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.     

Calculation of macroscopic first- and third-order optical susceptibilities for the benzene crystal

Starting from a set of high-level ab initio frequency-dependent molecular first- and third-order polarizabilities, the macroscopic first-order (linear) and third-order (cubic) susceptibilities of the benzene crystal are calculated. Environmental effects are taken into account using a rigorous local-field theory and are compared with the anisotropic Lorentz field factor approach. The experimentally determined first-order susceptibility of crystalline benzene is accurately reproduced. Dispersion curves for the first-order susceptibility and results for electric-field-induced second-harmonic generation and third-harmonic generation experiments are predicted. Comparison with similar calculations conducted in the course of molecular simulations of liquid benzene shows that the theoretical results for the two phases are of comparable accuracy. Overall, the results show that for the fairly compact nonpolar benzene molecules, environmental effects on the effective molecular response are small. Received: 11 February 1998 / Accepted: 6 July 1998 / Published online: 18 September 1998     

Calculation of the nonlinear optical properties of molecules

A finite-field method for the calculation of polarizabilities and hyperpolarizabilities is developed based on both an energy expansion and a dipole moment expansion. This procedure is implemented in the MOPAC semiempirical program. Values and components of the dipole moment (μ), polarizability (α), first hyperpolarizability (β), and second hyperpolarizability (γ) are calculated as an extension of the usual MOPAC run. Applications to benzene and substituted benzenes are shown as test cases utilizing both MNDO and AM1 Hamiltonians.     

Variational calculation of vibrational linear and nonlinear optical properties

A variational approach for reliably calculating vibrational linear and nonlinear optical properties of molecules with large electrical and/or mechanical anharmonicity is introduced. This approach utilizes a self-consistent solution of the vibrational Schrodinger equation for the complete field-dependent potential-energy surface and, then, adds higher-level vibrational correlation corrections as desired. An initial application is made to static properties for three molecules of widely varying anharmonicity using the lowest-level vibrational correlation treatment (i.e., vibrational M?ller-Plesset perturbation theory). Our results indicate when the conventional Bishop-Kirtman perturbation method can be expected to break down and when high-level vibrational correlation methods are likely to be required. Future improvements and extensions are discussed.     

Structural, spectral, linear and nonlinear optical properties of new nonlinear optical L-histidinium trichloroacetate crystals

Single crystals of a new histidinium salt: L-histidinium trichloroacetate {abbreviated as LHTCA; [(C(3)N(2)H(4))CH(2)CH(NH(3))(CO(2))](+)CCl(3)COO(-)} were grown by slow evaporation of an aqueous solution at room temperature. The compound crystallizes in a non-centrosymmetric space group P2(1) of monoclinic system with cell parameters a=5.4505(18) A, b=25.769(8) A, c=9.210(2) A and beta=99.98(2) degrees. The vibrational structure of the compound confirms the presence of various functional groups in the molecule. The UV-vis-NIR spectrum shows a good transparency in the whole of the region from ultraviolet to near IR. The Kurtz powder SHG measurement confirms the frequency doubling of the crystal. Thermal behaviour of the crystals has been investigated by DSC analysis. These preliminary results suggest that LHTCA crystal can act as a potential and promising candidate for frequency doubling applications even from the near UV region to the near IR.     

Mechanism of linear and nonlinear optical properties of the urea crystal family

First-principles calculations of the second-order optical response functions and the dielectric functions of urea [CO(NH(2))(2)] and some of its derivatives such as monomethylurea (H(2)NCONHCH(3), MMU), and N,N'-dimethylurea (H(3)CHNCONHCH(3), DMU) crystals are performed. On the basis of the density functional theory (DFT) in the local-density approximation (LDA), the highly accurate full-potential projected augmented wave (FP-PAW) method was used to obtain the electronic structure. Over a wide frequency range (0.0-10.0 eV), the dielectric constants and second-harmonic generation (SHG) susceptibilities of the urea crystal family have been obtained, and the results are in good agreement with the experimental values. The origin of the linear and nonlinear optical (NLO) properties of the urea crystal family has been analyzed by coupling the calculated electronic structure and optical spectrum. The prominent spectra of χ((2)) are successfully correlated with the dielectric function ε(ω) in terms of single-photon and double-photon resonances. The virtual electron (VE) and virtual hole (VH) processes have also been performed for the urea crystal family. From the research into the electron deformation density, crystal configuration, substitutional group, and so forth, it is found that the origin of the SHG of the urea crystal family is the charge transfer due to the strong "(?)push-pull" effect along the hydrogen bond, which favors a head-to-tail arrangement of the molecules and enhances the SHG response. The electron-donating substitutional group supplies more electrons to the electron-accepting group, and helps to form large dipoles in molecules. The influence on the NLO properties of the local symmetry of the substitutional group is also discussed in detail.     

Microcrystals of polydiacetylene derivatives and their linear and nonlinear optical properties

Organic microcrystals which are expected to have interesting and fascinating physical properties were fabricated by a reprecipitation method as aqueous dispersions. Many kinds of organic compounds have been microcrystallized by this convenient method. The size control has been extensively investigated for a polydiacetylene and succeeded in the range from several tens of nanometers to several micrometers by adjusting the temperature and concentration. Linear optical properties of these well-defined polydiacetylene microcrystals have been investigated and interesting size and temperature dependences of excitonic absorption are demonstrated. Nonlinear optical (NLO) properties of polydiacetylene microcrystals have also been evaluated by means of a Z-scan technique, and an extremely high nonlinear refractive index at the resonant wavelength was shown.     

Theoretical investigation on the linear and nonlinear susceptibilities of urea crystal

The linear and second-order nonlinear susceptibilities of the urea crystal have been evaluated by applying the supermolecule approach. Calculations performed at the time-dependent Hartree-Fock (TDHF) level using the Austin model (AM1) semiempirical Hamiltonian have first demonstrated the almost additive character of the essential polarizability and first hyperpolarizability components. In fact, the only exception concerns the chi(cc) ((1)) component when stacking urea molecules along the c axis, i.e., the axis of the hydrogen bonds. This behavior has been confirmed by ab initio calculations on small clusters. The macroscopic quantities have then been determined by adopting the multiplicative scheme and by correcting the TDHF/AM1 values for missing electron correlation by means of density functional theory and coupled cluster method. The reliability of the multiplicative scheme was demonstrated for clusters as large as 3ax3bx3c. While the electron correlation correction factors are similar for a single molecule and different small clusters, the global performance of the scheme differs for the linear and nonlinear responses. For the second-order nonlinear susceptibility, our predictions are in good agreement with experiment, while for the linear susceptibility and the associated refractive index, our predictions underestimate the experimental values. The limitations of our approach may be attributed to its inability to account for more subtle cooperative effects, like those associated with a network of hydrogen bonds. Together with other works, the supermolecule calculations confirm that the sign of chi(abc) ((2)) is negative, contrary to an estimate from band structure calculation.     

Electronic, linear, and nonlinear optical properties of III-V indium compound semiconductors

We have made an extensive theoretical study of the electronic, linear, and nonlinear optical properties of the III-V indium compound semiconductors InX (X=P, As, and Sb) with the use of full potential linear augmented plane wave method. The results for the band structure, density of states, and the frequency-dependent linear and nonlinear optical responses are presented here and compared with available experimental data. Good agreement is found. Our calculations show that these compounds have similar electronic structures. The valence band maximum and the conduction band minimum are located at Gamma resulting in a direct energy gap. The energy band gap of these compounds decreases when P is replaced by As and As by Sb. This can be attributed to the increase in bandwidth of the conduction bands. The linear and nonlinear optical spectra are analyzed and the origin of some of the peaks in the spectra is discussed in terms of the calculated electronic structure. The calculated linear optical properties show very good agreement with the available experimental data. We find that the intra-and interband contributions of the second-harmonic generation increase when moving from P to As to Sb. The smaller energy band gap compounds have larger values of chi(123) ((2))(0) in agreement with the experimental measurements and other theoretical calculations.     

Organometallic complexes for nonlinear optics. 30.1 electrochromic linear and nonlinear optical properties of alkynylbis(diphosphine)ruthenium complexes

A combination of cyclic voltammetry, UV-vis-NIR spectroelectrochemistry, time-dependent density functional theory (TD-DFT), and Z-scan measurements employing a modified optically transparent thin-layer electrochemical (OTTLE) cell has been used to identify and assign intense transitions of metal alkynyl complexes at technologically important wavelengths in the oxidized state and to utilize these transitions to demonstrate a facile electrochromic switching of optical nonlinearity. Cyclic voltammetric data for the ruthenium(II) complexes trans-[RuXY(dppe)(2)] [dppe = 1,2-bis(diphenylphosphino)ethane, X = Cl, Y = Cl (1), Ctbd1;CPh (2), 4-Ctbd1;CC(6)H(4)Ctbd1;CPh (3); X = Ctbd1;CPh, Y = Ctbd1;CPh (4), 4-Ctbd1;CC(6)H(4)Ctbd1;CPh (5)] show a quasi-reversible oxidation at 0.50-0.60 V (with respect to ferrocene/ferrocenium 0.56 V), which is assigned to the Ru(II/III) couple. The ruthenium(III) complex cations trans-[RuXY(dppe)(2)](+) were obtained by the in situ oxidation of complexes 1-5 using an OTTLE cell. The UV-vis-NIR optical spectra of 1(+)-5(+) contain a low-energy band in the near-IR region ( approximately 8000-16 000 cm(-)(1)), in contrast to 1-5, which are optically transparent at wavelengths < 22 000 cm(-)(1). TD-DFT calculations have been applied to model systems trans-[RuXY(PH(3))(4)] [X = Cl, Y = Cl, Ctbd1;CPh, or 4-Ctbd1;CC(6)H(4)Ctbd1;CPh; X = Ctbd1;CPh, Y = Ctbd1;CPh or 4-Ctbd1;CC(6)H(4)Ctbd1;CPh] to rationalize the optical spectra of 1-5 and 1(+)-5(+). The important low-energy bands in the electronic spectra of 1(+)-5(+) are assigned to the promotion of an electron from either a chloride p orbital or an ethynyl p orbital to the partially occupied HOMO. These absorption bands have been utilized to demonstrate a facile switching of cubic nonlinear optical (NLO) properties at 12 500 cm(-)(1) (corresponding to the wavelength of maximum transmission in biological materials such as tissue) using the OTTLE cell, the first electrochromic switching of molecular nonlinear refraction and absorption, and the first switching of optical nonlinearity using an electrochemical cell.     

Synthesis and linear and nonlinear optical properties of metal-terminated bis(dioxaborine) polymethines

Rh(III) and Ir(III) can be complexed to bipyridine groups attached to the termini of bis(dioxaborine)-capped heptamethines; these chromophores exhibit large third-order polarisabilities at 1.55 μm, while retaining good film-forming properties and linear optical transparency in the near infrared.     

A theoretical study on the third-order nonlinear optical properties of pi-conjugated linear porphyrin arrays

By using the Pariser-Parr-Pople (PPP) theory, the second hyperpolarizabilities (gamma) have been calculated for various pi-conjugated porphyrin arrays including "porphyrin tapes": the meso-beta doubly linked porphyrin array Dn and the meso-meso, beta-beta, beta-beta triply linked array Tn. The validity of the PPP theory is checked via a comparison with both the ab initio Hartree-Fock and the B3LYP theories in the case of porphyrin monomers and dimers. It is found that Dn and especially Tn exhibit much more remarkable evolution of gamma/n along with an increasing number of porphyrin units n compared with the butadiyne-bridged array, Yn. As a result, the static third-order susceptibilities chi((3)) of Dn and Tn are expected to be 1 and 3 orders of magnitude larger than that of Yn in the limit n --> infinity, and these advantages of porphyrin tapes become more prominent by taking into account geometrical relaxations of porphyrin units in the arrays. The structure-property relationship in various conjugated polymers including porphyrin arrays is interpreted on the basis of the scaling behaviors of chi((1)) and chi((3)) with the effective conjugation length (ECL) as well as the reciprocal HOMO-LUMO energy gap (1/E(g)). In particular, from the master plot of chi((3)) (and even chi((1))) versus 1/E(g), the pi-conjugation of Tn is noted to indeed be exceptional, because its large susceptibilities cannot be expected from the scaling behavior of ordinary one-dimensional conjugated systems. We also point out that the theory of scaling relationship, chi((3)) approximately 1/E(g)(x)(), is significantly improved by taking into account electron-electron interactions based on the comparison with experiments.     

Highly unusual effects of pi-conjugation extension on the molecular linear and quadratic nonlinear optical properties of ruthenium(II) ammine complexes

We have used several techniques, including hyper-Rayleigh scattering and Stark spectroscopy, to investigate the effects of polyene chain length on the optical properties of complexes containing ruthenium(II) electron donor groups and pyridinium electron acceptors. In marked contrast with all other known donor-acceptor polyenes, conjugation extension beyond a single double bond in the dipolar complexes studied leads to blue-shifting of the intramolecular charge-transfer absorptions. Furthermore, the static first hyperpolarizabilities beta0 become maximized with trans-1,3-butadienyl linkages and then decrease in complexes with three CH=CH bonds. Our results clearly demonstrate that the molecular engineering criteria for metal-containing nonlinear optical chromophores can differ dramatically from those for purely organic compounds.     

Calculation of the nonlinear stress of polymers in oscillatory shear fields

Complex moduli are calculated for the lowest-order deviations from linearity of the stress in an oscillatory shear field. The calculations involve solution of an equation, recently proposed by Doi, which goes beyond the “independent alignment approximation” of the Doi-Edwards theory of polymer dynamics. The new equation incorporates various reptative motions of a polymer in the effective constraining tube induced by entanglements, viz. Brownian motion along the tube and the systematic motion in response to changes in the length of the tube accompanying affine deformation.     

Dispersion of linear and nonlinear optical susceptibilities and the hyperpolarizability of 3-methyl-4-phenyl-5-(2-pyridyl)-1,2,4-triazole

As a starting point for our calculation of 3-methyl-4-phenyl-5-(2-pyridyl)-1,2,4-triazole we used the XRD data obtained by C. Liu, Z. Wang, H. Xiao, Y. Lan, X. Li, S. Wang, Jie Tang, Z. Chen, J. Chem. Crystallogr., 2009 39 881. The structure was optimized by minimization of the forces acting on the atoms keeping the lattice parameters fixed with the experimental values. Using the relaxed geometry we have performed a comprehensive theoretical investigation of dispersion of the linear and nonlinear optical susceptibilities of 3-methyl-4-phenyl-5-(2-pyridyl)-1,2,4-triazole using the full potential linear augmented plane wave method. The local density approximation by Ceperley-Alder (CA) exchange-correlation potential was applied. The full potential calculations show that this material possesses a direct energy gap of 3.4 eV for the original experimental structure and 3.2 eV for the optimized structure. We have calculated the complex's dielectric susceptibility ε(ω) dispersion, its zero-frequency limit ε(1)(0) and the birefringence. We find that a 3-methyl-4-phenyl-5-(2-pyridyl)-1,2,4-triazole crystal possesses a negative birefringence at the low-frequency limit Δn(0) which is equal to about -0.182 (-0.192) and at λ = 1064 nm is -0.193 (-0.21) for the non-optimized structure (optimized one), respectively. We also report calculations of the complex second-order optical susceptibility dispersions for the principal tensor components: χ(ω), χ(ω) and χ(ω). The intra- and inter-band contributions to these susceptibilities are evaluated. The calculated total second order susceptibility tensor components at the low-frequency limit |χ(0)| and |χ(ω)| at λ = 1064 nm for all the three tensor components are evaluated. We established that the calculated microscopic second order hyperpolarizability, β(ijk), the vector component along the dipole moment direction, at the low-frequency limit and at λ = 1064 nm, for the dominant component |χ(ω)| is 4.99 × 10(-30) esu (3.4 × 10(-30) esu) and 7.72 × 10(-30) esu (5.1 × 10(-30) esu), respectively for the non-optimized structure (optimized structure).     

Theoretical study in gas phase of linear and nonlinear optical properties of the ortho-, meta- and para-nitrophenol isomers

The linear (α), and nonlinear (β, γ) optical NLO properties of ortho-, meta- and para-nitrophenol (ONP, MNP and PNP) isomers have been calculated in gas phase by using ab initio (HF, MP2 and MP4) and density functional theory (DFT) (B3LYP, CAM-B3LYP) methods, with the 6-31+G(d,p) and 6-311+G(3d,3p) standard and the Sadlej specialized basis sets. These properties were evaluated both at static and at dynamic regime within the finite field FF numerical techniques and the time-dependent-Hartree–Fock approach at 1,910 nm, respectively. Additional calculations were performed for the β static hyperpolarizability of these isomers in presence of p-dioxane solvent with the Onsager Model and the SCRF-PCM approach, using B3LYP/6-31+G(d,p) and MP2/6-31+G(d,p) levels of theory. Additionally, CCSD/6-31+G(d,p) calculations were performed for the α, β and γ properties of PNP isomer. The B3LYP and MP2 α _ave results of the nitrophenol isomers are comparable to the experimental α _ave reports; while the tendency for the β _v calculated values (β _v PNP > β _v MNP > β _v ONP), that can be explained in terms of the O _x atomic charge of the –NO₂ group, does not follow exactly the experimental ones. The B3LYP γ _ave results are in correspondence to the experimental measurements, the correlation of which is r ² = 0.99. The use of FF methodology in conjunction with the B3LYP and MP2 methods and the 6-31+G(d,p) basis set show to be appropriate approaches to predict qualitative optical properties of Push–Pull like organic molecules, provided are considered the solvent effects or frequency dependence. However, to have a clear picture of the NLO properties of an isolated molecule, higher order correlation effects combined with specialized basis sets, frequency and solvent effects should be employed. We have demonstrated that MP4/Sadlej level of theory is able to reproduce NLO properties that can be considered equivalent to those from more sophisticated approaches, such as CCSD together with extended basis sets.     

Two-photon absorption and nonlinear optical properties of octupolar molecules.

Two-photon absorption (TPA) cross sections of four representative series of octupolar molecules are theoretically investigated. The general structure--TPA-property relationship is described by using the effective four-state valence-bond three-charge-transfer model. As the charge-transfer character of the ground electronic state increases due to the strong donors or acceptors, (i) the transition dipole matrix elements between the ground and 2-fold degenerate excited states increase, (ii) the energy gap decreases, and consequently (iii) the TPA transition amplitude monotonically increases. Thus, the design strategy to maximize the TPA cross section of the octupolar molecule is established. On the basis of the four-state model, the first hyperpolarizability of the octupolar molecule is found to be linearly proportional to the TPA cross section. This theoretical relationship is confirmed by using the ab initio calculation results. The Hammett correlation analysis of the TPA cross section and first hyperpolarizability is also presented.