Point Dipole Interaction Research Articles

Determining Local Magnetic Susceptibility Tensors in Paramagnetic Lanthanide Crystalline Powders from Solid-State NMR Chemical Shift Anisotropies

Exploring magnetic properties at the molecular level is a challenge that has been met by developing many experimental and theoretical solutions, such as polarized neutron diffraction (PND), muon-spin rotation (μ-SR), electron paramagnetic resonance (EPR), SQUID-based magnetometry measurements, and advanced modeling on open-shell systems and relativistic calculations. These methods are powerful tools that shed light on the local magnetic response in specifically designed magnetic materials such as contrast agents, for MRI, molecular magnets, magnetic tags for biological NMR, etc. All of these methods have their advantages and disadvantages. In order to complement the possibilities offered by these methods, we propose a new tool that implements a new approach combining simulation and fitting for high-resolution solid-state NMR spectra of lanthanide-based paramagnetic species. This method relies on a rigorous acquisition thanks to short high-power adiabatic pulses (SHAP) of high-resolution solid-state NMR isotropic and anisotropic data on a powdered magnetic material. It is also based on an efficient modeling of this data thanks to a semiempirical model based on a parametrization of the local magnetism and the crystal structure provided by diffraction methods. The efficiency of the calculation relies on a thorough simplification of the electron-nucleus interactions (point-dipole interaction, no Fermi contact) which is validated by experimental analysis. By taking advantage of the efficient calculation possibilities offered by our method, we can compare a great number of simulated spectra to experimental data and find the best-matching local magnetic susceptibility tensor. This method was applied to a series of isostructural lanthanide oxalates which are used as a benchmark system for many analytical methods. We present the results of thorough solid-state NMR and extensive modeling of the hyperfine interaction (including up to 400 paramagnetic centers) that yield local magnetic susceptibility tensor measurements that are self-consistent as well as consistent with bulk susceptibility measurements.

A CRYSTAL-based parameterization of carbon atom dynamic polarizabilities to compute optical properties of curved carbonaceous nanostructures

The radiative forcing of dust particles in Earth atmosphere is still poorly characterized. A better estimation of the absorption cross section of dust particles in the UV-visible part of the spectrum is thus needed. Among the methods used for this purpose, the Atomic Point Dipole Interaction model has the distinctive advantage of being sensitive to the atomistic geometry of the particle and to the chemical functions it contains. However, this requires an adequate parameterization of the atomic polarizabilities for all the atomic species forming the particle, over the UV-visible spectrum. In this paper, we illustrate how new methodological improvements based on quantum chemistry, allow taking into account the curvature of the carbon network in the parametrization of the carbon atomic polarizabilities, using the C $$_{60}$$ molecule to fit the adequate set of parameters. We thus show how this leads to significant differences in the computed curves of the absorption cross section of pure carbonaceous nanoparticles as a function of the frequency, with respect to calculations performed using parameters issued from graphite.

Soot light absorption and refractive index during agglomeration and surface growth

Abstract Optical characterization of soot (e.g., Laser Induced Incandescence, LII) and its impact on climate largely depend on light absorption. As soot grows, its morphology changes affecting its optical or radiative properties. Here, the impact of soot maturity on its light absorption is investigated by coupling Discrete Element Modeling (DEM) with Discrete Dipole Approximation (DDA) during soot surface growth and agglomeration. The Mass Absorption Cross-section, MAC, of nascent and mature soot agglomerates is estimated by DDA and validated against atomistic point dipole interactions and mesoscale DDA calculations. Using a refractive index, RI, for mature soot yields constant average and absorption function overestimating the nascent soot light absorption up to 75%. The RI is interpolated between those of nascent and mature soot for wavelengths, λ = 532 and 1064 nm to account for quantum confinement and evolving number of clustered sp2-bonded rings that affect the optical band gap, Eg. This results in excellent agreement of the DEM-derived evolutions of , and ratio R = E ( λ = 532 nm ) > E ( λ = 1064 nm ) > with the corresponding LII measurements in methane and ethylene premixed flames. The nascent soot Eg decreases during aging and agglomeration, increasing and by 65%. The R decreases from 1.34 to 0.95 by aging and coagulation and slowly converges to the asymptotic 0.89 of mature soot measured in diffusion flames. The good agreement between DEM and LII data confirms that soot dynamics by surface growth and agglomeration strongly correlate with soot maturity, composition and RI that are essential for quantifying soot light absorption and scattering.

Local Field Factors and Dielectric Properties of Liquid Benzene.

Local electric field factors are calculated for liquid benzene by combining molecular dynamic simulations with a subsequent force-field model based on a combined charge-transfer and point-dipole interaction model for the local field factor. The local field factor is obtained as a linear response of the local field to an external electric field, and the response is calculated at frequencies through the first absorption maximum. It is found that the largest static local field factor is around 2.4, while it is around 6.4 at the absorption frequency. The linear susceptibility, the dielectric constant, and the first absorption maximum of liquid benzene are also studied. The electronic contribution to the dielectric constant is around 2.3 at zero frequency, in good agreement with the experimental value around 2.2, while it increases to 6.3 at the absorption frequency. The π → π* excitation energy is around 6.0 eV, as compared to the gas-phase value of around 6.3 eV, while the experimental values are 6.5 and 6.9 eV for the liquid and gas phase, respectively, demonstrating that the gas-to-liquid shift is well-described.

Rectangular dipoles in the discrete dipole approximation

We performed a comprehensive analysis of the extension of the discrete dipole approximation (DDA) to a rectangular cuboid lattice of dipoles. The theoretical analysis of two different approaches, based either on the point–dipole interaction or on the integration of Green׳s tensor (IGT), was performed starting with the rigorous integral equation for the electric field. We showed that the expressions for polarizability and interaction terms must strictly conform to each other, which resolves the existing controversy in the literature. Moreover, there are large differences between the spectra of the interaction matrix in the static limit for those DDA formulations. In particular, the point–dipole formulation leads to unphysical edges of the spectrum that deteriorate the convergence of the iterative solver with increasing refractive index. This severely limits the applicability of point–dipole DDA formulations with rectangular dipoles in contrast to the case of cubic dipoles. We implemented both above formulations in the open-source code ADDA and illustrated their performance on a number of test cases. In particular, we considered a graphene sheet, with thickness much smaller than the wavelength. The use of rectangular dipoles (with IGT) resulted in up to 100-times decrease of both simulation time and memory requirements, keeping the satisfactory accuracy. Similar improvements are expected for any strongly oblate or prolate particles in which the smallest dimension is much smaller than the wavelength.

Local electric field factors by a combined charge-transfer and point–dipole interaction model

A model for the local electric field as a linear response to a frequency-dependent external electric field is presented based on a combined charge-transfer and point–dipole interaction force-field model.

Complex frequency-dependent polarizability through the π → π* excitation energy of azobenzene molecules by a combined charge-transfer and point-dipole interaction model.

The complex frequency-dependent polarizability and π → π* excitation energy of azobenzene compounds are investigated by a combined charge-transfer and point-dipole interaction (CT/PDI) model. To parametrize the model, we adopted time-dependent density functional theory (TDDFT) calculations of the frequency-dependent polarizability extended with excited-state lifetimes to include also its imaginary part. The results of the CT/PDI model are compared with the TDDFT calculations and experimental data demonstrating that the CT/PDI model is fully capable to reproduce the static polarizability as well as the π → π* excitation energy for these compounds. In particular, azobenzene molecules with different functional groups in the para-position have been included serving as a severe test of the model. The π → π* excitation is to a large extent localized to the azo bond, and substituting with electron-donating or electron-attracting groups on the phenyl rings results in charge-transfer effects and a shift in the excitation energy giving rise to azobenzene compounds with a range of different colors. In the CT/PDI model, the π → π* excitation in azobenzenes is manifested as drastically increasing atomic induced dipole moments in the azo group as well as in the adjacent carbon atoms, whereas the shifts in the excitation energies are due to charge-transfer effects.

Combined nonmetallic electronegativity equalisation and point–dipole interaction model for the frequency-dependent polarisability

A molecular mechanics model for the frequency-dependent polarisability is presented. It is a combination of a recent model for the frequency dependence in a charge-dipole model [Nanotechnology 19, 025203, 2008] and a nonmetallic modification of the electronegativity equalisation model rephrased as atom–atom charge-transfer terms [J. Chem. Phys. 131, 044101, 2009]. An accurate model for the frequency-dependent polarisability requires a more accurate partitioning into charge and dipole contributions than the static polarisability, which has resulted in several modifications of the charge-transfer model. Results are presented for hydrocarbons, including among others, alkanes, polyenes and aromatic systems. Although their responses to an electric field are quite different in terms of the importance of charge-transfer contributions, it is demonstrated that their frequency-dependent polarisabilities can be described with the same model and the same set of atom-type parameters.

Temperature dependence of the energy of point dipole interaction with the surfaces of solids

The effect of temperature on the energy of the interaction of mirror image forces of a point dipole with the surfaces of metals and dielectrics is considered. It is shown that as a dipole approaches a surface and/or the temperature falls, the chaotic motion of the dipole axis becomes more and more ordered, establishing the conditions for the dependence of the dipole interaction energy not only on the distance to the surface but also on the temperature.

THE ELECTROMAGNETIC RESPONSE OF A METAMATERIAL SLAB IN THE CASE OF NORMAL INCIDENCE

In this paper, we analyze the electromagnetic response of a metamaterial slab in the case of normal incidence using the point-dipole interaction model and an expansion of polarization by eigenmodes. The problem is simplifled by assuming that the lattice dimensions are smaller than a half wavelength and invoking the nearest neighbor approximation. In this manner, we flnd the structure supports three modes: an ordinary mode and two extraordinary modes. A systematic method is presented to flnd the scattering from the slab, and the results are conflrmed by full wave simulation using Ansoft HFSS.

A quasi-free position-dependent mass jump and self-scattering correspondence

A quasi-free quantum particle endowed with a Heaviside position-dependent mass jump is observed to experience scattering effects manifested by its by-product introduction of the derivative of the Dirac delta point dipole interaction, δ′(x)=∂xδ(x). Using proper parametric mappings, the reflection and transmission coefficients are obtained. A new ordering ambiguity parameter set is reported.

Nonmetallic electronegativity equalization and point-dipole interaction model including exchange interactions for molecular dipole moments and polarizabilities

The electronegativity equalization model (EEM) has been combined with a point-dipole interaction model to obtain a molecular mechanics model consisting of atomic charges, atomic dipole moments, and two-atom relay tensors to describe molecular dipole moments and molecular dipole-dipole polarizabilities. The EEM has been phrased as an atom-atom charge-transfer model allowing for a modification of the charge-transfer terms to avoid that the polarizability approaches infinity for two particles at infinite distance and for long chains. In the present work, these shortcomings have been resolved by adding an energy term for transporting charges through individual atoms. A Gaussian distribution is adopted for the atomic charge distributions, resulting in a damping of the electrostatic interactions at short distances. Assuming that an interatomic exchange term may be described as the overlap between two electronic charge distributions, the EEM has also been extended by a short-range exchange term. The result is a molecular mechanics model where the difference of charge transfer in insulating and metallic systems is modeled regarding the difference in bond length between different types of system. For example, the model is capable of modeling charge transfer in both alkanes and alkenes with alternating double bonds with the same set of carbon parameters only relying on the difference in bond length between carbon sigma- and pi-bonds. Analytical results have been obtained for the polarizability of a long linear chain. These results show that the model is capable of describing the polarizability scaling both linearly and nonlinearly with the size of the system. Similarly, a linear chain with an end atom with a high electronegativity has been analyzed analytically. The dipole moment of this model system can either be independent of the length or increase linearly with the length of the chain. In addition, the model has been parametrized for alkane and alkene chains with data from density functional theory calculations, where the polarizability behaves differently with the chain length. For the molecular dipole moment, the same two systems have been studied with an aldehyde end group. Both the molecular polarizability and the dipole moment are well described as a function of the chain length for both alkane and alkene chains demonstrating the power of the presented model.

Extracting the bulk effective parameters of a metamaterial via the scattering from a single planar array of particles

In this paper we present a method for retrieving the effective parameters of a metamaterial composed of a regular rectangular orthorhombic lattice of linear biaxially anisotropic particles suspended in free space. By assuming the point–dipole interaction approximation, equations are derived which extract the electric and magnetic polarizabilities of the individual particles given the measured or simulated scattering parameters of a single planar array of particles. These results are in turn substituted into the Clausius–Mossotti equations to find the bulk effective permittivity and effective permeability. To demonstrate our approach, the extraction method is applied to a metamaterial consisting of a cubic arrangement of magnetodielectric spheres using the scattering parameters obtained by simulating the structure with Ansoft HFSS. Our results show good agreement with a known analytical solution at frequencies in which the Clausius–Mossotti approximation is valid.

BOUNDARY EFFECTS IN THE ELECTROMAGNETIC RESPONSE OF A METAMATERIAL IN THE CASE OF NORMAL INCIDENCE

In this paper we investigate boundary effects and other consequences of spatial dispersion by analyzing in detail the response of a metamaterial half-space to a monochromatic plane wave normally incident from free-space. The metamaterial is composed of an orthorhombic lattice of identical particles, each of which exhibits both an electric and magnetic response. Rather than relying on the conventional boundary conditions and the Clausius-Mossotti equations, we use instead the point-dipole interaction model and an expansion of polarization in eigenmodes to determine the structure's dispersion relation and electromagnetic response. Using the nearest- neighbor approximation, we show how truncating the crystal lattice excites an ordinary mode and two modes that are necessary to satisfy the boundary conditions at the interface. For most cases, the extraordinary modes are evanescent, and thus form a thin transition layer at the surface. However, under certain conditions, typically near particle resonances, either one or both of these modes can be propagating.

Microscopic polarization in ropes and films of aligned carbon nanotubes

The microscopic electric polarization in terms of the dipole-dipole polarizability and its second hyperpolarizability of aligned films and ropes of carbon nanotubes has been studied theoretically by a point-dipole interaction model. The results show clearly the influence of intertube interactions on the microscopic polarization demonstrating the sensitivity of the electronic structure of carbon nanotubes to the surroundings. Both the polarizability and the second hyperpolarizability are screened due to the intertube interactions and deviate substantially from an additive model. It is noted that both the polarizability and the second hyperpolarizability reach their minimum values around the van der Waals separation. In the rope arrangement the polarizability of a tube is reduced by 10% and the second hyperpolarizability by as much as 50% as compared to an unperturbed tube.

Electronic Excited States of Polynucleotides: A Study by Electroabsorption Spectroscopy

Electroabsorption spectra were obtained for single-stranded polynucleotides poly(U), poly(C), poly(A), and poly(G) in glycerol/water glass at low temperature, and the differences in permanent dipole moment (Deltamu) and polarizability (Deltaalpha) were estimated for several spectral ranges covering the lowest energy absorption band around 260 nm. In each spectral range, the electrooptical parameters associated with apparent features in the absorption spectrum exhibit distinct values representing either a dominant single transition or the resultant value for a group of a relatively narrow cluster of overlapping transitions. The estimated spacing in energy between electronic origins of these transitions is larger than the electronic coupling within the Coulombic interaction model which is usually adopted in computational studies. The electroabsorption data allow us to distinguish a weak electronic transition associated with a wing in polynucleotide absorption spectra, at an energy below the electronic origin in absorption spectra of monomeric nucleobases. In poly(C) and poly(G), these low-energy transitions are related to increased values of Deltamu and Deltaalpha, possibly indicating a weak involvement of charge resonance in the respective excited states. A model capable of explaining the origin of low-energy excited states, based on the interaction of pipi* and npi* transitions in neighboring bases, is introduced and briefly discussed on the grounds of point dipole interaction.

High-Resolution ESR Study of the H···CH3, H···CHD2, D···CH2D, and D···CD3 Radical Pairs in Solid Argon

High-resolution electron spin resonance (ESR) spectra of radical pairs of a hydrogen atom that coupled with a methyl radical (H...CH3, H...CHD2, D...CH2D, and D...CD3) were observed for X-ray irradiated solid argon containing selectively deuterium-labeled methanes, CH4, CH2D2, and CD4, at 4.2 K. The double-quartet 1H-hyperfine (hf) splittings of ca. 26 and 1.16 mT at the Deltam(s) = +/-1 and Deltam(s) = +/-2 transitions, which are one-half of the isotropic 1H-hf splittings of an isolated H-atom and a CH3 radical, were attributed to the H...CH3 pair. The 1H-hf splittings at the Deltam(s) = +/-1 transition were further split by the fine structure (fs) due to the electron dipole-dipole coupling. Because of the high-resolution spectra, three different sets of the fs splitting, d, are clearly resolved in the spectra of both the H...CH3 and the D...CD3 pairs. The separation distance (inter-spin distance), R, between the H-atom and the CH3 radical being in pairs was evaluated from the d values based on a point-dipole interaction model. For the case of the H...CH3 pair, the observed d values of 4.2, 4.9, and 5.1 mT yield the respective separations, R = 0.87, 0.83, and 0.82 nm, to probe the trapping site of the pair in an Ar crystalline lattice (fcc). For the pair with R = 0.87 nm, for example, we propose that the CH3 radical occupies a substitutional site and the counter H-atom occupies either the interstitial tetrahedral sites directed away from the CH3 radicals by a distance of 0.87 nm or the interstitial octahedral sites by a distance of 0.88 nm. When a mixture of CH4 and CD4 in a solid Ar matrix was irradiated, only two different radical pairs, H...CH3 and D...CD3, were observed. This result clearly demonstrates that the hydrogen atom and methyl radicals, which undergo a pairwise trapping, can originate from the same methane molecule.

Analysis of the Cob(II)alamin−5‘-Deoxy-3‘,4‘-anhydroadenosyl Radical Triplet Spin System in the Active Site of Diol Dehydrase

A triplet spin system (S=1) is detected by low-temperature electron paramagnetic resonance (EPR) spectroscopy in samples of diol dehydrase and the functional adenosylcobalamin (AdoCbl) analogue 5'-deoxy-3',4'-anhydroadenosylcobalamin (anAdoCbl). Different spectra are observed in the presence and absence of the substrate (R,S)-1,2-propanediol. In both cases, the spectra include a prominent half-field transition (DeltaM(S) = 2) that is a hallmark of strongly coupled triplet spin systems. The appearance of 59Co hyperfine splitting in the EPR signals and the positions (g values) of the signals in the spectra show that half of the triplet spin is contributed by the low-spin Co2+ of cob(II)alamin. Line width effects from isotopic labeling (13C and 2H) in the 5'-deoxy-3',4'-anhydroribosyl ring demonstrate that the other half of the spin triplet is from an allylic 5'-deoxy-3',4'-anhydroadenosyl (anhydroadenosyl) radical. The zero-field splitting (ZFS) tensors describing the magnetic dipole-dipole interactions of the component spins of the triplets have rhombic symmetry because of electron spin delocalization within the organic radical component and the proximity of the radical to the low-spin Co2+. The dipole-dipole interaction was modeled as a summation of point-dipole interactions involving the spin-bearing orbitals of the anhydroadenosyl radical and cob(II)alamin. Geometries which are consistent with the ZFS tensors in the presence and absence of the substrate position the 5'-carbon of the anhydroadenosyl radical 3.5 and 4.1 A from Co2+, respectively. Homolytic cleavage of the cobalt-carbon bond of the analogue in the absence of the substrate indicates that, in diol dehydrase, binding of the coenzyme to the protein weakens the bond prior to binding of the substrate.

Computation of the static polarizabilities of multi-wall carbon nanotubes and fullerites using a Gaussian regularized point dipole interaction model

A Gaussian regularized dipolar model has been developed for carbon sp 2 structures. It is based on three parameters: the two components of the local polarizability tensor of the carbon atoms and a regularization parameter related to the size of the electronic clouds. The parameters of the model have been adjusted to reproduce the polarizability of isolated and FCC aggregates of C 60 and C 70 molecules, while avoiding any polarization catastrophes. The model has been applied to semiconducting single-wall nanotubes of finite and infinite length. Asymptotically, the axial and transverse polarizability per unit length vary linearly and quadratically with the tube radius, respectively, as already predicted by a tight-binding model and ab initio methods. As for multi-wall nanotubes, we show that the transverse polarizability is close to the transverse polarizability of the external layer taken alone, while the axial polarizability is close to the sum of the axial polarizabilities of the individual layers.

Scattering properties of point dipole interactions

The scattering properties of a three-parameter family of point dipole-like interactions constructed from a sequence of barrier-well rectangles are studied in the zero-range limit. Besides the real (unrenormalized) δ'-interaction, the derivative of Dirac's delta function, a whole family of point dipole interactions with a renormalized coupling constant are analysed. Depending on the parameter values, all these interactions being self-adjoint extensions of the one-dimensional Schrodinger operator are shown to be divided into four types: (i) interactions will full transparency, (ii) non-transparent interactions, (iii) partially transparent interactions acting effectively as a δ-interaction and (iv) interactions with partial transparency at discrete resonant values of the coupling constant.