Molecular dynamics simulations of local field factors

In the present work, the authors evaluate a scheme based on molecular dynamics to derive local field factors. These are given without any assumption of a cavity by fitting the Langevin functions to the order parameters obtained from the molecular dynamics simulations. The local field factors so obtained, with the detailed chromophore-solvent interactions and solvent structures taken into account, are much smaller than those calculated from the conventional Onsager and Lorentz models. A numerical demonstration is given for two typical organic chromophore molecules, p-nitroaniline and p-nitro-N,N-dimethylaniline dissolved in chloroform.     

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

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

Problems in the comparison of theoretical and experimental hyperpolarizabilities revisited

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

Environmental and excitonic effects on the first hyperpolarizability of polar molecules and related dimers

We investigate the second-order nonlinear optical properties of a push-pull chromophore in different external and supramolecular environments, through a combined experimental and theoretical approach. In particular, we compare the first hyperpolarizability (beta) of a model dipolar and polarizable chromophore with that of a charged analogue and of a molecular dimer based on the chromophore itself. We find that the beta value of the model chromophore in solutions of low-polarity solvents is strongly affected by association effects, already at concentrations of 10 (-3) M. The presence of a positive charge in close proximity to the chromophore is found to lead to a 100% increase of the beta response of the model push-pull chromophore. This effect is of major importance for biological applications, in particular when chromophores are used as markers in charged anisotropic environments. Finally, excitonic effects, beyond the Frenkel exciton approximation, are discussed for the dimer and found to be more important the higher the order of nonlinearity is.     

Macroscopic order and electro-optic response of dipolar chromophore-polymer materials.

This Minireview considers the key factors that govern the organization of macroscopic polarization in nonlinear optical systems obtained by electric poling of organic dipolar chromophores dissolved in polymer matrices. The macroscopic electric polarization depends on the thermodynamic state of the dipole system. The dependence of the paraelectric and antiferroelectric states of dipolar chromophores on the chromophore concentration and the strength of the poling field is discussed. Phase transitions between the para- and antiferroelectric states are investigated within the limits of the Ising and isotropic models for the chromophore dipoles and are considered for varying chromophore concentration, poling field strength, and macroscopic shape of the sample used for poling. The macroscopic polarization and electro-optic coefficient of the material change drastically upon phase transition. The theories are compared with the experimental data on the electro-optic coefficient dependence on the chromophore concentration. The isotropic dipole model shows excellent agreement with experiment for the chromophore systems most commonly used in nonlinear optics.     

Local and nonlocal contributions to molecular first-order hyperpolarizability: a Hirshfeld partitioning analysis

Based on first-principles calculations, a decomposition scheme is proposed to investigate the molecular site-specific first-order hyperpolarizability (β) responses by means of Hirshfeld population analysis and finite field method. For a molecule, its β is decomposed into local and nonlocal contributions of individual atoms or groups. The former describes the response within the atomic sphere, while the latter describes the contributions from interatomic charge transfer. This scheme is then applied to six prototypical donor-acceptor (D-A) or D-π-A molecules for which the local and nonlocal hyperpolarizabilities are evaluated based on their MP2 density. Both the local and nonlocal parts exhibit site-specific characteristics, but vary differently with molecular structures. The local part depends mainly on the atomic attributes such as electronegativity and charge state, as well as its location in the molecule, while the nonlocal part relates to the ability and distance of charge delocalization within the molecule, increasing rapidly with molecular size. The proposed decomposition scheme provides a way to distinguish atomic or group contributions to molecular hyperpolarizabilities, which is useful in the molecular design for organic nonlinear optical materials.     

A sum-over-state scheme of analysis of hyperpolarizabilities and its application to spiroconjugated molecular system

The static first and second hyperpolarizabilities of a number of spiromolecules with varying degree of polarity have been calculated at the HF and MP2 level using the 6-31+G* basis set and the B3LYP/6-31+G* optimized geometry. The variation of mean second hyperpolarizability in these molecular systems has been explained in terms of the ground state dipole moment, mean linear polarizability and second-order polarizability. A number of relationships among these quantities have been derived in the framework of the sum-over-state scheme and the generalized Thomas–Kuhn sum rule. The spiroconjugation results in the significant increase of the mean polarizability. The appreciable enhancement of first hyperpolarizability due to the spiroconjugation between two dipolar monomer units has been accounted for the rather significant increase of the mean polarizability tensor and the ground state dipole moment. The relatively larger value of the average second hyperpolarizability of the spiroconjugated molecules compared to that of the corresponding monomers arises from the rather significant increase of the nonaxial component γ _xxyy . The replacement of spirocarbon by spirosilicon results in the enhancement of the cubic polarizability manifold. The donor–acceptor substituted spirocompounds are predicted to be the superior third-order nonlinear optical (NLO) phores. The nature of π-conjugation in the monomer units around the spirocenter shows a strong modulation of the NLO properties of spirocompounds. The influence of electron correlation on the NLO properties at the MP2 level has been found to be rather significant.     

Combined molecular and supramolecular bottom-up nanoengineering for enhanced nonlinear optical response: experiments, modeling, and approaching the fundamental limit

The authors study the combination of two independent strategies that enhance the hyperpolarizability of ionic organic chromophores. The first molecular-level strategy is the extension of the conjugation path in the active chromophore. The second supramolecular-level strategy is the bottom-up nanoengineering of an inclusion complex of the chromophore in an amylose helix by self-assembly. The authors study a series of five (dimethylamino)stilbazolium-type chromophores with increasing conjugation length between the (dimethylamino)phenyl donor ring and the pyridinium acceptor ring in conjunction with four amylose helices of differing molecular weights. The first hyperpolarizabilities of the self-assembled inclusion complexes, as determined with frequency-resolved femtosecond hyper-Rayleigh scattering at 800 and 1300 nm, are compared with experimental values for the free chromophores in solution and with theoretical values. While the experimental values for the hyperpolarizability in solution are lower than the theoretically predicted values, an enhancement upon inclusion is observed, with the longest chromophore in the best amylose helix showing an enhancement by one order of magnitude. Molecular modeling of the inclusion of the chromophore suggests that the coplanarity of the two rings is more important than all-trans configuration in the conjugation path. The fundamental limit analysis indicates that the inclusion inside the amylose helix results in an optimal excited-level energy spacing that is responsible for breaching the apparent limit.     

Three-coupled-oscillator model for nonlinear optical response of chiral molecules with tripod-like structure

In this paper, we further study on the relation between the first hyperpolarizability and molecular configuration based on the three-coupled-oscillator model proposed by us. The model is suitable for chiral molecules with the tripod-like structure. We numerically simulate the spectra of first hyperpolarizabilities, and investigate the effects of molecular chiral parameters and coupling coefficients on the hyperpolarizabilities. As an example, we show a calculation of the first-hyperpolarizability spectra for NPAN molecules, which accord well with the experimental result obtained by Barzoukas et al. [M. Barzoukas, D. Josse, P. Fremaux, J. Zyss, J. Opt. Soc. Am. B 4 (1987) 977–986].     

Wavelength dependence of first molecular hyperpolarizability of a dendrimer in solution

The frequency dependence of the first molecular hyperpolarizability of a dendrimer incorporated with thiophene-stilbene based charge-transfer chromophores is investigated by using a nanosecond 1907 nm laser and a number of wavelengths ranging from 1160 to 1760 nm emitted from an optical parametric amplifier pumped by a 1 kHz 130 fs Ti:sapphire laser. The measured hyperpolarizabilities are compared with those calculated from the charge-transfer absorption spectrum involving a Kramers-Kronig transformation scheme. The Kramers-Kronig transformation analysis provides a satisfactory account of the dispersion of the first molecular hyperpolarizability over the entire excitation wavelength range measured. The Kramers-Kronig technique extends the Oudar-Chemla two-level model previously proposed for the first molecular hyperpolarizability and it can be used in the nonresonance as well as the resonance region where the Oudar-Chemla model fails. The Kramers-Kronig transformation scheme allows a consistent intrinsic hyperpolarizability beta(0) to be obtained from the measured beta(HRS) using different excitation wavelengths for the dendrimer. The comparison of beta(0) for the dendrimer, which contains three chromophores, with that of corresponding monomer chromophore suggests that the chromophores inside the dendrimer are independent. This gives the evidence of the site isolation effect of the dendrimer and substantiates the larger macroscopic optical nonlinearity recently obtained for the dendrimer.     

Reference molecules for nonlinear optics: a joint experimental and theoretical investigation

Hyper-Rayleigh scattering (HRS) experiments and quantum chemical calculations are combined to investigate the second-order nonlinear optical responses of a series of reference molecules, namely, carbon tetrachloride, chloroform, trichloroacetonitrile, acetonitrile, and dichloromethane. The multipolar decomposition of the first hyperpolarizability tensor through the use of the spherical harmonics formalism is employed to highlight the impact of the symmetry of the molecular scatterers on their nonlinear optical responses. It is demonstrated that HRS is a technique of choice to probe the molecular symmetry of the compounds. Coupled-cluster calculations performed at the coupled-cluster level with singles, doubles, and perturbative triples in combination with highly extended basis sets and including environment effects by using the polarizable continuum model qualitatively reproduce the molecular first hyperpolarizabilities and depolarization ratios of the molecular scatterers.     

Surface enhanced second harmonic generation from macrocycle, catenane, and rotaxane thin films: experiments and theory

Surface enhanced second harmonic generation (SE SHG) experiments on molecular structures, macrocycles, catenanes, and rotaxanes, deposited as monolayers and multilayers by vacuum sublimation on silver, are reported. The measurements show that the molecules form ordered thin films, where the highest degree of order is observed in the case of macrocycle monolayers and the lowest in the case of rotaxane multilayers. The second harmonic generation activity is interpreted in terms of electric field induced second harmonic (EFISH) generation where the electric field is created by the substrate silver atoms. The measured second order nonlinear optical susceptibility for a rotaxane thin film is compared with that obtained by considering only EFISH contribution to SHG intensity. The electric field on the surface of a silver layer is calculated by using the Delphi4 program for structures obtained with TINKER molecular mechanics/dynamics simulations. An excellent agreement is observed between the calculated and the measured SHG susceptibilities.     

Dipolar donor-acceptor-substituted schiff base complexes with large off-diagonal second-order nonlinear optical tensor components

The synthesis, characterization, and two-dimensional second-order nonlinear optical (NLO) response of a dipolar NiII donor- acceptor Schiff base complex and the related ligand are reported. Electric-field-induced second-harmonic generation and harmonic light (hyper-Rayleigh) scattering techniques, in combination with INDO/SCI-SOS theoretical calculations, were used to investigate the vector part of the hyperpolarizability tensor and the two-dimensional character of the molecular nonlinearity, respectively. Off-diagonal hyperpolarizability tensors can be related to charge-transfer transitions that are polarized perpendicular to the molecular dipolar axis, while parallel transitions account for the diagonal hyperpolarizability tensor. The role of the metal center in enhancing the two-dimensional NLO response of such molecules is twofold since it acts both as the donor and the bridging moiety of the planar donor-(pi-conjugate-bridge)-acceptor system. These dipolar two-dimensional molecules are interesting candidates from the perspective of polarization-independent NLO materials.     

On the determination of molecular hyperpolarizabilities by combining data from the Kerr effect and from electrically induced NMR line splitting

It is shown that in the calculation of the contribution to the Kerr effect in polar liquids by the hyperpolarizabilities, the effective field should be taken equal to the sum of the Lorentz field and the reaction field. Calculation of first hyperpolarizabilities on this basis by combining values of the Kerr constant with values of the alignment from electrically induced line splitting in NMR, yields for strongly polar molecules (μ ≈ 4 D) values that are smaller by an order of magnitude than those from previous calculations on the same effects, but that compare more favourably with other data.     

A new hybrid DFT approach to electronic excitation and first hyperpolarizabilities of transition metal complexes

The electronic excitations and the static first hyperpolarizability of three typical transition metal (TM) aromatic carbonyl complexes, two tungsten pentacarbonyl derivatives (W(CO)₅L, L = Py and PyCHO) and one chromium tricarbonyl arene derivative (Cr(CO)₃Bz, Bz = benzene), have been theoretically studied by a variety of density functional methods. The assessments reveal that most of the conventional DFT methods including local density approximation, generalized gradient approximation (GGA), and the various kinds of hybrid exchange‐correlation (xc) methods present the first hyperpolarizabilities of these TM‐containing molecules with large deviations from the experiments. A one‐parameter hybrid xc functional is introduced by using the Perdew‐Wang 1991 gradient‐corrected correlation functional (PW91) and the Barone's‐modified PW91 exchange functional (mPW). The ratio between the exact and the density functional exchange is determined to be 0.40 by the adiabatic connection method. The application of the new hybrid functional to the three organometallic carbonyl molecules results in the satisfactory agreement between the calculated first hyperpolarizabilities and the experimental ones. The second‐order nonlinear optical properties of the three organometallic complexes are addressed to the metal‐to‐ligand charge transfers, and the extended π‐delocalization ligands benefit the enhancement of the first hyperpolarizability. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009     

Determination of the quadratic hyperpolarizability of trans-4-[4-(dimethylamino)styryl]pyridine and 5-dimethylamino-1,10-phenanthroline from solvatochromism of absorption and fluorescence spectra: a comparison with the electric-field-induced second-harmonic generation technique.

For fluorescent compounds, the combined use of absorption and emission solvatochromic data allows to estimate indirectly the cavity radius of the molecule in solution, a very critical parameter in the application of the solvatochromic method for the determination of the quadratic hyperpolarizability beta of dipolar molecules. For two test compounds, trans-4-[4-(dimethylamino)styryl]pyridine (DASP) and 5-dimethylamino-1,10-phenanthroline (DAPHEN), the beta values so obtained are compared with those obtained by the EFISH (Electric Field Induced Second-Harmonic generation) technique. For DAPHEN, the versatility of the method described in this work in the presence of more than one electronic transition contributing to the non-linear optical response is demonstrated.     

Direct metal-metal interaction contributions to quadratic hyperpolarizability: a study on dirhenium complexes

We present a comparative study of the metal-metal interaction effect on the static quadratic hyperpolarizabilities of two typical dinuclear rhenium clusters. The electronic structures, excitation spectra, dipolar moments, static polarizabilities, and quadratic hyperpolarizabilities of the two complexes with direct metal-metal interactions have been computed and analyzed with the use of high-level DFT/TDDFT methods. The geometries and the first intense excitations agree with the relevant reported measurements. The orbital decomposition scheme ( J. Phys. Chem. A 2006, 110, 1014-1021) has been applied to analyze the relationship between the electronic structures and nonlinear optical (NLO) properties of these two complexes. We propose an unprecedented NLO response mechanism featuring the contribution of the direct metal-metal interaction transition process in these dinuclear rhenium complexes. This contribution positively enhances the quadratic hyperpolarizability and relates to the intensity of the metal-metal interactions of the complexes. The results are helpful to the development of NLO chromophores in polynuclear metal clusters through the molecular design technique.     

Effects of external electric field and self-aggregations on conformational transition and optical properties of azobenzene-based D-π-A type chromophore in THF solution

The influence of environments (THF solvents and electric field) and molecular self-aggregations on the structure and optical properties of 4-(4-hydroxyphenylazo)nitrobenzene has been investigated by molecular dynamics (MD) simulations and quantum chemical calculations. Long-range electrostatic effects and the hydrogen bond interactions between the solute and the THF solvent molecules lead to the augments of nonlinear optical (NLO) response by about two times from the gas phase to THF solution, accompanied by considerable red-shift of more than 40 nm in the maximum absorption wavelengths of the ground (S(0)) and low-lying excited states (S(1), S(2), and S(3)). The solvated chromophore reorients quickly (within 300 ps) under external electric field of 1.0 V/nm, even when the direction of the applied electric field is antiparallel to the dipole moment of the solute. Nonequilibrium MD simulations demonstrate that the light-induced cis-trans isomerization in THF solution and external electric field need longer relaxation time (about 1.0 ps) than that in gas phase (about 500 fs). The dipole-dipole interactions and intermolecular hydrogen bonds facilitate the self-aggregations of solute molecules in solution. The V-shaped dimer exhibits higher hyperpolarizability value by about 1.2 times of the monomer, whereas the antiparallel alignment leads to a cancellation of dipole moment and hence dramatic decrease in hyperpolarizability (one-third of the monomer). However, the Boltzmann-weighted contribution to hyperpolarizability from these two aggregations (with 82% V-shaped and 18% antiparallel) is close to that of the monomer. Orientations of D-π-A dipoles in various environments and molecular aggregations are important to modulate the optical properties of materials.