Third-order Nonlinear Optical Polarizabilities Research Articles

Designing the electron push-pull chromophores through the joining of triphenylamine and triphenylborane for efficient nonlinear optical and photovoltaic properties

The benzoxadiazole class of organic compounds demonstrates exceptional versatility, particularly in the realm of nonlinear optical (NLO) materials, where their unique properties find impactful applications. In the present study, we have focused on systematically designed six benzoxadiazole (BDZ) derivatives named as BDZ-1 to BDZ-6 by using 2,3,1-benzoxadiazole as a central core/π-spacer between the donor and acceptor. Triphenylamine and triphenylborane are used as donor and acceptor in all derivatives with addition of nitro and methoxy group as substitutions. B3LYP/6-311G* method of density functional theory (DFT) is employed for optimization of purposed systems while M06/6-311G* is used to check the NLO properties. The isotropic polarizability (αiso) and anisotropic polarizability (αaniso) of BDZ-6, were found to be 110.1 × 10−24 esu and 106.3 × 10−24 esu, respectively. Among our designed compounds, the BDZ-6 exhibits the highest third-order NLO polarizability, which was found to be 5954.8 × 10−36 esu corresponding to lowest transition energy of 2.00 eV. Additionally, frontier molecular orbitals (FMOs), molecular electrostatic potential maps (MEPs), electron difference density maps (EDD) and UV–Vis analysis were performed. BDZ-6 shows minimum energy gap of 2.24 eV, while it shows maximum absorption at 620 nm. The density of states (DOS) analysis reveals distinct electronic contributions of various fragments in the formation of HOMO and LUMO orbitals resulting in efficient intramolecular charge transfer (ICT). Photovoltaic findings revealed that BDZ-4 have maximum open circuit voltage of 1.70 eV with minimum dye regeneration value (0.30 eV). Our findings shed light on the design and development of novel NLO materials with BDZ derivatives.

Acid catalyzed one-pot approach towards the synthesis of curcuminoid systems: unsymmetrical diarylidene cycloalkanones, exploration of their single crystals, optical and nonlinear optical properties.

In the present study crystalline unsymmetrical diarylidene ketone derivatives BNTP and BDBC have been prepared by two sequential acid catalyzed aldol condensation reactions in a one pot manner. The crystal structures of both compounds were confirmed by single crystal X-ray diffraction analysis which revealed the presence of H-bonding interactions of type C-H⋯O, along with weak C-H⋯π and weak π⋯π stacking interactions that are involved in the crystal stabilization of both organic compounds. Hirshfeld surface analysis is carried out for the broad investigation of the intermolecular interactions in both compounds. The quantum chemical investigation was performed on the optimized molecular geometries of BNTP and BDBC to calculate optical and nonlinear optical (NLO) properties. The density functional theory (DFT) study showed that the third-order NLO polarizabilities of compounds BNTP and BDBC are found to be 226.45 × 10-36 esu and 238.72 × 10-36 esu, respectively, which indicates noticeable good NLO response properties. Additionally, the BNTP and BDBC molecules also showed the HOMO-LUMO orbital gaps of 5.96 eV and 6.06 eV, respectively. Furthermore, the computation of UV-visible spectra of the titled compounds indicated a limited and/or no absorption above the 400 nm region, directing a good transparency and NLO property trade-off for both synthesized compounds that may play a significant contribution in the future for optoelectronic technologies.

Insights into the nonlinear optical (NLO) response of pure Aum (2 ≥ m ≤ 7) and copper-doped Au m -xCu x clusters.

A series of small pure Aum (2 ≥ m ≤ 7) and copper-doped Aum−xCux clusters was evaluated by density functional theory (DFT) at the CAM-B3LYP/LANL2DZ level for their geometric, electronic, and nonlinear optical (NLO) properties. The charge transfer for the Au cluster significantly improved by reducing the HOMO–LUMO energy gap from 3.67 eV to 0.91 eV after doping with Cu atoms. The doping of Cu also showed noteworthy impacts on other optical and NLO properties, including a decrease in the excitation energy and increase in the dipole moment and oscillator strength. Furthermore, changes in the linear isotropic and anisotropic polarizabilities (αiso and αaniso) and first and second NLO hyperpolarizabilities (βstatic, γstatic) were also observed in the pure and Cu-doped clusters, which enhanced the NLO response. The nonlinear optical properties of the clusters were evaluated by calculating the static and frequency dependent second- and third-order NLO polarizabilities at 1064 nm wavelength. Among all the doped structures, the Au3Cu1 cluster showed the largest static first hyperpolarizability of β(total) = 4.73 × 103 au, while the Au1Cu6 cluster showed frequency dependent first hyperpolarizability of β(−2w;w,w) = 1.26 × 106 au. Besides this, large static and frequency-dependent second hyperpolarizability values of 6.30 × 105 au and 1.05 × 10 au were exhibited by Cu7 and Au1Cu6, respectively. This study offers an effective approach to design high-performance NLO materials utilizing mixed metal clusters which might have broad applications in the fields of optoelectronics and electronics.

Chemically Modified Quinoidal Oligothiophenes for Enhanced Linear and Third-Order Nonlinear Optical Properties.

In the present investigation, quantum chemical calculations have been performed in a systematic way to explore the optoelectronic, charge transfer, and nonlinear optical (NLO) properties of different bis(dicyanomethylene) end-functionalized quinoidal oligothiophenes. The effect of different conformations (linking modes of thiophene rings) on conformational, optoelectronic, and NLO properties are studied from the best-performed dimer to octamer. The optical and NLO properties of all the selected systems (1–7) are calculated by means of density functional theory (DFT) methods. Among all the designed compounds, the largest linear isotropic (αiso) polarizability value of 603.1 × 10–24 esu is shown by compound 7 which is ∼12, ∼16, ∼9, ∼11, ∼10, and ∼4 times larger as compared to compounds 1–6, respectively. A relative investigation is performed considering the expansion in third-order NLO polarizability as a function of size and conformational modes. Among all the investigated systems, system 7 shows the highest value of static second hyperpolarizability ⟨γ⟩ with an amplitude of 7607 × 10–36 esu at the M06/6-311G** level of theory, which is ∼521, ∼505, ∼38, ∼884, ∼185, and ∼15 times more than that of compounds 1–6, respectively. The extensively larger ⟨γ⟩ amplitude of compound 7 with higher oscillator strength and lower transition energy indicates that NLO properties are remarkably dependent upon linking modes of thiophene rings and its chain length. Furthermore, to trace the origin of higher nonlinearities, TD-DFT calculations are also performed at the same TD-M06/6-311G** level of theory. Additionally, a comprehensive understanding of the effect of structure/property relationship on the NLO polarizabilities of these investigated quinoidal oligothiophenes is obtained through the inspection of Frontier molecular orbitals, the density of states (TDOS and PDOS), and molecular electrostatic potential diagrams including the transition density matrix. Hence, the current examination will not just feature the NLO capability of entitled compounds yet additionally incite the interest of experimentalists to adequately modify the structure of these oligothiophenes for efficient optical and NLO applications.

Experimental and computational study of naphthalimide derivatives: Synthesis, optical, nonlinear optical and antiviral properties

The nonlinear optical (NLO) and antiviral properties of naphthalimide Schiff base compounds (5a–c) were experimentally and computationally investigated. The synthesized compounds (5a–c) were successfully characterized via UV–Vis, FTIR, 1H NMR, fluorescence spectroscopy, and elemental analysis. The calculated average third-order NLO polarizabilities (˂γ˃) of 5a, 5b, and 5c were found to be 5, 9, and 21 times greater than the ˂γ˃ amplitude of p-NA, respectively. The computed results revealed the potential of the synthesized compounds for NLO applications. Additionally, molecular docking studies of the synthesized compounds with two crucial SARS-CoV-2 proteins were performed to examine their biochemical properties. Compound 5c exhibited a higher binding affinity with the spike protein compared to that with Mᴾᴿᴼ. The results obtained herein indicate the potential of the synthesized naphthalimide derivatives for optoelectronic and drug design applications.

Exploring the twisted molecular configurations for tuning their optical and nonlinear optical response properties: A quantum chemical approach

Unlike the previous several investigations on planar donor-π-acceptor chromophores, the present investigation highlights the importance of twisted molecular configurations to effectively tune the optical and nonlinear optical (NLO) response properties. A variety of substitutions are made to design several twisted molecular compounds (1–7). These compounds are designed using pyrenyl and naphthalimide moieties, which are twisted with each other in their molecular configurations. The calculated versus experimental highest intensity absorption energy peaks (3.482 V. 3.444 eV) and experimental ionization potentials (6.07 V. 5.93 eV) of parent compound 1 reproduced reasonably well at M06/6-311G∗∗ methodology. The twisted chromophores show significantly larger amplitudes of third-order NLO polarizabilities (<γ>), which are found to be as large as 778.31 × 10−36 esu for compound 7 at the M06/6-311G∗∗ methodology. The <γ> amplitudes were also compared with planar donor-π-acceptor prototype para-nitroaniline (p-NA) molecule to provide the semi-quantitative assessment. For instance, the <γ> amplitudes of all compounds are about ∼7–∼39 times bigger from the amplitude of p-NA at the same computational level. The origin of larger amplitudes has been traced though three-level model using the TD-DFT results. The larger oscillator strengths, lower transitions energies and larger change between the electronic dipole moment between the ground and the excited states. We believe the present study will not only put these compounds under the spotlight of material science but also provide structure-property relationships in designed compounds.

An efficient and eco-friendly synthesis, computational assay and antimicrobial evaluation of some novel diastereoselective monocyclic cis-β-lactams

This paper outlines the efficient and eco-friendly synthesis of twenty monocyclic cis-β-lactam derivatives, their spectral analysis, X-ray crystallographic study, computational analysis and antimicrobial activity assay. This is the first time that, 2-methoxy carbonyl DCPN has been used as an activator of acid to generate in situ ketene in synthesis of β-lactams. The synthesis of β-lactam derivatives was completely diastereoselective leading to the formation of cis-stereoisomers exclusively. All these novel cis-β-lactam derivatives were fully characterized by FT-IR, 1H NMR, 13C NMR, HRMS, CHNS and X-ray crystallography study. we use quantum chemical analysis on selected derivatives from both the series to explore their potential optical and nonlinear optical (NLO) properties by calculating their absorption energies and third-order NLO polarizability, respectively. The third-order NLO polarizability values for derivatives 5ad and 5bd (with NO2 fragments) are found to be as large as 205.05 × 10−36 and 203.88 × 10−36 esu, respectively, which are about 10 times larger than that of p-NA (a prototype NLO molecule). The calculation of frontier molecular orbitals (FMOs) and molecular electrostatic potential (MEPs) maps indicates the intramolecular charge process as origin of larger NLO amplitudes. Additionally, all this novel compound was also evaluated for their antimicrobial activities against certain strains of bacteria and fungi. These derivatives displayed, comparatively good to moderate activity against selected microbial strains. Thus, it is believed that the present newly synthesized monocyclic cis-β-lactam derivatives are multifunctional in nature and prove to be very important in material science and chemistry.

Synthesis, characterizations, crystal structures, and theoretical studies of copper(II) and nickel(II) coordination complexes

In the present study, we report synthesis, characterization, structural and theoretical studies of two copper(II) complexes, [Cu(py)2(L1)2] (1) and [Cu(phen)(Ac)2-Cu2(Ac)4]n (2), and a nickel(II) complex, [Ni(bipy)(L)(Ac)] (3), where py = pyridine, L1 = 3,5-dichloro-2-hydroxybenzaldehyde, phen = 1,10-phenanthroline, Ac = acetate ion, bipy = 2,2’-bipyridine and HL = 4-bromo-2-(Z)-(naphthalene-2-ylimino)methyl) phenol. The new complexes were fully characterized using microanalysis, FAB-mas (m/z), FT-IR, UV-Vis and fluorescence spectra, X-band EPR spectroscopy and then by single crystal X-ray diffraction studies. X-ray studies of 1 and 3 revealed distorted octahedral geometries. Complex 2 is a coordination polymer built by an octahedral copper unit Cu(phen)(Ac)2 alternating with paddle wheel species Cu2(Ac)4, located on a crystallographic center of symmetry, where an acetate anion bridges the two crystallographic independent copper ions. The fluorescence intensities and quantum yields of 1 and 2 were found to be more compared to 3. The preliminary tests in the potential application for theoretical biological activities of compounds have also been studied. Furthermore, we also performed quantum chemical calculations to get insights into the structure-property relationships of the synthesized complexes. The quantum chemical calculations were used for theoretical calculations of linear polarizability and third-order nonlinear optical polarizability (γ) for 1, 2 and 3. Besides this, the theoretical calculations, including the analysis of frontier molecular orbitals and electrostatic potential diagrams, are used to highlight the theoretical aspects of metal to ligand charge transfer (MLCT) processes in the studied complexes.

Synthesis, characterization, Hirshfeld surface analysis and computational studies of 1-methylpiperazine-1,4-diium bis(hydrogen oxalate): [C5H14N2](HC2O4)2

A new organic,1-methylpiperazine-1,4-diium bis(hydrogen oxalate) (compound 1) has been synthesized at room temperature. This compound was subject to various characterization studies such as elemental analysis, powder X-ray diffraction, FTIR, UV–Vis and NMR spectroscopy. The structure of the crystal was confirmed by powder X-ray diffraction analysis. The 13C CP-MASNMR spectrum confirms the results predicted by X-ray diffraction. The Hirshfeld surface analysis and fingerprint plot of the compound has been presented to explore the nature of non-covalent interactions and their relative contributions in building the solid-state architecture. Furthermore, the density functional theory (DFT) methods were used to explore the optical and nonlinear optical (NLO) properties of compound 1. The calculated isotropic (αiso) and anisotropic (αaniso) linear polarizabilities are found to be28.42 × 10−24 esu and 4.81 × 10−24 esu, respectively. While the average third-order NLO polarizability <γ>of compound 1 is found to be 40.64 × 10−36 esu at M06/6-31 + G∗ level of theory. A comparison of <γ> amplitude of the studied compound with a prototype NLO molecule of para-Nitroaniline (7.41 × 10−36 esu) showed that <γ> amplitude of compound 1 is ∼5 times larger as compared to that of p-NA. Moreover, the frontier molecular orbitals, molecular electrostatic potential maps are drawn to get several structure-property insights for compound 1.

Exploring the potential of novel transition metal complexes derived from ONO donor type ligand: a quantum chemical study.

In the present quantum chemical investigation, we predict several novel transition metal complexes which are designed using tridentate ONO donor type Schiff base ligand (2-((E)-((Z)-4-hydroxypent-3-en-2-ylidene) amino) phenol). The stable molecular geometries of newly designed metal complexes are obtained using density functional theory (DFT) methods. Several properties including geometrical parameters, energies of frontier molecular orbitals (FMOs), and interaction energies are calculated for optimized metal complexes. The more negative interaction energies illustrate more susceptibilities of the reaction of metal cations with ligand. The charge transfers from ligand to metals are observed in the d7 and d8 metal complexes while it is seen as backdonation of charge from metal to ligand in the d10 complexes. The quantum chemical characterizations are performed for calculating UV-visible spectra and IR frequencies for all the designed metal complexes. All designed metal complexes show multiple absorption peaks in UV region ranging from 184 to 376nm, which are related to metal to ligand and ligand to metal charge transfer processes. The IR frequency analysis shows that the -C=N- stretching frequency of ligand in the region of 1650-1580cm-1 is decreased by between 50 and 100cm-1, which may assign the coordination of ligand with metal via nitrogen. Moreover, the investigations of nonlinear optical (NLO) polarizabilities among selected complexes show that these complexes may possess good potential for NLO applications. The most interesting results are found about the third-order NLO polarizabilities (γ||) where the γ|| amplitudes are found to be 60.01 × 10-36, 56.48 × 10-36, 90.04 × 10-36, and 64.57 × 10-36esu for complexes 1, 2, 9, and 10, respectively. Thus, we believe that the present investigation may bring the newly designed metal complexes in the limelight of scientific interest for their practical realization in optical and nonlinear optical applications. Graphical abstract Several novel transition metal complexes are designed using tridentate ONO donor type Schiff base ligand as efficient NLO materials.

A dual approach to study the synthesis, crystal structure, thermal, optical and nonlinear optical properties of copper (II) malonate complex {(C7H8O2N)2[Cu(C3H2O4)2(H2O)2

A copper (II) malonate complex{[(C7H8O2N)2][Cu(C3H2O4)2(H2O)2]}, 1 has been synthesized and characterized by IR spectroscopy, elemental analysis, TGA/DSC and X-ray crystallography. The X-ray analysis reveals that the complex is anionic species in which copper is coordinated by six oxygen atoms having octahedral coordination geometry that is tetragonally compressed due to Jahn Teller effect. To balance the charge on the complex ion two molecules of 4-carboxybenzeneammonium ions are present as counter ions. The density functional theory methods are applied to explore the linear and nonlinear optical (NLO) properties of 1 using M06 method and 6-31G*/LANL2DZ basis set. The calculated linear molecular polarizability and third-order NLO polarizability of 1 are found to be 43.98 × 10−24 esu and 33.93 × 10−36 esu, respectively, which interestingly better than some standard NLO molecules. To comprehend more understanding, the optical properties from molecule to material levels, we also calculated the optical properties (dielectric function, refractive index and absorption spectrum) in solid-state at bulk-level within periodic boundary conditions (PBC). The calculated optical properties show that the complex 1 possesses static dielectric function and refractive index values of 2.0 and 1.4, respectively. The absorption wavelength from 3 eV to 6 eV illustrates that the complex 1 has strong absorption and larger reflectivity values in UV region, which may be potential for using complex 1 as coating materials. It is credible that the synthesized complex 1 may possess reasonable potential for its application as optical and NLO material.

A dual approach to study the synthesis, crystal structure and nonlinear optical properties of binuclear Pd(II) complex of 3-methyl-5-(trifluoromethyl) pyrazole and its potential quantum chemical analogues

The transition metal complexes are playing the crucial role in advancement of modern chemical science. In the present study, we synthesized the Pd(II) complex [Pd2 (C5H5F3N2)2(C5H4F3N2)2Cl2]·3(C2H6O), 1 with 3-Methyl-5-(trifluoromethyl) pyrazoleligand. The complex 1 has been characterized by IR spectroscopy, elemental analysis and X-ray crystallography. The complex 1 crystallizes in triclinic space group P-1. Moreover, density functional theory (DFT) methods are successfully used not only to study the optical and nonlinear optical (NLO) properties of complex 1 but also to design its potential derivatives with Ni(II) and Pt(II) metals as complexes 2 and 3, respectively. The interaction energies are calculated for optimized complexes that are found to be −400, −524.41 and −504.16 kcal/mol for complexes 1, 2 and 3, respectively. The calculations for third-order nonlinear optical polarizability (γ) show that the average γ amplitudes for compounds 1, 2 and 3 are found to be 79.89 × 10−36, 71.24 × 10−36 and 102.09 × 10−36 esu, respectively. The γ amplitudes of compounds 1, 2 and 3 are about 4 times, 3 times and 5 times larger than that of para-nitroaniline (pNA), which is a prototype NLO molecule, respectively. The calculations of UV–Visible spectra show that the maximum absorption wavelength for complex 3 is around 260 nm with a significantly larger oscillator strength, which is about 4 times larger than the absorption spectra of complexes 1 and 2. The analysis of FMOs shows the ligand to metal intramolecular charge transfer (LMCT) process which might be the reason of larger NLO response properties in complex 3. Additionally, the calculations of global chemical reactivity descriptors indicate that the complexes are thermally and kinetically stable. Thus, we believe the present study will intrigue the scientific community to explore the designed complexes for optical and NLO applications.

Exploring the functional properties of Trimethoxy-Phenylpyridine as efficient optical and nonlinear optical material: A quantum chemical approach

In the current study, the 2,6-diphenyl-4-(3,4,5-trimethoxyphenyl)pyridine (compound 1) has been investigated as proficient material for optoelectronic and nonlinear optical (NLO) applications. In order to highlight the potential at both solid-state (bulk) and molecular levels, different electronic and optical parameters were investigated. The optical and electronic parameters such as refractive index, reflectivity, dielectric function, extinction coefficient, conductivity, electronic band structure, density of states (DOS) of newly reported trimethoxy-phenylpyridine at bulk (solid-state) level have been studied. The band gap is found to be 2.817 eV, which revealed the photon absorption competency has been improved in compound 1 due to narrow band gap and has the capability of containing the absorbed energy. Other calculated optoelectronic properties also revealed that the compound 1 might be better for semiconductor applications. Additionally, the geometric parameters, polarizability (isotropic and anisotropic) and third-order NLO polarizability have been computed at molecular level. For compound 1, its isotropic and anisotropic values are found to be 63.41 × 10−24 esu and 46.22 × 10−24 esu, respectively. The calculated γ amplitude for studied material has been computed as 187.53 × 10−36 esu that is about 25 times bigger than that of the γ amplitude for pNA (a prototype NLO molecule). The third order NLO response for compound 1 has been further tuned through the designing of its further derivatives in the form of compounds 1a, 1b and 1c. Thus, the present study highlights the important optoelectronic and NLO properties of compound 1 and its derivatives.

A comparative analysis of the optical and nonlinear optical properties of cross-shaped chromophores: Quantum chemical approach

Using the first principles calculations, optical and nonlinear optical (NLO) properties are calculated for three crossed shaped chromophores having alike benzoic acid π-conjugated side chains but different central cores i.e. phenyl in 1-Ph, pyrazino[2,3-g]quinoxaline in 2-PyQ and tetrathiafulvalene in 3-TTF. Molecular geometries are effectively reproduced and compared to their experimental crystallographic structures. The third-order NLO polarizability is calculated with three different DFT functionals including M06, PBE0 and B3LYP using 6-311G* basis set. Our calculated third-order NLO polarizability amplitudes and their comparison to those of standard and contemporary NLO chromophores indicate that all the three compounds have remarkably larger NLO response. The γ amplitudes of compounds 1-Ph, 2-PyQ and 3-TTF are 429.6×10−36, 1871.7×10−36 and 967.5×10−36 esu, respectively, at M06/6-311G* level of theory. Interestingly, in present investigation the γ amplitude of the best-studied NLO compound 2-PyQ is 257 times larger than that of para nitroaniline (7.279×10−36 esu) at the same M06/6-311G* level of theory. The TD-DFT calculations are used to trace the origin of larger NLO response. Additionally, total and partial densities of states are calculated to compare the effect and contributions of central cores in all adopted compounds. Thus, the present investigation will not only highlight the NLO potential of entitled compounds but also provoke the interest of experimentalists to effectively modify the central cores for such other applications.

Preparation of Two Carbazole Derivatives and its Third-Order Nonlinear Optical Properties

Carbazole derivative is one sort of important nonlinear optical materials. In this work, new symmetric-type D-π-D carbazole derivatives, 3, 6 - di- substituted carbazole chromophores with two styryl bridges of the two-dimensional conjugated D-π-D system were synthesized via Witting reaction and characterized by IR, NMR and MS. The third-order nonlinear optical properties of the material were investigated using single-beam Z-scan technique with Sapphire femtosecond laser pulses at 800nm, repetition rate of 1 KHz and pulse width of 140fs. The results of Z-scan with and without an aperture showed that larger third-order nonlinear optical polarizabilities γ can be readily obtained in such carbazole chromophores because of the incorporation with two styryl bridges, increasing of conformational planarity and molecular conjugation length.

Theoretical study on photophysical property of C60M(CO)5 (M=Cr, Mo and W)

Configurations of three η2 models of transition-metal [60]fullerene derivatives C60M(CO)5 (M=Cr, Mo and W) have been optimized at B3LYP/LanL2DZ level. On the basis of the optimized geometrical structures, their electronic spectra and the frequency dependence of third-order nonlinear optical polarizabilities γ in different optical processes of third-harmonic generation (THG), electric-field-induced second-harmonic generation (EFISHG) and degenerate four-wave mixing (DFWM) are calculated by using TDB3LYP model based on LanL2DZ level coupled with the SOS (sum-over-state) method. The obtained results show that their electronic spectra have a red shift compared with that of [60]fullerene and different transition-metal functional groups added to C60 cage may result in different spectrum properties. For the three studied species, (η2-C60)Mo(CO)5 has the largest third-order nonlinear optical polarizability.

SIZE EFFECT OF ENCASED ATOM ON ABSORPTION AND NONLINEAR OPTICAL PROPERTIES OF EMBEDDED METALLOFULLERENES M@C82 (M = Sc, Y, La)

The linear absorption spectra and third-order nonlinear optical properties of M@ C 82 (M = Sc , Y , La ) nanostructural materials, whose configurations were optimized at the unrestricted open shell UB3LYP level, are simulated by the sum-over-states combined with the time-dependent UB3LYP methods. The obtained results show that the electronic absorption bands have redshifts, and the values of third-order nonlinear optical polarizabilities and two-photon absorption cross sections increase for M@ C 82 fullerenes (M = Sc , Y , La ) as the atomic radius of encased metal M increase in the order of Sc → Y → La . It is indicated that the electron-donating ability from the encased M atom to cage C 82 decreases or the electron-accepting ability from C 82 to M atom increases as the atomic radius of M increases, which results in third-order nonlinear optical response enhancement in the order of Sc @ C 82 &lt; Y @ C 82 &lt; La @ C 82. This gives a clue to design the nanostructural materials of encased fullerenes having a large nonlinear optical response.

SOS∥TDDFT study on the dynamic third-order nonlinear optical properties of aniline oligomers based on the optimized configurations

In this paper, we employ the sum-over-states formula to calculate the dynamic third-order nonlinear optical polarizabilities of three optical processes, third-harmonic generation, electric-field-induced second-harmonic generation, and degenerate four-wave mixing, at the ground state of aniline oligomers. The ground state configurations of these compounds are obtained by the geometrical optimizations based on the B3LYP/6-31G** level. The transition moment elements and the transition energies are obtained by using the time-dependent density functional theory at the B3LYP/6-31G* level. The calculated results show that the third-order polarizability 〈 γ〉 at the ground singlet state is increasing with the increase of repeat units number N of aniline oligomers and it approaches saturation at chain length around N=7–8.

Theoretical studies of third-order nonlinear optical response for B 12N 12, B 24N 24 and B 36N 36 clusters

In this paper, we have calculated the third-order nonlinear optical polarizabilities corresponding to three optical processes: third-harmonic generation (THG), electric-field-induced second-harmonic generation (EFISHG) and degenerate four-wave mixing (DFWM) for B 12N 12, B 24N 24 and B 36N 36 clusters. The calculations have been performed by employing ab initio time-dependent density functional theory combined with sum-over-states method (SOS//TDDFT). We obtained the similar dynamic behavior of third-order NLO polarizabilities for three BN clusters. At input photon energy below 1.25 eV, the resonance enhancements of response haven't occurred. This is due to the fact that the calculated BN clusters have the large transition energy. B 24N 24 cluster has the larger transition dipole moments and the third-order polarizabilities of B 24N 24 are much larger than those of B 12N 12 and B 36N 36. We also estimate the static third-order optical susceptibility χ (3) for BN fullerene materials from the average static third-order polarizability < γ>. The static χ (3) of B 24N 24 fullerene materials are 1.36×10 −14 esu for three NLO processes.

Modeling of configurations and third-order nonlinear optical properties of methyl silsesquioxanes

Configuration optimizations, excited state properties, and the frequency-dependent third-order nonlinear optical polarizabilities have been investigated on a series of methyl-silsesquioxane (MeT) cages [CH(3)SiO(1.5)](n) (n=4, 6, 8, and 10) using ab initio quantum mechanical methods coupled with the sum-over-states methods. The obtained electronic absorption spectra show a redshift as the cage size increases, and the absorption spectra are assigned as charge transfers from oxygen p type to silicon s type atomic orbitals. The calculated average third-order polarizabilities of <gamma> in the three optical physical processes (third-harmonic generation, the electric-field-induced second-harmonic generation, and degenerate four-wave mixing) have wide nonresonance regions. For all the considered species, the values of gamma decrease in the order of [MeT](4)>[MeT](8)(C(2v))=[MeT](10)>[MeT](6)>[MeT](8)(O(h)).