Nanosecond laser measurements of optical absorption coefficients of electrons in polar fluids

Direct measurements of the optical absorption coefficients of the short-lived electrons in polar fluids have been made. Laser-induced photoionization of pyrene in alcohols at 293 K generated equal numbers of electrons (e_s^?) and pyrene positive ions (P⁺). The ?_max(e_s^?) were derived by measuring the relative absorption intensities of e_s^? and P⁺, which had been independently characterised. The ?_max values for e_s^? in methanol to 1-decanol fell within the range (1.0–2.0) × 10⁴ M^?1 cm^?1, the implications of which are discussed.     

Exact relations between the electron density and external potential for systems of interacting and noninteracting electrons

The differential virial theorem (DVT) is an explicit relation between the electron density ρ( r ), the external potential, kinetic energy density tensor, and (for interacting electrons) the pair function. The time‐dependent generalization of this relation also involves the paramagnetic current density. We present a detailed unified derivation of all known variants of the DVT starting from a modified equation of motion for the current density. To emphasize the practical significance of the theorem for noninteracting electrons, we cast it in a form best suited for recovering the Kohn–Sham effective potential v_s( r ) from a given electron density. The resulting expression contains only ρ( r ), v_s( r ), kinetic energy density, and a new orbital‐dependent ingredient containing only occupied Kohn–Sham orbitals. Other possible applications of the theorem are also briefly discussed. © 2012 Wiley Periodicals, Inc.     

Estimation of electrostriction coefficients of a nonlinear optical polymer electret

The effect of organic chromophores incorporated into a polymer electret and responsible for its nonlinear optical (NLO) response to an applied electric field on the electrostriction coefficients (ESC) of the material is studied. Analytical expressions for the ESC were derived in the framework of a model proposed earlier, which includes the effect of a locally anisotropic, polarizable and deformable environment on the electric characteristics of the chromophore. The dependence of the ESC on both macroscopic and microscopic parameters of the molecular system is established. Numerical estimates of the ESC for poly(methyl methacrylate) doped with the dye Disperse Red 1 and dimethylaminonitrostilbene-doped polycarbonate agree with experimental data in order of magnitude. The relations obtained can be used in the design of novel organic NLO materials. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 7, pp. 1324–1329, July, 2008.     

Effect of magnetic field on diamagnetic susceptibility of two interacting electrons in a quantum dot

We have estimated the energy levels of the low‐lying states as a function of magnetic field when two electrons are introduced in a quantum dot (QD). Oscillator strength of interacting electrons for different magnetic field strengths has been calculated. There is no appreciable change in oscillator strength for stronger confinements for all the magnetic field strengths. We present the shift of diamagnetic susceptibility of a hydrogenic donor impurity in GaAs/Ga_1?xAl_xAs QD systems for the ground and low lying excited states. The effect of magnetic field on diamagnetic susceptibilities is estimated by two different methods and it has been found that values obtained from both the methods resemble each other. The diamagnetic shift is in good agreement with the other investigators. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Very high third-order nonlinear optical activities of intrazeolite PbS quantum dots

Zeolite-intercalated semiconductor quantum dots (QDs) have long been proposed to give very high third-order nonlinear optical (3NLO) responses. However, measurements of their 3NLO responses have not been possible due to the lack of methods to prepare optically transparent QD-incorporating zeolite films supported on optically transparent substrates and to confine QDs only within zeolite interiors. We found that the zeolite-Y films grown on indium-tin-oxide-coated glass plates (Ygs) remain firmly bonded to the substrates during ion exchange with Pb2+ ions, drying, and formation of PbS QDs by treating Pb2+ ions with H2S. A series of Ygs encapsulating different numbers (n = 0, 8, 14, 23, and 33) of PbS in a unit cell [(PbS)n-Yg] were prepared. The PbS QDs were expelled by adsorbed moisture to the external surfaces, and the expelled QDs formed large QDs. Coating of the (PbS)n-Ygs with octadecyltrimethoxysilane results in effective confinement of the QDs within the internal pores. The zeolite-encapsulated PbS QDs showed remarkably high 3NLO activities at 532 and 1064 nm which are unparalleled by other PbS QDs dispersed in other matrixes.     

MNDO calculations of molecular electric polarizabilities,hyperpolarizabilities, and nonlinear optical coefficients

Molecular electric polarizabilities, hyperpolarizabilities, and nonlinear optical coefficients have been calculated by the MNDO SCF MO method with reasonably satisfactory results.     

Quantum dot with N interacting electrons confined in a power-law external potential

The ground-state physical properties, such as electron density, chemical potential, and total energy, of a two-dimensional quantum dot with N interacting electrons confined in a power-law external potential are numerically determined by the Thomas-Fermi approximation. The effect of the confining potential on properties such as electron density and chemical potential is examined for both interacting and non-interacting systems. It is shown that the results of the calculations are in excellent agreement with those given in the literature. The results indicate that interactions and the shape of the confinement affect the density and thus the ground-state properties of the electrons significantly.     

Vibrational contributions to static linear and nonlinear optical coefficients: from two-level to two-band systems

The importance of vibrational contributions to the static linear and nonlinear optical coefficients is investigated. We apply the exact sum-over-state (SOS) formulas for polarizabilities and hyperpolarizabilities expressed in terms of vibronic states to a two-level system with a single vibrational mode. The Herzberg–Teller expansion is applied to the SOS formulas including vibrational energy levels without employing the Placzek’s approximation within both the Born–Oppenheimer approximation and electrical and mechanical harmonicities. The results include not only the vibrational contribution from the lattice relaxation expression but also the contribution arising from the higher-order correction terms. Model calculations on a diatomic system with two electronic states show that the contribution of these correction terms is small. Moreover, most of these higher-order terms are negligible in the solid-state limit. In polyacetylene, the contribution of the lattice relaxation expression is much larger than that in the diatomic case. Within the tight-binding approximation, the contribution of the lattice relaxation expression is 44% of the pure electronic contribution for the second hyperpolarizability.     

Linear and nonlinear optical studies of CdS1−x Se x quantum dots

In this contribution we present and discuss our measurements on CdS_1?x Se _x quantum dots in a glass matrix. In linear absorption measurements we find the typical blue shift of the transitions with decreasing crystallite radius due to quantization. The luminescence shows a significant Stokes shift with respect to absorption, which is interpreted in terms of strong exciton-phonon coupling and allows to deduce the Huang-Rhys factor S. Under high excitation we find an additional emission band on the high energy side, which can be attributed to the recombination of an excited two electron-hole pair state to a one electron-hole pair state in agreement with theory. Pump and probe beam experiments give a bleaching but no hole burning. Finally we discuss some open questions especially concerning the high energy structures in the absorption spectrum.     

Exact solutions of lattice polymer models

We consider directed path models of a selection of polymer and vesicle problems. Each model is used to illustrate an important method of solving lattice path enumeration problems. In particular, the Temperley method is used for the polymer collapse problem. The ZL method is used to solve the semi-continuous vesicle model. The Constant Term method is used to solve a set of partial difference equations for the polymer adsorption problem. The Kernel method is used to solve the functional equation that arises in the polymer force problem. Finally, the Transfer Matrix method is used to solve a problem in colloid dispersions. All these methods are combinatorially similar as they all construct equations by considering the action of adding an additional column to the set of objects.     

Size-dependent extinction coefficients of PbS quantum dots

We report here on a detailed study on PbS colloidal quantum dots. A characterization via X-ray diffraction (XRD) and high-resolution transmission electron microscopy (HRTEM) allowed us to reliably determine the diameter and the shape of the nanocrystals. These data, together with second-derivative analysis of the absorption spectra, allowed us to determine the size dependence of seven transitions in the absorption spectrum; some of these transitions were identified on the basis of their normalized confinement energy. The size dependence of the first excitonic transition was best modeled by a four-band envelope approach which considers the anisotropy of the band edges (Andreev, A. D.; Lipovskii, A. A. Phys. Rev. B: Condens. Matter Mater. Phys. 1999, 59, 15402-15404). The extinction coefficients were calculated using concentrations obtained from inductively coupled plasma atomic emission spectrometry (ICP-AES), and their size dependence was found to follow a power law with exponent equal to approximately 2.5. In contrast with what was expected from the effective mass approximation, the per particle absorption cross section of the lowest transition was found to be strongly dependent on the particle size.     

共轭杂环对席夫碱体系结构和非线性光学性质影响的量子化学研究

采用量子化学半经验FF/AM1,FF/PM3,ZIDO-SOS方法,讨论了杂环取代对水杨醛缩苯胺结构、电子光谱、非线性光学系数的影响,得到这类化合物的特征吸收峰位于294-303nm,符合非线性光学材料对透明性的要求,且给电性杂环指点入可改善体系的非线性光学性质,是一类有意义的分子设计基团。     

Theoretical study on quantum dynamics of bose system interacting with photon field

We investigate the quantum dynamics of two‐boson and two‐level systems interacting with a one‐mode photon field. The time evolution of the population for each state is calculated in terms of the Jaynes–Cummings model. We find the collapses and revivals of the order parameter for the Bose–Einstein condensation. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem 84: 401–408, 2001     

Synthesis of conjugated dendrons with nonlinear optical activity

New dipolar conjugated dendrons with electron-withdrawing groups on the periphery and electron-donating groups distributed at the core and throughout the dendritic skeleton have been conveniently synthesized. The pi-conjugated dendritic skeleton provides extended conjugation between each electron donor-acceptor pair, resulting in numerous traditional nonlinear optically active chromophores in one single dendron.     

Higher-order virial coefficients of water models

We use the Mayer sampling method, with both direct and overlap sampling, to calculate and compare classical virial coefficients up to B6 for various water models (SPC, SPC/E, MSPC/E, TIP3P, and TIP4P). The precision of the computed values ranges from 0.1% for B2 to an average of 25% for B6. When expressed in a form scaled by the critical properties, the values of the coefficients for SPC water are observed to greatly exceed the magnitude of corresponding coefficients for the simple Lennard-Jones model. We examine the coefficients in the context of the equation of state and the Joule-Thomson coefficient. Comparisons of these properties are made both to established molecular simulation data for each respective model and to real water. For all models, the virial series up to B5 describes the equation of state along the saturated vapor line better than the series that includes B6. At supercritical temperatures, however, the sixth-order series often describes pressure-volume-temperature behavior better than the fifth-order series. For example, the sixth-order virial equation of state for SPC/E water predicts the 673 K isotherm within 8% of published molecular simulation values up to a density of 9 mol/L (roughly half the critical density of SPC/E water).     

Preparation of polymer optical fibers doped with nonlinear optical active organic chromophores

We synthesized two novel organic nonlinear optical chromophores—chiral S(+)‐N‐[p‐(4‐nitrostyryl) phenyl] prolinol and non‐chiral [p‐(4‐nitrostyryl) phenyl] piperdine—as potential laser‐active dyes for photonic applications. Both materials show good optical transmittance in the telecommunication frequency region, desirable solubility in acrylic polymer optical fiber matrices, and attractive fluorescence properties that are advantageous for laser‐gain materials and devices. Subsequently, these two chromophores were incorporated into poly(methyl methacrylate) and poly(ethyl methacrylate) and drawn into polymer optical fibers. The relevant properties of these organic dye‐doped fibers have been studied, revealing essential attributes of laser‐active characteristics. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 1794–1801, 2001     

Exact linearization of some nonlinear least squares fittings

The nonlinear least squares fit for the sum of two Gaussians is exactly linearized by means of difference equations. The efficiency of the method is demonstrated.     

Exact stationary response of SDOF nonlinear stochastic oscillators

In this paper, a systematic procedure is developed to obtain the stationary probability density function for the response of a general single-degree-of-freedom (SDOF) nonlinear oscillators under parametric and external Gaussian white-noise excitations. Wang and Zhang (1998) expressed the nonlinear function of oscillators by a polynomial formula. The nonlinear system described here has the following form: $\text{x}\text{̈}\text{+g(x,}\text{x}\text{̇}\text{)=k}{}_1\text{ξ}{}_1\text{(t)+k}{}_2\text{xξ}{}_2\text{(t)}$ , where $\text{g(x,}\text{x}\text{̇}\text{)=}\text{∑}\text{i=0}\text{∞}\text{g}{}_{\mathrm{i}}\text{(x)}\text{x}\text{̇}{}^{\mathrm{i}}$ and ξ₁,ξ₂ are Gaussian white noises. Thus, this paper is a generalization for the results obtained by Wang and Zhang (1998). The reduced Fokker–Planck (FP) equation is employed to get the governing equation of the probability density function. Based on this procedure, the exact stationary probability densities of many nonlinear stochastic oscillators are obtained, and it is shown that some of the exact stationary solutions described in the literature are only particular cases of the presented generalized results.     

Exact quantum solutions of general driven time‐dependent quantum quadratic system

We studied the general time‐dependent linear and quadratic system via dynamical symmetries. In an algebraic framework, we obtained exact solutions of the evolution operators, propagators, and wave functions of the general time‐dependent linear and quadratic system. To illustrate our calculations, we discuss a few special cases, including a particle driven by a monochromatic electric field, and cases of oscillatory, linear, or monotonic with respect to the time of the quadratic system. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007