Orbital Character Research Articles

Insulator-to-metal transition, magnetic anisotropy, and improved TC in a ferrimagnetic La2CoIrO6: strain influence.

The elegant interactions between Coulomb repulsion and spin-orbit coupling in Ir-based double perovskite oxides (DPO) normally induce peculiar magnetic behavior. Herein, we investigate the effect of the development of biaxial [110] strain on the formation energetics, and electronic and magnetic properties of the La2CoIrO6 DPO employing density functional theory calculations. Our results reveal that the unstrained motif is a Mott-insulator achieving an energy band gap of 0.35 eV with a ferrimagnetic (FiM) ground state, which essentially arises due to anti-ferromagnetic (AFM) coupling between the half-occupied Co t2g and partially occupied Ir t2g/empty eg orbitals via oxygen 2p states. Along with this, it is found that [001] (c-axis) is the easy magnetic axis, which results in 12.5 meV total energy per u.c., obtaining a large anisotropy constant of 0.8 × 108 erg cm-3. The computed partial spin-magnetic moments on the Co/Ir ion are 2.64/-0.46 μB, where the negative sign on the Ir ion moment confirms the AFM interactions between them. Additionally, the t2g/eg and t2g orbital characteristics of Co2+ and Ir4+ ions are visible in the spin-magnetization density isosurfaces plot, respectively. Likewise, the estimated Curie temperature (TC) using the Heisenberg model is 104 K, which is in agreement with the experimentally observed value of 94/97 K. Interestingly, an insulator-to-metal transition is achieved at a critical compressive strain of -6% with a robust FiM state, where the Co 3dxy and Ir 5dx2-y2 orbitals are mainly responsible for metallicity. Simultaneously, the magnetocrystalline anisotropy energy and TC can be sufficiently enhanced by applying compressive strain due to enhancement in the structural distortions. So this work suggested that the strain strategy is an efficient approach to tuning the properties of the compounds for their feasible realization in spintronics.

Assembly of multilayer phthalocyanine vanadium oxide molecules on Ag<sub>2</sub>Sb alloy monolayer

Fabricating ordered molecular films and further tuning their assembly behavior is important for constructing organic devices with diverse performances. By using high-resolution scanning tunneling microscopy, in this work, we demonstrate that well-organized vanadyl phthalocyanine (VOPc) films can be formed <i>via</i> ‘bottom-up’ molecular self-assembly on a binary alloy Ag<sub>2</sub>Sb/Ag(111). The Ag<sub>2</sub>Sb monolayer is prepared by evaporating Sb atoms on clean Ag(111) and followed by annealing. The VOPc molecules are deposited on the Ag<sub>2</sub>Sb layer <i>via</i> thermal evaporation. The molecular configuration, structural and orbital characteristics of VOPc are clearly clarified at a submolecular level. It is found that initially the ordered VOPc membrane only exhibits the O-up adsorption configuration. Its square-shaped unit cell consists of five VOPc molecules where two adsorption orientations coexist with the horizontal axis of VOPc which is rotated by about 11° or 21° relative to the side of the unit cell. Due to the molecular dipole-dipole interaction, further-deposited molecules result in the assembly of the second-layer VOPc films with the O-down configuration and the square-shaped unit cell that contains only one VOPc molecule. Subsequently, due to the dipole-dipole interaction between layered molecules, following VOPc molecular layers adopt alternating O-up and O-down configurations as well as the square-shaped unit cell, similar to the case of the second layer. In addition, we find that the molecular orbitals overlap in each assembled molecular layer due to the π-π interaction which could facilitate the charge transport along the π stacking direction of VOPc. This research provides possibility to regulate the adsorption configuration and assembly behavior of functional organic molecules on metal surfaces by forming surface alloys.

Cumulant Green's function methods for molecules.

The cumulant expansion of the Green's function is a computationally efficient beyond-GW approach renowned for its significant enhancement of satellite features in materials. In contrast to the ubiquitous GW approximation of many-body perturbation theory, ab initio cumulant expansions performed on top of GW (GW + C) have demonstrated the capability to handle multi-particle processes by incorporating higher-order correlation effects or vertex corrections, yielding better agreements between experiment and theory for satellite structures. While widely employed in condensed matter physics, very few applications of GW + C have been published on molecular systems. Here, we assess the performance of this scheme on a series of 10-electron molecular systems (Ne, HF, H2O, NH3, and CH4) where full configuration interaction estimates of the outer-valence quasiparticle and satellite energies are available.

Theoretical study of the spin-orbit coupled molecular states of the Mg-He dimer.

The primary objective of this study is to conduct precise ab initio calculations of the spin-orbit interaction between Mg and He atoms. Our investigation centers on identifying the first low-lying electronic states of the Mg-He molecule through high-level theoretical methods such as CCSD(T) and RCCSD(T) and SA-CASSCF/MRCI, while also integrating Davidson and BSSE corrections to refine our findings further. Additionally, we employ the state-interacting method to comprehensively account for the influence of spin-orbit coupling (SO) on molecular states. We carefully characterize the potential energy curves (PECs) of these molecular states by deriving crucial spectroscopic parameters including Re, De, Be and Te, which are then compared against data from prior studies. Moreover, our analysis extends to evaluating vibrational levels, radiative lifetimes, and transition dipole moments (TDMs), offering a comprehensive understanding of the system's dynamics. Notably, we locate the positions of satellite features within the absorption spectra of brown and white dwarfs. To validate the precision and reliability of our findings, extensive comparisons are made with both theoretical predictions and experimental observations, ensuring robustness and accuracy in our conclusions.

Formation of Transitional cE/UCD Galaxies through Massive/Dwarf Disc Galaxy Mergers

The dynamics of the merger of a dwarf disc galaxy with a massive spiral galaxy of the Milky Way type were studied in detail. The remnant of such interaction after numerous crossings of the satellite through the disc of the main galaxy was a compact stellar core, the characteristics of which were close to small compact elliptical galaxies (cEs) or large ultra-compact dwarfs (UCDs). Such transitional cE/UCD objects with an effective radius of 100–200 pc arise as a result of stripping the outer layers of the stellar core during the destruction of a dwarf disc galaxy. Numerical models of the satellite before interaction included baryonic matter (stars and gas) and dark mass. We used N-body to describe the dynamics of stars and dark matter, and we used smoothed-particle hydrodynamics to model the gas components of both galaxies. The direct method of calculating the gravitational force between all particles provided a qualitative resolution of spatial structures up to 10 pc. The dwarf galaxy fell onto the gas and stellar discs of the main galaxy almost along a radial trajectory with a large eccentricity. This ensured that the dwarf crossed the disc of the main galaxy at each pericentric approach over a time interval of more than 9 billion years. We varied the gas mass and the initial orbital characteristics of the satellite over a wide range, studying the features of mass loss in the core. The presence of the initial gas component in a dwarf galaxy significantly affects the nature of the formation and evolution of the compact stellar core. The gas-rich satellite gives birth to a more compact elliptical galaxy compared to the merging gas-free dwarf galaxy. The initial gas content in the satellite also affects the internal rotation in the stripped nucleus. The simulated cE/UCD galaxies contained very little gas and dark matter at the end of their evolution.

EGMT-CD: Edge-Guided Multimodal Transformers Change Detection from Satellite and Aerial Images

Change detection from heterogeneous satellite and aerial images plays a progressively important role in many fields, including disaster assessment, urban construction, and land use monitoring. Currently, researchers have mainly devoted their attention to change detection using homologous image pairs and achieved many remarkable results. It is sometimes necessary to use heterogeneous images for change detection in practical scenarios due to missing images, emergency situations, and cloud and fog occlusion. However, heterogeneous change detection still faces great challenges, especially using satellite and aerial images. The main challenges in satellite and aerial image change detection are related to the resolution gap and blurred edge. Previous studies used interpolation or shallow feature alignment before traditional homologous change detection methods, which ignored the high-level feature interaction and edge information. Therefore, we propose a new heterogeneous change detection model based on multimodal transformers combined with edge guidance. In order to alleviate the resolution gap between satellite and aerial images, we design an improved spatially aligned transformer (SP-T) with a sub-pixel module to align the satellite features to the same size of the aerial ones supervised by a token loss. Moreover, we introduce an edge detection branch to guide change features using the object edge with an auxiliary edge-change loss. Finally, we conduct considerable experiments to verify the effectiveness and superiority of our proposed model (EGMT-CD) on a new satellite–aerial heterogeneous change dataset, named SACD. The experiments show that our method (EGMT-CD) outperforms many previously superior change detection methods and fully demonstrates its potential in heterogeneous change detection from satellite–aerial images.

(Invited) DFT Studies on Interactions between Heteropolyacids, Noble Metal Ions, and TiO2 Support

Heteropolycompounds of Keggin structure have been used as homogeneous and heterogeneous catalysts for decades. Recently, they gained popularity in photo- and electrocatalysis where they can be used as components of complex materials e.g., composed of metal ions/heteropolyacids/oxide-based supports.The aim of the current theoretical studies is to characterize systems comprising of free and TiO2-supported heteropolyanions (PW12O40 3-, PMo12O40 3-) with embedded noble metal ions (Ag, Au, Cu, Pd, and Pt) acting as single atom catalysts. Their ground-state geometric and electronic structures were elucidated. Next, their redox and photochemical properties were determined: frontier (HOMO, LUMO) orbitals were defined, energy gaps and UV-VIS spectra were calculated, total and partial density of states were plotted and analysed. The interactions between components of the systems, in particular the influence of the support on the heteropolycompound electronic structure, were investigated. Next, the reactivity of the noble metal cations towards typical reagents (CO, H2, CH3, and C6H6) was studied.The performed calculations demonstrated that the type of the metal and its oxidation state determines the energetics and character of the frontier orbitals, bond lengths and bond orders in their first coordination sphere, incl. the strength of their interactions with common reagents. The presence of TiO2 as the support is manifested by the emergence of new metal ion sitting sites, usually located at the interface between the heteropolyacid and the support, and modification of the redox properties of the systems.Acknowledgements: This work was supported by the National Science Centre, Poland within Solar-Driven Chemistry project no 2019/01/Y/ST4/00024.

DFT Studies on Cun/TiO2 (n=1-7) System for Water Splitting

Copper deposited on titania is active in numerous catalytic reactions, incl. water splitting [1]. The activity of the system depends on the size of the copper phase, whether it is present as single atoms, sub-nanometer clusters, or nanoparticles.The aim of the current contribution is to elucidate the relationship between the size of the copper active phase and its electronic and geometric properties by performing Density Functional Theory (DFT) calculations with PBE functional and the def2-TZVP basis set.Theoretical model of the system comprised of a cluster model of anatase phase of titania – (TiO2)34 - with clusters of copper of varying sizes on top of it. The ground-state geometric and electronic structures were elucidated. Next, their redox and photochemical properties were determined: frontier (HOMO, LUMO) orbitals were defined, energy gaps, total and partial density of states were plotted and analysed. The interactions between components of the systems, in particular the influence of the support on the copper electronic structure, were investigated. Next, the reactivity of the metal phase towards typical intermediates observed during water splitting (H2O, OH, O, and H) was studied.The performed calculations demonstrated that the presence of metal determines the energetics and character of the frontier orbitals of the catalyst. The size of copper active phase influences the bond lengths and bond orders with studied reagents.Acknowledgements: This work was supported by the National Science Centre, Poland within Solar-Driven Chemistry project no 2019/01/Y/ST4/00024. This publication is based upon work from COST Action CA 18234 “Computational materials sciences for efficient water splitting with nanocrystals from abundant elements”, supported by COST (European Cooperation in Science and Technology). We gratefully acknowledge Polish high-performance computing infrastructure PLGrid (HPC Centers: ACK Cyfronet AGH) for providing computer facilities and support within computational grant no. PLG/2020/013927.Literature:[1] Cheng Cheng, Wei-Hai Fang, Run Long, and Oleg V. Prezhdo, JACS Au 2021, 1, 5, 550–559

Resurgence of superconductivity and the role of dxy hole band in FeSe1−xTex

Iron-chalcogenide superconductors display rich phenomena caused by orbital-dependent band shifts and electronic correlations. Additionally, they are potential candidates for topological superconductivity due to the band inversion between the Fe d bands and the chalcogen pz band. Here we present a detailed study of the electronic structure of the nematic superconductors FeSe1−xTex (0 < x < 0.4) using angle-resolved photoemission spectroscopy to understand the role of orbital-dependent band shifts, electronic correlations and the chalcogen band. We assess the changes in the effective masses using a three-band low energy model, and the band renormalization via comparison with DFT band structure calculations. The effective masses decrease for all three-hole bands inside the nematic phase, followed by a strong increase for the band with dxy orbital character. Interestingly, this nearly-flat dxy band becomes more correlated as it shifts towards the Fermi level with increasing Te concentrations and as the second superconducting dome emerges. Our findings suggests that the dxy hole band, which is very sensitive to the chalcogen height, could be involved in promoting an additional pairing channel and increasing the density of states to stabilize the second superconducting dome in FeSe1−xTex. This simultaneous shift of the dxy hole band and enhanced superconductivity is in contrast with FeSe1−xSx.

Dynamical substructures of local metal-poor halo

ABSTRACT Based on 4098 very metal poor (VMP) stars with six-dimensional phase-space and chemical information from Gaia Data Release 3 (DR3) and Large sky Area Multi-Object fiber Spectroscopic Telescope DR9 as tracers, we apply an unsupervised machine learning algorithm, shared nearest neighbour, to identify stellar groups in the action–energy (J–E) space. We detect seven previously known mergers in local samples, including Helmi Stream, Gaia-Sausage/Enceladus (GSE), metal-weak thick disc (MWTD), Pontus, Wukong, Thamnos, and I’itoi + Sequoia + Arjuna. According to energy, we further divide GSE and Wukong into smaller parts to explore the orbital characteristics of individual fragments. Similarly, the division of Thamnos is based on action. It can be found that the apocentric distances of GSE parts of high and medium energy levels are located at $29.5\pm 3.6$ and $13.0\pm 2.7\ {\rm kpc}$, respectively, which suggests that GSE could account for breaks in the density profile of the Galactic halo at both ≈30 and 15–18 kpc. The VMP stars of MWTD move along prograde orbits with larger eccentricities than those of its more metal-rich stars, which indicates that the VMP part of MWTD may be formed by accreting with dwarf galaxies. Finally, we summarize all substructures discovered in our local VMP samples. Our results provide a reference for the formation and evolution of the inner halo of the Milky Way.

Spin-Vibronic Coupling Controls the Intersystem Crossing of Iodine-Substituted BODIPY Triplet Chromophores.

4,4-Difluoro-4-borata-3a-azonia-4a-aza-s-indacene (BODIPY) dyes are extensively used in various applications of their triplet states, ranging from photoredox catalysis, through triplet sensitization to photodynamic therapy. However, the rational design of BODIPY triplet chromophores by ab initio modelling is limited by their strong interactions of spin, electronic and vibrational dynamics. In particular, spin-vibronic coupling is often overlooked when estimating intersystem crossing (ISC) rates. In this study, a combined experimental and theoretical approach using spin-vibronic coupling to correctly describe ISC in BODIPY dyes was developed. For this purpose, seven π-extended BODIPY derivatives with iodine atoms in different positions were examined. It was found that the heavy-atom effect of iodine atoms is site specific, causing high triplet yields in only some positions. This site-specific ISC was explained by El-Sayed rules, so both the contribution and character of the molecular orbitals involved in the excitation must be considered when predicting the ISC rates. Overall, the rational design of BODIPY triplet chromophores requires using (i) the high-quality electronic structure theory, including both static and dynamical correlations; and (ii) the two-component wave function Hamiltonian, and rationalizing; and (iii) ISC based on the character of the molecular orbitals of heavy atoms involved in the excitation, expanding El-Sayed rules beyond their traditional applications.

Insights into orbital morphological features and fracture patterns in medial and inferior wall fracture: a retrospective cohort study

This study investigated the orbital morphological features that lead to fractures at different sites by comparing patients with isolated inferior wall fracture (IWF) to patients with isolated medial wall fracture (MWF). This study analyzed the orbital morphologic characteristics of all orbital fracture patients who underwent orbital computed tomography (CT) scans between January 2017 and October 2022. On CT scans, the bony structures of the orbit were measured. We investigated the bilateral symmetry of orbital. In addition, orbital morphological differences were compared between patients with fractures of the medial wall and those with fractures of the inferior wall. A total of 135 patients with orbital fractures were included in the study. Of these, 91 were isolated MWFs and 44 were isolated IWF. We confirmed the symmetry of bilateral orbits and measured the orbit of the uninjured side. No differences were found between the MWF group and the IWF group in terms of ocular prominence, horizontal orbital diameter, orbital rim angle, sagittal orbital depth, sagittal orbital depth, and angle of inferior wall inclination. The distance between the infraorbital nerve (ION) entry point and the orbital rim was significantly smaller in the inferior lateral wall fracture group than in the MWF group (11.87 ± 2.54 vs 14.90 ± 4.64, P < 0.001), and the percentage of type 1 ION was significantly lower in the IWF group than in the MWF group (40.9% vs 65.9%, P = 0.012). We demonstrated the symmetry of bilateral orbits and found that when the point where the ION enters the infraorbital canal is near the orbital rim, patients are more prone to suffering a fracture of the inferior wall after orbital trauma. It is less likely for patients with type 1 ION to suffer an IWF following an orbital fracture.

Imaginary Intelligence Via Satellites

This article gives basic information about all types of satellites. The types of satellites reveal the functions, purposes and applications. Information is provided on the sections required to use a satellite. The features of reconnaissance satellites are characterized. Analytical factors of satellite imagery, their pros and cons were compared. The role and functions of satellite imagery in current and probable future wars are declared.

Dual spherical-spherical aromaticity in [M(η2-P4)2]+ (M = Cu, Ag, Au) and [P(P4)2]+. Evaluation of bonding nature and spherical aromatic character of the P4 aggregates from DFT calculations

The favorable coordination of two P4 units to a coinage metal center, given by [M(η2–P4)2]+ and [P(P4)2]+ clusters, offers an interesting template for evaluating how two spherical aromatic units interact when bridged by either a metal or a main-group element center. Our results indicate a M+–(P4)2 stabilization trend in the order Au > Cu > Ag, involving mainly electrostatic character, followed by a sizable contribution from covalent (orbital) character, with a slight London dispersion type stabilization. The coordination scheme is based on a σ- M+←(η2-P4)2 charge transfer, followed by σ-metal-to-ligand backbonding, in addition to a set of two σ-ligand-to-metal and π-ligand-to-metal charge transfer bonds. Such structural features bring together two spherical aromatic P4 units, leading to the formation of a dual aromatic cluster mediated by a coinage metal center, i.e. two independent aromatic units within the same cluster. However, in [P(P4)2]+ involving stronger covalent P4–P bonds, the spherical aromatic character decreases, owing to the larger distortion of the P4 units, as result of the larger bonding interaction towards the central P atom. Hence, the coordination towards a coinage metal center of the P4 unit incorporates multiple aromatic units into a single molecular entity. This provides a model to envisage larger connected spherical-aromatic species serving as building blocks while retaining their inherent characteristics.

Field-induced structural and orbital transformations leading to large bulk photovoltaic response in modified barium titanate

Ferroelectric systems are gaining importance in the perspective of capitalizing on their potential in energy applications. In particular, the ferroelectric photovoltaic effect is one of the attractive fields because of the reported above bandgap photovoltage. Although numerous efforts are being made to understand the ferroelectric photovoltaic mechanism, correlations among the structural, orbital, and photovoltaic characteristics, useful to engineer the system for applications, are rarely being investigated. Here, such correlations are established in electric field-induced studies carried out on the lead-free ferroelectric Ba0.875(Bi0.5Li0.5)0.125TiO3 system. Upon poling, x-ray diffraction studies reveal a twofold enhancement in the orthorhombic phase fraction at the expense of the tetragonal phase in comparison with the unpoled sample. The ex situ and in situ Raman studies demonstrate the field-induced changes in the structural characteristics. Furthermore, the Rayleigh analysis validates the field-induced lattice deformation in accordance with x-ray diffraction and Raman studies. Notably, the Ba0.875(Bi0.5Li0.5)0.125TiO3 sample exhibits anomalous open-circuit voltage (12 V) under the poling condition. To substantiate the experimental finding, density functional theory calculations are carried out. The theoretical calculations elucidate that the conduction band edge of the orthorhombic phase has a vital contribution from z character orbitals, which is further enhanced under poling to give rise to a higher shift current and, hence, a better photovoltaic response. However, the tetragonal phase's orbital characters are robust upon poling. Overall, these studies pave the way for designing ferroelectric systems for better photovoltaic properties.

Intra-Zero-Energy Landau Level Crossings in Bilayer Graphene at High Electric Fields.

The highly tunable band structure of the zero-energy Landau level (zLL) of bilayer graphene makes it an ideal platform for engineering novel quantum states. However, the zero-energy Landau level at high electric fields has remained largely unexplored. Here we present magnetotransport measurements of bilayer graphene in high transverse electric fields. We observe previously undetected Landau level crossings at filling factors ν = -2, 1, and 3 at high electric fields. These crossings provide constraints for theoretical models of the zero-energy Landau level and show that the orbital, valley, and spin character of the quantum Hall states at high electric fields is very different from low electric fields. At high E, new transitions between states at ν = -2 with different orbital and spin polarization can be controlled by the gate bias, while the transitions between ν = 0 → 1 and ν = 2 → 3 show anomalous behavior.

Achieving the Reverse Intersystem Crossing in Chalcone Based Donor-Acceptor System through Down-Conversion of Triplet Exciton.

In recent years, understanding the mechanism of thermally activated delayed fluorescence (TADF) has become the primary choice for designing high-efficiency, low-cost, metal-free organic light emitting diodes (OLEDs). Herein, we propose a strategically designed chalcone based donor-acceptor system, where intensification of delayed fluorescence with decrease in temperature (300 K to 100 K) is observed; the theoretical investigations of electronic states and orbital characters uncovered a new cold rISC pathway in donor-acceptor system, where rISC occurs through the down-conversation of higher triplet exciton (from T3 ) to lowest singlet state (S1 ), having negative energy splitting, thus no thermal energy is required. The comprehensive research described herein might open-up new avenues in donor-acceptor system over the conventional up-convention of triplet exciton and demonstrates that not necessarily all delayed fluorescence are thermally activated (TADF).

Estimation of historical daily airborne pollen concentrations across Switzerland using a spatio temporal random forest model

High concentrations of airborne pollen trigger seasonal allergies and possibly more severe adverse respiratory and cardiovascular health events. Predicting pollen concentration accurately is valuable for epidemiological studies, in order to study the effects of pollen exposure. We aimed to develop a spatiotemporal machine learning model predicting daily pollen concentrations at a spatial resolution of 1 × 1 km across Switzerland between 2000 and 2019. Daily pollen concentrations for five common, highly allergenic pollen types (hazel, alder, birch ash, and grasses) were available from fourteen measurement sites across Switzerland. We considered several predictors such as elevation, species distribution, wind speed, wind direction, temperature, precipitation, relative humidity, satellite-observed Normalized Difference Vegetation Index, and land-use (CORINE, Landsat satellite) to explain variation in pollen concentration. We employed feature engineering techniques to encode categorical variables and fill in missing values. We applied a random forest machine learning model with 5-fold cross-validation. The 5th–99th percentiles for concentrations of hazel, alder, birch, ash, and grass pollen at the pollen monitoring stations were 0–298, 0–306, 0–1153, 0–800, and 0–290 pollen grains/m3, respectively. The results of a predictive model for these concentrations yielded overall R2 values of 0.87, 0.84, 0.89, 0.88, and 0.91, and temporal root mean squared errors (RMSEs) of 16.07, 16.72, 69.04, 41.50, and 22.45 pollen grains/m3. An analysis of predictor variable importance indicates that the average national daily pollen concentration is the most important predictor of pollen concentrations for all pollen types. Furthermore, meteorological variables including temperature, total precipitation, humidity, boundary layer height, wind speed, and wind direction, as well as date and satellite features, are important factors in pollen concentration prediction. These spatiotemporal pollen models will serve to estimate individual residential pollen exposure for epidemiological studies. Resulting estimates will enable us to study respiratory and cardiovascular mortality and hospital admissions in Switzerland.

Stacking effect on the orbital characters and transition probability of bilayer MoS2

In this paper, employing the van der Waals (vdW) corrected density functional method, the electronic and optical properties of bilayer MoS2 are calculated for five different stacking patterns ( and ). In this regard, the structural stability and the van der Waals interlayer distance are investigated. The minimum formation energy has indicated the overall trend of relative stability to be as This means and have the most and and have the least stable structures. The band structure and probability distribution for finding electrons in atomic orbitals have also been calculated in the Brillouin zone. The results obtained from band structures and orbital characters show the same trend in the three most stable and a different but the same trend for the two least stable orders. In addition, the oscillator strength has been derived from the calculation of the momentum operator matrix elements using first-principles methods. The calculation of transition probabilities from matrix elements indicates that and have higher transition probabilities than that of and The study of transition probability also shows the y-polarized light is stronger than the x-polarized light for all stacking patterns.

A Close Binary Supermassive Black Hole Model for the Galaxy 3C 273

The data from the last 60 years on the programs of long-term multi-frequency monitoring of active galactic nucleus (AGN) 3C 273 were analyzed. A model is proposed for finding the parameters of close binary systems (CBSs) from supermassive black holes (SMBHs), including a harmonic analysis of observational data series obtained in the optical and radio ranges. The purpose of this research was to show that in the absence of optical information on AGNs, only radio data can be used and the necessary information on the physical objects can be obtained. Regarding the example of the blazar 3C 273, the following parameters were obtained: the masses of the companions; their orbital characteristics, such as the speeds of movement in orbits; the reserves of the kinetic energy of the system; and others. It was found that AGN 3C 273 can be a very massive binary system at the stage of evolution close to merging. Based on the obtained parameters, the characteristics of the gravitational waves (GWs) of this system, its lifetime before the merger, and the possible observation of 3C 273 using gravitational wave detectors were considered.