Components Of Polarizability Tensor Research Articles

Radiative transfer in atmospheres with a large chaotic magnetic field

ABSTRACT We derive the radiative transfer equations for all Stokes parameters of continuum radiation in atmospheres with any value of homogeneous magnetic field $\boldsymbol{B}$. The explicit formulas for cross-sections and the phase shifts are given with allowance for absorption effects. We consider the scattering of non-polarized radiation in an optically thin envelope with a dipole magnetic field. The presented theory is valid for magnetic fields B ≤ 1010G. In general, a magnetic field consists of the mean value $\boldsymbol{B_0}$ and the chaotic part $\boldsymbol{ B^{\prime }}$. The latter is assumed to have an isotropic distribution over directions and a Gaussian-type distribution over the value B′. It is shown that for B0(G)λ(μm) ≪ 108, the fluctuations play a dominating role. This case is considered in detail. First of all, we derive the system of transfer equations for observed averaged Stokes parameters. The averaging procedure consists of two stages: the averaging of fluctuations $\boldsymbol{B }^{\prime }$ over values and the averaging of these over all directions. The averaging over Gaussian fluctuations B′ is carried out using the exponential Fourier transform of polarizability tensor components and the known formula for the averaged exponential. This technique is available for arbitrary values of a magnetic field, both large and small. The system of transfer equations for four averaged Stokes parameters, I, Q, U and V, splits up into two independent systems – for I, Q and V, U parameters. The form of equations for the case of large magnetic fluctuations differs strongly from the Thomson scattering. These equations describe the large decrease of linear and circular polarization of observed radiation.

A computational quantum chemical and polarizability calculations of liquid crystal 4-cyano-4-pentylbiphenyl with water molecule (H2O)

In this paper, we investigate the quantum chemical parameters such as energy of the highest occupied molecular orbital (EHOMO), energy of the lowest unoccupied molecular orbital (ELUMO), HOMO-LUMO energy gap (△Egap), ionization potential (I), electron affinity (A), chemical potential (μ), electronegativity (χ), hardness (η), softness (S), and electrophilicity index (ω) of liquid crystal (LC) 4-cyano-4-pentylbiphenyl with water molecule (H2O). Above quantum chemical parameters have been calculated at Becke's three-parameter hybrid exchange functional and the Lee–Yang–Parr correlation functional (B3LYP) with 6-31G(d) and 6-31G++(d,p) basis sets in the framework of density-functional theory (DFT). For comparative purposes, we also optimize 4-cyano-4-pentylbiphenyl with water molecule at Perdew-Burke-Ernzerhof (PBEPBE) with 6-31++G(d,p) level. Mulliken charge analysis infer that (-0.03e) amount of charge is being associated with the H2O at B3LYP/6-31G(d) level. This fact indicates a considerable amount of electron population is transferred from pristine 4-cyano-4- pentylbiphenyl to H2O molecule. Polarizability tensor components such as αxx, αyy, αzz, average polarizability (αav), and polarizability anisotropy (Δα) have been calculated. The most intense IR spectral characteristics of 4-cyano-4-pentylbiphenyl with water molecule are accommodated in between 3000 cm−1 to 3920 cm−1at all presented levels.

Anisotropic Stark shift, field-induced dissociation, and electroabsorption of excitons in phosphorene

We compute binding energies, Stark shifts, electric-field-induced dissociation rates, and the Franz-Keldysh effect for excitons in phosphorene in various dielectric surroundings. All three effects show a pronounced dependence on the direction of the in-plane electric field, with the dissociation rates in particular decreasing by several orders of magnitude upon rotating the electric field from the armchair to the zigzag axis. To better understand the numerical dissociation rates, we derive an analytical approximation to the anisotropic rates induced by weak electric fields, thereby generalizing the previously obtained result for isotropic two-dimensional semiconductors. This approximation is shown to be valid in the weak-field limit by comparing it to the exact rates. The anisotropy is also apparent in the large difference between armchair and zigzag components of the exciton polarizability tensor, which we compute for the five lowest lying states. As expected, we also find much more pronounced Stark shifts in either the armchair or zigzag direction, depending on the symmetry of the state in question. Finally, an isotropic interaction potential is shown to be an excellent approximation to a more accurate anisotropic interaction derived from the Poisson equation, confirming that the anisotropy of phosphorene is largely due to the direction dependence of the effective masses.

Dynamic Polarizability and Higher-Order Electric Properties of Fluorene, Carbazole, and Dibenzofuran

Static electric properties, from the dipole moment to the second-hyperpolarizability tensor γ, of the 3-membered, isoelectronic ring molecules, fluorene (FL), carbazole (CR), and dibenzofuran (DBF), have been calculated at various levels of approximation. The electron correlation effects have been included at the coupled-cluster (CC) level, using CCSD and CC2 versions of the method. DFT calculations with the CAM-B3LYP functional have also been performed, and the results are compared to the CC values. The electric property-tailored Pol basis set and its more compact Z3Pol version have been employed in all static calculations. Differences between dipole polarizability values computed at the Pol and Z3Pol bases have been found to be almost negligible. Therefore, all components of the frequency-dependent dipole polarizability tensor α(-ω;ω) have been determined at the CAM-B3LYP/Z3Pol level. Divergence occurring at electronic resonances has been eliminated using the complex polarization propagator (CPP) formalism, explicitly introducing an imaginary iΓ parameter to account approximately for the finite lifetime of the excited state. The imaginary part of the dipole polarizability Im α(-ω;ω) has been calculated for a wide range of external radiation energies up to 10 eV, and its maxima have been compared to the calculated vertical electronic excitation energies.

First Principles Investigation of the Polarizability and First Hyperpolarizability of Anhydride Derivatives

The electrical properties (dipole moment, polarizability, and first hyperpolarizabilities) of anhydride derivatives are studied using theoretical chemistry methods. Several DFT XC functionals have been used while reliable atomic basis sets have been selected for their evaluations. The variations of (hyper)polarizabilities as a function of the anhydride structure are consistent among the different functionals, which facilitates the deduction of structure–property relationships. It has been observed that (1) The dipole moment of maleic anhydride (2) increases when adding a methyl group (3) and even more when fusing a phenyl ring to get phthalic anhydride (1), in good agreement with experiment. (2) The average polarizability is mostly driven by the molecular size while the polarizability anisotropy presents more subtle variations as a function of the compound. (3) For 1 and 2, the calculated polarizability tensor components are in close agreement with the experimental data. (4) To a good extend, the HRS first hyperpolarizabilities follow the same ordering as the polarizability anisotropy. (5) The EFISHG first hyperpolarizabilities exhibit a completely different ordering while its sign depends on the orientation of the CO double bonds. Finally, since the first hyperpolarizability values of these anhydride derivatives are of moderate amplitude, like those of amino acids, several design strategies have been discussed for achieving their enhancement.

Imaging small polarizable scatterers with polarization data

We present a method for imaging small scatterers in a homogeneous medium from polarization measurements of the electric field at an array. The electric field comes from illuminating the scatterers with a point source with known location and polarization. We view this problem as a generalized phase retrieval problem with data being the coherency matrix or Stokes parameters of the electric field at the array. We introduce a simple preprocessing of the coherency matrix data that partially recovers the ideal data where all the components of the electric field are known for different source dipole moments. We prove that the images obtained using an electromagnetic version of Kirchhoff migration applied to the partial data are, for high frequencies, asymptotically identical to the images obtained from ideal data. We analyze the image resolution and show that polarizability tensor components in an appropriate basis can be recovered from the Kirchhoff images, which are tensor fields. A time domain interpretation of this imaging problem is provided and numerical experiments are used to illustrate the theory.

Formation of a Spin Texture in a Quantum Gas Coupled to a Cavity.

We observe cavity mediated spin-dependent interactions in an off-resonantly driven multilevel atomic Bose-Einstein condensate that is strongly coupled to an optical cavity. Applying a driving field with adjustable polarization, we identify the roles of the scalar and the vectorial components of the atomic polarizability tensor for single and multicomponent condensates. Beyond a critical strength of the vectorial coupling, we infer the formation of a spin texture in a condensate of two internal states from the analysis of the cavity output field. Our work provides perspectives for global dynamical gauge fields and self-consistently spin-orbit coupled gases.

Structural stability and vibrational analysis of beryllium sulfide BeS from the bulk to the (n,0) nanotubes. An ab initio description

Beryllium sulfide (BeS) in different forms from molecule, bulk, monolayer (h-BeS), to the single-walled nanotube obtained by wrapping the h-BeS monolayer along the (n,0) hexagonal lattice vector for n varying from n = 6 to 64, has been examined. Density functional theory (DFT) with an all electron basis set and the hybrid DFT/B3LYP level have been applied to compute energetic and geometrical, electronic and vibrational, elastic and piezoelectric properties, where the trend towards the hexagonal monolayer (h-BeS) in the limit of large tube radius is obtained. The vibrational properties including Raman spectra and polarizabilities are evaluated via the Coupled Perturbed Hartree–Fock and Kohn–Sham (CPHF/KS) computational schemes. For the first time, the IR vibrational modes at higher tube diameter and their convergence to the h-BeS monolayer limit are reported where the vibrational and electronic contributions to both perpendicular and parallel components of polarizability tensor are additionally discussed. For the (n,0) BeS nanotube family, three ranges of IR active phonon modes are determined. The first one located in the 0–300 cm−1frequency domain, goes regularly to zero when the tube diameter increases. Both the second (300–400 cm−1) and the third (700–800 cm−1) ones tend smoothly with different slope, towards the two optical vibrational modes of the h-BeS layer. These theoretical models can be extended to investigate further issues, such as the effect caused by the addition of a dopant, the influence of the substitutional fraction of nanotube atoms and the interaction of molecules outside and/or inside of the nanotube.

Anharmonic vibrational analysis of s-trans and s-cis conformers of acryloyl fluoride using numerical-analytic Van Vleck operator perturbation theory

A new gas-phase infrared (IR) spectrum of acryloyl fluoride (ACRF, CH2CHCFO) with a resolution of 0.1cm−1 in the range 4000–450cm−1 was measured. Theoretical ab initio molecular structures, full quartic potential energy surfaces (PES), and cubic surfaces of dipole moments and polarizability tensor components (electro-optical properties, EOP) of the s-trans and s-cis conformers of the ACRF were calculated by the second-order Møller-Plesset electronic perturbation theory with a correlation consistent Dunning triple-ζ basis set. The numerical-analytic implementation of the second-order operator canonical Van Vleck perturbation theory was employed for predicting anharmonic IR and Raman scattering (RS) spectra of ACRF. To improve the anharmonic predictions, harmonic frequencies were replaced by their counterparts evaluated with the higher-level CCSD(T)/cc-pVTZ model, to form a “hybrid” PES. The original operator representation of the Hamiltonian is analytically reduced to a quasi-diagonal form, integrated in the harmonic oscillator basis and diagonalized to account for strong resonance couplings. Double canonical transformations of EOP expansions enabled prediction of integral intensities of both fundamental and multi-quanta transitions in IR/RS spectra. Enhanced band shape analysis reinforced the assignments. A thorough interpretation of the new IR experimental spectra and existing matrix-isolation literature data for the mixture of two conformers of ACRF was accomplished, and a number of assignments clarified.

Electrostatic model of the LiТаO3 ferroelectric

Possible combinations of the electronic polarizability tensor components for oxygen and tantalum ions have been established based on the analysis of the refraction coefficients of LiТаO3 crystal in the far-IR region. The local electric field on structurally nonequivalent ions in the LiТаO3 unit cell was calculated within the modified point-multipole model. A combination of the electronic polarizability tensor components for oxygen and tantalum ions and their effective charges is established, which provides a good correspondence of the calculation results with the experimental data on LiТаO3 crystals obtained by 7Li nuclear magnetic resonance and 181Та nuclear quadrupole resonance and with the known value of the crystal spontaneous polarization.

Dipole and quadrupole polarizabilities of the water molecule as a function of geometry.

Dipolar, dipole-quadrupole and quadrupole-quadrupole static polarizabilities of the water molecule have been determined by ab initio calculations at coupled cluster level of theory with single, double and perturbative triple excitations CCSD(T) with an aug-cc-pVTZ basis set using a finite field and field-gradient method. The geometry dependence of polarizability tensor components has been explored and modeled by power series expansion in bond length and angle variations up to sum of powers equal to 4. The results provide a very detailed description of the static polarizability of water up to quadrupolar rank which can be used for the test and development of novel accurate polarizable interaction potentials for modeling aqueous solutions. © 2016 Wiley Periodicals, Inc.

Elastic dipoles in the model of single-crystal and amorphous copper

The characteristic values of the elastic polarizability tensor components of point defects in crystalline and amorphous copper, which determine changes in the elasticity tensor components upon introduction of defects, have been found using the molecular dynamics method. A relation of the elastic polarizability tensor with the main parameter of the interstitialcy theory, i.e., shear susceptibility, has been established. An analysis of the elastic polarizability tensors of defects in crystalline and amorphous copper has demonstrated that, in a noncrystalline structure, there are specific atomic configurations that under deformation manifest themselves similarly to elastic dipoles (interstitial atoms in a dumbbell configuration) in single-crystal copper.

On the determination of the diagonal components of the optical activity tensor in chiral molecules

It is shown that the diagonal components of the mixed electric-magnetic dipole polarizability tensor, used to rationalize the optical rotatory power of chiral molecules, are origin independent, if they are referred to the coordinate system defined by the eigenvectors of the dynamic electric dipole polarizability, for a given value ω of the frequency of a monochromatic wave impinging on an ordered sample. Within this reference frame, the individual diagonal components of the mixed electric-magnetic dipole polarizability are separately measurable properties. The theoretical method is applied via a test calculation to the cyclic 1,2-M enantiomer of the dioxin molecule, using a large Gaussian basis set to estimate near Hartree-Fock values within a series of dipole length, velocity, and acceleration representations.

Change in the polarizability of MBBA molecules upon the nematic-isotropic liquid transition and physical consequences

The Lorentz tensor components Lj and the polarizability tensor components γj of 4-methoxyben-zylidene-4′-butylaniline (MBBA) liquid crystal molecules in nematic and isotropic phases have been determined experimentally. The quadratic dependences of the mean value \(\bar \gamma \) (S) and anisotropy Δγ(S) of the polarizability in the nematic phase on the orientational order parameter S of molecules have been established. Within the phenomenological approach, the dependences \(\bar \gamma \) (S) and Δγ(S) have been derived, and their features for MBBA and other known objects have been interpreted. The relation of the dependences \(\bar \gamma \) (S) and Δγ(S) to the features of the nematic-isotropic liquid phase transition has been found.

A density functional theory study of the reactivity descriptors and antioxidant behavior of Crocin

The molecular characteristics of Crocin (digentiobiosyl-8,8′-diapocarotene-8,8′-oate; C44H64O24), naturally occurring carotenoid pigment compound, such as: the ionization potential (I), electron affinity (A), electronegativity (χ), electrophicility (ω), and hardness have been calculated using Density Functional Theory (DFT) approach with B3LYP/6-31G(d,p) level of theory. The plots of Frontier Molecular Orbital and molecular electrostatic potential (MEP) for Crocin molecule along with the spin density distribution for its cation radical have been demonstrated. For the first time, we indicated the chemically active sites of the Crocin molecule by Fukui functions. Calculated components of polarizability tensor illustrate that sugar moiety in Crocin molecule has a vital role in its chemical reactivity. To conclude, our calculations are in accordance with the previous experimental reports (Papandreou et al. [5]) which reveal Crocin is an effective antioxidant and its gentiobiose terminals affect its antioxidant performance.

Mechanism of near-field Raman enhancement in two-dimensional systems

A theory describing the near-field Raman enhancement in two-dimensional (2D) systems is presented. The analysis quantifies the near-field Raman intensity as a function of the tip-sample distance, Raman polarizability tensor components, incident laser beam configuration, and tip orientation relative to the sample plane. Our results show that the near-field Raman intensity is inversely proportional to the 10th and 8th power of the tip-sample distance in the incoherent and coherent scattering regimes, respectively. Optimal conditions for the tip inclination angle for different configurations are determined, and the results can be used as a guide for tip-enhanced Raman spectroscopy (TERS) experiments in 2D systems such as graphene, two-dimensional electron gases, and topological insulators.

Theoretical investigation on two-dimensional molecule-based second-order nonlinear optical materials of the disubstituted o-carborane derivatives

Recent studies show that non-dipolar molecular structures, having multidimensional (nD) nonlinear optical (NLO) characteristics, can be regarded as excellent candidates for the second-order NLO applications. Then, the second-order NLO response of a series of o-carborane (C2B10H12) derivatives was investigated by density functional theory (DFT) method. The results suggest that their second-order nonlinearities are dominated by two second-order polarizability tensor components (βzzz and βzyy). Electronic transitions to crucial excited states show that y-polarized transition, contributed to the off-diagonal second-order polarizability tensor (βzyy), possesses lower transition energy compared with z-polarized transition accounted for the diagonal second-order polarizability tensor (βzzz), which led to the large in-plane nonlinear anisotropy (μ=βzyy/βzzz) value, as well as good 2D second-order NLO properties. Moreover, the βtot values gradually increase from the monosubstituted (MS) to disubstituted (DS) o-carboranes. With increasing the strength of donor groups in DS molecules, the βtot values are also enhanced. The micromechanism of the second-order NLO properties has been analyzed from the standpoint of dipole moment, transition electronic dipole moment and transition energy. Our studies show that these complexes can be used as excellent 2D second-order NLO materials from the standpoint of large β, high transparency, and μ values.

Re-radiation Enhancement in Polarized Surface-Enhanced Resonant Raman Scattering of Randomly Oriented Molecules on Self-Organized Gold Nanowires

We explore the effect of re-radiation in surface-enhanced Raman scattering (SERS) through polarization-sensitive experiments on self-organized gold nanowires on which randomly oriented Methylene Blue molecules are adsorbed. We provide the exact laws ruling the polarized, unpolarized, and parallel- and cross-polarized SERS intensity as a function of the field polarizations. We show that SERS is polarized along the wire-to-wire nanocavity axis, independently from the excitation polarization. This proves the selective enhancement of the Raman dipole component parallel to the nanocavity at the single molecule level. Introducing a field enhancement tensor to account for the anisotropic polarization response of the nanowires, we work out a model that correctly predicts the experimental results for any excitation/detection polarization and goes beyond the E(4) approximation. We also show how polarization-sensitive SERS experiments permit one to evaluate independently the excitation and the re-radiation enhancement factors accessing the orientation-averaged non-diagonal components of the molecular Raman polarizability tensor.

Calculation of torsional and rotational raman spectra of hydrogen peroxide

We present calculated intensity distributions in torsional, rotational, and torsional-rotational Raman lines in spectra of hydrogen peroxide. Ab initio calculations of polarizability tensor components as functions of internal rotation angle were carried out in the HF/6-311G approximation. It is shown that the structure and transformational properties of the polarizability tensor components of hydrogen peroxide in extended molecular symmetry group G4(EM) permit formation of purely rotational and torsional and rotational-torsional Raman spectra. Common expressions to calculate Raman line intensities governed by torsional and rotational motions of the non-rigid symmetric top molecule are obtained. The torsional components of the line intensities have been calculated by estimating the appropriate matrix elements. The contribution of rotational components has been calculated using the 3j-symbols technique.

Modelling the polarizability of the dihydrogen–argon pair

The collision-induced (CI) pair polarizability of dihydrogen–argon ( H 2 – Ar ) pair has been studied using quantum-chemical and analytical methods. We have proposed a procedure to determine the rotationally adapted (symmetry adapted) components of the CI polarizability tensor. The corresponding irreducible spherical symmetry adapted components are computed for the H 2 – Ar pair. We have analyzed the dipole-induced dipole (DID) model pair polarizability tensor for H 2 – Ar . Good agreement between the DID allowed rotationally adapted CI H 2 – Ar polarizability components and those computed by quantum-chemical methods is found.