The polarizability and the second hyperpolarizability of tetrakis(phenylethynyl)ethene and several of its lithiated derivatives

The polarizability (α) and the second hyperpolarizability (γ) of tetrakis(phenylethynyl)ethene (TPEE) are compared and analyzed in connection with the properties (α, γ) of a series of selected/designed molecules having different conjugation patterns. Several lithiated derivatives of TPEE are designed and shown to have very enhanced second hyperpolarizabilities; for example, one of the lithiated TPEE has a 1.6×10³ times larger second hyperpolarizability than that of benzene. The potential of the proposed derivatives for applications in photonics is noted. The polarizabilities and the hyperpolarizabilities of the considered molecules have been computed employing the PM3 method which has been proven to be adequate for the present comparative study. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 72: 177–187, 1999     

Theoretical study on nonlinear optical properties of the Li+[calix[4]pyrrole]Li−dimer,trimer and its polymer with diffuse excess electrons

The static (hyper)polarizabilities of the dimer and trimer with diffuse excess electrons, [Li⁺[calix[4]pyrrole]Li^?]_n, are firstly investigated by the DFT(B3LYP) method in detail. For the dimer and trimer, a Li atom inside each calix[4]pyrrole unit is ionized to form a diffuse excess electron. The results show that the dimer and trimer containing two and three excess electrons, respectively, have very large first hyperpolarizablities as 2.3 × 10⁴ and 4.0 × 10⁴ au, which are 30 and 40 times larger than that of the corresponding [calix[4]pyrrole]_n (n = 2, 3) without Li atom. Also, β values of dimer and trimer are twice and four times as large as that of monomer containing one excess electron. Obviously, not only excess electron but also the number of excess electron plays an important role in increasing the first hyperpolarizability. Moreover, the (hyper)polarizabilities of the [Li⁺[calix[4]pyrrole]Li^?]_n polymer are investigated at ab initio level by using the elongation finite‐field (elongation FF) method. All the oligomers of the [Li⁺[calix[4]pyrrole]Li^?]_n with many excess electrons exhibit very large first hyperpolarizability and large second hyperpolarizability. The present investigation shows that by introducing several and more excess electrons into the nonlinear optical (NLO) materials will be an important strategy for improving their NLO properties, which will be helpful for design of NLO materials. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Structures and considerable static first hyperpolarizabilities: new organic alkalides (M+@n6adz)M'- (M, M'=Li, Na, K; n=2, 3) with cation inside and anion outside of the cage complexants

Eighteen structures of new organic alkalides (M+@n6adz)M'- (M, M'=Li, Na, K; n=2, 3) with the alkali-metal cation M+ lying near the center of the adz cage and the alkali-metal anion M'- located outside are obtained with all real frequencies. They exhibit very large static first hyperpolarizabilities (beta0) up to 3.2x10(5) au, which exceeds the record value of beta0=1.7x10(5) au for nonlinear optical compounds [Chem.-Eur. J. 1997, 3, 1091]. All potassides (M+@n6adz)K- (M=Li, Na, K; n=2, 3) have considerably large beta0 values (1.6x10(5)-3.2x10(5) au) much larger than the beta0 value (3.6x10(4) au) of the previously designed cuplike alkalide Li+(calix[4]pyrrole)K- [J. Am. Chem. Soc. 2006, 128, 1072]. This shows that the 26adz and 36adz cage complexants are preferable to cuplike calix[4]pyrrole complexant in enhancing the first hyperpolarizability. The effect of cage size of the complexant on the first hyperpolarizability is also presented here: in most cases, the smaller cage complexant corresponds to the larger beta0 value. Moreover, the crucial role by the alkali-metal anion in the large first hyperpolarizability of these alkalides is revealed. These results may provide new means for designing high-performance nonlinear optical materials.     

Charge transfer interactions in polymers and the fabrication of high frequency electro-optic modulators

The synthesis and processing of second order nonlinear optical polymeric materials for application in electro-optic devices is described with particular emphasis on (1) the synthesis and incorporation into hardened polymer lattices of chromophores characterized by large μβ (where μ is the dipole moment and β is the molecular first hyperpolarizability) values; (2) the synthesis and incorporation into hardened polymer lattices of chromophores which are capable of undergoing photo-induced conformational changes and which can be processed by new multi-color photolithography techniques into buried channel active waveguides; and (3) the processing of polymeric nonlinear optical materials appropriate for the realization of full integration with very large scale integration (VLSI) drive electronics and with silica fiber optic transmission lines. Prototype modulators have been fabricated and shown to be suitable for broadband operation from 0 to 113 GHz. Optical losses associated with waveguide wall roughness and with mode mismatch in transitioning between silica and polymeric waveguides are reduced by control of the conditions of reactive ion etching and by use of the new technique of multi-color photochemical lithography.     

Twisted π-system chromophores for all-optical switching

Molecular chromophores with twisted π-electron systems have been shown to possess unprecedented values of the quadratic hyperpolarizability, β, with very large real parts and much smaller imaginary parts. We report here an experimental and theoretical study which shows that these twisted chromophores also possess very large values of the real part of the cubic hyperpolarizability, γ, which is responsible for nonlinear refraction. Thus, for the two-ring twisted chromophore TMC-2 at 775 nm, relatively close to one-photon resonance, n(2) extrapolated to neat substance is large and positive (1.87 × 10(-13) cm(2)/W), leading to self-focusing. Furthermore, the third-order response includes a remarkably low two-photon absorption coefficient, which means minimal nonlinear optical losses: the T factor, α(2)λ/n(2), is 0.308. These characteristics are attributed to closely spaced singlet biradical and zwitterionic states and offer promise for applications in all-optical switching.     

Static hyperpolarizability of the van der Waals complex CH4?N2

The static first hyperpolarizability of the van der Waals CH₄ N₂ complex was calculated. The calculations were carried out in the approximation of the rigid interacting molecules for a broad range of intermolecular separations (R = 6–40 a₀) and for six configurations at CCSD(T) level of theory using the correlation consistent aug-cc-pVTZ basis set with the basis set superposition error correction. It was shown that the long-range classical approximation, including the terms up to R⁻⁶, is in a good agreement with ab initio calculations for R > 11 a₀. It was found out that for the family of most stable configurations of the complex, the first hyperpolarizability invariants practically do not change (the changes are less than 0.1%). Under forming the stable van der Waals CH₄ N₂ complex, the intensity and degree of depolarization of the hyper-Rayleigh scattering are noticeable decreased (by ∼10%) to be compared with the free CH₄ and N₂ molecules. © 2012 Wiley Periodicals, Inc.     

Geometrical structure and nonlinear response variations of metal (M = Ni2+, Pd2+, Pt2+) octaphyrin complex derivatives: A DFT study

Nonlinear optical response of designed organometallic complexes of Ni²⁺, Pd²⁺, and Pt²⁺ metal ions with octaphyrin (OP) as ligand were explored by using DFT at CAM-B3LYP/6–311G++(d, p)/LANL2DZ/DEF2SV level of theory. The geometries of these organometallic complexes were studied in terms of effect on molecular framework by metal ion and substituent groups. The optimized geometry of free ligand displays that one of the four pyrrole rings orients out of plane to reduce the steric hindrance. The effect of the substituents on the geometry was found more prominent in the Ni²⁺-OP complexes. The calculations reveal enhancement in the values of dipole moment and hyperpolarizability on introducing electron withdrawing and electron donating groups in ligand framework with maximum enhancement in case of Pt²⁺-OP derivatives. In this study no regular trend was observed for the HOMO and LUMO energies with the second-order hyperpolarizability of M²⁺-OP complexes. However, we have observed that the excited-state properties calculated by using TD-DFT correlate well with the second-order hyperpolarizability values and the dependence was rationalized in terms of two-level model. Thus, from overall calculations we have observed that the designed organometallic complexes display higher polarizability and hyperpolarizability values and can be effective candidates for nonlinear response.     

First hyperpolarizability of a sesquifulvalene transition metal complex by time-dependent density-functional theory

The first hyperpolarizability and electronic excitation spectrum of sesquifulvalene and a sesquifulvalene ruthenium complex have been computed and analyzed with use of time-dependent density-functional theory. A new orbital decomposition scheme is introduced that allows the computed first hyperpolarizability to be related to the electronic structure of complex molecules. The analysis shows that the first hyperpolarizability of sesquifulvalene is not associated with the first intense absorption, with HOMO-1 --> LUMO+1 character, but is dominated by the lowest energy transition, with HOMO --> LUMO character, despite its very low intensity. In the ruthenium complex, the analysis reveals that the strong enhancement of the nonlinear optical response compared to free sesquifulvalene should not be attributed to the effect of complexation on the hyperpolarizability of sesquifulvalene. The strong hyperpolarizability originates from MLCT transitions from ruthenium d-orbitals to an empty orbital located at the seven ring of sesquifulvalene, transitions that have no analogue in free sequifulvalene.     

Three-propeller-blade-shaped electride: remarkable alkali-metal-doped effect on the first hyperpolarizability

Significant alkali-metal-doped effects on the structure and the first hyperpolarizability (β ₀) of effective multi-nitrogen complexant tris[(2-imidazolyl)methyl]amine (TIMA) are investigated. Three imidazoles of TIMA like three blades of propeller connect with methyls by the C–C single bonds. Because of the three C–C single-bond cooperative rotations, the TIMA behaves with great flexibility, and it is a high-performance multi-nitrogen complexant for the alkali metal doping. Thus, the new complexes A_m-TIMA (A_m = Li, Na, and K) with electride characteristic have diffuse excess electron than the reported electride-type system due to the strong interaction between the complexant TIMA and alkali metal. For the first hyperpolarizability, three engaging electrides A_m-TIMA with the diffuse excess electrons exhibit considerably large β ₀ values using the MP2 (full) method and the β ₀ values of new electrides are greatly larger (3,464–29,705 times) than that (338 au) of TIMA. Surprisingly, the K-TIMA sets a new record β ₀ value to be 1.00 × 10⁷ au which far exceeds than that (3,694–76,978 au) of the reported electride-type system Li@calix[4]pyrrole (J Am Chem Soc 127:10977–10981, 2005) and Li_n−H−(CF₂−CH₂)₃−H (n = 1, 2) (J Am Chem Soc 129:2967–2970, 2007) and 31,123 au of the organometallic system (J Am Chem Soc 121:4047–4053, 1999) Ru(trans-4,4′-diethylaminostyryl-2,2′-bipyridine)₃²⁺, as well as 1.23 × 10⁶ au of the large donor-CNT systems (Nano Lett 8:2814–2818, 2008). Clearly, the alkali-metal-doped effect on the first hyperpolarizability is very dramatic for the high-performance multi-nitrogen complexant TIMA. Considering simple possibility from molecule to material, the β ₀ values of optimized Li-TIMA-dimer and Li-TIMA-tetramer are investigated by BHandHLYP method. Interestingly, results show that the order of β ₀ value is Li-TIMA-monomer < Li-TIMA-dimer < Li-TIMA-tetramer. So the new three-propeller-blade-shaped electrides can be considered as candidates for high-performance nonlinear optical materials.     

The structure and the large nonlinear optical properties of Li@calix[4]pyrrole

A new compound with electride characteristics, Li@calix[4]pyrrole, is designed in theory. The Li atom in Li@calix[4]pyrrole is ionized to form a cation and an excess electron anion. Its structure with C(4v) symmetry resembles a cup-like shape. It may be a stable organic electride at room temperature. The first hyperpolarizability of the cup-like electride molecule is first investigated by the DFT (B3LYP) method. The result shows that this electride molecule has a considerably large first hyperpolarizability with beta(0) = 7326 au (63.3 x 10(-30) esu), while the beta(0) value of the related calix[4]pyrrole system is only 390 au. Obviously, the Li atom doped in calix[4]pyrrole brings a dramatic change to the electronic structure, so that the first hyperpolarizability of Li@calix[4]pyrrole is almost 20 times larger than that of calix[4]pyrrole. We find that the excess electron from the Li atom plays an important role in the large first hyperpolarizability of Li@calix[4]pyrrole. The present investigation reveals a new idea and different means for designing and synthesizing high-performance NLO materials.     

Analysis of vibrational spectra (FT-IR and VCD) and nonlinear optical properties of [Ru(L)3]2+ complexes

Density functional theory calculations were performed on [Ru(L)₃]²⁺ (L = 1,10-phenanthroline, 2,2′-bipyridine, 2,2′-bipyrimidine, 2,2′-bipyrazine) complexes by employing B3PW91 functional and LAN2DZ basis set to predict their spectra and nonlinear optical response. The geometrical and coordination energy studies explained that the stability of [Ru(L)₃]²⁺ metal complexes depends on the extent of interaction of the dπ orbitals of Ru²⁺ with the π* ligand orbitals, which is maximum for 1,10-phenanthroline. The two enantiomers of the [Ru(L)₃]²⁺ show IR absorption peaks in the region of 1100–1800 cm^?1, and a slight shift occurs to lower frequency by solvent. The vibrational circular dichroism peaks of [Ru(phen)₃]²⁺ had major contribution from out-of-phase stretching of 1,10-phenanthroline rings and a minor contribution from H–C=C–H wagging and C=C stretching of rings. Maximum hyperpolarizability was observed for [Ru(phen)₃]²⁺ due to stronger anharmonicity in the π-electron system. Among the [Ru(L)₃]²⁺ (L = bpy, bpm, and bpz) complexes, [Ru(bpm)₃]²⁺ shows enhanced hyperpolarizability due to increase in the dipole along the X-direction. In derivative Ru²⁺ complexes, we found that hyperpolarizability depends on electron-donating capability of the substituent. As per FMOs study, the HOMO is predominantly metal fragment based, the LUMO is primarily ligand based, and the larger value of hyperpolarizability corresponds to the lower E_LUMO–E_HOMO gap, reflecting that nonlinear optical response is a consequence of additive dipolar responses of charge transfer and hyperpolarizability.     

Irreducible tensor analysis of sum- and difference-frequency generation in partially oriented samples

The macroscopic non-liner optical susceptibility _X⁽²⁾ for a system of partially oriented molecules is written as the ensemble average of molecular hyperpolarizability tensors β. The orientational distribution of these molecules is described by a probability function expanded in Wigner matrices. For a rotationally invariant system _X⁽²⁾ has seven non-vanishing components, and a method is outlined to determine these by sum- or difference-frequency mixing experiments. The method could be applied to electrically poled samples, adsorbates liquid crystals and membranes to determine several components of the molecular hyperpolarizability tensor, or to extract information about the orientational distribution.     

Role played by the organometallic fragment on the first hyperpolarizability of iron–acetylide complexes: A TD-DFT study

The static first hyperpolarizabilities (β) for a series of both substituted thiophene-acetylide ligands and the corresponding η⁵–monocyclopentadienyliron(II) complexes were determined by density functional theory (DFT) calculations. The effect on the hyperpolarizabilities by various donor and acceptor substituents in the thiophene-acetylide ligands was studied. The nature and role of the electronic excitation contributions to the first hyperpolarizability, using time-dependent DFT (TD-DFT) calculations, are rationalized in terms of the two-level model. Our calculations show that the organometallic fragment can form a very effective push-pull system in combination with electron-withdrawing substituents in the thiophene-acetylide moiety, leading to enhanced static first hyperpolarizabilities. Also, an improvement of the magnitude of β is expected if solvation effects are taken into account.     

How does hybrid bridging core modification enhance the nonlinear optical properties in donor‐π‐acceptor configuration? A case study of dinitrophenol derivatives

This study spotlights the fundamental insights about the structure and static first hyperpolarizability (β) of a series of 2,4‐dinitrophenol derivatives (1–5), which are designed by novel bridging core modifications. The central bridging core modifications show noteworthy effects to modulate the optical and nonlinear optical properties in these derivatives. The derivative systems show significantly large amplitudes of first hyperpolarizability as compared to parent system 1 , which are 4, 46, 66, and 90% larger for systems 2, 3, 4 , and 5 , respectively, at Moller–Plesset (MP2)/6‐31G* level of theory. The static first hyperpolarizability and frequency dependent coupled‐perturbed Kohn–Sham first hyperpolarizability are calculated by means of MP2 and density functional theory methods and compared with respective experimental values wherever possible. Using two‐level model with full‐set of parameters dependence of transition energy (ΔΕ), transition dipole moment (μ⁰) as well as change in dipole moment from ground to excited state (Δμ), the origin of increase in β amplitudes is traced from the change in dipole moment from ground to excited state. The causes of change in dipole moments are further discovered through sum of Mulliken atomic charges and intermolecular charge transfer spotted in frontier molecular orbitals analysis. Additionally, analysis of conformational isomers and UV‐Visible spectra has been also performed for all designed derivatives. Thus, our present investigation provides novel and explanatory insights on the chemical nature and origin of intrinsic nonlinear optical (NLO) properties of 2,4‐dinitrophenol derivatives. © 2014 Wiley Periodicals, Inc.     

Resonant Raman spectra and first molecular hyperpolarizabilities of strongly charge-transfer molecules

The effect of vibrational structure on the frequency dependence of the first molecular hyperpolarizability of two thiophene-based charge-transfer chromophores is investigated. A time domain formulation is used to express the polarizability. The new expression includes the solvent-induced inhomogeneous distribution of electronic transition frequencies as well as the effect of the motion of solvent molecules that modulates the vibrational and electronic transition frequencies of the nonlinear optical molecule on which the first molecular hyperpolarizability depends. Resonance Raman scattering and one-photon absorption spectra of the chromophores are measured. By simultaneously fitting the experimental one-photon absorption spectrum and Raman cross sections of vibrational lines derived from resonance Raman scattering to a theoretical model, important parameters needed for the calculation of the first molecular hyperpolarizability are obtained. The first molecular hyperpolarizability is calculated as a function of frequency covering both nonresonance and two-photon resonance regions. The calculated result is compared with the measured hyperpolarizability as a function of frequency of the excitation laser. The resonance Raman-based analysis is shown to account reasonably well for the dispersion of the hyperpolarizability of the two charge transfer chromophores.     

Linear phosphorus–boron chains: model system with huge electronic first hyperpolarizability

The longitudinal electronic static first hyperpolarizability of model linear phosphorus–boron chains is investigated using ab initio tools, including dynamic electron correlation corrections. The polymer presents an extremely large first hyperpolarizability (1700 × 10^?30 esu per unit cell) that can be rationalized in terms of delocalization and asymmetry (unit cell and chain‐ends contributions). © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Revisiting the relationship between the bond length alternation and the first hyperpolarizability with range-separated hybrid functionals

We monitor the influence of the bond length alternation (BLA) modification on the static electronic polarizability and first hyperpolarizability of two polymethineimine oligomers. Four theoretical approaches are compared: HF, PBE0, LC-omegaPBE, and MP2. For the dodecamer, both HF and PBE0 are unable to foresee even the qualitative evolution of the first hyperpolarizability when varying the BLA. On the contrary, LC-omegaPBE provides (non)linear optics properties in agreement with MP2 results, especially for the longer chains. This confirms the interest of range-separated hybrids for the computation of the (hyper)polarizabilities of extended pi-conjugated compounds.     

Effect of modified donor units on molecular hyperpolarizability of thienyl-vinylene nonlinear optical chromophores

Highly efficient and thermally stable nonlinear optical chromophores based on the phenyl vinylene thiophene vinylene (FTC) donor-π-acceptor structure have been synthesized and investigated. The donor part of the chromophores was modified with additional donor units, resulting in the enhanced nonlinear optical property with large molecular hyperpolarizability. Hyper-Rayleigh scattering measurement indicated nearly threefold increase of the molecular hyperpolarizability for novel chromophores compared with the benchmark FTC chromophore. Furthermore, measurement of the electro-optic coefficient confirmed that enhancement of microscopic molecular hyperpolarizability of the chromophores can be effectively translated into macroscopic electro-optic property. Measured electro-optic coefficients were nearly twofold larger than that for the benchmark FTC. Thermal analysis indicated that the synthesized chromophores showed the excellent temperature stability with decomposition temperatures up to 280 °C.     

Theoretical study of spectroscopic properties of insulated molecular wires formed by substituted oligothiophenes and cross‐linked α‐cyclodextrin

The inclusion compound formed between cross‐linked α‐cyclodextrin dimer and substituted oligothiophene, was investigated using density functional theory (DFT). Energy gap, spectroscopy (IR, UV–vis, ¹³C NMR, and ¹H NMR) and first hyperpolarizability data were analyzed for the free species and inclusion compound, pp‐PT@(αCD–αCD). The semiconducting property of the included pp‐PT was not substantially affected on inclusion, with the energy gap increasing by only 10% after interaction with αCD–αCD. On the other hand, the nonlinear optical (NLO) response was significantly decreased, with the first hyperpolarizability, β, predicted to be just more than 60% lower for the [2]rotaxane than for free pp‐PT, but still having considerable magnitude. This was explained by the two‐state model based on the charge‐transfer contribution to the electronic transitions. The sensitivity of electronic spectra might also be useful for the inclusion complex characterization. The IR spectrum was slightly sensitive to the host–guest interaction and the calculated ¹³C NMR and ¹H NMR chemical shifts for the pp‐PT guest showed appreciable variations of 5–10 and 1–1.5 ppm, respectively, and so can be used for the characterization of inclusion compounds. We concluded that the formation of inclusion complexes with CDs, seems indeed very promising and the use of encapsulating conducting material should be experimentally pursued. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Synthesis, structure and quantum chemical calculations on p-trifluoromethylphenyl thioacid amide

The title compound of p-trifluoromethylphenyl thioacid amide has been synthesized in one step and characterized by elemental analysis, UV and X-ray single crystal diffraction. Ab initio calculations indicate that both HF/6-311G^** and B3LYP/6-311G^** methods can reproduce the title compound well. Electronic absorption spectra calculated by the time-dependent density functional theory (TD-DFT) show that the two absorption bands are mainly derived from the contribution of bands π → π^*. Thermodynamic properties of the title compound have been predicted based on the optimized structure. The calculation of the second order optical nonlinearity also has been carried out, and the molecular hyperpolarizability is 2.31770 × 10⁻³⁰ esu.