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.     

Ab initio CPHF calculations of the static polarizability and second hyperpolarizability of small molecules: Comparisons between standard and moderately large basis sets augmented with diffuse functions

Static polarizability and second hyperpolarizability have been calculated for a number of small molecules? CO₂, OCS, CS₂, C₂H₂, C₂H₆, C₃H₈, cyclo-C₃H₆, C₃H₄, C₃H₆, SiH₄, Si₂H₆? in the framework of the coupled-perturbed Hartree-Fock (CPHF ) theory. The linear and nonlinear coefficients have been calculated with standard Gaussian basis sets and 3-21G bases moderately enlarged with diffuse functions. It is shown that the parallel component of the polarizability saturates rapidly, which suggests that a 3-21G basis containing s and p diffuse functions is sufficient to reproduce α_zz. For the α_xx and α_yy components, a 3-21G basis with s, p, and d diffuse functions is required. In general, the concordance between α computed with this basis set and the experimental static polarizability is at least of the order of 80%. On the contrary, the computation of the second hyperpolarizability with the same basis set for CO₂, CS₂, and C₂H₂ gives values that are 30% too low, compared to the experimental value. Better results are observed for ethane, propane, and cyclopropane for which the error is lower than 50%. The better agreement observed for the saturated compounds can probably be explained by their saturated character.     

Structural,electrical and optical properties of Lin@C20 (n = 1–6) nanoclusters

The current research was undertaken to investigate the structural, electrical, and optical properties of C₂₀ fullerene decorated with different numbers of lithium (Li) atoms on its surface. The stability of the structure increased as the number of lithium atoms increased. Increasing the number of lithium atoms around C₂₀ from one to four slightly increased the E_g (energy gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital). Increasing the number to five or six narrowed the E_g. The electrical properties such as ionization potential (I), electron affinity (A), chemical potential (μ), global hardness (η), global softness (γ), global electrophilicity (ω), and electronegativity (χ) were also calculated. The polarizability (α) and first hyperpolarizability (β₀), which correspond to the linear optical and nonlinear optical properties, respectively, were also calculated. An intense increase in β₀ was recorded as the effect of five Li atoms adsorbed onto the C₂₀ surface. The results of this study can be used to design and fabricate nanomaterials with adjustable electro-optical properties.     

Free-electron model for hyperpolarizability of the π-electron system in benzene

The hyperpolarizabilities of benzene have been calculated using a free-electron model for the π-electron system. The first hyperpolarizability is identically zero. For the second hyperpolarizability only the components γ_zzzz; γ_xxxx; γ_yyyy; γ_zzxx; γ_zzyy; γ_xxyy are non-zero. Some of these γ quantities show dispersion near the characteristic absorption band of the benzene molecule. The polarizability α of the π-electron system also shows similer dispersion.     

Computational investigation of solvent effect on the structure,spectroscopic properties (13C, 1H NMR and IR,UV), NLO properties and HOMO–LUMO analysis of Ru(NHC)2Cl2(=CH-p-C6H5) complex

This paper presents, a theoretical study of the structural, ¹³C and ¹H NMR chemical shifts, electronic transitions, vibrational analysis, and first hyperpolarizability for Ru(NHC)₂Cl₂(=CH-p-C₆H₅) complex in gas phase and different solvents. The solvent effect on structural parameters, frontier orbital energies, Ru=C_carbene and C_carbene-H stretching frequencies, and chemical shifts of C_carbene, C_NHC and H_carbene of complex was explored based on Polarizable Continuum Model (PCM). The wavenumbers of υ(Ru=C_carbene) and υ(C_carbene-H) of complex in different solvents were correlated with the Kirkwood–Bauer–Magat equation (KBM). As well as, the polarizability and the first order hyperpolarizability values of the investigated compound were computed in various solvents.     

两个二茂铁基查尔酮衍生物的合成及超快三阶非线性光学响应

合成两种新颖的含二茂铁基团的查尔酮衍生物：1-二茂铁基-3-(4-叔丁基苯基)丙烯酮(a)和1-二茂铁基-3-联苯基丙烯酮(b),经₁H NMR、₁₃C NMR、HR-MS对其结构进行了表征;测定了该两化合物的热力学性质;采用量子化学方法计算了它们的分子轨道能量和极化率,给出了轨道电子云图;采用紫外-可见吸收光谱和Z-扫描技术测定了其线性和非线性光学性质。结果表明：与原料相比,化合物a和b的紫外吸收明显增加,且b的吸收波长更长;化合物a和b均存在分子内电荷转移现象,表现出超快三阶非线性光学响应。     

Synthesis,crystal structure and photophysical properties of 1,4‐bis(1,3‐diazaazulen‐2‐yl)benzene: a new π building block

A dimerized 1,3‐diazaazulene derivative, namely 1,4‐bis(1,3‐diazaazulen‐2‐yl)benzene [or 2,2′‐(1,4‐phenylene)bis(1,3‐diazaazulene)], C₂₂H₁₄N₄, (I), has been synthesized successfully through the condensation reaction between 2‐methoxytropone and benzene‐1,4‐dicarboximidamide hydrochloride, and was characterized by ¹H NMR and ¹³C NMR spectroscopies, and ESI–MS. X‐ray diffraction analysis reveals that (I) has a nearly planar structure with good π‐electron delocalization, indicating that it might serve as a π building block. The crystal belongs to the monoclinic system. One‐dimensional chains were formed along the a axis through π–π interactions and adjacent chains are stabilized by C—H…N interactions, forming a three‐dimensional architecture. The solid emission of (I) in the crystalline form exhibited a 170 nm red shift compared with that in the solution state. The observed optical bandgap for (I) is 3.22 eV and a cyclic voltammetry experiment confirmed the energy levels of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). The calculated bandgap for (I) is 3.37 eV, which is very close to the experimental result. In addition, the polarizability and hyperpolarizability of (I) were appraised for its further application in second‐order nonlinear optical materials.     

Solubilization of benzene and cyclohexane in aqueous solutions of hexadecyltrimethylammonium bromide: a deuterium magnetic resonance study

Quadrupole splittings in the ²H NMR spectrum from C₆D₆ and C₆D₁₂ solubilized in aqueous solutions of hexadecyltrimethylammonium bromide (CTAB) have been observed in the hexagonal liquid crystalline phase (E) as well as in the concentrated micellar phase (L₁). The order parameter that is obtained for solubilized C₆D₆ is more than two orders of magnitude greater than previously reported from measurements of linear dichroism spectra. Various possibilities for the nature of the solubilization sites are discussed.     

Electronic structures and nonlinear optical properties of highly deformed halofullerenes C3v C60F18 and D3d C60Cl30

Electronic structures and nonlinear optical properties of two highly deformed halofullerenes C_3v C₆₀F₁₈ and D_3d C₆₀Cl₃₀ have been systematically studied by means of density functional theory. The large energy gaps (3.62 and 2.61 eV) between the highest occupied and lowest unoccupied molecular orbitals (HOMOs and LUMOs) and the strong aromatic character (with nucleus‐independent chemical shifts varying from ?15.08 to ?23.71 ppm) of C₆₀F₁₈ and C₆₀Cl₃₀ indicate their high stabilities. Further investigations of electronic property show that C₆₀F₁₈ and C₆₀Cl₃₀ could be excellent electron acceptors for potential photonic/photovoltaic applications in consequence of their large vertical electron affinities. The density of states and frontier molecular orbitals are also calculated, which present that HOMOs and LUMOs are mainly distributed in the tortoise shell subunit of C₆₀F₁₈ and the aromatic [18] trannulene ring of C₆₀Cl₃₀, and the influence from halogen atoms is secondary. In addition, the static linear polarizability and second‐order hyperpolarizability of C₆₀F₁₈ and C₆₀Cl₃₀ are calculated using finite‐field approach. The values of and for C₆₀F₁₈ and C₆₀Cl₃₀ molecules are significantly larger than those of C₆₀ because of their lower symmetric structures and high delocalization of π electrons. © 2010 Wiley Periodicals, Inc. J Comput Chem 2010     

M···π-conjugated complexes: simple materials with dramatic NLO features (M = Li,Na, K,and π = butadiene,cyclobutadiene, hexatriene,benzene)

Theoretical investigation of linear and nonlinear optical (NLO) properties in simple complexes consist of alkali metals and π-conjugated systems have been studied at MP2/6-311++G(2d,2p) computational level. Lithium, sodium, and potassium as alkali metals were chosen for interaction with some non-aromatic, aromatic and anti-aromatic systems. For better comparison of results, the π-systems were chosen with the same carbon number: butadiene as a non-aromatic in comparison with cyclobutadiene as an anti-aromatic and hexatriene as a non-aromatic in comparison with benzene as an aromatic system. Results revealed that gap energy of studied π-systems was decreased under the interacting with alkali metals. Furthermore all designed complexes were shown very good results in average polarizability (α) and first hyperpolarizability (β ₀) parameters. So these very simple dimer complexes could be introduced as promising innovative nonlinear optical materials.     

Calculations on the Nonlinear Second—Order Optical Polarizabilities for Series of Donor—C60 Molecules

IntroductionThebulkpreparation1ofC6 0 andC70 clusters(fullerenes)hasstimulatedawidevarietyofexperimentalandtheoreticalstudies .2 5Wehavesuccessfullyexaminedthestructures ,UV visiblespectraandthenonlinearthird orderopticalpolarizabilities (γ)ofC6 0 andC70 .6 ,7Byin troductionofsubstituents ,thecentrosymmetriesofC6 0 andC70 arebrokenandthesecond orderopticalnonlinearitiesareinduced .ThechargeseparationinsubstitutedC6 0whichleadstoenhancementofβvaluehasalsobeendis cussed .5Inrecentyears ,a…     

Nonlinear optical properties of benzofurobenzofurans

The geometric structure, dipole moment, μ, linear polarizability, α and first hyperpolarizability, β, of symmetrically substituted amino-and cyanobenzofurobenzofurans and dihydrobenzofurobenzofurans have been calculated by ab initio coupled perturbed Hartree-Fock methods. Singlet electronic transition energies and excited state dipole moments have been calculated by the AMI program. The benzofurobenzofuran derivatives are planar, while dihydrobenzofurobenzofuran derivatives have a V-shaped form, in agreement with experimental X-ray data. The molecular structure is rather unaffected by substitution. The linear polarizability is weakly sensitive to the substituent and substituent position, while β value changes over about 1 order of magnitude. Although both series of compounds have relatively modest hyperpolarizability, reaching ca. 60% β of para-nitroaniline, they have good properties for second harmonic generation devices: transparency in the visible spectral region, thermal stability and conformational rigidity.     

Calculations of induced moments in large molecules I. Polarizabilities and second hyperpolarizabilities in some alkanes

We report the results of coupled Hartree-Fock computations for the average polarizability, , and hyperpolarizability, , of CH₄, C₂H₆, C₃H₆ and C₃H₈. The Hamiltonian matrices are constructed from an extended CNDO model. Small as well as large basis sets were tested. Agreement with available experimental values is within 13% for and 31% for .     

Effect of the formation of silver nano‐binuclear complex on the refinement of cytotoxic and antibacterial potency of coumarin Schiff base: Spectroscopy,thermal, X‐ray diffraction analyses and density functional theory calculations

A new Schiff base (SCH) was prepared using 8‐acetyl‐7‐hydroxy‐4‐methylcoumarin and sulfaclozine. Its silver complex was also synthesized. These compounds were subjected to elemental and spectral analyses. The silver complex was also subjected to thermogravimetric analysis, molar conductance measurements, scanning electron microscopy, energy‐dispersive X‐ray analysis and X‐ray diffraction measurements. The formula of the complex was determined as [(Ag₂SCH(NO₃)₂]. The molar conductance indicates its non‐electrolyte character. The electronic structure and nonlinear optical parameters of SCH and its complex were investigated theoretically at the B3LYP/GENECP level. The geometry of the studied complex is non‐planar as indicated from the dihedral angles between central Ag metal ion and coordinated centres of SCH. Density functional theory calculations were also carried out to calculate the global properties of hardness, global softness and electronegativity. The calculated energy gap between HOMO and LUMO energies shows that charge transfer occurs within the studied complex. The total static dipole moment, the mean polarizability, the anisotropy of the polarizability and the mean first‐order hyperpolarizability were calculated and compared with those of urea as a reference material. The results of the mean first‐order hyperpolarizability showed that SCH and its silver complex are excellent candidates as nonlinear optical materials. The compounds were screened for their antimicrobial effect against various species of bacteria and fungi. Their anticancer activities were evaluated in vitro against the human cancer cell line MCF‐7 (human breast adenocarcinoma).     

Nonlinear optical properties of the M @ C60 endohedrals (M = Cs,Li, and Na)

The Hartree–Fock (HF) approximation and the Single‐excitation configuration interaction (single‐CI) method are used, with sum‐over‐state (SOS) approach, in order to determine the static (ω = 0) and frequency dependent linear and non linear optical (NLO) properties of the M @ C₆₀ endohedrals (M = Cs, Li, and Na). We discuss the effects of displacement, movement direction, and type of atom on the (hyper) polarizability of the M at C₆₀ endohedrals. A HF‐single‐CI model yields the (hyper) polarizability magnitudes and spectra, which are in agreement with experiment. Our results indicate that the movement of the atom (M) effect on the NLO spectra of M @ C₆₀ endohedrals is dramatic. These results may provide new means to design some new types of NLO materials. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Borazine-based conjugated derivatives: Structural,electronic, and optical properties

The structural characteristics, electronic properties, and nonlinear optical properties of borazine-based conjugated derivatives have been explored at B3LYP/6-311G(d,p) level. The effects of various electron donor and acceptor substituents (H, F, Cl, Br, Me, CF₃, NH₂, OH, COOH, CHO, NO₂) on the structure, polarizability, frontier orbitals, the most intense electronic transition, and hyperpolarizabilities have studied. Calculations show that NO₂-substituted molecules have lowest hardness, the largest isotropic polarizability and anisotropy of polarizability, and first hyperpolarizability.     

Constructing a novel nonlinear optical materials: substituents and heteroatoms in π-π systems effect on the first hyperpolarizability

By doping π-π systems with Li atom, a series of Li@sandwich configuration and Li@T-shaped configuration compounds have been theoretically designed and investigated using density functional theory. It is revealed that energy gaps (E _gap) between highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) of all compounds are in a range of 0.4–0.9 ev. When Li atom is introduced into different sandwich configuration π-π systems (C₆₀-toluene, C₆₀-fluorobenzene, C₆₀-phenol, C₆₀-benzonitrile), Li@C₆₀-benzonitrile exhibits considerable first hyperpolarizability as large as 19,759 au, which is larger by about 18,372–18,664 au than those of other compounds. When Li atom is introduced into different T-shaped configuration π-π systems (C₆₀-pyridine, C₆₀-pyrazine, C₆₀-1, 3, 5-triazine, C₆₀-pyridazine), Li@C₆₀-pyridazine is found to present largest first hyperpolarizability up to 67,945 au in all compounds. All compounds are transparency in the deep ultraviolet spectrum range. We hope that this study could provide a new idea for designing nonlinear optical materials using π-π systems as building blocks.     

Synthesis, molecular conformation, vibrational and electronic transition, isometric chemical shift, polarizability and hyperpolarizability analysis of 3-(4-methoxy-phenyl)-2-(4-nitro-phenyl)-acrylonitrile: a combined experimental and theoretical analysis

This work presents the synthesis and characterization of a novel compound, 3-(4-Methoxy-phenyl)-2-(4-nitro-phenyl)-acrylonitrile (abbreviated as 3-(4MP)-2-(4-NP)-AN, C₁₆H₁₂N₂O₃). The spectroscopic properties of the compound were examined by FT-IR, UV–vis and NMR (¹H and ¹³C) techniques. FT-IR spectrum in solid state was observed in the region 4000–400 cm⁻¹. The UV–vis absorption spectrum of the compound which dissolved in chloroform was recorded in the range of 200–800 nm. The ¹H and ¹³C NMR spectra were recorded in CDCl₃ solution. To determine lowest-energy molecular conformation of the title molecule, the selected torsion angle is varied every 10° and molecular energy profile is calculated from 0° to 360°. The structural and spectroscopic data of the molecule in the ground state were calculated using density functional theory (DFT) employing B3LYP/6-31G(d,p) basis set. The dipole moment, linear polarizability and first hyperpolarizability values were also computed using the same basis set. A study on the electronic properties, such as HOMO and LUMO energies, were performed by time-dependent DFT (TD-DFT) approach. The HOMO and LUMO analysis were used to elucidate information regarding charge transfer within the molecule. The vibrational wavenumbers were calculated and scaled values were compared with experimental FT-IR spectrum. The complete assignments were performed on the basis of the experimental results and total energy distribution (TED) of the vibrational modes, calculated with scaled quantum mechanics (SQM) method. Isotropic chemical shifts were calculated using the gauge-invariant atomic orbital (GIAO) method. Comparison of the calculated frequencies, NMR chemical shifts, absorption wavelengths with the experimental values revealed that DFT and TD-DFT method produce good results. The linear polarizabilities and first hyperpolarizabilities of the studied molecule indicate that the title compound can be used as a good nonlinear optical material. The thermodynamic properties of the studied compound at different temperatures were calculated, revealing the correlations between standard heat capacity, standard entropy, standard enthalpy changes and temperatures.     

Multipole polarizabilities of Ar

The four lowest multipole polarizabilities of Ar have been calculated by using the complete fourth-order many-body perturbation theory approach and a large GTO/CGTO basis set including a number of diffuse and polarization functions. The present results for the dipole polarizability (α =11.23 au), quadrupole polarizability (C= 26.79 au), dipole-quadrupole polarizability (B = -164.3), and the dipole hyperpolarizability (γ =1329 au) are compared with other theoretical data and experimental values.     

A Quantum Chemical Study on the Enormously Large Nonlinear Optical Response of Doped Endohedral Superalkali Na2F and Superhalogens MF4 (M = B,Al) with CNT (C56H16) Cage

In the present communication, the interaction of single-wall carbon nanotubes (SWCNTs) CNT (C56H16) with endohedral doped superhalogens (MF₄:M = B, Al) placed outside of CNT cage and superalkali (Na₂F) placed inside the cage has been studied by using a combination of DFT/B3LYP method and 6–311G(d, p) basis set. The geometry and stability of MF₄@CNT-Li₂F have been studied using optimization parameters, highest occupied molecular orbit (HOMO), lowest unoccupied molecular orbital (LUMO), vibration frequencies, and thermodynamic parameters of absorption reactions. The quantum theory in atoms in molecules (QTAIM) analysis is used to analyze the nature of interactions between MF₄ (M = B, Al) and Na₂F@CNT. Several electronic parameters are computed by using HOMO–LUMO energy. The dipole moment, polarizability, hyperpolarizability, order parameters, anisotropic polarizability, and molar refractivity of MF4@CNT-Li₂F (M = Al, B) are used to calculate the nonlinear optical parameters (MR). The NBO analysis is used to calculate the transfer of charge to stabilized system. The calculated hyperpolarizability of Na₂F@CNT-BF₄/Na₂F@CNT-AlF₄ is nearly 81 times that of reference material urea (40 a.u.). The intramolecular charge transfer (ICT) moment of π electron cloud is responsible for the nonlinear optical behavior of the system.