Multipole Model Research Articles

From unipolarity to G-Zero and beyond: Political economy of the world without superpowers

The erosion of the unipolar system of international relations, accelerated as a result of the turbulent events of 2022, is returning experts in the field of international relations to discuss the phenomenon of the balance of power and its embodiment in various models. During the thirty-year period, following the end of the Cold War (1991–2021), the system of interstate relations went through periods when unipolar, bipolar and multipolar models were considered optimal. This article, based on the author’s address at the plenary session of the First Saint-Petersburg Congress of International Studies, proposes a political and economic interpretation of the consequences that the member states of the world community will face at a new stage in the transformation of the modern architecture of international relations in the 21st century through the mechanism of the balance of power. The trend of reducing state power in comparison with the growing economic power of market institutions and business structures in the modern era has been replaced by a reverse trend. It is characterized by the “return of the state” against the backdrop of a global system in crisis. The absence of a hegemonic state in the new system leads to the destruction of the foundations of the international liberal order, the formation of a decentralized system of alliances of states, an increase in the number and scale of economic conflicts, expressed both in the formation of regional trade blocks and in the expansion of the practice of applying economic sanctions as a substitute for armed conflicts of the past. A new era in the political and economic development of the planet, in which new actors will replace the superpowers of the past, should be characterized as a period of competitive interdependence. The coming years will show what will prevail — competition, extolled by representatives of the realistic school of the theory of international relations, i. e. inter-country/inter-bloc rivalry, or interdependence raised to the shield by the liberals.

Investigation of C–F···F–C Interactions Using Experimental and Theoretical Charge Density Analyses

Among the halogens, fluorine plays a crucial role in governing the potency of drugs and pharmaceuticals. In this study, experimental and theoretical charge density analyses have been performed on N-(2,5-difluorophenyl)-3,5-difluoro-N-(3-methoxyphenethyl)benzamide to study the nature of weak intermolecular interactions, especially the F···F interactions, mediated by organic fluorine. The kind of C–F···F–C interactions analyzed in this study are Type I and quasi Type I/Type II. For this, the quantitative and qualitative analyses of electron densities have been performed based on the multipole modeling of high-resolution experimental X-ray diffraction data and theoretical structure factors generated from periodic calculations. The interactions have been analyzed based on the topological properties of electron densities using quantum theory of atoms in molecules (QTAIM). Thus, the nature of organic fluorine has been investigated by studying deformation of electron densities, Laplacian, and topological parameters.

Foreign Policy and «Diplomacy of the World Power with Chinese Characteristics»: Based on the Report of the CPC Central Committee to the XX Congress

The article analyzes the text of the report of the Central Committee of the Communist Party of China, which Xi Jinping delivered at the XX Party Congress, in the context of the current state and prospects of the foreign policy strategy of the People’s Republic of China, as well as the challenges to the country’s foreign policy in recent years. Based on the results of the analysis of the report, changes in China’s strategic positions are discussed. It is concluded that the main strategy of the foreign policy of the People’s Republic of China as a whole will remain unchanged: the country in foreign affairs relies on the domestic political situation, the ideology of the Communist Party of China and the role of the national leader, openness, modernization of the system and the potential to ensure national security and social stability. The main challenge for the People’s Republic of China remains the Taiwan issue, which is supposed to be resolved peacefully in the “one countrytwo systems” format, but the use of force is not ruled out. Relations with the United States of America are defined as a restrained global confrontation without open counteraction. The Russian-Chinese strategic partnership is understood as the choice of the People’s Republic of China, which meets its national interests, which will contribute to the formation of a multipolar model of the modern world. The actualization of the country’s foreign policy strategy at the XX Congress of the CPC is shown in its dynamics and comparison with previous strategies.

Electron Density Analysis of Metal–Metal Bonding in a Ni4 Cluster Featuring Ferromagnetic Exchange

We present a combined experimental and theoretical study of the nature of the proposed metal-metal bonding in the tetranuclear cluster Ni4(NPtBu3)4, which features four nickel(I) centers engaged in strong ferromagnetic coupling. High-resolution single-crystal synchrotron X-ray diffraction data collected at 25 K provide an accurate geometrical structure and a multipole model electron density description. Topological analysis of the electron density in the Ni4N4 core using the quantum theory of atoms in molecules clearly identifies the bonding as an eight-membered ring of type [Ni-N-]4 without direct Ni-Ni bonding, and this result is generally corroborated by an analysis of the energy density distribution. In contrast, the calculated bond delocalization index of ∼0.6 between neighboring Ni atoms is larger than what has been found for other bridged metal-metal bonds and implies direct Ni-Ni bonding. Similar support for the presence of direct Ni-Ni bonding is found in the interacting quantum atom approach, an energy decomposition scheme, which suggests the presence of stabilizing Ni-Ni bonding interactions with an exchange-correlation energy contribution approximately 50% of that of the Ni-N interactions. Altogether, while the direct interactions between neighboring Ni centers are too weak and sterically constrained to bear the signature of a topological bond critical point, other continuous measures clearly indicate significant Ni-Ni bonding. These metal-metal bonding interactions likely mediate direct ferromagnetic exchange, giving rise to the high-spin ground state of the molecule.

Features of the socio-political consolidation of Russian society and the state in the conditions of a special military operation: sociological analysis

In the article, the author examines the risks and reserves of socio-political consolidation of Russian society and the state in the conditions of sanctions and a special military operation in Ukraine. The study is based on the analysis of a wide range of literature, sources of official information and statistics, the results of sociological research of Russian and international organizations. The analysis of global trends allowed us to fix the destructive nature of the consolidation processes of society and government taking place in most countries of the world. Their characteristic features are the decline in the level of trust of citizens, the growing alienation of the state and society, the crisis of democracy around the world. According to citizens, their governments, intentionally spreading false information, contribute to the disunity and division of the national civil society. In modern conditions, citizens of countries share a multipolar model of the world order. The plans of the political leaders of unfriendly states to tighten the sanctions policy against Russia and strengthen the provision of military assistance to Ukraine have not found active support of the population in a number of countries around the world. Russia is not an aggressor in the consciousness of the society of most states. In our country, the markers of socio-political consolidation of society and the state were the increase in the levels of trust of citizens in state structures and loyalty to the policy pursued by the authorities. The Russian state managed to contain a sharp decline in the quality of life of citizens and establish a dialogue in the information space. The key reserve for the socio-political consolidation of Russian society and the state is the formation of a unified national idea, ideology, stable moral guidelines based on the values of justice, peace, law and patriotism.

Multipolar Modeling of Spatially Dispersive Metasurfaces

There is today a growing need to accurately model the angular scattering response of metasurfaces for optical analog processing applications. However, the current metasurface modeling techniques are not well suited for such a task since they are limited to small angular spectrum transformations, as shall be demonstrated. The goal of this work is to overcome this limitation by improving the modeling accuracy of these techniques and, specifically, to provide a better description of the angular response of metasurfaces. This is achieved by extending the current methods, which are restricted to dipolar responses and weak spatially dispersive effects, so as to include quadrupolar responses and higher-order spatially dispersive components. The accuracy of the newly derived multipolar model is demonstrated by predicting the angular scattering of a dielectric metasurface. This results in a modeling accuracy that is at least two times better than the standard dipolar model.

Accelerating multimodal gravitational waveforms from precessing compact binaries with artificial neural networks

Gravitational waves from the coalescences of black hole and neutron stars afford us the unique opportunity to determine the sources' properties, such as their masses and spins, with unprecedented accuracy. To do so, however, theoretical models of the emitted signal that are i) extremely accurate and ii) computationally highly efficient are necessary. The inclusion of more detailed physics such as higher-order multipoles and relativistic spin-induced orbital precession increases the complexity and hence also computational cost of waveform models, which presents a severe bottleneck to the parameter inference problem. A popular method to generate waveforms more efficiently is to build a fast surrogate model of a slower one. In this paper, we show that traditional surrogate modelling methods combined with artificial neural networks can be used to build a computationally highly efficient while still accurate emulation of multipolar time-domain waveform models of precessing binary black holes. We apply this method to the state-of-the-art waveform model SEOBNRv4PHM and find significant computational improvements: On a traditional CPU, the typical generation of a single waveform using our neural network surrogate SEOBNN_v4PHM_4dq2 takes 18ms for a binary black hole with a total mass of $44 M_{\odot}$ when generated from 20Hz. In comparison to SEOBNRv4PHM itself, this amounts to an improvement in computational efficiency by two orders of magnitude. Utilising additional GPU acceleration, we find that this speed-up can be increased further with the generation of batches of waveforms simultaneously. Even without additional GPU acceleration, this dramatic decrease in waveform generation cost can reduce the inference timescale from weeks to hours.

Experimental X-ray Charge-Density Studies─A Suitable Probe for Superconductivity? A Case Study on MgB2.

Case studies of 1T-TiSe2 and YBa2Cu3O7-δ have demonstrated that X-ray diffraction (XRD) studies can be used to trace even subtle structural phase transitions which are inherently connected with the onset of superconductivity in these benchmark systems. However, the utility of XRD in the investigation of superconductors like MgB2 lacking an additional symmetry-breaking structural phase transition is not immediately evident. Nevertheless, high-resolution powder XRD experiments on MgB2 in combination with maximum entropy method analyses hinted at differences between the electron density distributions at room temperature and 15 K, that is, below the Tc of approx. 39 K. The high-resolution single-crystal XRD experiments in combination with multipolar refinements presented here can reproduce these results but show that the observed temperature-dependent density changes are almost entirely due to a decrease of atomic displacement parameters as a natural consequence of a reduced thermal vibration amplitude with decreasing temperature. Our investigations also shed new light on the presence or absence of magnesium vacancies in MgB2 samples─a defect type claimed to control the superconducting properties of the compound. We propose that previous reports on the tendency of MgB2 to form non-stoichiometric Mg1-xB2 phases (1 - x ∼ 0.95) during high-temperature (HT) synthesis might result from the interpretation of XRD data of insufficient resolution and/or usage of inflexible refinement models. Indeed, advanced refinements based on an Extended Hansen-Coppens multipolar model and high-resolution X-ray data, which consider explicitly the contraction of core and valence shells of the magnesium cations, do not provide any significant evidence for the formation of non-stoichiometric Mg1-xB2 phases during HT synthesis.

New refinement strategies for a pseudoatom databank – toward rapid electrostatic interaction energy estimations

Pseudoatom databanks, collections of parameters from the multipole model of electron densities for various atom types, are used to replace the Independent Atom Model with the more accurate Transferable Aspherical Atom Model (TAAM) in crystal structure refinements. The databanks are also employed to reconstruct the electron density of a molecule, crystal or biomacromolecular complex in a fast yet accurate way and compute various properties such as the energy of electrostatic interactions, for example. A even faster but similarly accurate model for estimations of electrostatic energy exists called aug-PROmol [Bojarowski, Kumar & Dominiak (2016). ChemPhysChem, 17, 2455–2460]. A model analogous to aug-PROmol cannot be built from the current pseudoatom databanks, as they perform badly when truncated to the monopole level. Here, new strategies for multipole model refinements were sought, leading to better parametrization at the monopole level. This would allow the creation of a pseudoatom databank in a single route of model parametrization, which would be suitable for both crystal structure refinement and rapid electrostatic energy calculations. Here it is shown that the cumulative approach to multipole model refinements, as opposed to simultaneous or iterative refinements of all multipole model parameters (Pv , κ, Plm , κ′), leads to substantially different models of electron density. Cumulative refinement of two blocks of parameters, the first with Pv and κ and then the second with Plm and κ′, leads to the P v κ|P lm κ′ model having promising properties. The P v κ|P lm κ′ model is as good as the University at Buffalo DataBank (UBDB) in X-ray structure TAAM refinements and electrostatic energy estimations, especially for less polar molecules. When truncated to the monopole level, the P v κ model has a chance to replace aug-PROmol in fast yet accurate electrostatics energy calculations, although some improvements in κ parametrization for polar functional groups are still needed. The P v κ model is also a source of point charges which behave similarly to restrained electrostatic potential (RESP) charges in electrostatic interaction energy estimations.

Synthesis, crystal structure and Hirshfeld surface analysis of tert-butyl N-acetyl-carbamate.

This article reports a practical synthesis of tert-butyl acetyl-carbamate, C7H13NO3, from N-Boc-thio-acetamide and the study of its crystal structure. The reaction proceeds in the presence of natural phosphate as a catalyst, with excellent yield, simple workup and benign environment. The crystal structure was refined using a transferred multipolar atom model. In the crystal, symmetrical pairs of strong N-H⋯O hydrogen bonds connect the mol-ecules into dimers with an R 2 2(8) ring motif. The inter-actions between neighbouring dimers are mostly van der Waals, between hydro-phobic methyl groups. Hirshfeld surface analysis shows the major contributions to the crystal packing are from H⋯H (42.6%) and O⋯H (26.7%) contacts.

Accurate Reproduction of Quantum Mechanical Many-Body Interactions in Peptide Main-Chain Hydrogen-Bonding Oligomers by the Polarizable Gaussian Multipole Model.

A key advantage of polarizable force fields is their ability to model the atomic polarization effects that play key roles in the atomic many-body interactions. In this work, we assessed the accuracy of the recently developed polarizable Gaussian Multipole (pGM) models in reproducing quantum mechanical (QM) interaction energies, many-body interaction energies, as well as the nonadditive and additive contributions to the many-body interactions for peptide main-chain hydrogen-bonding conformers, using glycine dipeptide oligomers as the model systems. Two types of pGM models were considered, including that with (pGM-perm) and without (pGM-ind) permanent atomic dipoles. The performances of the pGM models were compared with several widely used force fields, including two polarizable (Amoeba13 and ff12pol) and three additive (ff19SB, ff15ipq, and ff03) force fields. Encouragingly, the pGM models outperform all other force fields in terms of reproducing QM interaction energies, many-body interaction energies, as well as the nonadditive and additive contributions to the many-body interactions, as measured by the root-mean-square errors (RMSEs) and mean absolute errors (MAEs). Furthermore, we tested the robustness of the pGM models against polarizability parameterization errors by employing alternative polarizabilities that are either scaled or obtained from other force fields. The results show that the pGM models with alternative polarizabilities exhibit improved accuracy in reproducing QM many-body interaction energies as well as the nonadditive and additive contributions compared with other polarizable force fields, suggesting that the pGM models are robust against the errors in polarizability parameterizations. This work shows that the pGM models are capable of accurately modeling polarization effects and have the potential to serve as templates for developing next-generation polarizable force fields for modeling various biological systems.

Латиноамериканская интеграция в условиях становления многополярной конфигурации международных отношений

Within the framework of the dynamically changing conditions of world politics and the long-term trend towards the formation of a multipolar model of international relations, as well as to the transition to a downward wave of the globalization cycle, the search for alternative foundations for socio-political, economic, cultural and civilizational development, one of which is integration in the separate self-sufficient region. One of these regions is Latin America, which has significant integration opportunities, as well as a deep potential for development in all areas of public life.

Multipolar Atom Types from Theory and Statistical Clustering (MATTS) Data Bank: Impact of Surrounding Atoms on Electron Density from Cluster Analysis.

The multipole model (MM) uses an aspherical approach to describe electron density and can be used to interpret data from X-ray diffraction in a more accurate manner than using the spherical approximation. The MATTS (multipolar atom types from theory and statistical clustering) data bank gathers MM parameters specific for atom types in proteins, nucleic acids, and organic molecules. However, it was not fully understood how the electron density of particular atoms responds to their surroundings and which factors describe the electron density in molecules within the MM. In this work, by applying clustering using descriptors available in the MATTS data bank, that is, topology and multipole parameters, we found the topology features with the biggest impact on the multipole parameters: the element of the central atom, the number of first neighbors, and planarity of the group. The similarities in the spatial distribution of electron density between and within atom type classes revealed distinct and unique atom types. The quality of existing types can be improved by adding better parametrization, definitions, and local coordinate systems. Future development of the MATTS data bank should lead to a wider range of atom types necessary to construct the electron density of any molecule.

Multipolar Atom Types from Theory and Statistical Clustering (MATTS) Data Bank: Restructurization and Extension of UBDB.

A fast and accurate operational model of electron density is crucial in many scientific disciplines including crystallography, molecular biology, pharmaceutical, and structural chemistry. In quantum crystallography, the aspherical refinement of crystal structures is becoming increasingly popular because of its accurate description in terms of physically meaningful properties. The transferable aspherical atom model (TAAM) is quick and precise, though it requires a robust algorithm for atom typing and coverage of the most popular atom types present in small organic molecules. Thus, the University at Buffalo Databank (UBDB) has been renamed to the Multipolar Atom Types from Theory and Statistical clustering (MATTS) data bank, broadened, restructured, and implemented into the software DiSCaMB with 651 atom types obtained from 2316 small-molecule crystal structures containing C, H, N, O, P, S, F, Cl, and Br atoms. MATTS2021 data bank now covers most of the small molecules, peptides, RNA, DNA, and some frequently occurring cations and anions in biological, pharmaceutical, and organic materials, including the majority of known crystal structures composed of the above elements. The multipole model parameters (Pval, κ, κ′, Plm) obtained for different atom types were greatly influenced by neighboring atom types, hybridization, geometrical strain in the ring system, and charges on the molecule. Contrary to previous findings, the atoms showing variable oxidation states and ions deviate from the linear dependence of monopole-derived charges on the expansion–contraction κ parameter.

Boundary admittance estimation for wave-based acoustic simulations using Bayesian inference.

Acoustic surface admittance/impedance at domain boundaries is essential for wave-based acoustic simulations. This work applies two levels of Bayesian inference to estimate the order and the parameter values of the multipole admittance model. The frequency-dependent acoustic admittance is experimentally measured. Incorporating the maximum entropy strategy, the unified Bayesian framework is applied to the multipole approximation. Analysis results demonstrate that multipole model-based Bayesian inference is well suited to estimating the arbitrary frequency-dependent boundary condition within a wave-based simulation framework.

The Relevance of Experimental Charge Density Analysis in Unraveling Noncovalent Interactions in Molecular Crystals.

The work carried out by our research group over the last couple of decades in the context of quantitative crystal engineering involves the analysis of intermolecular interactions such as carbon (tetrel) bonding, pnicogen bonding, chalcogen bonding, and halogen bonding using experimental charge density methodology is reviewed. The focus is to extract electron density distribution in the intermolecular space and to obtain guidelines to evaluate the strength and directionality of such interactions towards the design of molecular crystals with desired properties. Following the early studies on halogen bonding interactions, several “sigma-hole” interaction types with similar electrostatic origins have been explored in recent times for their strength, origin, and structural consequences. These include interactions such as carbon (tetrel) bonding, pnicogen bonding, chalcogen bonding, and halogen bonding. Experimental X-ray charge density analysis has proved to be a powerful tool in unraveling the strength and electronic origin of such interactions, providing insights beyond the theoretical estimates from gas-phase molecular dimer calculations. In this mini-review, we outline some selected contributions from the X-ray charge density studies to the field of non-covalent interactions (NCIs) involving elements of the groups 14–17 of the periodic table. Quantitative insights into the nature of these interactions obtained from the experimental electron density distribution and subsequent topological analysis by the quantum theory of atoms in molecules (QTAIM) have been discussed. A few notable examples of weak interactions have been presented in terms of their experimental charge density features. These examples reveal not only the strength and beauty of X-ray charge density multipole modeling as an advanced structural chemistry tool but also its utility in providing experimental benchmarks for the theoretical studies of weak interactions in crystals.

Концептуальні аспекти міждисциплінарного підходу до регіональних студій у системі глобальної е

The dynamic development of the processes of economic transformation in the conditions of aggravation of world security is accompanied by the change in the geopolitical situation at the international level. There is a formation of the basis of systemic changes at the level of polarization and regionalization of the modern world with the formation of a new multipolar model and new regional centers in the global economy system. The development of new scientific approaches to the regional studies is becoming especially important in order to ensure the effective development of foreign policy and international relations. In the course of research, it has been noted that the scientific basis of regional studies consists of several modern concepts, theories and conceptual views. Conceptual aspects of interdisciplinary scientific approach to regional studies in the system of global economy have been determined. The sequence of formation of the conceptual apparatus of the region taking into account general and specific features, as well as identification of links in the regional system has been proposed. As conceptual aspects of the interdisciplinary approach to regional studies, the following components of the subsystem have been proposed, which provide conditions for effective use of potential and formation of mechanisms to increase the competitiveness of regions in various fields, including international, economic, social, environmental and sustainable socioeconomic development. It has been proposed to quantify the potential of the region and the effectiveness of its use as a basis for ensuring the competitiveness of the regional economic system. On the basis of the analysis of numerous scientific researches the systematization of the factors influencing potential of regional economic system and efficiency of its use has been carried out. Based on the interdisciplinary nature of the conceptual aspects, a methodological approach to quantitative assessment of the region’s potential and efficiency of its use has been developed. Practical application of the proposed approach allows identifying ways to increase the efficiency of the potential of the regions and form the basis for ensuring the competitiveness of the regional economic system in the context of global transformation.

Benzene and Borazine, so Different, yet so Similar: Insight from Experimental Charge Density Analysis.

Although benzene and borazine are isoelectronic and isostructural, they have very different electronic structures, mainly due to the polar nature of the B-N bond. Herein, we present an experimental study of the charge density distribution obtained from the multipole model formalism and Hirshfeld atom refinement (HAR) based on high-resolution X-ray diffraction data of borazine B3N3H6 (1) and B,B',B″-trichloroborazine (2) crystals. These data are compared to those obtained from HAR for benzene (4) and 1,3,5-trichlorobenzene (5) and further compared with values obtained from density functional theory calculations in the gas phase, where N,N',N″-trichloroborazine (3) was also included. The results confirm that, unlike benzene, borazines are only weakly aromatic with an island-like electronic delocalization within the B3N3 ring involving only the nitrogen atoms. Furthermore, delocalization indices and interacting quantum atom energy for bonded and non-bonded atoms were found to be highly suitable indicators capable of describing the origin of the discrepancies observed when the degree of aromaticity in 2 and 3 is evaluated using common aromaticity indices. Additionally, analysis of intermolecular interactions in the crystals brings further evidence of a weakly aromatic character of the borazines as it reveals surprising similarities between the crystal packing of borazine and benzene and also between B,B',B″-trichloroborazine and 1,3,5-trichlorobenzene.

A multipole model-based boundary admittance estimation for wave-based room-acoustic simulations using Bayesian inference

Room-acoustic simulations for sound wave propagation require significant knowledge of the boundary conditions for the room boundary surface. This work presents the application of model-based Bayesian inference on the surface admittance estimation problem. First, this work deals with selecting the multipole admittance model through the higher level of inference, Bayesian model selection. And the parameters of the chosen multipole admittance model are estimated through the first (lower) level of inference, Bayesian parameter estimation. This work focuses on the approximation of the surface admittance as a function of frequency given a set of acoustic admittance. This frequency-dependent admittance is deduced either from the experimental measurements of a porous material or numerical predictions in order to demonstrate wave-based boundary conditions to incorporate arbitrary admittance functions with frequency ranges under consideration. According to the analytical results and numerical verifications conducted in this work, Bayesian inference based on the multipole model is well-suited for the estimation of the frequency-dependent boundary conditions within a wave-based simulation framework.

Global ecological and economic policy: strategic management in the conditions of economic transformation

This article is devoted to the most important issue of achieving an innovative breakthrough in the context of the transformation of the economic environment against the background of the formation of the information society in the context of the deployment of the sixth technological order. Humanity, which is entering a completely new era, characterized by a fundamentally different system of social relations, values and meanings, is forced today to give priority to the search for solutions to global problems. The transition to a multipolar world model aggravates the competition of developed countries, on the one hand, and weakens the role of developing countries, making them dependent, subordinate. At the same time, the role of the state in the life of society is significantly reduced. Globalization abolishes borders, eliminates inequalities, and at the same time deprives entire peoples of their national, cultural, and linguistic identity, and erases historical memory. Today, the world is divided into globalists and anti-globalists, but civilization still faces the need to move to sustainable development, which requires an innovative breakthrough not only on the scale of individual countries, but also on a broader, planetary scale. The proposed article is an attempt to answer the question of whose forces this innovative breakthrough should be achieved. It deals with the problem of developing a new theoretical and methodological basis for staffing an innovative breakthrough in the context of the deployment of the sixth technological order against the background of the greening of public and, in particular, economic relations.