Longitudinal Polarizability Research Articles

An explicit solution for the electric potential of the asymmetric dielectric double sphere

An explicit solution for the longitudinal and transverse polarizability of the asymmetric dielectric intersecting double sphere is obtained as a rapidly converging series of integral operators, which can be implemented efficiently, for example, in Java Applet. This article generalizes the results of the paper (Pitkonen M 2006 J. Math. Phys. 47 102901) to the asymmetric case and also allows the permittivities of the spheres to have different values.

Static polarizability and second hyperpolarizability of closed- and open-shell π-conjugated polymers

The static longitudinal linear polarizability (alpha) and second order hyperpolarizability (gamma) for neutral and charged, closed- and open-shell trans-polyacetylene (PA) chains C(2n)H(2n+2), C(2n-1)H(2n+1), C(2n-1)H(2n+1) (+), C(2n)H(2n+2) (+), and C(2n)H(2n+2) (2+) are systematically investigated and compared. The polarizabilities are calculated within the Pariser-Parr-Pople model, and the electron correlation effect is included through density matrix renormalization group. It turns out that for both alpha, and gamma, two neutral PA chains C(2n)H(2n+2) and C(2n-1)H(2n+1) give similar values, while both singly charged and doubly charged systems present significantly larger magnitude of alpha and gamma values than the two neutral chains. The two singly charged PA chains C(2n-1)H(2n+1) (+) and C(2n)H(2n+2) (+) give more apparent nonlinear optical responses than doubly charged case C(2n)H(2n+2) (2+) and both present negative second order hyperpolarizabilities for short to medium sized oligomers. The sign inversion of gamma values in singly charged PA molecules is anticipated to take place at the much longer length than ever observed due to the significant effects of electron correlation and geometry.

Polarizability of the dielectric double-sphere

An explicit solution for the longitudinal and transverse polarizability of the symmetric dielectric intersecting double sphere is obtained as a rapidly converging series of integral operators, which is fast enough for real time calculation in Java Applet.

Longitudinal Polarizability of Carbon Nanotubes

The longitudinal polarizabilities of carbon nanotubes are determined using first principles density functional theory. These results demonstrate that the polarizability per atom of a nanotube in the axial direction is primarily determined by the band gap. In fact, polarizability per atom versus inverse band gap yields a linear trend for all nanotubes and methods utilized in this study, creating a universal relationship for longitudinal polarizability. This can be explained by examining the terms in the sum over states equation used to determine polarizability and noting that the vast majority of the polarizability arises from a few elements near the band gap. This universal trend is then used with experimentally determined band gaps to predict the experimental polarizability of carbon nanotubes.

Static Dielectric Properties of Carbon Nanotubes from First Principles

We characterize the response of isolated single-wall (SWNT) and multiwall (MWNT) carbon nanotubes and nanotube bundles to static electric fields using first-principles calculations and density-functional theory. The longitudinal polarizability of SWNTs scales as the inverse square of the band gap, while in MWNTs and bundles it is given by the sum of the polarizabilities of the constituent tubes. The transverse polarizability of SWNTs is insensitive to band gaps and chiralities and is proportional to the square of the effective radius; in MWNTs, the outer layers dominate the response. The transverse response is intermediate between metallic and insulating, and a simple electrostatic model based on a scale-invariance relation captures accurately the first-principles results. The dielectric response of nonchiral SWNTs in both directions remains linear up to very high values of applied field.

Rotational diffusion and orientation relaxation of rodlike molecules in a biaxial liquid crystal phase

The longitudinal relaxation time and the complex dielectric polarizability of rod-like molecules with dipole moment parallel to the long axis in a biaxial nematic liquid crystal are calculated using as model the rotational Brownian motion in a mean field potential so reducing the problem to a solution of a set of linear differential-recurrence relations for statistical moments (the appropriate equilibrium orientational correlation functions). The solution of this set is obtained by matrix continued fractions. Moreover, simple analytic equations (based on the exponential separation of the time scales of the intrawell and overbarrier (interwell) relaxation processes), allowing one to understand the qualitative behavior of the system and accurately predicting the longitudinal complex polarizability for wide range of the barrier height and anisotropy parameters, are proposed.

Longitudinal polarizability of long polymeric chains: Quasi-one-dimensional electrostatics as the origin of slow convergence

The longitudinal linear polarizability alpha(N) of a stereoregular oligomer of size N is proportional to N in the large-N limit, provided the system is nonconducting in that limit. It has long been known that the convergence of alpha(N)/N to the asymptotic alpha(infinity) value is slow. We show that the leading term in the difference between alpha(N)/N and alpha(infinity) is of the order of 1/N. The difference [alpha(N)-alpha(N-1)], as well as alpha(center)(N) (when computationally accessible), also converge to alpha(infinity), but faster, the leading term being of the order of 1/N(2). We also present evidence that in these cases the power law convergence behavior is due to quasi-one-dimensional electrostatics, with one exception. Specifically, in molecular systems the difference between alpha(N)/N and alpha(infinity) has not just one but two sources of the O(1/N) term, with one being due to the aforementioned Coulomb interactions, and the second due to the short ranged exponentially decaying perturbations on chain ends. The major role of electrostatics in the convergence of the remainders is demonstrated by means of a Clausius-Mossotti-type classical model. The conclusions derived from the model are also shown to be applicable in molecular systems, by means of test-case ab initio calculations on linear stacks of H(2) molecules, and on polyacetylene chains. The implications of the modern theory of polarization for extended systems are also discussed.

MP2 static longitudinal (hyper)polarizabilities of polydifluoroacetylene

Results for the static longitudinal linear polarizability, α L, and second hyperpolarizability, γ L, of planar and twisted fluorinated polyacetylene chains, obtained at MP2/6-31G level, are presented. Our correlated calculations indicate that the geometric modifications implied by the substitution of H atoms of polyacetylene by F atoms, leads to a substantial increase on γ L. As observed in a previous work, HF converged geometries give a rapid convergence pattern for the MP2/HF polarizability values, showing that the inclusion of the electron correlation effects on the polarizabilities per subunit of the polymeric polydifluoroacetylene chains, can be accurately determined from HF extrapolated results.

Modeling the electric field third-order nonlinear responses of an infinite aggregate of hexatriene chains using the electrostatic interaction model

A classical electrostatic polarization scheme using the additive distribution procedure has been applied to determine the static longitudinal polarizability and second hyperpolarizability of a all-trans hexatriene molecule in an infinite stretched fiber. The parameters have been derived from ab initio coupled-perturbed Hartree-Fock calculations and the electrostatic scheme has been validated via comparison with ab initio results on small clusters. Upon packing, the polarizability of all-trans hexatriene increases by 7% whereas the second hyperpolarizability increases by as much as 61%. These increases result from the balance between the enhancement of the (hyper)polarizability due to collinear packing and the reduction associated with lateral packing.

Electronic and vibrational polarizability and first hyperpolarizability of charge transfer chromophores: Quantum chemistry investigation

Static vibrational and electronic contributions to the longitudinal polarizability (α) and first hyperpolarizability (β) have been calculated, within the double harmonic oscillator approximation, at the HF/6-31G for a set of polyconjugated, D-linker-A, compounds. Effects due to the nature of the linker and of the D/A-pair type, on the geometrical structures and the electrical properties, are investigated. It turns out that, for a given linker, in almost all cases, the static β$^e_L$ (0) and β$^v_L$ (0) vary in the same order, with the type of the acceptor group A (A # NO$_2$, COH, CF$_3$). As well, the pair HO/NO$_2$ was associated the greatest β$^e_L$ (0) and β$^v_L$ (0) values. The analysis upon the SOM expressions, due to Bishop and Kirtman, demonstrates that, more than 50% of β$^v_L$ owes to three, two or even to only one vibrational normal mode contribution. Moreover, the vibrational modes with frequencies at, or more than, 3000 cm$^{-1}$ present a null individual vibrational first hyperpolarizability.

Modelisation of the Electric Field Linear Response of an Infinite Aggregate of All-Trans Hexatriene Chains by Electrostatic Interaction Model

A classical electrostatic polarization scheme using the additive distribution procedure has been applied to determine the longitudinal polarizability of an all-trans hexatriene molecule in an infinite stretched fiber. The parameters have been derived from ab initio CPHF/6-31G calculations and the electrostatic scheme has been validated via comparison with ab initio results on small clusters. Upon packing the polarizability of all-trans hexatriene increases by 7%. This small increase results from the balance between the enhancement of the polarizability due to collinear packing and the reduction associated with lateral packing.

Geometry, dipole moment, polarizability and first hyperpolarizability of polymethineimine: an assessment of electron correlation contributions.

We have investigated the geometries as well as the longitudinal dipole moment (micro), polarizability (alpha), and first hyperpolarizability (beta) of polymethineimine oligomers using different approaches [Hartree-Fock (HF), second-order Møller-Plesset (MP2), and hybrid density functional theory (DFT) methods (B3LYP and PBE0)] for evaluating the geometries and the nonlinear optical properties. It turns out that (i) HF and the selected DFT methods provide the incorrect sign for beta of short and medium size oligomers. (ii) The B3LYP and PBE0 electron correlation correction are too small for micro, too large for alpha, and for some oligomer lengths, they are in the wrong direction for beta. (iii) On the contrary to polyacetylene, the hybrid-DFT geometries are in poor agreement with MP2 geometries; the former showing much smaller bond length alternations.

Hartree–Fock static longitudinal polarizabilities of fluorinated polyacetylene chains

Abstract This work presents ab initio results for the static longitudinal linear polarizability, α , and second hyperpolarizability, γ , of planar and twisted fluorinated polyacetylene chains. These electric properties were calculated by the finite field (FF) method, in the framework of the Hartree–Fock approximation. Our calculations, using different basis sets (6-31G and its standard extensions) indicate that inclusion of polarization functions, through the 6-31G(d) basis set, is important in the determination of the geometric parameters, specially dihedral angles. Nevertheless for both, planar and twisted F-substituted chains, our results show that the 6-31G basis set is sufficient to provide consistent estimates for α and γ . It is observed that the twisted conformation of F-substituted compounds leads to a marked reduction on the polarizabilities, specially on the second hyperpolarizability. Using converged geometries, the polarizabilities for the polymeric polydifluoroacetylene chains were obtained by extrapolation and compared with those of polymeric polyacetylene chains.

Calculation of refractive indices for the (NH2CH2COOH)2 · HNO3 crystal

The refraction R of the diglycine nitrate (DGN) crystal, (NH2CH2COOH)2 · HNO3, in the para-and ferroelectric phases has been calculated in the model of noninteracting diatomic chemical bonds of the elementary unit cell of the crystal on the basis of the longitudinal and transversal polarizabilities of these bonds. The calculated magnitudes of the principal refractive indices n p , n m , and n g and the orientations of the optical indicatrix of the crystal agree satisfactorily with experimentally observed values. Introducing the coefficient of Lorenz-Lorentz interaction x into the corresponding formula permits better agreement of the calculated and experimental refractive indices of DGN crystal to be obtained. The temperature changes of these x coefficients upon the ferroelectric phase transition in the DGN crystal have been analyzed.

Static polarizabilities of doubly charged polyacetylene oligomers: basis set and electron correlation effects

Abstract Ab initio calculations, carried out with different basis sets, for the static longitudinal linear polarizability, αL, and second order hyperpolarizability, γL, of small doubly charged polyacetylene (PA) chains, are presented. The polarizabilities were calculated using the Hartree–Fock (HF) method while the electron correlation effects were included through the second-order Moller–Plesset perturbation theory (MP2). Positively and negatively charged bipolarons were studied. The results obtained for positive and negative chains show that the ionization state effect decreases more rapidly, as the chain length is increased, for αL than for γL. For both types of charged chains, the incorporation of the electron correlation increases the αL and γL values, as compared to the HF values. A comparison between the results obtained using the standard 6-31G basis set and augmented versions of this set, obtained by the addition of diffuse and polarization functions, shows that 6-31G basis set does not provide a good description of the negative chains studied here and that the addition of extra diffuse functions on the basis set is needed in order to obtain reliable estimates for polarizabilities, specially for γL.

Irreversible temperature-induced changes in purple membranes studied by electrooptics

The thermal stability of purple membranes is studied by electric light scattering. Information on the polarization mechanisms is obtained. Incomplete recovery of the initial electric state (i.e., of permanent dipole moment, p ⊥, and electric polarizability, γ fast,‖) after the membranes are heated at temperatures above 60 °C is revealed. Additional slow polarizability components, γ slow,⊥ and γ slow,‖, relaxing at different characteristic frequencies than the fast longitudinal polarizability γ fast,‖ appear in the temperature range where the order–disorder transition takes place. The slow polarizability γ slow,⊥ is probably connected with counterion displacement in the electrical double layer perpendicular to the disk plane. The results are important for understanding the polarization mechanisms and the origin of slow orienting moments.

Electron correlation corrected static polarizabilities of polymers with linear and cyclic conjugated elementary cells

We have calculated the static polarizabilities of polymers with small linear and medium-size cyclic elementary cells and their constituent molecules. The basis set dependence has been investigated for the average and the longitudinal polarizabilities. The influence on the results of the selected method for the calculation (finite field or coupled perturbed Hartree–Fock) was analyzed. The effect of the electron correlation for this property in these systems has been calculated for the first time in the frames of the crystal orbital approach. The results show that this correction amounts up to 35% of the ab initio Hartree–Fock values.

Initial convergence of the perturbation series expansion for vibrational nonlinear optical properties

Ab initio Hartree–Fock and MP2 calculations of the longitudinal (hyper)polarizability—including the static electronic, static zero-point vibrational average (ZPVA), and pure vibrational (static and dynamic) contributions—have been carried out on a set of seven typical medium size conjugated nonlinear optical (NLO) molecules. The ZPVA is obtained through first-order in mechanical plus electrical anharmonicity. Based on physical “nuclear relaxation” considerations the individual (square bracket) terms that contribute to the pure vibrational (hyper)polarizability are then taken into account through third-, fourth-, or fifth-order depending upon the type of term. In order to carry out the correlated treatment, field-induced coordinates and a special finite field technique are utilized. Correlation leads to very substantial differences in the absolute and relative values of the various contributions. In comparison to the electronic term the ZPVA correction is usually small but in one case is over two-thirds as large. On the other hand, both static and dynamic pure vibrational contributions are commonly of a magnitude that is comparable to, or are larger than, the electronic term. The higher-order pure vibration terms are often large. For dynamic processes they can be almost as important as the lowest-order terms; for static (hyper)polarizabilities they can be more important. Thus, for typical NLO molecules, the initial convergence behavior of the perturbation series in mechanical and electrical anharmonicity requires further investigation.

The effect of varied ion distributions on long-range DNA charge transport.

Long-range oxidative damage to DNA was utilized as a probe to delineate the effects of different ion distributions on DNA charge transport. DNA assemblies were constructed, containing a tethered rhodium intercalating photooxidant, spatially separated from two 5'-GG-3' sites of oxidative damage, with either an A6-tract or a mixed DNA sequence intervening between the guanine doublets; the extent of charge transport was assessed through measurements of the ratio of yields of damage at the guanine doublet distal versus that proximal to the metal binding site. The distal/proximal damage ratios were compared after photooxidation of otherwise identical Rh-tethered assemblies, except for 32P-labeling either at the 5'- or 3'-end; this labeling difference corresponds, in the absence of charge neutralization by condensed counterions, to a shift in negative charge from one end of the duplex to the other. Both with assemblies containing the mixed sequence and the A6-tract, we observed that moving the negative charges to the proximal end of the duplex significantly decreased hole transport to the distal end. We propose that these results reflect variations in the thermodynamic potential at the proximal and distal guanine sites because of the change in charges at the termini of the oligomer. High values for the internal dielectric constant of the stacked base pairs are suggested by these data. Hence, the longitudinal polarizability of DNA may be important to consider in mechanisms for long-range DNA charge transport.

Substitution effects on the molecular structures and the longitudinal molecular polarizabilities of all-trans polyacetylene oligomers of increasing size

AM1 calculations have been performed on all-trans polyacetylene (PA) oligomers with an increasing number of unit cells to study the effect of donor or acceptor groups capped at opposite ends of PA chains, substituents included in the monomers, substituents' number and position in the monomers, on the molecular structures, and the static longitudinal polarizabilities (αL) and second-order hyperpolarizabilities (γL). Substitution of CH3, Cl, or F group at opposite ends of an oligomer results in an increase of αL and γL, but the substitution effects on ΔαL(N) and ΔγL(N) are very small. The asymptotic limit values are unaffected by the substitution. F substituent included in the monomer of an oligomer enhances the ΔαL(N) and ΔγL(N) values, especially at large N, but including monomers with CH3 or Cl substituents substantially reduces the ΔαL(N) and ΔγL(N) values. We alter the number of F substituents included in the monomers of oligomers and find that including two F substituents in the monomer leads to the larger enhancement of ΔγL(N). The effect of F substituents' position in the monomers of oligomers on ΔαL and ΔγL is obvious. The results may be helpful for the design of new materials for applications in nonlinear optics, particularly in the area of poled polymer films. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001