Dipole polarizability,structure, and stability of [2+2]-linked fullerene nanostructures (C60)n (n≤7)

In the present work, structural features, dipole polarizability, and stability of two most promising oligomeric series (C₆₀)_n with zigzag and linear arrangement of the fullerene cages have been studied by the PBE/3ζ density functional theory method. Their mean polarizabilities and polarizability exaltations are linearly correlated with the molecular size (maximal intercage distance). Linear (C₆₀)_n have higher polarizability than zigzag oligomers with the same n. Based on the example of hexamers (C₆₀)₆, we have shown that connectivity (number of connections) has no effect on the resulting polarizability but maximal remoteness does, i.e. the geometric factor is more decisive for mean polarizability of such fullerene nanostructures. Stability of (C₆₀)_n decreases with growing molecular size for linear structures and slowly increases in the case of zigzag (C₆₀)_n. The found dependences of polarizability and stability on the molecular size may be used for assessing these parameters of larger fullerene nanostructures, hardly computable with quantum chemical methods.     

Orientational order parameter estimated from molecular polarizabilities – an optical study

An optical study of N-(p-n-alkyloxybenzylidene)-p-n-butyloxyanilines, nO.O4 compounds with the alkoxy chain number n?=?1, 3, 6, 7, and 10 has been carried out by measuring the refractive indices using modified spectrometer and direct measurement of birefringence employing the Newton's rings method. Further, the molecular polarizability anisotropies are evaluated using Lippincott δ-function model, the molecular vibration method, Haller's extrapolation method, and scaling factor method. The molecular polarizabilities α _e and α ₀ are calculated using Vuk's isotropic and Neugebauer anisotropic local field models. The order parameter S is estimated by employing the molecular polarizability values determined from experimental refractive indices and density data and the polarizability anisotropy values. Further, the order parameter S is also obtained directly from the birefringence data. A comparison has been carried out among the order parameter obtained from different ways and the results are compared with the body of the data available in the literature.     

Ab initio calculations of multipole moments,polarizabilities and long-range interaction coefficients for the azabenzene molecules

Using LCAO-SCF wave functions on the monomers and a non-empirical Unsöld procedure for the second-order properties we have calculated the (2 ^l ) multipole moments (up to l=6), the (l,l') multipole polarizabilities (up to l + l' = 6) and the related long-range coefficients describing the electrostatic, induction and dispersion interactions for the different azabenzene molecules. The agreement with available experimental data is good, in particular for the dipole polarizabilities. The anisotropy of the long-range interaction potential is dominated by the electrostatic contributions, although the dispersion terms, especially the mixed-pole terms (l≠l') for even n (C₈, C₁₀), also contribute significantly; the induction energy is rather small. The π contributions to the polarizabilities and the dispersion interactions are found to be larger than earlier estimates. Moreover, it is shown by calculating the dipole polarizabilities of some (aza)naphthalenes and (aza)anthracenes, that a bond polarizability model can be applied effectively only if the delocalized π electrons are considered separately from the σ electrons.     

Vibration-rotation effects on the polarizabilities of CH4 and CD4 calculated from an ab initio polarizability surface

A polarizability surface has been calculated for the methane molecule using a Hartree-Fock wavefunction. Coefficients of the surface are given to second order in terms of both symmetry coordinates and internal coordinates. The polarizability is sensitive to bond stretching and angle bending. The effects of nuclear motion on the polarizabilitles of ¹²CH₄ and ¹²CD₄ have been calculated from the coefficients of the surface. Some of the second order coefficients are found to be significant in contributing to the nuclear motion corrections. The ν₃ mode is the dominant contributor to the corrections. The temperature dependences of the mean molecular polarizabilities of ¹²CH₄ and ¹²CD₄ are also calculated. The results suggest that modern methods of measurement could distinguish between the isotopomers CH_4-n D _n (n=0–4) thereby enabling an experimental surface to be obtained.     

Interferometric measurements of the dipole polarizability α of molecules between 300 K and 1100 K

The temperature dependence of the dipole polarizability α(λ, T) of free atoms and molecules is determined by precise measurements of the refractive index n of gases in the extended temperature range between 300 K and 1100 K for wavelength λ = 632·99 nm, using a specially constructed Michelson twin interferometer. α of the noble gases is observed to be independent of T. α of the molecular gases H₂, N₂, O₂, and CH₄ increases with increasing temperature by an amount of approximately 1 per cent per 1000 K. These results are in excellent agreement with theoretical predictions. They will be compared to previously measured temperature dependent polarizabilities.     

Orientational ordering from molecular polarizabilities and an odd-even effect in nCB homologous series

The molecular polarizabilities of the homologous series of cyano-alkyl-biphenyl (C _n H_2n+1.φφ.CN for n = 5 to 9) have been calculated using two different internal field models. From these values the orientational order parameters have been obtained. The orientational ordering exhibits an odd-even alteration along the series. The variations of different parameters with the increase of alkyl chain length are discussed. The relative stabilities of the alkyl-cyano-biphenyls are also discussed in terms of the molecular parameters.     

Size effects on cation heats of formation. IV. Methyl and ethyl substitutions in methyl,methylene, acetylene and ethene

An empirical relation between the heat of formation of molecular ions and cation size is used to study the effects of methyl and ethyl substitution of hydrogen atoms on the cations of the C_nH_m hydrocarbons methyl, methylene, acetylene and ethene. The results provide tests of the graphical method, revealing regularities and irregularities in the empirical size relation used, as well as its value as a predictive tool for determining cation and neutral heats of formation. Of the 36 C_nH_m cations studied, only 5 have heats of formation listed in the renowned ATcT tables. Some C_nH_m cation heats of formation are questioned or eliminated, mainly in cases where multiple choices are available in the literature. Proposals are made for investigating or re-investigating the ionisation energies and the heats of formation of several of the molecules studied where no data previously exist or where our analysis suggests that more reliable values are needed. The relative effects of methyl and ethyl substitution on the thermodynamic stability of the series of alkyl-substituted C_nH_m cations are discussed.     

Spectroscopic dissociation energies of diatomic alkaline earth oxides

Numerical procedures are employed to determine uncoupled hartree-Fock polarizabilities α₀ for members of the Ne, Mg and Ar isoelectronic sequences. For each system the first-order correction (α₁) to the polarizability is evaluated and it is found that both α₀ + α₁ and the ‘geometric approximation’ α₀/(1 - α₁/α₀) are generally in accord with polarizabilities determined from the fully coupled Hartree-Fock scheme. It is concluded that, as for smaller systems, this approach provides an economical means of obtaining a satisfactory approximation to the coupled Hartree-Fock polarizability of an atom.     

Correlation between electronic polarizabilities and ionic radii in alkali halides

An analysis of the electronic polarizabilities and sizes of ions in alkali halides has been carried out by considering a relationship according to which the electronic polarizability of an ion should vary as the n th power of its radius. The values of crystal radii, polarizabilities and the exponent “n”have been calculated using the free ion data reported by Pauling. The values of “n” are found to be nearly 3 in most of the crystals suggesting the validity of the polarizability radius cube relation. The polarizabilities and crystal radii calculated in the present study agree well with those estimated by earlier investigators.     

On the application of the theory of the brownian movement in a periodic potential to the study of inertial effects and dipole coupling

For a series of ten electron molecules (HF, H₂O, NH₃, CH₄) the molecular polarizability tensor and the derivatives with respect to the symmetry coordinates have been calculated from ab initio SCF wavefunctions using the finite field method as well as perturbation theory approaches. Raman intensities and degrees of depolarization derived from the finite field results agree well with the available experimental data.

The zeroth order bond polarizability model and the atom dipole interaction model have been analysed. Both models can be used to describe the computed static polarizabilities and the derivatives with respect to bond stretching, but fail for the derivatives with respect to the bending coordinates.     

手性分子2, 3-丁二醇的旋光拉曼光谱研究

本文从拉曼峰和旋光拉曼峰出发,通过键极化率和微分键极化率分析研究(2R, 3R)-2, 3-丁二醇. 通过分子C₁和C₂两种点群的优化结构,获得不依赖于这两种结构的结果 和有关这个手性系统物理图像的丰富信息.对分子拉曼键极化率分析,得出在拉曼弛豫过程中, 电荷主要从外围流向骨架结构.对分子微分键极化率的分析,显示在不对称C原子和与其相联系的H原子 两侧化学键, C-O和C-CH₃的微分键极化率的符号正好相反,意味着这个分子具有相当好的手性 不对称性质.对比对称和反对称的键极化率、微分键极化率,本文得到这样的结论: 对于(特别是键伸缩的)键极化率,(大体上是)对称的大于反对称的; 而对于微分键极化率则是反对称的大于对称的. 关键词： 旋光拉曼 键极化率 微分键极化率 2,3-丁二醇     

PNO-CI and PNO-CEPA studies of electron correlation effects

Dipole moments and static dipole polarizabilities are calculated for neon and the molecules HF, H₂O, NH₃, CH₄ and CO from SCF and correlated wavefunctions.

The construction of appropriate gaussian-type basis sets is discussed and the convergence of the correlation contributions to the polarizability is analysed. The effect of vibrational averaging is also investigated. The polarizabilities as obtained from the coupled electron pair approximation (CEPA) with the most extended basis sets differ from experimental values by less than 1·5 per cent in all cases. The calculated polarizability anisotropies appear to be correct to about 5–15 per cent. The correlation contributions to the polarizabilities are found to vary from 3 to 12 per cent.     

The influence of intermolecular interactions on the Kerr effect in gases

Expressions are derived for the second and third Kerr virial coefficients, B _K and C _K, of spherical top molecules in terms of irreducible cluster polarizabilities, and values are calculated using the dipole-induced dipole model for argon, krypton, xenon, methane, tetrafluoromethane, neopentane and sulphur hexafluoride. For mixtures of rare gases it is shown that the collision-induced dipole moment makes a negligible contribution to B _K. The effect of the choice of intermolecular potential function on the calculated second Kerr virial coefficients is also demonstrated. It is found that the predominant contributions to C _K arise from the pair polarizability, and that the triplet polarizability is only of minor importance.     

Fine-structure effects in relativistic calculations of the static polarizability of the helium atom

We use the relativistic configuration-interaction method and the model potential method to calculate the scalar and tensor components of the dipole polarizabilities for the excited states 1s3p ³ P ₀ and 1s3p ³ P ₂ of the helium atom. The calculations of the reduced matrix elements for the resonant terms in the spectral expansion of the polarizabilities are derived using two-electron basis functions of the relativistic Hamiltonian of the atom, a Hamiltonian that incorporates the Coulomb and Breit electron-electron interactions. We formulate a new approach to determining the parameters of the Fuss model potential. Finally, we show that the polarizability values are sensitive to the choice of the wave functions used in the calculations. Zh. éksp. Teor. Fiz. 115, 494–504 (February 1999)     

Tuning the absorption spectra and nonlinear optical properties of D‐π‐A azobenzene derivatives by changing the dipole moment and conjugation length: a theoretical study

The optical properties of several azobenzene derivatives were modulated by varying the dipole moments and conjugation lengths of the D‐π‐A systems. The relationship between the structure and absorption spectrum and polarizability was studied in the gas phase, THF and MeOH solutions, respectively, by using the density functional theory. The calculated absorption spectra and second‐order polarizabilities are in good agreement with the available experimental observations. In comparison with the D‐π‐A monomer, the H‐shaped D‐π‐A dimer almost doubles the dipole moments and hence increases the second‐order polarizabilities, without a significant shift in the maximum absorption bands. The addition of another azobenzol group between electron‐donating and ‐accepting groups increases the second‐order polarizabilities by 4–6 times, but leads to an evident red‐shift of about 65–80 nm in spectra. The relative second‐order polarizability of the halogen‐substituted derivatives is in the sequence of ? CF₃ > ? F > ? Cl > ? Br, without obvious substituent effects on the optical transparency. The D‐π‐A chromophores with the strong electron‐donating (amino) and ‐accepting (acetyl) substituent present the larger second‐order polarizabilities, at the cost of about 20 nm red‐shift of the maximum absorption lengths relative to the halogen‐substituted species. It is also demonstrated that both the linear and nonlinear optical properties augment with the increase in solvent polarity, accompanied by a red‐shift in the wavelengths of maximum absorption by about 18 and 23 nm, respectively, in THF and MeOH solutions. The changes in optical properties upon the structural modifications are further rationalized by the electronic structures of various H‐shaped dimers. Copyright © 2010 John Wiley & Sons, Ltd.     

The effect of choice of basis set in molecular pseudopotential calculations

The long tails at high Stokes and anti-Stokes frequencies observed in Rayleigh scattering from compressed methane, carbon tetrafluoride and sulphur hexafluoride are attributed to induced rotational transitions. The longest-range contribution to the collision-induced polarizability, the dipoleinduced-dipole term in R ^-3, where R is the separation of a pair of molecules, does not fluctuate with molecular rotation. However, the dipole-quadrupole polarizability A of the tetrahedron leads to a rotating contribution in R ^-4. The dipole-octopole polarizability E of an octahedron and a tetrahedron leads to a contribution in R ^-5 which also rotates with the molecule. The rotational transitions associated with these polarizabilities can explain both the intensity and the shape of the long tails. Approximate values of A for CH₄ and CF₄ and of E for SF₆ are deduced. As in the monatomic case, there is a simple relationship between the total scattered intensity and the second Kerr virial coefficient.     

Electronic and elastic properties of expanded radialenes carbon nanotubes

The series of expanded radialenes of molecular formulae C_2n H _n and C_3n H _n are obtained by inserting acetylene or diacetylene groups between each pair of methylene units of radialenes C _n H _n . This paper reports on the new theoretical investigation of electronic and elastic properties of some carbon nanotubes based on expanded radialenes with different diameters and with the armchair and zigzag edges Using the ABINIT software package, which is based on the density functional theory (DFT), we found that all studied carbon nanotubes based on expanded radialenes possess metallic behavior. Also, the calculations show that the elastic properties of the nanotubes depend on the form of the rolling up (armchair (m,m) or zigzag (m,0)). The Young’s modulus is slightly smaller for the (m,0) nanotubes and a bit larger for (m,m) nanotubes.     

Density functional study of structural and electronic properties of Al<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>P (2 ≤ <Emphasis Type="Italic">n</Emphasis> ≤ 12) clusters

Low-lying equilibrium geometric structures of Phosphorus-doped aluminum cluster Al _n P (n = 2–12) clusters obtained by an all-electron linear combination of atomic orbital approach, within spin-polarized density functional theory, are reported. The binding energy, dissociation energy, and stability of these clusters are studied within the local spin density approximation (LSDA) and the three-parameter hybrid generalized gradient approximation (GGA) due to Becke-Lee-Yang-Parr (B3LYP). Ionization potentials, electron affinities, hardness, and static polarizabilities are calculated for the ground-state structures within the GGA. It is observed that symmetric structures with the P atom occupying a peripheral position are lowest-energy geometries of Al _n P (n = 2, 4–11), while the P impurities of Al₃P and Al₁₂P prefer to occupy internal sites in the aluminum clusters. Generalized gradient approximation extends bond lengths as compared to the LSDA lengths. The odd-even oscillations in the dissociation energy, the second differences in energy, the HOMO–LUMO gaps, the ionization potential, the electron affinity, and the hardness are more pronounced within both GGA and LSDA. The stability analysis based on the energies clearly shows the clusters with an even number of valence electrons are more stable than clusters with odd number of valence electrons.     

Analysis of crystal binding of ammonium halides

Electronic polarizabilities and sizes of ions in NH₄Cl, NH₄Br and NH₄I crystals are calculated using Ruffa's theory and an empirical relation between polarizability and radius. Using the electronic polarizabilities we have estimated the van der Waals dipole-dipole and dipole-quadrupole potentials following the Slater-Kirkwood varitional method. These potentials and ionic radii are then used to calculate the cohesive energies of ammonium halides. The results are discussed and compared with those of other investigators.     

NMR chemical shifts of129Xe dissolved in various oxygen and nitrogen substituted straight chain aliphatic compounds

Xenon-129 NMR spectra have been measured for dilute solutions of¹²⁹Xe dissolved in a series of n-alcohols and primary n-alkyl amines, as well as ethylene glycol and water. The chemical shifts recorded for¹²⁹Xe in the alcohols and amines are found to be linearly related to solvent composition expressed in terms of the individual methyl and methylene groups as well as the nitrogen and oxygen bearing functional groups making up these compounds. This behavior is consistent with a simple model which considers the van der Waals contribution to the chemical shift of¹²⁹Xe to result from pair interactions between a dissolved Xe atom and the individual methyl, methylene, and functional groups from which the solvent molecules are derived. The¹²⁹Xe chemical shifts caused by the ?CH₂?, ?NH₂, and ?OH groups are found to be quite similar in magnitude, each being approximately twice that of a ?CH₃ group.