Quadrupole Contributions Research Articles

Second Harmonic Scattering of Molecular Aggregates

A general model is developed to describe the polarization-resolved second harmonic scattering (SHS) response from a liquid solution of molecular aggregates. In particular, the molecular spatial order is introduced to consider the coherent contribution, also known as the retarded contribution, besides the incoherent contribution. The model is based on the description of a liquid suspension of molecular dyes represented by point-like nonlinear dipoles, locally excited by the fundamental field and radiating at the harmonic frequency. It is shown that for a non-centrosymmetrical spatial arrangement of the nonlinear dipoles, the SHS response is very similar to the purely incoherent response, and is of electric dipole origin. However, for centrosymmetrical or close to centrosymmetrical spatial arrangements of the nonlinear dipoles, the near cancellation of the incoherent contribution due to the inversion symmetry rule allows the observation of the coherent contribution of the SHS response, also known as the electric quadrupole contribution. This model is illustrated with experimental data obtained for aqueous solutions of the dye Crystal Violet (CV) in the presence of sodium dodecyl sulfate (SDS) and mixed water-methanol solutions of the dye 4-(4–dihexadecylaminostyryl)-N-methylpyridinium iodide (DiA), a cationic amphiphilic probe molecule with a strong first hyper-polarizability; both CV and DiA form molecular aggregates in these conditions. The quantitative determination of a retardation parameter opens a window into the spatial arrangements of the dyes in the aggregates, despite the small nanoscale dimensions of the latter.

Power spectrum multipole expansion for H i intensity mapping experiments: unbiased parameter estimation

ABSTRACT We assess the performance of the multipole expansion formalism in the case of single-dish H i intensity mapping, including instrumental and foreground removal effects. This formalism is used to provide Markov chain Monte Carlo forecasts for a range of H i and cosmological parameters, including redshift space distortions and the Alcock–Paczynski effect. We first determine the range of validity of our power spectrum modelling by fitting to simulation data, concentrating on the monopole, quadrupole, and hexadecapole contributions. We then show that foreground subtraction effects can lead to severe biases in the determination of cosmological parameters, in particular the parameters relating to the transverse Baryon Acoustic Oscillations (BAO) rescaling, the growth rate, and the H i bias (α⊥, $\overline{T}_\rm{H{\small I}}f\sigma _8$, and $\overline{T}_{\mathrm {H}\,{\small I}}b_{\mathrm {H}\,{\small I}}\sigma _8$, respectively). We attempt to account for these biases by constructing a two-parameter foreground modelling prescription, and find that our prescription leads to unbiased parameter estimation at the expense of increasing the estimated uncertainties on cosmological parameters. In addition, we confirm that instrumental and foreground removal effects significantly impact the theoretical covariance matrix, and cause the covariance between different multipoles to become non-negligible. Finally, we show the effect of including higher order multipoles in our analysis, and how these can be used to investigate the presence of instrumental and systematic effects in H i intensity mapping data.

Design of High-Q Passband Filters Implemented Through Multipolar All-Dielectric Metasurfaces

We propose a novel class of ultrathin high Q passband filters designed by properly combining different multipolar resonances sustained by an all dielectric metasurface. A rigorous analytical model, based on surface impedance homogenization and accounting for the effects of both dipolar and the quadrupolar contributions to the overall scattering response, is derived and verified through numerical simulations. Then, it is described how it is possible to engineer the interactions between dipoles and quadrupoles in a metasurface made by core shell spherical elements to design ultrathin and broadband dielectric mirrors with a narrow transmission band. The proposed filters exhibit high Q factor resonances and can be implemented using realistic materials at either microwave or optical frequencies. Finally, we discuss how the proposed dielectric filters can be used to design self filtering aperture antennas exhibiting higher out of band selectivity compared with those implemented through metallic resonators.

Shape and Size Tuning of BiIII-Centered Polyoxopalladates: High Resolution 209Bi NMR and 205/206Bi Radiolabeling for Potential Pharmaceutical Applications.

We have discovered five bismuth(III)-containing polyoxopalladates (POPs) which were fully characterized by solution and solid-state physicochemical techniques: the cube-shaped [BiPd12O32(AsPh)8]5- (BiPd12AsL), [BiPd12O32(AsC6H4N3)8]5- (BiPd12AsLN), and [BiPd12O32(AsC6H4COO)8]13- (BiPd12AsLC) as well as the star-shaped [BiPd15O40(PO)10H6]11- (BiPd15P) and [BiPd15O40(PPh)10]7- (BiPd15PL), respectively. The organically modified capping groups phenylarsonate, p-azidophenylarsonate, and p-carboxyphenylarsonate were chosen as the azido (-N3) and carboxyl (-COOH) groups open up opportunities to covalently conjugate (via click reaction, amide coupling, etc.) with targeting vectors. The synthesis of p-azidophenylarsonate is reported here for the first time. The effects of the BiIII template and the organoarsonate vs -posphonate capping groups on the resulting POP shape (cube vs star) are discussed. The 209Bi NMR (I = 9/2) spectra of BiPd12AsL, BiPd12AsLN, and BiPd12AsLC revealed narrow peaks (ν1/2 ∼ 200 Hz) at 5470 ppm with a longitudinal relaxation time in the millisecond range (at 8.46 T). The absence of a quadrupolar relaxation contribution could be attributed to the allocation of BiIII in the highly symmetrical cuboid POP host cage. Similar peaks were absent in the 209Bi-NMR spectra of the star-shaped POPs BiPd15P and BiPd15PL due to the less symmetric coordination environment around the central BiIII ion. Further, 205/206Bi-radiolabeled POPs have been synthesized by incorporating a 205/206BiIII ion in the center of the POP structures. Carrier-free 205/206Bi radioisotopes (as surrogates of α-emitting 213Bi) were incorporated into the POP host-cage for the preparation of 205/206BiPd12AsL, 205/206BiPd12AsLN, 205/206BiPd12AsLC, and 205/206BiPd15PL, respectively. The radiometal incorporation was complete (>99% radiochemical yield) in 10 min according to radio-thin-layer chromatography. The 205/206BiPd12AsL polyanion was purified by solid-phase extraction. The incubation in rat serum showed the formation of a 205/206BiPd12AsL-protein aggregate.

Revisiting the basic theory of sum-frequency generation.

The basic theory of sum-frequency generation (SFG) is revisited. A rigorous derivation showing that linear optical transmission and reflection at an interface result from the interference of the incident wave and induced radiation wave in a medium is presented. The derivation is extended to SFG in a medium with a finite interface layer to see how SFG evolves. Detailed description on interface vs bulk and electric dipole (ED) vs electric quadrupole (EQ) contribution to SFG are provided with essentially no model dependence, putting the theory of SFG on a solid ground and removing possible existing confusions. Electric-quadrupole contributions to SFG from the interface and bulk are discussed. It is seen that there is a relevant bulk EQ contribution intrinsically inseparable in measurement from the interface ED contribution but plays a major role among all EQ contributions; its importance relative to the ED part can only be judged by referring to the established reference cases.

Nuclear magnetic resonance spin-lattice relaxation of lithium ions in aqueous solution by NMR and molecular dynamics.

We study the aqueous solvation dynamics of lithium ions using nuclear magnetic resonance spectroscopy, molecular dynamics, and viscosity measurements. Several relaxation mechanisms are examined to explain the strong increases of spin-lattice relaxation toward high concentrations. The use of both 6Li and 7Li isotopes is helpful to identify the quadrupolar contribution to the relaxation rate. In particular, it is found that the quadrupolar interaction constitutes the strongest contribution above a concentration of ∼10 molal. The next-strongest contribution arises from interactions that scale with the square of the gyromagnetic ratio (mostly the dipolar interaction), and the experimental relaxation rates appear to be fully accounted for when these mechanisms are combined over the concentration range up to the saturation concentration. The study of solvation dynamics, particularly at high concentrations, could be of relevance for electrolyte dynamics in aqueous Li-ion rechargeable batteries.

An extensive thermodynamic study on amino acids aqueous solutions and their CO2 solubility by taking into account dipolar and quadrupolar contributions

Amino acids are significant biological components that in water form predominant species named zwitterions. They are highly dipolar molecules with negative and positive charges. Aqueous solutions of amino acids have numerous practical applications where knowing their thermodynamic behavior is essential to model, design, and optimize processes concerned with them. Although, dipole-dipole interactions play important roles in aqueous solution of amino acids, dipole-quadrupole and quadrupole-quadrupole ones make significant contributions when considering the solubility a highly quadrupolar component such as carbon dioxide in aqueous solution of amino acids, i.e., CO2 capture by an amino acid aqueous solution. According to the literature, there is still room to apply a more simple and effective thermodynamic model considering dipole-dipole interactions for water + amino acid systems where this work did so by applying Cubic-Plus-Polar (CPP) Equation of State (EoS). Moreover, water + amino acid + carbon dioxide systems were thermodynamically modeled by taking into account dipole-dipole, dipole-quadrupole, and quadrupole-quadrupole contributions which such investigation has not yet been carried out in the literature. The predictive capability of the proposed model were extensively examined by evaluating the model-calculated data of activity coefficient, osmotic coefficient, density, and water activity of numerous aqueous solutions of amino acids including glycine, alanine, α-aminobutyric acid, valine, serine, proline, threonine, leucine, cysteine, methionine, glutamic acid, histidine, and arginine at various temperatures. The osmotic coefficient of water + valine + alanine and water + valine + glycine systems were also predicted by CPP EoS. The solubility of CO2 in aqueous solution of methionine was finally calculated by the proposed model over a wide range of pressure. The quantitative and qualitative results provided by CPP EoS verified its reliability in all studied situations.

Gravitational-wave detectors as particle-physics laboratories: Constraining scalar interactions with a coherent inspiral model of boson-star binaries

Gravitational-wave (GW) detections of binary neutron star coalescences play a crucial role to constrain the microscopic interaction of matter at ultrahigh density. Similarly, if boson stars exist in the universe their coalescence can be used to constrain the fundamental coupling constants of a scalar field theory. We develop the first coherent waveform model for the inspiral of boson stars with quartic interactions. The waveform includes coherently spin-induced quadrupolar and tidal-deformability contributions in terms of the masses and spins of the binary and of a single coupling constant of the theory. We show that future instruments such as the Einstein Telescope and the Laser Interferometer Space Antenna can provide strong complementary bounds on bosonic self-interactions, while the constraining power of current detectors is marginal.

Piezoelectric Electron-Phonon Interaction from AbInitio Dynamical Quadrupoles: Impact on Charge Transport in Wurtzite GaN.

First-principles calculations of e-ph interactions are becoming a pillar of electronic structure theory. However, the current approach is incomplete. The piezoelectric (PE) e-ph interaction, a long-range scattering mechanism due to acoustic phonons in noncentrosymmetric polar materials, is not accurately described at present. Current calculations include short-range e-ph interactions (obtained by interpolation) and the dipolelike Frölich long-range coupling in polar materials, but lack important quadrupole effects for acoustic modes and PE materials. Here we derive and compute the long-range e-ph interaction due to dynamical quadrupoles, and apply this framework to investigate e-ph interactions and the carrier mobility in the PE material wurtzite GaN. We show that the quadrupole contribution is essential to obtain accurate e-ph matrix elements for acoustic modes and to compute PE scattering. Our work resolves the outstanding problem of correctly computing e-ph interactions for acoustic modes from first principles, and enables studies of e-ph coupling and charge transport in PE materials.

Quadrupole Contribution of C═O Vibrational Band in Sum Frequency Generation Spectra of Organic Carbonates.

Sum Frequency Generation (SFG) is usually governed by surface-selective signals of dipole origin, but it can also contain some bulk signals of quadrupole origin. In this work, we examined the dipole and quadrupole contributions in the C═O stretching band of organic carbonate liquids with collaboration of heterodyne SFG measurement and theoretical analysis. As a result, we found that these spectra are substantially affected by the quadrupole contribution of the bulk, which resolved the discrepancy between the experimental and computational SFG spectra.

Interaction of atomic systems with quantum vacuum beyond electric dipole approximation

The photonic environment can significantly influence emission properties and interactions among atomic systems. In such scenarios, frequently the electric dipole approximation is assumed that is justified as long as the spatial extent of the atomic system is negligible compared to the spatial variations of the field. While this holds true for many canonical systems, it ceases to be applicable for more contemporary nanophotonic structures. To go beyond the electric dipole approximation, we propose and develop in this article an analytical framework to describe the impact of the photonic environment on emission and interaction properties of atomic systems beyond the electric dipole approximation. Particularly, we retain explicitly magnetic dipolar and electric quadrupolar contributions to the light-matter interactions. We exploit a field quantization scheme based on electromagnetic Green’s tensors, suited for dispersive materials. We obtain expressions for spontaneous emission rate, Lamb shift, multipole-multipole shift and superradiance rate, all being modified with dispersive environment. The considered influence could be substantial for suitably tailored nanostructured photonic environments, as demonstrated exemplarily.

Energy momentum tensor and the D term in the bag model

The energy-momentum tensor (EMT) form factors pave new ways for exploring hadron structure. Especially the D-term related to the EMT form factor D(t) has received a lot of attention due to its attractive physical interpretation in terms of mechanical properties. We study the nucleon EMT form factors and the associated densities in the bag model which we formulate for an arbitrary number of colors Nc and show that the EMT form factors are consistently described in this model in the large-Nc limit. The simplicity of the model allows us to test in a lucid way many theoretical concepts related to EMT form factors and densities including recently introduced concepts like normal and tangential forces, or monopole and quadrupole contributions to the angular momentum distribution. We also study the D-terms of rho-meson, Roper resonance, other N* states and Delta-resonances. Among the most interesting outcomes is the lucid demonstration of the deeper connection of EMT conservation, stability, the virial theorem and the negative sign of the D-term.

Fundamental Spin Interactions Underlying the Magnetic Anisotropy in the Kitaev Ferromagnet CrI_{3}.

We lay the foundation for determining the microscopic spin interactions in two-dimensional (2D) ferromagnets by combining angle-dependent ferromagnetic resonance (FMR) experiments on high quality CrI_{3} single crystals with theoretical modeling based on symmetries. We discover that the Kitaev interaction is the strongest in this material with K∼-5.2 meV, 25 times larger than the Heisenberg exchange J∼-0.2 meV, and responsible for opening the ∼5 meV gap at the Dirac points in the spin-wave dispersion. Furthermore, we find that the symmetric off-diagonal anisotropy Γ∼-67.5 μeV, though small, is crucial for opening a ∼0.3 meV gap in the magnon spectrum at the zone center and stabilizing ferromagnetism in the 2D limit. The high resolution of the FMR data further reveals a μeV-scale quadrupolar contribution to the S=3/2 magnetism. Our identification of the underlying exchange anisotropies opens paths toward 2D ferromagnets with higher T_{C} as well as magnetically frustrated quantum spin liquids based on Kitaev physics.

How surface-specific is 2nd-order non-linear spectroscopy?

Surfaces and interfaces play important roles in many processes and reactions and are therefore intensively studied, often with the aim of obtaining molecular-level information from just the interfacial layer. Generally, only the first few molecular layers next to the interface are relevant for the surface processes. In the past decades, 2nd-order nonlinear spectroscopies including sum-frequency generation and second harmonic generation have developed into powerful tools for obtaining molecularly specific insights into the interfacial region. These approaches have contributed substantially to our understanding of a wide range of physical phenomena. However, along with their wide-ranging applications, it has been realized that the implied surface-specificity of these approaches may not always be warranted. Specifically, the bulk quadrupole contribution beyond the electric dipole-approximation for a system with a weak nonlinear interface signal, as well as the diffuse layer contribution at charged interfaces, could mask the surface information. In this perspective paper, we discuss the surface-specificity of 2nd-order nonlinear spectroscopy, especially considering these two contributions.

Eccentric-orbit extreme-mass-ratio-inspiral radiation: Analytic forms of leading-logarithm and subleading-logarithm flux terms at high PN orders

We present new results on the analytic eccentricity dependence of several sequences of gravitational wave flux terms at high post-Newtonian (PN) order for extreme-mass-ratio inspirals. These sequences are the leading logarithms, which appear at PN orders $x^{3k} \log^k(x)$ and $x^{3k+3/2} \log^k(x)$ for integers $k\ge 0$ ($x$ a PN compactness parameter), and the subleading logarithms, which appear at orders $x^{3k} \log^{k-1}(x)$ and $x^{3k+3/2} \log^{k-1}(x)$ ($k\ge 1$), in both the energy and angular momentum radiated to infinity. For the energy flux leading logarithms, we show that to arbitrarily high PN order their eccentricity dependence is determined by particular sums over the function $g(n,e_t)$, derived from the Newtonian mass quadrupole moment, that normally gives the spectral content of the Peters-Mathews flux as a function of radial harmonic $n$. An analogous power spectrum $\tilde{g}(n,e_t)$ determines the leading logarithms of the angular momentum flux. For subleading logs, the quadrupole power spectra are again shown to play a role, providing a distinguishable part of the eccentricity dependence of these flux terms to high PN order. With the quadrupole contribution understood, the remaining analytic eccentricity dependence of the subleading logs can in principle be determined more easily using black hole perturbation theory. We show this procedure in action, deriving the complete analytic structure of the $x^6 \log(x)$ subleading-log term and an analytic expansion of the $x^{9/2}$ subleading log to high order in a power series in eccentricity. We discuss how these methods might be extended to other sequences of terms in the PN expansion involving logarithms.

Observation of a ferro-rotational order coupled with second-order nonlinear optical fields

Ferroic orders can be classified by the symmetry of their order parameters, and ferroelectric, ferromagnetic and ferro-toroidal orders have already been observed. The ferro-rotational order1–3, whose order parameter is an axial vector invariant under both time-reversal and spatial-inversion operations, is the final ferroic to be identified and has a vector order parameter. This order is closely related to a number of phenomena such as polar vortices4, giant magnetoelectric coupling5 and spin-helicity-driven ferroelectricity6, but it has received little attention so far. Here, using high-sensitivity rotational-anisotropy second-harmonic generation, we have exploited the electric quadrupole contribution to the second-harmonic generation to directly couple to this centrosymmetric ferro-rotational order in an archetype of type-II multiferroics, RbFe(MoO4)2. We found that two domain states with opposite ferro-rotational vectors emerge with distinct populations at the critical temperature Tc ≈ 195 K and gradually evolve to reach an even ratio at lower temperatures. Moreover, we have identified the ferro-rotational order phase transition as weakly first order and have revealed its coupling field as a unique combination of the induced electric quadrupole second-harmonic generation and the incident fundamental electric fields. The authors use optical spectroscopy to show that RbFe(MoO4)2 hosts a ferro-rotational phase. This is the final form of ferroic order to be observed.

Synchrotron x-ray scattering of magnetic and electronic structure of UN and U2N3 epitaxial films

We examine the magnetic ordering of UN and of a closely related nitride, U2N3, by preparing thin epitaxial films and using synchrotron x-ray techniques. The magnetic configuration and subsequent coupling to the lattice are key features of the electronic structure. The well-known antiferromagnetic (AF) ordering of UN is confirmed, but the expected accompanying distortion at Tn is not observed. Instead, we propose that the strong magneto-elastic interaction at low temperature involves changes in the strain of the material. These strains vary as a function of the sample form. As a consequence, the accepted AF configuration of UN may be incorrect. In the case of cubic a-U2N3, no single crystals have been previously prepared, and we have determined the AF ordering wave-vector. The AF Tn is close to that previously reported. In addition, resonant diffraction methods have identified an aspherical quadrupolar charge contribution in U2N3 involving the 5f electrons; the first time this has been observed in an actinide compound.

Symmetrized Normal Mode Analysis of the Spin–Lattice Relaxation of Metal Borohydrides in Solids

The spin–lattice relaxation of a quadrupolar nucleus 11B of solid borohydrides was measured by using solid‐state NMR techniques and the experimental data were analyzed with a newly‐constructed relaxation matrix. The spectral densities for dipole–dipole, quadrupolar, and random‐field interactions were obtained, and the quadrupolar contribution to the spin–lattice relaxation of 11B nucleus of solid borohydrides were calculated as well. The quadrupolar contribution was less than 10% in solid LiBH4, as has been reported. In addition, the quadrupolar contribution was more than 30% in solid Mg(BH4)2, as was expected. The symmetrized normal mode analysis for the spin–lattice relaxation of a quadrupolar nucleus could provide more accurate spectroscopic parameters, and is expected to improve accuracy of the description of the rotational motion of the local chemical unit containing the quadrupolar nucleus.

Quadrupolar mechanism for vibrational sum frequency generation at air/liquid interfaces: Theory and experiment

Vibrational sum frequency generation (VSFG) spectroscopy has been widely utilized to investigate various interfaces through molecular vibration. VSFG is usually attributed to the breakdown of the inversion symmetry at the interface within the electric dipole approximation. Although the electric dipole approximation is a very good approximation in the isotropic bulk, its validity is questionable at the interface because a large electric field gradient exists in the thin interface region. Thus, the quadrupole contribution may become significant at the interface. Here, we discuss the quadrupole contribution in VSFG from theoretical and experimental viewpoints. We describe a theory as to how the quadrupole contribution appears in experimental VSFG spectra by deriving the vibrational selection rule and discussing the interface selectivity. With this theoretical framework, we examine the mechanism of VSFG at the air/benzene and air/decane interfaces. The accurate determination of the vibrational frequencies realized by heterodyne-detected VSFG spectroscopy reveals that VSFG at the air/benzene interface arises from the quadrupolar mechanism. This means that the observation of VSFG does not imply a molecular alignment so that interfacial benzene molecules may be randomly oriented. Meanwhile, at the air/decane interface, it is concluded that the VSFG signal arises from the ordinary dipolar mechanism. This implies that decane molecules are aligned in a preferential direction at the interface despite their low polarity. This study demonstrates the importance of examining the mechanism of VSFG before discussing the interfacial structure based on VSFG spectra. A strategy to distinguish different mechanisms is also proposed. The present study further shows that the quadrupolar mechanism, if properly taken into consideration, enables us to obtain information about interfacial molecules beyond the restriction of the inversion symmetry breaking required by the dipolar mechanism, through the large electric field gradient localized at the interface.

Quantitative Susceptibility Mapping of Magnetic Quadrupole Moments

We modeled the magnetic field up to the quadrupole term to investigate not only the average susceptibility (dipole), but also the susceptibility distribution (quadrupole) contribution. Expanding the magnetic field up to the 2nd order provides the quadrupole (0th: monopole, 1st: dipole). Numerical simulations were performed to investigate the quadrupole contribution with subvoxel nonuniformity. Conventional dipole and our dipole + quadrupole models were compared in the simulation, the phantom and human brain. Furthermore, the quadrupole field was compared with the anisotropic susceptibility field in the dipole tensor model. In a nonuniformity case, numerical simulations showed a nonnegligible quadrupole field contribution. Our study showed a difference between the two methods in the susceptibility map at the edges; both the phantom and human studies showed sharper structural edges with the dipole + quadrupole model. Quadrupole moments showed contrast mainly at the structural boundaries. The quadrupole moment field contribution was smaller but nonnegligible compared to the anisotropic susceptibility contribution. Nonuniform and uniform source distributions can be separately considered by quadrupole expansion, which were mixed together in the dipole model. In the presence of nonuniformity, the susceptibility maps may be different between the two models. For a comprehensive field model, the quadrupole might need to be considered along with susceptibility anisotropy and microstructure effects.