TDDFT-SOS Studies on the Polarizabilities and Second-order Hyperpolarizabilities of Zn_3O_3 II-VI Semiconductor Clusters

The geometrical structure of semiconductor clusters including Zn3O3 was optimized by the DFT B3LYP method. With the same basis sets, dipole moments, polarizabilities and secondorder hyperpolarizabilities have been calculated and compared with the results obtained by TDDFT B3LYP method combined with sum-over-state （SOS） formula. The calculation results indicate that the dipole moments of the ground state depend on the atom radius and electronegative differences between elements and are their balance point as well. The polarizabilities of the clusters accord with the rule of the corresponding energy transformation from ground to excited state. The results predict an increase of second-order hyperpolarizabilities with increasing the distances between atoms in the clusters as well as a decrease of the polarizabilities and second-order hyperpolarizabilities in the same serial of semiconductor clusters with increasing the dipole moments of the ground states. The changes of dipole moments in ground states are inconsistent with transition moments. Spatial structure, charge transfer and other factors play an important role in composing the transition moments.

Calculations of Hyperpolarizabilities for Para-disubstituted Benzeneswith the QSPR

A quantitative structure-property relationship (QSPR) was made for the prediction of the hyperpolarizabilities(β) ofpara-disubstituted benzenes with the nonlinear optical properties, and the βca12 calculated by this model accorded better with the experimental values (βexpt) compared with theβcall calculated at the CPHF/6-31G*//HF/STO-3G level of theory, especially whenβ was big.

Theoretical Study on First Hyperpolarizabilities of End-Capped Triply Branched Dendrimers

A series of end-capped triply branched dendritic chromophores have been studied by means of density functional theory calculations. It is found that the second order nonlinear optical properties of the end-capped dendrimers are strongly dependent on the mutual orientations of the three chromophores, numbers of caps and the conjugation length of the ehromophores. Large enhancement of the first hyperpolarizability can be obtained when dipole moments of three branches in the dendrimers are highly parallelized.

Heavy Atom Effect on the First Hyperpolarizabilities of Squaric Acid Homologues Studied by Ab Initio and DFT Methods

We have calculated the first hyperpolarizabilities of four squaric acid homologue molecules: 3,4-dithiohydroxy-3-cyclobutene-1,2-dione (OSSQ), 3,4-dithiohydroxy-3-cyclobutene-1, 2-dithione (SSSQ), 3,4-dithiohydroxy-3-cyclobutene-1,2-diselenone (SeSSQ) and 3,4-dithiohydroxy- 3-cyclobutene-1,2-ditellurone (TeSSQ). The correlation effect was investigated at the second-order Mller-Plesset (MP2) perturbation and density functional theory (DFT) levels. The frequency disper- sion and solvent effect were considered to compare the theoretical values with the experimental observations. Based on all of these studies, it is worthy to point out that the heavy atom effect dis- covered for furan homologues is an influence on the first hyperpolarizabilities of squaric acid homologues.

Theoretical Studies on the First Hyperpolarizabilities of One-dimensional Donor-bridge-acceptor Chromophores and New Applications of BLA in Determining Molecular First Hyperpolarizabilities

We present a quantum-chemical analysis of the relationship between the bond length alteration （BLA） and the static first hyperpolarizability of a series of one-dimensional （1D） chromophores with donor-bridge-acceptor （D-B-A） structures. The calculated results show that the parameter BLA can be considered as an indicator to evaluate the molecular first hyper- polarizability. Along the direction of molecular ground-state dipole moments, the evolutions of BLA can be classified into three categories： the first is a non-monotonic line, which represents most chromophores; the second is monotonic increasing; and the third, contrarily, is monotonic decreasing. On the whole, the first hyperpolarizabilities of these studied chromophores are the monotonic functions of BLA along the direction of dipole moments. Therefore, the first hyperpolarizability of these 1D chromophores can be preliminarily evaluated in terms of the development of BLA without a rigorous computation. In other words, one can roughly estimate the relative magnitude of the first hyperpolarizability according to the optimized geometry.

Theoretical Studies on the First Hyperpolarizabilities of One-dimensional Donor-bridge-acceptor Chromophores

The ground-state dipole moments and second-order nonlinear optical （NLO） properties of a series of one-dimensional （1D） chromophores with donor-bridge-acceptor （D-B-A） structures have been investigated by using the second-order MФller-Plesset （MP2） and density functional theory （DFT） methods with the basis set of 6-31＋G（d）. According to the calculated results, the relationship between the molecular static first hyperpolarizability （βμ） and the directions of electron transition has been summarized. In terms of the sign of βμ, these 1D organic chromophores were classified into two categories： type Ⅰ with negative βμ and type Ⅱ bearing positive βμ. The analyses show that the remarkable difference of the first hyperpolarizabilities between Ⅰ and Ⅱ chromophores is associated mainly with the electrostatic interaction between terminal groups and the transport electrons in excited states. Moreover, different from the popular viewpoint, the obtained results also show that most of this series of 1D D-B-A molecules are more charge-separated in the ground states than in the excited states. As a whole, this theoretical investigation, to some extent, can be considered as a useful reference in designing the NLO chromophores with large first hyperpolarizabilities.

Natural Bond Orbital(NBO)Population Analysis,First Order Hyperpolarizabilities and Thermodynamic Properties of Cyclohexanone

The molecular structure of cyclohexanone was calculated by the B3LYP density functional model with 6-31G(d,p)and 6-311++G(d,p)basis set by Gaussian program.The results from natural bond orbital(NBO)analysis have been analyzed in terms of the hybridization of atoms and the electronic structure of the title molecule.The electron density based local reactivity descriptors such as Fukui functions were calculated.The dipole moment(μ)and polarizability(α),anisotropy polarizability(Δα)and first order hyperpolarizability(βtot)of the molecule have been reported.Thermodynamic properties of the title compound were calculated at different temperatures.

The First Hyperpolarizabilities of Merocarbocyanines

The dot products mu(g)beta(CT) of first hyperpolarizability and ground state dipole moment of two merocarbocyanines were measured experimentally with solvatochromism and compared to the values obtained by AM1/FF calculation. The comparable result was also obtained by the measurement of second harmonic generation (SHG) for LB film of dye II. The mu(g)beta(CT) of dye II is larger than that of the well known NLO chromophore 4-N, N-dimethylamino-4'-nitrostilbene (DANS).

Semiempirical prediction of the hyperpolarizabilities for cyanovinyl-substituted donor-acceptor molecules

We present here a systematically theoretical study on the nonlinearities and their structure-property relationship of cyanovinyl-substituted donor-acceptor molecules by virtue of semiempirical PM3/AM1-FF approach. Good consistency between measured and calculated hyperpolarizabilities is obtained. Results show that conformation has a significant effect on hyperpolarizabilities. The torsion angle change between two conjugated parts of the molecular systems can substantially alter the nonlinearities. The total amount of charge transfer difference from donor to acceptor has been introduced to understand the microscopic nature of the nonlinear optical properties for the title molecules. General guidelines may be sought out in the search of molecules with large values of beta. Some molecules with large molecular hyperpolarizabilities can be predicted by the optimization for the longer pi-electron systems with both acceptor and donor groups.

Hyperpolarizabilities of alkaline-earth metal ions Be^+, Mg^+, and Ca^+

The knowledge of the hyperpolarizabilities of atoms and ions is helpful for the analysis of the high order effects of the frequency shifts in precision spectroscopy experiments. Liu et al. [Phys. Rev. Lett. 114, 223001 （2015）] proposed to establish all-optical trapped ion clocks using laser at the magic wavelength for clock transition. To evaluate the high-order frequency shifts in this new scheme of optical clocks, hyperpolarizabilities are needed, but absent. Using the finite field method based on the B-spline basis set and model potentials, we calculated the electric-field-dependent energy shifts of the ground and low-lying excited states in Be＋, Mg＋, and Ca＋ in the field strength range of 0.0-6×10-5 a.u.. The scalar and tensor polarizabilities （α0, α2） and hyperpolarizabilities （Y0,Y2, 74） were deduced. The results of the hyperpolarizabilities for Be＋ showed good agreement with the values in literature, implying that the present method can be applied for the effective estimation of the atomic hyperpolarizabilities, which are rarely reported but needed in experiments. The feasibility of optical trapping of Ca＋ is discussed, and the contributions of hyperpolarizabilities to the transition frequency shift for Ca＋ in the optical dipole trap are estimated using quasi-electrostatic approximation.

Third-Order Nonlinear Optical Responses of Bis(15-crown-5)-stilbenes Binding to One-or Two-Alkali Metal Cation(Li^(+),Na^(+)and K^(+))

Bis(15-crown-5)-stilbenes containing crown ether parts have been widely used in a variety of chemical applications,such as cation detectors,because of their ability to selectively bind to alkali metal cations,Bis(15-crown-5)-stilbenes and its derivatives with complexation of one-or two-alkali metal cation(Li^(+),Na^(+)and K^(+))have been theoretically investigat-ed by quantum chemistry methods.The coordination of alkali cations results in partial shrinkage of crown ethers,which directly affected natural distribution analysis charges and molecular orbital energy levels.The number of alkali metal ions has significant effects on absorption spectra and mean second hyperpolarizability.When one alkali metal ion was added to the anticonformer of bis(15-crown-5)-stilbene,the absorption spectra were obvious-ly redshifted and the mean second hyperpolarizability values were slightly increased;while two alkali metal ions were added to bis(15-crown-5)-stilbene,the absorption spectra were ob-viously blue shifted and the mean second hyperpolarizability values decreased.On the other hand,as the radius of the alkali ions increased,the mean second hyperpolarizability values of the compounds increased gradually.It is indicated that the mean second hyperpolarizability value is sensitive to the number and radius of the alkali metal cations,thus the third order nonlinear optical response can be used as a signal to detect the number and type of alkali met-al ions.

The Spectroscopic and Electronic Properties of Dimethylpyrazole and Its Derivatives Using the Experimental and Computational Methods

In this paper the spectroscopic and the geometric properties of four ligands with pyrazole unit are studied at both experimental and computational levels.The computational results are perfectly in good agreement with the experimental results especially in terms of the IR,1 H-NMR and 13 C-NMR shifts.The spectroscopic features as well as the computed properties help to establish the successful synthesis of ligands bdmpzm and bdmpza.The theoretical and the experimental IR and Raman significantly help in distinguishing the four ligands.The results show that the Raman spectral is better applicable in characterising the CH3deformation,the C-H,CNN and CCNNout of the ligands but vibrations like N-H in dmpz and O-H,CO in bdmpza are observed to be Raman inactive.A significant variations are observed among the two available*N atoms characterising the bidentate features of bdmpzm,bdmpza and bdcpzm which indicates a possible different affinities for metal coordination.Also the result suggest that bdmpza will be the best starting material for NLO application than other while bdcpzm is predicted to have potential of been a poor coordinating ligand.The computed variations in the properties of*N atoms that are the characteristic features of their power of coordination can be of immense help since these type of ligands have a wide application in transition metal coordination.

Theoretical Investigation of Nonlinear Optical Properties of Organicand Transition Metal Hybrid Azobenzene Dendrimers

In this work, we report a theoretical exploration of the responses of organic azobenzene dendrimers. The polarizabilities, the first and second hyperpolarizabilities of the azobenzene monomers （GO）, and the first, second and third generation （G1, G2 and G3, respectively） are investigated by semi-empirical methods. The calculated results show that the nonlinear optical （NLO） properties of these organic dendrimers are mainly determined by the azobenzene chromospheres. Additionally, the values oft and y increase almost in proportion to the number of chromophores. On the other hand, two types of transition metal hybrid azobenzene dendrimers （core-hybrid and branch-end hybrid according to the sites combined with transition metals） are simulated and discussed in detail in the framework of time-dependent density functional theory （TDDFT）. The calculated results reveal that the NLO responses of these metal dendrimers distinctly varied as a result of altering the charge transfer transition scale and the excitation energies.

NLO response of derivatives of benzene, stilbene and diphenylacetylene：MP2 and DFT calculations

MP2 method and different functionals such as M06-HF, M06-2X, CAM-B3 LYP, PBE0, B3 LYP and M06 L incorporating different XC amounts were used to calculate the static first hyperpolarizabilies β(0) of eight molecules which are derivatives of benzene, stilbene and diphenylacetylene. The values were then compared to the experimental ones. The M06-2X functional was then selected for further calculations. NBO calculations were also performed to define the intramolecular charge transfer in each molecule. TD-DFT calculations were performed taking into account the solvent effect using the IEF-PCM formalism. Some parameters characterizing the vertical transitions such as the wavelength of the maximum absorption λ_(max) were compared to the experimental ones. Finally,solvation Gibbs free enthalpy ΔG_(solv) values have also been examined in order to determine which the specific solvent for a given molecule is.

Influences of adsorptions of some inorganic molecules on electronic, optical, and thermodynamic properties of Mg_(12)O_(12) nanocage: A computational approach

According to density functional theory, we investigate the effects of BF3, BF4, BCI3, A1F3, AICI3, A1Br3, 13eF3, GaF3, GaC13, GaBr3, NO3, BS2, BSO, BO2, F2, PFs, PC15, and ASF5 molecules on the geometric, electronic, linear, and nonlinear optical properties of an Mg12012 nanocage. The thermodynamic stability and feasibility of the adsorption process are investigated by analyzing the free energy. It is shown that the adsorptions of almost all molecules on the Mg12OI2 surface are exothermic. The calculations of the polarizability of these nanoclusters show that among the studied molecules, BeF3 has the largest influence on the polarizability value （a≈315 a.u., the unit a.u. is short for atomic unit）. The static first hyperpolarizability （β0） value is increased in the presence of these superhalogens. This increase is greatest for BeF3 and BF4 of which the highest value of the first hyperpolarizability （βO≈ 5775 a.u.） is related to a BeF3_c（e@Mgl2Ol2） nanocluster. The adsorption position is a key to estimating the value of increasing the first hyperpolarizability.

Nonlinear Optical Properties of Novel C60 Derivatives under Picosecond Laser Excitation

We investigate the third-order nonlinear optical properties of six novel fullerene derivatives under picosecond laser excitation by Z-scan technique. The experimental results reveal that all the derivatives have very large nonlinear absorption coefficient under 532 nm pulses excitation and great third-order nonlinear refraction index under 1064 nm pulses excitation. The molecular second hyperpolarizabilities are obtained from the experimental results.

SYNTHESIS AND CHARACTERIZATION OF A NOVEL STYRYLTHIOPHENE MONOMER AND CORRESPONDING POLYURETHANE FOR NLO MATERIALS

A novel monomer, (trans)-7-[4-N,N-(di-beta-hydroxyethyl) amino-benzene]-ethenyl-3,5-dinitrothiophene (HBDT), was synthesized and characterized. The details of synthesizing the monomer and prepolymer, polyurethane with the monomer covalently incorporated are presented. The prepolymer and polyurethane exhibited good solubility in common organic solvents. Molecular nonlinear optical properties of the monomer (HBDT) substituted thiophene based stilbenes is presented.

Orientation Angle of Molecules at Hexadecane-Water Interface Studied with Total Internal Reflection Second Harmonic Generation

The orientation angle is an important parameter that reflects the structure of molecules at interfaces. In order to obtain this parameter, second order nonlinear spectroscopic techniques including second harmonic generation （SHG） and sum frequency generation-vibrational spec- troscopy （SFG-VS） have been successfully applied through analysis of the nonlinear signal from various polarizations. In some SHG and SFG-VS experiments, total internal reflection （TIR） configuration has been adopted to get enhanced signals. However, the reports on the detailed procedure of the polarization analysis and the calculation of the orientation angle of interracial molecules under TIR configuration are still very few. In this paper, we mea- sured the orientation angles of two molecules at the hexadecane-water interface under TIR and Non-TIR experimental configurations. The results measured from polarization analysis in TIR configuration consist with those obtained from Non-TIR configuration. This work demonstrates the feasibility and accuracy of polarization analysis in the determination of the orientation angle of molecules at the interfaces under TIR-SHG configuration.

Second-order Nonlinearities of CdS Nanoparticles Studied by Hyper-Rayleigh Scattering Technique

A series of CdS nanoparticles with different surfaces were prepared by colloidal chemical method and reverse micelle method. Their second-order nonlinear optical (NLO) properties were experimentally studied in solution by newly developed hyper-Rayleigh scattering (HRS) technique. The results show that 'per particle' first-order hyperpolarizability beta values are sensitive To the synthetic method and the surface chemical modification.

A modeling analysis of molecular orientation at interfaces by polarization-dependent sum frequency generation vibrational spectroscopy

Sum frequency generation(SFG) vibrational spectroscopy has been proven an excellent tool to measure the molecular structures, symmetries and orientations at surfaces/interfaces because of its strong polarization dependence. However, a precise quantitative analysis of SFG spectral intensity and molecular orientation at interfaces must be carefully performed. In this work, we summarized the parameters and factors that are often ignored and illustrated them by evaluating studies of CO adsorption on the(111) facet of platinum(Pt) and palladium(Pd) single crystals at the gas(ultra-high vacuum, UHV)/solid interfaces and methanol(water) adsorption at the air/liquid(solid/liquid) interfaces in the presence of sodium iodide(chloride) salts. To intuitively estimate the influence of incidence angles and refractive indices on the SFG intensity, solely a defined factor of|Fyyz| was discussed, which can be individually separated from the macroscopic second-order non-linear susceptibility χ yyz^(2) term and represents the SSP intensity. Moreover, effects of refractive indices and the molecular hyperpolarizability ratio(R) were discussed in the orientational analysis of interfacial CO and methanol molecules. When IPPP/ISSP was identical, molecules with a larger R had smaller tilting angles(q) on Pt(assuming q < 51°), and CO molecules on Pd would tilt much closer to the surface than they did on Pt. A total internal reflection(TIR) geometry enhanced the SFG intensity, but it also amplified the influence of refractive index on SFG intensity at the solid(silica)/liquid interface. The refractive index and R-value had similar influence on the methanol orientation in the presence of sodium iodide salts at air/liquid and solid/liquid interfaces. This work should provide a guideline for analyzing the orientation of molecules with different R, which are adsorbed on catalysts or located at liquid interfaces involving changes of refractive indices.