Multipole Model Research Articles

X-ray charge density study of the 6-methyluracil derivative in the crystal: Revealing, consequences, and multipole refinement of minor static disorder

The accurate X-ray diffraction experiment was performed on the crystal of 1,6-dimethyl-3-propargyl-2,4-pyrimidinedione at 100 K. The static electron density (ED) was obtained via multipole refinement against these data. The presence of low-intense but nonrandom positive residual density peaks revealed that the structure was complicated by the minor conformational static disorder. Further analysis of the number and positions of critical points (CPs) (3, +3) of Laplacian of ED ∇2ρ(r) and the ratio of eigenvalues of its Hessian matrix unambiguously proved that the multipole-modeled ED of the main disorder component was contaminated by the second one. A method of visualizing the Laplacian minima as CP-ellipsoids with semiaxes inversely proportional to the eigenvalues of Hessian matrix of ∇2ρ(r) was applied to evaluate the correctness of modeled ED. Extra Laplacian CPs (3, +3) were attributed to the incorrect multipole populations, while the elongated shape of the corresponding discoid CP-ellipsoids was mainly considered to be the effect of troublesome kappa-parameters. A number of different multipole models were constructed in order to minimize the undesirable effects of disorder on the multipole ED. The two-component multipole model showed that the heterocyclic moiety of the minor component with an occupancy of 2% underwent the 180° rotation about the N3–C7 bond axis. Furthermore, the partial transfer of multipole parameters from the model refined against theoretical structure factors was utilized on the most problematic atoms, which massively contributed to disorder treatment. This approach allowed us to restore the ED of the main component in the crystal environment, which quality was gauged by the quantum-topological analysis as well as by its conformity to the data obtained from ab initio periodic calculations. Attempts to speculate on reasons for the limited disordering observed were made: theoretical calculations suggest that moderate hydrogen bonds support the disordering in the structure, while multiple weak noncovalent contacts, e.g., pi interactions, may provide the restrictions on the 50:50 disorder.

Acoustical characterization of a portable pneumatic infrasound source.

A portable infrasound source based on a pneumatic siren design is described. The source is capable of producing narrowband tone bursts over a frequency range of approximately 0.25-10 Hz. The acoustical characteristics of the infrasound source are presented, including measured sound pressure levels and horizontal directivity. The methodologies for processing the received acoustic signals are reported, and comparisons of measurements are made with a simple multipole model of the source. Measurements indicate that the pneumatic infrasound siren can be useful for a variety of applications for which a controlled, known infrasound source is required.

Polarizable Multipolar Molecular Dynamics Using Distributed Point Charges.

Distributed point charge models (DCM) and their minimal variants (MDCM) have been integrated with tools widely used for condensed-phase simulations, including a virial-based barostat and a slow-growth algorithm for thermodynamic integration. Minimal DCM is further developed in a systematic fashion to reduce fitting errors in the electrostatic interaction energy, and a new fragment-based approach offers considerable speedup of the MDCM fitting process for larger molecules with increased numbers of off-centered charged sites. Finally, polarizable (M)DCM is also introduced in the present work. The developments are used in condensed-phase simulations of popular force fields with commonly applied simulation conditions. (M)DCM equivalents for a range of widely used water force fields and for fluorobenzene (PhF) are developed and applied along with the original models to evaluate the impact of reformulating the electrostatic term. Comparisons of the molecular electrostatic potential (MEP), electrostatic interaction energies, and bulk properties from molecular dynamics simulations for a range of models from simple TIPnP (n = 3-5) to the polarizable, multipolar iAMOEBA models for water and an existing quadrupolar model for PhF confirm that DCMs retain the accuracy of the original models, providing a homogeneous, efficient, and generic point charge alternative to a multipolar electrostatic model for force field development and multilevel simulations.

Charge density of difluorides from synchrotron diffraction data and investigation of bonding in low valent binary fluorides

The experimental charge density analysis of two isostructural transition metal difluorides, CoF2 and NiF2 has been performed using single crystal synchrotron X-ray diffraction data. The multipole and MEM models of electron density and the thermal vibration parameters suggest that the difluoride of nickel is a hard molecule with more shared shell interaction nature than the difluoride of cobalt. In the course of study, a comparative study on fluorine bonding in low valent binary fluorides with metal cations of oxidation states, ranging from +1 to +3 have been accomplished and thoroughly analysed. The explored topological features derived from the Bader's theory of Atoms In Molecules (AIM) approach reveals the existence of ionic nature of bonding at +1 valence state of metal, as viewed in LiF and NaF and as the oxidation on metals ascends, intermediate interaction with increase in covalent nature is evidenced.

Efficient formulation of polarizable Gaussian multipole electrostatics for biomolecular simulations.

Molecular dynamics simulations of biomolecules have been widely adopted in biomedical studies. As classical point-charge models continue to be used in routine biomolecular applications, there have been growing demands on developing polarizable force fields for handling more complicated biomolecular processes. Here, we focus on a recently proposed polarizable Gaussian Multipole (pGM) model for biomolecular simulations. A key benefit of pGM is its screening of all short-range electrostatic interactions in a physically consistent manner, which is critical for stable charge-fitting and is needed to reproduce molecular anisotropy. Another advantage of pGM is that each atom's multipoles are represented by a single Gaussian function or its derivatives, allowing for more efficient electrostatics than other Gaussian-based models. In this study, we present an efficient formulation for the pGM model defined with respect to a local frame formed with a set of covalent basis vectors. The covalent basis vectors are chosen to be along each atom's covalent bonding directions. The new local frame can better accommodate the fact that permanent dipoles are primarily aligned along covalent bonds due to the differences in electronegativity of bonded atoms. It also allows molecular flexibility during molecular simulations and facilitates an efficient formulation of analytical electrostatic forces without explicit torque computation. Subsequent numerical tests show that analytical atomic forces agree excellently with numerical finite-difference forces for the tested system. Finally, the new pGM electrostatics algorithm is interfaced with the particle mesh Ewald (PME) implementation in Amber for molecular simulations under the periodic boundary conditions. To validate the overall pGM/PME electrostatics, we conducted an NVE simulation for a small water box of 512 water molecules. Our results show that to achieve energy conservation in the polarizable model, it is important to ensure enough accuracy on both PME and induction iteration. It is hoped that the reformulated pGM model will facilitate the development of future force fields based on the pGM electrostatics for applications in biomolecular systems and processes where polarization plays crucial roles.

Understanding how water models affect the anomalous pressure dependence of their diffusion coefficients

The self-diffusion coefficient of water shows an anomalous increase with increasing hydrostatic pressure up to a broad maximum (PmD) near 1 kbar at 298 K, which has been attributed to pressure effects on the tetrahedral hydrogen bond network of water. Moreover, the ability of a water model to reproduce anomalous properties of water is a signature that it is reproducing the network. Here, water was simulated between 1 bar and 5 kbar using three water models, two four-site (with all charges in the molecular plane) and one single-site multipole (which accounts for out-of-molecular plane charge), that have reasonable pressure-temperature properties. For these three models, the diffusion coefficients display a maximum in the pressure dependence and the radial distribution functions show good agreement with the limited experimental structural data at high pressure that are available. In addition, a variety of properties associated with the network are examined, including hydrogen bond lifetimes and occupancies, three-body angle distributions, and tetrahedral order parameters. Results suggest that the initial increasing diffusion with pressure is because hydrogen bonds are distorted and thus weakened by pressure, but above PmD, the hydrogen bonds are weakened to the point it behaves more like a normal liquid. In other words, the PmD may be a measure of the angular strength of hydrogen bonds. In addition, since the four-site models over-predict the values of PmD while the multipole model under-predicts it, out-of-plane charge may improve four-site models.

Multipolar effective-one-body waveforms for precessing binary black holes: Construction and validation

As gravitational-wave detectors become more sensitive, we will access a greater variety of signals emitted by compact binary systems, shedding light on their astrophysical origin and environment. A key physical effect that can distinguish among formation scenarios is the misalignment of the spins with the orbital angular momentum, causing the spins and the binary's orbital plane to precess. To accurately model such systems, it is crucial to include multipoles beyond the dominant quadrupole. Here, we develop the first multipolar precessing waveform model in the effective-one-body (EOB) formalism for the inspiral, merger and ringdown (IMR) of binary black holes: SEOBNRv4PHM. In the nonprecessing limit, the model reduces to SEOBNRv4HM, which was calibrated to numerical-relativity (NR) simulations, and waveforms from perturbation theory. We validate SEOBNRv4PHM by comparing it to the public catalog of 1405 precessing NR waveforms of the Simulating eXtreme Spacetimes (SXS) collaboration, and also to new 118 precessing NR waveforms, which span mass ratios 1-4 and spins up to 0.9. We stress that SEOBNRv4PHM is not calibrated to NR simulations in the precessing sector. We compute the unfaithfulness against the 1523 SXS precessing NR waveforms, and find that, for $94\%$ ($57\%$) of the cases, the maximum value, in the total mass range $20-200 M_\odot$, is below $3\%$ ($1\%$). Those numbers become $83\%$ ($20\%$) when using the IMR, multipolar, precessing phenomenological model IMRPhenomPv3HM. We investigate the impact of such unfaithfulness values with two parameter-estimation studies on synthetic signals. We also compute the unfaithfulness between those waveform models and identify in which part of the parameter space they differ the most. We validate them also against the multipolar, precessing NR surrogate model NRSur7dq4, and find that the SEOBNRv4PHM model outperforms IMRPhenomPv3HM.

Multipole analysis of substrate-supported dielectric nanoresonator metasurfaces via the T -matrix method

Substrates, and layered media in general, are ubiquitous and affect the properties of any object in their vicinity. However, their influence is, in an arbitrary framework, challenging to quantify analytically, especially for large arrays which additionally escape explicit numerical treatment due to the computational burden. In this work, we utilize a versatile $T$-matrix-based framework to generalize the coupled multipole model toward arbitrarily high multipole orders and substrate-supported arrays. We then employ it to study substrate-supported random/amorphous arrays of high index dielectric nanoparticles which are of wide interest due to relatively low losses and a highly tunable optical response, making them promising elements for nanophotonic devices. We discuss how multipole coupling rules evolve in the presence of a substrate in amorphous arrays for three interaction mechanisms: direct coupling between particles, substrate-mediated interparticle coupling, and substrate-mediated self-coupling. We show how the interplay of array density, distance from the substrate, and the latter's refractive index determine the optical response of an array. As an example, we use this framework to analyze refractometric sensing with substrate-supported arrays and demonstrate that the substrate plays a crucial role in determining the array sensitivity.

On the accuracy and precision of X-ray and neutron diffraction results as a function of resolution and the electron density model.

X-ray diffraction is the main source of three-dimensional structural information. In total, more than 1.5 million crystal structures have been refined and deposited in structural databanks (PDB, CSD and ICSD) to date. Almost 99.7% of them were obtained by approximating atoms as spheres within the independent atom model (IAM) introduced over a century ago. In this study, X-ray datasets for single crystals of hydrated α-oxalic acid were refined using several alternative electron density models that abandon the crude spherical approximation: the multipole model (MM), the transferable aspherical atom model (TAAM) and the Hirshfeld atom refinement (HAR) model as a function of the resolution of X-ray data. The aspherical models (MM, TAAM, HAR) give far more accurate and precise single-crystal X-ray results than IAM, sometimes identical to results obtained from neutron diffraction and at low resolution. Hence, aspherical approaches open new routes for improving existing structural information collected over the last century.

Magnetization Density Distribution of Sr_{2}IrO_{4}: Deviation from a Local j_{eff}=1/2 Picture.

5d iridium oxides are of huge interest due to the potential for new quantum states driven by strong spin-orbit coupling. The strontium iridate Sr_{2}IrO_{4} is particularly in the spotlight because of the so-called j_{eff}=1/2 state consisting of a quantum superposition of the three local t_{2g} orbitals with, in its simplest version, nearly equal populations, which stabilizes an unconventional Mott insulating state. Here, we report an anisotropic and aspherical magnetization density distribution measured by polarized neutron diffraction in a magnetic field up to 5T at 4K, which strongly deviates from a local j_{eff}=1/2 picture even when distortion-induced deviations from the equal weights of the orbital populations are taken into account. Once reconstructed by the maximum entropy method and multipole expansion model refinement, the magnetization density shows four cross-shaped positive lobes along the crystallographic tetragonal axes with a large spatial extent, showing that the xy orbital contribution is dominant. The analogy to the superconducting copper oxide systems might then be weaker than commonly thought.

Multipolar second-harmonic generation from high-Q quasi-BIC states in subwavelength resonators

Abstract We put forward the multipolar model which captures the physics behind linear and nonlinear response driven by high-quality (high-Q) supercavity modes in subwavelength particles. We show that the formation of such trapped states associated with bound states in the continuum (quasi-BIC) can be understood through multipolar transformations of coupled leaky modes. The quasi-BIC state appears with increasing the order of the dominating multipole, where dipolar losses are completely suppressed. The efficient optical coupling to this state in the AlGaAs nanodisk is implemented via azimuthally polarized beam illumination matching its multipolar origin. We establish a one-to-one correspondence between the standard phenomenological non-Hermitian coupled-mode theory and multipolar models. The derived multipolar composition of the generated second-harmonic radiation from the AlGaAs nanodisk is then validated with full-wave numerical simulations. Back-action of the second-harmonic radiation onto the fundamental frequency is taken into account in the coupled nonlinear model with pump depletion. A hybrid metal-dielectric nanoantenna is proposed to augment the conversion efficiency up to tens of per cent due to increasing quality factors of the involved resonant states. Our findings delineate novel promising strategies in the design of functional elements for nonlinear nanophotonics applications.

Russia’s Growth as a Regional Power in the Context of the Eurasian Economic Union

Abstract We are currently witnessing the emergence of new poles of power, practically from the bi-polar model of the post-World War 2 world, the Russian Federation has made in the last years made great efforts to introduce a multi-polar model, in other words it is seeking to affirm itself again on the world stage and gain leadership as a pole of power for the eastern Europe. There is a direct correlation between the status of „regional leader” and the economic power of the country who wants to achieve this status. Taking into account a set of indicators such as: share in the world GDP, trade and investment flows, the European Union, USA and China are at the moment the biggest poles of economic power in the world. Russia aspires to expand its influence and within the context of the Eurasian Economic Union seeks to reach the status of regional economic power. The main research questions of the article is if Russia can achieve through the Eurasian Economic Union and strategic partnership with China, the status of regional power and be a serios contender to the European Union. The article follows a qualitative methodology and examines the possible implications of the European Union- Eurasian economic Union competition at a regional level and Russia’s perspectives to achieve, as the leading force of the Union, a greater influence from an economic and geo-political perspective. The final section analyses the impact that the growth of the Chinese economy has had on the European Union as well as the Eurasian Economic Union. In this context, Russia has moved its attention towards Asia, particularly towards China, with whom all evidence points, is trying to form an alliance against the West, and is trying to capitalize on the ongoing trade war that is enfolding between the USA and China. The article concludes that Russia needs China, as the world’s second largest economy and important regional power more than China needs Russia and their current relationship is based more on their personal need to undermine other powers than any true common visions.

Multipolar superconductivity in Luttinger semimetals

Topological superconductivity in multiband systems has received much attention due to a variety of possible exotic superconducting order parameters as well as non-trivial bulk and surface states. While the impact of coexisting magnetic order on superconductivity has been studied for many years, such as ferromagnetic superconductors, the implication of coexisting multipolar order has not been explored much despite the possibility of multipolar hidden order in a number of $f$-electron materials. In this work, we investigate topological properties of multipolar superconductors that may arise when quadrupolar local moments are coupled to conduction electrons in the multiband Luttinger semimetal. We show that the multipolar ordering of local moments leads to various multipolar superconductors with distinct topological properties. We apply these results to the quadrupolar Kondo semimetal system, PrBi, by deriving the microscopic multipolar Kondo model and examining the possible superconducting order parameters. We also discuss how to experimentally probe the topological nature of the Bogoliubov quasiparticles in distinct multipolar superconductors via doping and external pressure, especially in the context of PrBi.

Design of Port Enterprise Financial Shared Service Center Based on Nested Logit Model

Liu, Y., 2020. Design of port enterprise financial Shared service center based on nested logit model. In: Yang, Y.; Mi, C.; Zhao, L., and Lam, S. (eds.), Global Topics and New Trends in Coastal Research: Port, Coastal and Ocean Engineering. Journal of Coastal Research, Special Issue No. 103, pp. 29–32. Coconut Creek (Florida), ISSN 0749-0208.The port enterprise financial Shared service center under the traditional design, has the characteristics of centralized management, but with the rapid improvement of the economic level, the service center cannot meet the diversified business model, so according to the hierarchical characteristics of the nested Logit model, the design of a new port enterprise financial Shared service center. This design USES elastic analysis method to obtain the working behavior characteristics of enterprise employees. Based on the nested Logit model, the multi-polarization comprehensive service model of financial Shared service center is designed. By changing the strategic positioning, the optimization design of the port enterprise financial Shared service center is realized. Experimental test results: taking 6 conditions in the four business modes as the test target, the financial center designed fails to meet only 3 test conditions, while the financial center designed by the traditional method fails to meet more than 50% of test conditions. It can be seen that the financial sharing service center designed this time meets the diversified development requirements of enterprises.

Investigation of bond topological and electrostatic properties of plumbagin molecule: An experimental and theoretical charge density study

Plumbagin is a naturally occurring derivative with several medicinal properties including antioxidants, antifungal, antimalarial, leprosy and antitumor properties; their structural and electrostatic properties are yet to be determined. The crystal structure of plumbagin has been solved; it shows that the compound crystallizes in P21/c space group with two molecules in the asymmetric unit. The electron density distribution of both molecules have determined from multipole model refinement. Among all the C–O bonds of both molecules (I & II), the OH group connected C–O bond and the methyl group connected C–C bond exhibits less electron density and the negative Laplacian of electron density as well. Further, the electrostatic potential (ESP) surface of two plumbagin molecules show some difference in their electronegative regions. The carbonyl O-atoms exhibit high electronegative ESP regions which are the key reactive locations of plumbagin when bind with the active site of target protein and in the ESP map, an aromatic π-cloud also observed in one of the molecule. The electron density distribution of O–H⋅⋅⋅O intermolecular interactions between the molecules I and II, reveals that these interactions are found very stronger than the other interactions in the crystal.

Charge density studies of energetic material: RDX

Experimental charge density study has been carried out for Cyclotrimethylene-trinitramine (space group Pbca), an explosive material from a low temperature X-ray diffraction experiment. The electron density was modeled using the Hansen-Coppens multipole model and refined to R=0.032 for 6226 unique observed reflections. The electron density, laplacian and electrostatic potential distributions are reported and discussed, especially, the properties of the bond (3,-1) critical points, which are thought to play a key role in the decomposition of the molecule. From the bond topological analysis of all the bonds, it is observed that the N–N bond is the weakest. The dominating nature of the oxygen atoms was clearly well understood from isosurface electrostatic potential of isolated and symmetrically sitting molecules in the crystal.

Charge density of 4-methyl-3-[(tetrahydro-2H-pyran-2-yl)oxy]thiazole-2(3H)-thione. A comprehensive multipole refinement, maximum entropy method and density functional theory study.

The structure of 4-methyl-3-[(tetrahydro-2H-pyran-2-yl)oxy]thiazole-2(3H)-thione (MTTOTHP) was investigated using X-ray diffraction and computational chemistry methods for determining properties of the nitrogen-oxygen bond, which is the least stable entity upon photochemical excitation. Experimentally measured structure factors have been used to determine and characterize charge density via the multipole model (MM) and the maximum entropy method (MEM). Theoretical investigation of the electron density and the electronic structure has been performed in the finite basis set density functional theory (DFT) framework. Quantum Theory of Atoms In Molecules (QTAIM), deformation densities and Laplacians maps have been used to compare theoretical and experimental results. MM experimental results and predictions from theory differ with respect to the sign and/or magnitude of the Laplacian at the N-O bond critical point (BCP), depending on the treatment of n values of the MM radial functions. Such Laplacian differences in the N-O bond case are discussed with respect to a lack of flexibility in the MM radial functions also reported by Rykounov et al. [Acta Cryst. (2011), B67, 425-436]. BCP Hessian eigenvalues show qualitatively matching results between MM and DFT. In addition, the theoretical analysis used domain-averaged fermi holes (DAFH), natural bond orbital (NBO) analysis and localized (LOC) orbitals to characterize the N-O bond as a single σ bond with marginal π character. Hirshfeld atom refinement (HAR) has been employed to compare to the MM refinement results and/or neutron dataset C-H bond lengths and to crystal or single molecule geometry optimizations, including considerations of anisotropy of H atoms. Our findings help to understand properties of molecules like MTTOTHP as progenitors of free oxygen radicals.

A Method to Determine Dielectric Model Parameters for Broadband Permittivity Characterization of Thin Film Substrates

This article introduces an efficient method to determine the dielectric model parameters of a thin film substrate from microstrip line measurements and electromagnetic analysis. The proposed method avoids using optimization algorithms which normally require extensive computation time. The complex permittivity is extracted through only one full-wave simulation. The multipole Debye model was employed to fit the extracted complex permittivity. The parameters of the best-fitting model obtained through this procedure are considered as the final results, which also ensure physically consistent characteristics. Polyimide was selected to validate the methodology. The best-fitting model generated by the proposed method has shown excellent agreement to the polyimide data sheet values at 1 MHz. Moreover, simulations using the parameters of the best-fitting model exhibit good agreement with the experimental propagation constant data of microstrip lines up to 60 GHz.

Regioselectivity of reduction of nitro groups in 3, 5-dinitrosalicylic acid monohydrate explored by experimental and theoretical charge density analysis

Preferential reduction of one of the two nitro groups in 3, 5-dinitrosalicylic acid monohydrate has been investigated using experimental charge density analysis from a high-resolution X-rays diffraction data at 100K combined with DFT theoretical calculations. The structure was refined using the classical Independent Atom Model as well as the Multipolar Atom Model. Bond characterization is performed in terms of charge density distribution and the associated topological properties. The theoretical (B3LYP/6-311++G(d,p), SMD/water) electrostatic potential molecular surfaces and atomic charges complimented the mechanism where one of the two nitro groups with higher negative charge gets preferentially reduced. The weak intermolecular interactions and hydrogen bonding are further quantified by the Hirshfeld surface analysis.

Vulnerability Assessment of Regional Water Resources

This paper established the regional water resources vulnerability impact factor system by selecting the impact factors and screening out the key factors based on principal component analysis and DPSIR model. Then combing with multipolar fuzzy pattern recognition model and improved fuzzy clustering iterative model, the regional water resource vulnerability assessment model was proposed. Taking Jinan city as an example, the results of water resource vulnerability assessment from 2000 to 2016 show that the water resource status of Jinan city has gone from bad to good, then to worse, and finally slowly getting better.