturbed Hartree-Fock method implemented at the Density Functional Theory (DFT) level of theory to determine the static and dynamic (at 1064 nm) first-order hyperpolarizability (βHRS) of nine triarylamine derivatives with distinct electron-withdrawing groups. In four of these derivatives, an azoaromatic unit is inserted and a pronounceable increase of the first-order hyperpolarizability is reported. Based on the theoretical results, the dipolar/octupolar character of the derivatives is determined. By using a polarizable continuum model in combination with the DFT calculations, it was found that although solvated in an aprotic and low dielectric constant solvent, due to solvent-induced polarization and the frequency dispersion effect, the environment substantially affects the first-order hyperpolarizability of all derivatives investigated. This statement is supported due to the solvent effects to be essential for the better agreement between theoretical results and experimental data concerning the dynamic first-order hyperpolarizability of the derivatives. The first-order hyperpolarizability of the derivatives was also modeled using the two- and three-level models, where the relationship between static and dynamic first hyperpolarizabilities is given by a frequency dispersion model. Using this approach, it was verified that the dynamic first hyperpolarizability of the derivatives is satisfactorily reproduced by the two-level model and that, in the case of the derivatives with an azoaromatic unit, the use of a damped few-level model is essential for, considering also the molecular size of such derivatives, a good quantitative agreement between theoretical results and experimental data to be observed.

Generalized gradient approximation exchange energy functional with correct asymptotic behavior of the corresponding potential.

A new non-empirical exchange energy functional of the generalized gradient approximation (GGA) type, which gives an exchange potential with the correct asymptotic behavior, is developed and explored. In combination with the Perdew-Burke-Ernzerhof (PBE) correlation energy functional, the new CAP-PBE (CAP stands for correct asymptotic potential) exchange-correlation functional gives heats of formation, ionization potentials, electron affinities, proton affinities, binding energies of weakly interacting systems, barrier heights for hydrogen and non-hydrogen transfer reactions, bond distances, and harmonic frequencies on standard test sets that are fully competitive with those obtained from other GGA-type functionals that do not have the correct asymptotic exchange potential behavior. Distinct from them, the new functional provides important improvements in quantities dependent upon response functions, e.g., static and dynamic polarizabilities and hyperpolarizabilities. CAP combined with the Lee-Yang-Parr correlation functional gives roughly equivalent results. Consideration of the computed dynamical polarizabilities in the context of the broad spectrum of other properties considered tips the balance to the non-empirical CAP-PBE combination. Intriguingly, these improvements arise primarily from improvements in the highest occupied and lowest unoccupied molecular orbitals, and not from shifts in the associated eigenvalues. Those eigenvalues do not change dramatically with respect to eigenvalues from other GGA-type functionals that do not provide the correct asymptotic behavior of the potential. Unexpected behavior of the potential at intermediate distances from the nucleus explains this unexpected result and indicates a clear route for improvement.

Resonant-convergent PCM response theory for the calculation of second harmonic generation in makaluvamines A-V: pyrroloiminoquinone marine natural products from poriferans of genus Zyzzya.

The first-order hyperpolarizability, β, has been calculated for a group of marine natural products, the makaluvamines. These compounds possess a common cationic pyrroloiminoquinone structure that is substituted to varying degrees. Calculations at the MP2 level indicate that makaluvamines possessing phenolic side chains conjugated with the pyrroloiminoquinone moiety display large β values, while breaking this conjugation leads to a dramatic decrease in the calculated hyperpolarizability. This is consistent with a charge-transfer donor-π-acceptor (D-π-A) structure type, characteristic of nonlinear optical chromophores. Dynamic hyperpolarizabilities calculated using resonance-convergent time-dependent density functional theory coupled to polarizable continuum model (PCM) solvation suggest that significant resonance enhancement effects can be expected for incident radiation with wavelengths around 800 nm. The results of the current work suggest that the pyrroloiminoquinone moiety represents a potentially useful new chromophore subunit, in particular for the development of molecular probes for biological imaging. The introduction of solvent-solute interactions in the theory is conventionally made in a density matrix formalism, and the present work will provide detailed account of the approximations that need to be introduced in wave function theory and our program implementation. The program implementation as such is achieved by a mere combination of existing modules from previous developments, and it is here only briefly reviewed.

High-precision nonadiabatic calculations of dynamic polarizabilities and hyperpolarizabilities for low-lying vibrational-rotational states of hydrogen molecular ions

The static and dynamic electric multipolar polarizabilities and second hyperpolarizabilities of the ${{\mathrm{H}}_{2}}^{+}$, ${{\mathrm{D}}_{2}}^{+}$, and ${\mathrm{HD}}^{+}$ molecular ions in the ground and first excited states are calculated nonrelativistically using explicitly correlated Hylleraas basis sets. The calculations are fully nonadiabatic; the Born-Oppenheimer approximation is not used. Comparisons are made with published theoretical and experimental results, where available. In our approach, no derivatives of energy functions nor derivatives of response functions are needed. In particular, we make contact with earlier calculations in the Born-Oppenheimer calculation where polarizabilities were decomposed into electronic, vibrational, and rotational contributions and where hyperpolarizabilities were determined from derivatives of energy functions. We find that the static hyperpolarizability for the ground state of ${\mathrm{HD}}^{+}$ is seven orders of magnitude larger than the corresponding dipole polarizability. For the dipole polarizability of ${\mathrm{HD}}^{+}$ in the first excited state the high precision of the present method facilitates treatment of a near cancellation between two terms. For applications to laser spectroscopy of trapped ions we find tune-out and magic wavelengths for the ${\mathrm{HD}}^{+}$ ion in a laser field. In addition, we also calculate the first few leading terms for long-range interactions of a hydrogen molecular ion and a ground state H, He, or Li atom.

Evaluation of the molecular static and dynamic first hyperpolarizabilities

By considering two prototypical π‐conjugated compounds, several technical aspects associated with the evaluation of the first hyperpolarizabilities have been addressed in this article, that is, (i) the automatization of the Romberg's scheme to improve the numerical accuracy in the finite field method, (ii) the evaluation of the frequency dispersion at correlated levels using approximate schemes, and (iii) the deviations from Kleinman's symmetry conditions. It results from this study that accurate numerical derivatives can be obtained by resorting to the Romberg's method and by analyzing the Romberg's table in terms of two quantities, the field error and the iteration error. Indeed, the resulting first hyperpolarizability values are in close agreement with those obtained using an analytical differentiation procedure. The reliability of the multiplicative and additive approximate schemes to describe the frequency dispersion at correlated levels from using HF (Hartree‐Fock) frequency dispersion has been confirmed to be limited to large wavelengths or far‐from‐resonance wavelength regions. Kleinman's symmetry conditions have been assessed, showing that for off‐diagonal components of these two π‐conjugated compounds, the deviations could be substantial. Nevertheless, good accuracy can be achieved for experimentally related quantities like βHRS because the diagonal tensor components are dominant. © 2014 Wiley Periodicals, Inc.

ABAB Homoleptic Bis(phthalocyaninato)lanthanide(III) Complexes: Original Octupolar Design Leading to Giant Quadratic Hyperpolarizability

The octupolar cube, a Td symmetry cube presenting alternating charges at its corners, is the generic point charge template of any octupolar molecule. So far, transposition into real molecular structures has yet to be achieved. We report here a first step toward the elaboration of fully cubic octupolar architectures. A series of octupolar bis(2,3,16,17-tetra(hexylthio)phthalocyaninato)lanthanide double-decker complexes [Pc2Ln], Ln = Nd (1), Eu (2), Dy (3), Y (4), and Lu (5), are described, whose original three-dimensional structures display the required alternation of ABAB type for one face of the cube and the delocalization between the two rings approximating to the electronic interaction along the edges of the cube. Synthesis, X-ray crystal structure, and study of the optical properties and of the first molecular hyperpolarizability β are reported. The size of the lanthanide (III) central ion modulates the ring-to-ring distance and the degree of coupling between the two phthalocyanine rings. As a consequence, the optical properties of these octupolar chromophores and in particular the strong near-infrared absorption due to the intervalence transition between the two rings also depend on the central lanthanide (III) ion. The first oxidized and reduced states of the complexes, while keeping a similar octupolar structure, display considerably changed optical properties compared to the neutral states. Second-order nonlinear properties were determined by nonpolarized harmonic light scattering in solution at 1907 nm. Exceptionally large dynamic molecular first hyperpolarizabilities √(<βHLS(2)>1907), among the highest ever reported, were found that showed a strong dependence on the number of 4f electrons.

Accurate calculations of dynamic first hyperpolarizability: Construction of physically justified slater‐type basis sets

An efficient procedure for construction of physically rationalized Slater‐type basis sets for calculations of dynamic hyperpolarizability is proposed. Their performance is evaluated for the DFT level calculations for model molecules, carried out with a series of functionals. Advantages of new basis sets over standard d‐aug‐cc‐pVTZ and recently developed LPOL‐(FL,FS) Gaussian‐type basis sets are discussed. © 2014 Wiley Periodicals, Inc.

Assessment of the global and range-separated hybrids for computing the dynamic second-order hyperpolarizability of solution-phase organic molecules

The dynamic second-order hyperpolarizability from the third-harmonic generation experiment, 〈γ〉(−3ω;ω;ω;ω), of 59 solution-phase organic molecules has been theoretically calculated and compared with available experimental data. The DFT/6-311+G(2d,p)//(CAM-)B3LYP/6-31G(2df,p) level of theory with the polarizable continuum model was employed to evaluate the static second-order hyperpolarizability. The theoretical static values were then corrected to dynamic estimates of 〈γ〉(−3ω;ω;ω;ω) by employing a two-level approximation (Chen et al. in J Chem Phys 101(7):5860–5864, 1994). Calculated results showed that for the property of interest, the range-separated hybrids provided more accurate and consistent estimate than the global hybrids and the CAM-B3LYP optimized geometry delivered more accurate estimate than the B3LYP optimized geometry.

Quantum chemistry study on the third-order nonlinear optical properties of spirobifluorene derivatives

We investigate the electronic properties and dynamic second hyperpolarizabilities of spirobifluorene derivatives by using quantum chemistry calculations. We find that studied spirobifluorene derivatives exhibit both large second hyperpolarizability and excellent transparency. In addition, the second hyperpolarizabilities 〈γ(−2ω;ω,ω,0)〉 and 〈γ(−ω;ω,0,0)〉 increase with raising the frequency of incident light, and the increasing extent of 〈γ(−2ω;ω,ω,0)〉 is larger than that of 〈γ(−ω;ω,0,0)〉. Resonance enhancement observed results in a significant dispersion of the 〈γ〉 values in visible region. The effects of the basis sets and substituent group on the polarizability and second hyperpolarizability are also discussed respectively.

An efficient method for calculating dynamical hyperpolarizabilities using real-time time-dependent density functional theory

In this paper we present a time-domain time-dependent density functional theory (TDDFT) approach to calculate frequency-dependent polarizability and hyperpolarizabilities. In this approach, the electronic degrees of freedom are propagated within the density matrix based TDDFT framework using the efficient modified midpoint and unitary transformation algorithm. We use monochromatic waves as external perturbations and apply the finite field method to extract various orders of the time-dependent dipole moment. By fitting each order of time-dependent dipole to sinusoidal waves with harmonic frequencies, one can obtain the corresponding (hyper)polarizability tensors. This approach avoids explicit Fourier transform and therefore does not require long simulation time. The method is illustrated with application to the optically active organic molecule para-nitroaniline, of which the frequency-dependent polarizability α(-ω; ω), second-harmonic generation β(-2ω; ω, ω), optical rectification β(0; -ω, ω), third-harmonic generation γ(-3ω; ω, ω, ω), and degenerate four-wave mixing γ(-ω; ω, ω, -ω) are calculated.

NLO chromophores containing dihydrobenzothiazolylidene and dihydroquinolinylidene donors with an azo linker: Synthesis and optical properties

We report the synthesis of a series of nonlinear optical chromophores containing either a dihydrobenzothiazolylidene or dihydroquinolinylidene donor with an azo linker. The results demonstrate the versatility of coupling a diazonium salt to a donor–methylidene nucleus in order to access novel materials with good thermal stabilities and high nonlinear optical responses. From hyper-Raleigh scattering studies it was found that the use of the well-known TCF acceptor yields the best performing chromophores, one of which has a dynamic first hyperpolarizability of 1900 × 10 −30 esu at 800 nm. The results from this study suggest the use of pro-aromatic donors such as dihydrobenzothiazolylidene or dihydroquinolinylidene results in compounds with higher nonlinear optical responses than those containing donors based on either indoline or aniline . ► A series of chromophores with aromatizable donors and azo linkers are reported. ► The methodology allows for the synthesis of the target molecules in high yield. ► The compounds have first hyperpolarizabilities of up to 1900 × 10 −30 esu. ► The compounds have decomposition temperatures between approx 215–250 °C.

Spectroscopic, quantum-chemical and X-ray diffraction studies of Piperidinium p-Hydroxybenzoate-combined experimental and theoretical studies on a novel NLO crystal

Large size and high quality single crystals of organic nonlinear optical material Piperidinium p-Hydroxybenzoate (PDPHB) have been grown by solution growth method. This crystal belongs to monoclinic system with a noncentrosymmetric space group of Cc. To confirm its structure and compositions this material was subjected to single and powder X-ray diffraction and microanalysis studies. Fourier transform infrared (FTIR), UV–VIS–NIR, photoluminescence and nuclear magnetic resonance spectra have been recorded and extensive spectroscopic investigations have been carried out. Frequency conversion property of the crystal was tested by using Kurtz and Perry powder technique and the relative conversion efficiency was about 19 times greater than that of KDP. Static and dynamic hyperpolarizability values were calculated to confirm the suitability of the crystal for nonlinear optical applications. In addition, frontier molecular orbital (FMO), Mulliken charge and molecular electrostatic potential (MEP) analyses were performed by density functional theory (DFT) at the B3LYP/6-31G (d) basis set.

Solvation Effects on the Static and Dynamic First-Order Electronic and Vibrational Hyperpolarizabilities of Uracil: A Polarized Continuum Model Investigation

Electronic (β e) and vibrational (β v) first-order hyperpolarizabilities of uracil were determined in gas and water solution using the Coulomb-attenuating Density Functional Theory level with the Dunning's correlation-consistent aug-cc-pVDZ basis set. Frequency-dependent β e values were computed for the Second Harmonic Generation (SHG) and Electric Optical Pockels Effect (EOPE) nonlinear optical phenomena. The Polarized Continuum Model was employed to study the solvent effects on the electronic and vibrational properties. The introduction of solvation contributions increases the β e(static) value by ca. 110%. In comparison, smaller enhancements are found for the β e(EOPE) and β e(SHG) data evaluated at the typical wavelength of 694 nm (by 40–50%). The gas-water hyperpolarizability difference was rationalised through a density analysis study. The magnitudes of the vibrational first-order hyperpolarizabilities are comparable to their electronic counterparts and noticeably increase in solution: β v(EOPE) ~ β e(EOPE) in aqueous phase at λ = 694 nm. Analysis of the IR and Raman spectra is useful to elucidate the most important contributing modes to the vibrational first-order hyperpolarizabilities.

Real-space, real-time calculation of dynamic hyperpolarizabilities

The finite-difference method to calculate hyperpolarizabilities is generalized for dynamical case. The calculation of the dynamical hyperpolarizabilities from non-perturbative, explicitly time-dependent single particle states obtained in the framework of the time-dependent density functional theory, is implemented in real space and real time. The optical response functions up to the third order are extracted in frequency domain. The present approach is free of deficiencies associated with atom centered basis sets and allows treatment of large molecules. The calculated results are in good agreement with experiments and with other theoretical calculations for various test cases.

Quantum chemical study on first hyperpolarizabilities of mono- and bimetal Pt(II) diimine complexes

The static first hyperpolarizabilities (βvec) of ligand L (N,N′-bis(4-methoxyphenyl)ethylenediimine) and its Pt(II) chelated complexes have been calculated by density functional theory (DFT) method. The results show that the βvec values of Pt(II) diimine complexes range from ∼4.2 to ∼198.8 times larger than that of ligand L, and the βvec values of Pt(II) complexes with coordinated atom O are larger than those of the corresponding complexes with S. Notably, the bimetallic complex 3a possesses the largest βvec value in the studied systems, ∼1498.86 × 10−30 esu, which is ∼46.6, ∼30.5, and ∼3.6 times as large as those of complexes 1a, 2a and 3b, respectively. In addition, the dynamic first hyperpolarizabilities (βvec(ω)) of complex 1a are also calculated at the input photon energy from 0.1 to 1.8 eV. Our present work would be beneficial for further theoretical and experimental studies on large second-order nonlinear optical (NLO) responses of metal complexes.

Electronic and Vibrational Nonlinear Optical Properties of Five Representative Electrides.

The electrides have a very special electronic structure with diffuse excess electrons not localized on any specific atom. Such systems are known to have huge electronic nonlinear optical (NLO) properties. Here, we determine and analyze the vibrational, as compared to the electronic, NLO properties for a representative set of electrides: Li@Calix, Na@Calix, Li@B10H14, Li2(•+)TCNQ(•-), and Na2(•+)TCNQ(•-). The static and dynamic vibrational (hyper)polarizabilities are computed by the nuclear relaxation method (with field-induced coordinates and the infinite optical frequency approximation) at the UB3LYP level using a hybrid Pople basis set. In general, the static vibrational βvec and γ∥ exceed the corresponding static electronic property values by up to an order of magnitude. The same comparison for dynamic vibrational hyperpolarizabilities shows a smaller ratio. For the intensity-dependent refractive index (IDRI) and dc-Kerr processes, the ratio is on the order of unity or somewhat larger; it is less for the dc-Pockels and the electric field induced second harmonic (EFISH) effects (as well as the static α̅) but still important. The role of anharmonicity, motion of the alkali atoms, and substitution of Na for Li is discussed along with specific aspects of the charge distribution associated with the excess electron.

Theoretical study on second-order nonlinear optical properties of 1,10-phenanthroline Ru(II) complexes

The dynamic first hyperpolarizabilities of a series of 1,10-phenanthroline Ru(II) complexes were carried out using density functional theory (DFT). The results indicate that these complexes have large second-order nonlinear optical (NLO) responses. Specially, complex 6b has a maximal first hyperpolarizability βtot value. The first hyperpolarizabilities can be tuned by changing the ancillary ligand, introducing electron-acceptor group NO2 and/or increasing π-conjugation on phenanthroline. Calculations on absorption spectra demonstrate that the second-order NLO responses of complexes in series a are ascribed to the intraligand charge transfer (ILCT), while the complexes in series b exhibit metal-to-ligand charge transfer (MLCT) and ligand-to-ligand charge transfer (LLCT) transition at relatively low-energy absorptions.

Development of Calculation and Analysis Methods for the Dynamic First Hyperpolarizability Based on the Ab Initio Molecular Orbital – Quantum Master Equation Method

We develop novel calculation and analysis methods for the dynamic first hyperpolarizabilities β [the second-order nonlinear optical (NLO) properties at the molecular level] in the second-harmonic generation based on the quantum master equation method combined with the ab initio molecular orbital (MO) configuration interaction method. As examples, we have evaluated off-resonant dynamic β values of donor (NH(2))- and/or acceptor (NO(2))-substituted benzenes using these methods, which are shown to reproduce those by the conventional summation-over-states method well. The spatial contributions of electrons to the dynamic β of these systems are also analyzed using the dynamic β density and its partition into the MO contributions. The present results demonstrate the advantage of these methods in unraveling the mechanism of dynamic NLO properties and in building the structure-dynamic NLO property relationships of real molecules.

Static and dynamic first hyperpolarizabilities from time‐dependent auxiliary density perturbation theory

AbstractA new approach for the calculation of static and dynamic hyperpolarizabilities in the framework of auxiliary density perturbation theory is derived. It takes advantage of the Wigner's 2n+1 rule. As a byproduct dynamic quadratic response equations are obtained. Even though the final equations are similar to other approaches they present subtle differences due to their rooting in auxiliary density functional theory. The numerical stability and accuracy of the new approach is validated with respect to other theoretical and experimental results. © 2012 Wiley Periodicals, Inc.

Dynamic hyperpolarizability calculations of large systems: The linear-scaling divide-and-conquer approach

We report a linear-scaling computation method for evaluating the dynamic first hyperpolarizability β based on the divide-and-conquer (DC) method. In the present scheme, we utilized the quasi-density-matrix expression derived from Wigner's (2n + 1) rule for β, where the quasi-density matrices are constructed from the solution obtained via the DC time-dependent self-consistent field (TD-SCF) method [T. Touma, M. Kobayashi, and H. Nakai, Chem. Phys. Lett. 485, 247 (2010)]. Numerical evaluation of π-conjugated and saturated organic chain systems verified that the present scheme considerably reduces the computational time for the β evaluation with a slight loss of accuracy, even around the singular frequency appearing at the electronic excitation energy. This evaluation indicates that the present linear-scaling TD-SCF scheme can also be used to estimate the molecular excitation energy. Furthermore, we succeeded in accurately evaluating the macroscopic second-harmonic generation coefficient of the polyvinylidene fluoride from the molecular (hyper)polarizabilities.