Relativistic Effects Research Articles

Highly Accurate and Robust Constraint-Based Orbital-Optimized Core Excitations.

We adapt our recently developed constraint-based orbital-optimized excited-state method (COOX) for the computation of core excitations. COOX is a constrained density functional theory (cDFT) approach based on excitation amplitudes from linear-response time-dependent DFT (LR-TDDFT), and has been shown to provide accurate excitation energies and excited-state properties for valence excitations within a spin-restricted formalism. To extend COOX to core-excited states, we introduce a spin-unrestricted variant which allows us to obtain orbital-optimized core excitations with a single constraint. Using a triplet purification scheme in combination with the constrained unrestricted Hartree-Fock formalism, scalar-relativistic zero-order regular approximation corrections, and a semiempirical treatment of spin-orbit coupling, COOX is shown to produce highly accurate results for K- and L-edge excitations of second- and third-period atoms with subelectronvolt errors despite being based on LR-TDDFT, for which core excitations pose a well-known challenge. L- and M-edge excitations of heavier atoms up to uranium are also computationally feasible and numerically stable, but may require more advanced treatment of relativistic effects. Furthermore, COOX is shown to perform on par with or better than the popular ΔSCF approach while exhibiting more robust convergence, highlighting it as a promising tool for inexpensive and accurate simulations of X-ray absorption spectra.

Metallo‐Surfactant Complex‐Assisted Biomimetic Synthesis of Silver Nanoparticles: Exploring Relativistic Effects in Catalytic and Sensing Applications

AbstractA biological reduction method for silver nanoparticles was employed using Cassia alata extract from plant leaves, which functions as a reducing agent and the metallo‐surfactant [Co(dqn)2(C12H27N)2]3+ (dqn = dipyrido[3,2‐f:2′,3′‐h]‐quinoxaline; C12H27N)2 = dodecylamine) acting as both stabilizing and capping agent. The ratio of Ag nanoparticles (AgNPs) formation was adjusted to be equal to the amount of AgNO3, along with variations in the amount of plant leaf extract, the metallo‐surfactant, pH, surrounding temperature, and the length of interaction periods. High‐resolution transmission electron microscopy (HRTEM), field emission scanning electron microscopy (FE‐SEM), energy‐dispersive spectroscopy (EDS), and energy‐dispersive X‐ray analysis (EDAX) were used to confirm the formation of AgNPs. The infrared results indicate the presence of hydroxyl, amine, and carboxylate groups in the extract plays a crucial role in the reduction process. Additionally, the metallo‐surfactant acts as a capping agent for the silver nanoparticles, preventing agglomeration. By adjusting the acidity of the solution and the quantity of the additive metallo‐surface active agent utilized, the size of AgNPs can be precisely regulated. The relativistic effects observed in this metallo‐surfactant‐assisted silver nanoparticle demonstrate excellent reduction capabilities for nitro compounds, effective dye degradation, and mercury sensing applications.

Ionization Limits and Upper Levels in P-XIV and in Cl-XVI

Abstract This study fills the gap of upper-level energies and the ionization limits of the following configurations: 1s3s1S0, 1s2p3Po0, 1s2p 1Po1, 1s3p1Po1, 1s4p 1Po1, 1s5p1Po1, 1s6p1Po1, 1s2p3Po1, 1s3s3S1, 1s4s3S1, 1s3d 1D2, 1s3d3D2, 1s5d3D2, 1s2p3Po2, 1s3d3D3, 1s4d3D3, 1s5d3D3 in P-XIV and in Cl-XVI currently not listed at NIST. Therefore, in this work the ionization limits with and without relativistic effects are computed for the Helium-like iso-spectrum levels series for the mentioned configurations, for Z = 2 - 17. A total of 254 ionization limits are computed and compared with the available data at National Institute of Standard and Technology. The yield limits departing from NIST ones by not more than 0.00001 eV.

Faraday rotation method improves the upper limit of the electron electric-dipole-moment sensitivity.

The electron electric-dipole-moment (eEDM) is a powerful tool for exploring new particles. The candidates for eEDM search are heavy atoms and their molecules, which are well known for the obvious relativistic effect. Lead atom is considered to be the most ideal relativistic atom [Park et al., Nat. Commun. 11(1), 815 (2020)]. PbH molecule is an important representative of the Pb compound and is considered a cold candidate molecule due to the high diagonal Franck-Condon factors. We systematically investigated the (eEDM) searches of PbH using a two-component approach. The parity- and time-reversal symmetry violation constants of ground and excited states, including internal effective electric field Eeff, electron-nucleon scalar-pseudoscalar interaction constant WP,T, and nuclear magnetic quadrupole moment, were obtained and compared to other molecules. In addition, we designed two experimental methods to measure the sensitivity of the eEDM, indicating that the Faraday rotation method could greatly improve its sensitivity.

Limits and Potentials of Special Relativity

This paper presents the application of special relativity to different thought experiments. Some issues will be noted and a modification of special relativity will be presented. That modification can be tested and one interpretation of the preliminary result supports the modification. After presenting the history of special relativity, the non-simultaneity of special relativity is questioned in our macro world. In addition, some issues between light-clocks and the application of Lorentz transformation are presented. All this indicates that there is something not right with special relativity. A new proposal is presented based on an adaptation of special relativity; this new proposal solves the anomalies and could be a solution to the twin paradox. It has a prediction: a difference with special relativity which has been tested with a new experiment and the preliminary results support the new proposal. Previously, a lack of special relativistic effects has been observed in the universe [Davis et al., 2004]; that second observation is also explained with the new proposal.

Observation of doping-induced spin–orbit coupling in gold cluster assembly to carrier-tuneable semiconductors and Schottky behaviors

The doping influenced carrier dynamics to maneuvering n-type to p-type semiconducting gold cluster assembly have been assessed. The resonance photoemission spectroscopic measurements corroborate an incremental rise in the density of states at the valence edge, the overlap of valence states due to doping, and the presence of distinct spin–orbit splitting and coupling in manganese-doping (Au7Mn) compared to gold clusters (Au8), originating from the relativistic effect resulted in a semiconducting property. The work function dependent current–voltage characteristics in metal–semiconductor configuration show Ohmic and Schottky behaviors assorting p-type carriers in Au7Mn in contrast to the n-type Au8 and are presenting an atomic cluster based fast electronic device.

Computational Exploration of the Impact of Low‐Spin and High‐Spin Ground State on the Chelating Ability of Dimethylglyoxime Ligand on Dihalo Transition Metal: A QTAIM, EDA, and CDA Analysis

ABSTRACTWe have explored the chelation of dimethylglyoxime ligand to divalent (ndx: x = 6, 7, 8) transition metal (TM) cations in two media (gas phase and water) at the B3LYP//LANL2DZ/6–311+G (d,p) and B3LYP/def2‐TZVP level at lower multiplicity and higher multiplicity states. Majority of the 18 optimized halide (chloride and bromide) complexes prefer square planar configuration. The correlations discerned between the experimental structural data and their estimated counterparts demonstrate a good credibility for complexes at lower multiplicity state. The basis set superposition errors (BSSEs) estimated is very small which reflects the fact that the choice of different basis sets (B3LYP//LANL2DZ/6–311+G (d,p)) introduces a slight bias in the calculation of energies. The ADMP (atom‐centered density matrix propagation) simulations in water on chloride complexes indicate the irreversible nature of these M—N dissociation in trajectory simulation process. This fact explains our exclusive focus on the examination of the [glyoxime ligand]…[MX2] interactions. In addition, the solvation of (3d and 4d) transition metal chloride complexes causes a sensitive augmentation of the metal ion affinity (MIA) with an average of 0.29 and 0.24 kcal/mol. In both multiplicity states, the topological parameters have illustrated that the M—N and M—X bonds are typical metal–ligand in both media. The average ΔEorb/ΔEsteric ratio equal to 0.45 and 0.11 in gas phase and water, respectively, reveals the predominance of the contributions from non‐covalent bonding interactions (NCI) compared to those of covalent bonding. But, the maximal value equal to 6.760 is obtained for bromide rhodium complex in water. NBO analysis in both media highlights the fact that a more pronounced ionic character is observed for the majority of the chloride complexes at both spin multiplicity states because of their higher retained charges on the metal atom. For [dimethylglyoxime]…[MX2] interaction (X = Cl and Br), the charge decomposition analysis demonstrates that the lowest value of the d/b ratio is found for the chloride platinum complex at lower multiplicity state in water. This is a proof of its strong relativistic effects.

Impact of correlations on the modeling and inference of beyond vacuum–general relativistic effects in extreme-mass-ratio inspirals

Impact of correlations on the modeling and inference of beyond vacuum–general relativistic effects in extreme-mass-ratio inspirals

Modelling absorption and emission profiles from accretion disc winds with WINE

Fast and massive winds are ubiquitously observed in the UV and X-ray spectra of active galactic nuclei (AGNs) and other accretion-powered sources. Several theoretical and observational pieces of evidence suggest they are launched at accretion disc scales, carrying significant mass and angular momentum. Thanks to such high-energy output, they may play an important role in transferring the energy released by accretion to the surrounding environment. In the case of AGNs, this process can help to set the so-called co-evolution between an AGN and its host galaxy, which mutually regulates their growth across cosmic time. To precisely assess the effective role of UV and X-ray winds at accretion disc scales, it is necessary to accurately measure their properties, including mass and energy rates. However, this is a challenging task, due to both the limited signal-to-noise ratio of available observations and the limitations of the models currently used in the spectral analysis. We aim to maximise the scientific return of current and future observations by improving the theoretical modelling of these winds through our Winds in the Ionised Nuclear Environment (WINE) model. WINE is a spectroscopic model specifically designed for disc winds in AGNs and compact accreting sources, which couples photoionisation and radiative transfer with special relativistic effects and a three-dimensional model of the emission profiles. We explore with WINE the main spectral features associated with the disc winds in AGNs, with a particular emphasis on the detectability of the wind emission in the total transmitted spectrum. We explore the impact of the wind ionisation, column density, velocity field, and geometry in shaping the emission profiles. We simulated observations with the X-ray microcalorimeter Resolve on board the recently launched XRISM satellite and the X-IFU on board the future Athena mission. This allows us to assess the capabilities of these telescopes in the study of disc winds in X-ray spectra of AGNs for the typical physical properties and exposure times of the sources included in the XRISM performance verification phase. The wind kinematic and geometry (together with the ionisation and column density) deeply affect both shape and strength of the wind spectral features. Thanks to this, both Resolve and, on a longer timescale X-IFU will be able to accurately constrain the main properties of disc winds over a broad range of ionisation, column densities, and covering factors. We also investigate the impact of the spectral energy distribution (SED) on the resulting appearance of the wind. Our findings reveal a dramatic difference in the gas opacity when using a soft, Narrow Line Seyfert 1-like SED compared to a canonical powerlaw SED with a spectral index of $

Ground and Excited Electronic Structure Analysis of FeH with Correlated Wave Function Theory and Density Functional Approximations.

FeH is one of the most challenging diatomic molecules to study under electronic structure theory. Here, we have successfully studied 22 electronic states of FeH using ab initio multireference configuration interaction (MRCI), Davidson-corrected MRCI (MRCI+Q), and coupled cluster singles, doubles, and perturbative triples [CCSD(T)] levels of theory. We report their potential energy curves (PECs), excitation energies, dissociation energies, equilibrium electronic configurations, and a series of spectroscopic constants with the use of augmented triple-ζ, quadruple-ζ, and quintuple-ζ quality correlation consistent basis sets. The scalar relativistic effects and active space and core electron correlation contribution on the properties of FeH are also explored. The use of a large CASSCF active space that includes 4s, 4p, 3d, and 4d orbitals of Fe and the 1s of H is critical for producing accurate full PECs with proper dissociations and predicting the exact order of the electronic states. Our findings are in harmony with the experimental results available in the literature and will serve as reference values for future studies of FeH. Furthermore, with the use of PECs, the total internal partition function sum (TIPS) of FeH was calculated across a range of temperatures. Finally, we exploited the single-reference nature of the a6Δ of FeH and its ionized product FeH+ (X5Δ) to evaluate the associated density functional theory (DFT) errors on their dissociation energies and spectroscopic parameters.

Theoretical study on the spectroscopic and transition properties of phosphorus dimer cation

The potential energy curves of 18 Λ-S states of the P2 + cation have been constructed using the internally contracted multi-reference configuration interaction approach combined with the Davidson correction. The basis-set extrapolation to the complete basis set limit is performed. The relativistic effect is considered in calculations. Treatment of scalar relativistic effect at the third-order Dkroll-Hess approximate and spin-orbit coupling with the state-average Breit-Pauli operator is made. Based on the obtained potential energy curves, the spectroscopic parameters for all bound Λ-S and Ω states are determined. These results are in agreement with experiment where the spectroscopic data are available. The transition dipole moments are calculated. The properties of the dipole-allowed transitions among doublet or quartet Λ-S states are evaluated, from which Einstein coefficients, Franck-Condon factors and radiative lifetimes are estimated. The spin-orbit coupling effect on the transition properties of the 12Πg→X2Πu system is also studied. The spectroscopic and transition properties reported in this study can be used to guide the detection of phosphorus dimer cation in spectroscopy experiments.

DMRG-Tailored Coupled Cluster Method in the 4c-Relativistic Domain: General Implementation and Application to the NUHFI and NUF3 Molecules.

Heavy atom compounds represent a challenge for computational chemistry due to the need for simultaneous treatment of relativistic and correlation effects. Often such systems also exhibit strong correlation, which hampers the application of perturbation theory or single-reference coupled cluster (CC) methods. As a viable alternative, we have proposed externally correcting the CC method using the density matrix renormalization group (DMRG) wave functions, yielding the DMRG-tailored CC method. In a previous paper [J. Chem. Phys. 2020, 152, 174107], we reported a first implementation of this method in the relativistic context, which was restricted to molecules with real double group symmetry. In this work, we present a fully general implementation of the method, covering complex and quaternion double groups as well. The 4c-TCC method thus becomes applicable to polyatomic molecules, including heavy atoms. For the assessment of the method, we performed calculations of the chiral uranium compound NUHFI, which was previously studied in the context of the enhancement of parity violation effects. In particular, we performed calculations of a cut of the potential energy surface of this molecule along the stretching of the N-U bond, where the system exhibits strong multireference character. Since there are no experimental data for NUHFI, we have performed also an analogous study of the (more symmetric) NUF3 molecule, where the vibrational frequency of the N-U bond can be compared with spectroscopic data.

Relativistic and electron-correlation effects in static dipole polarizabilities for main-group elements

Relativistic and electron-correlation effects in static dipole polarizabilities for main-group elements

Low-temperature oxidation of methane mediated by Al-doped ZnO cluster and nanowire: a first-principles investigation.

First-principles calculations are performed to investigate the catalytic oxidation of methane by using N2O as an oxidizing agent over aluminum (Al)-doped Zn12O12 cluster and (Zn12O12)2 nanowire. The impact of Al impurity on the geometry, electronic structure, and surface reactivity of Zn12O12 and (Zn12O12)2 is thoroughly studied. Our study demonstrates that Al-doped ZnO systems have a better adsorption ability than the corresponding pristine counterparts. It is found that N2O molecule is initially decomposed on the Al site to provide the N2 molecule, and an Al-O intermediate which is an active species for the CH4 oxidation. The conversion of CH4 into CH3OH over AlZn11O12 and (AlZn11O12)2 requires an activation energy of 0.45 and 0.29eV, respectively, indicating it can be easily performed at normal temperatures. Besides, the overoxidation of methanol into formaldehyde cannot take place over the AlZn11O12 and (AlZn11O12)2, due to the high energy barrier needed to dissociate C-H bond of the CH3O intermediate. Dispersion-corrected density functional theory calculations were performed through GGA-PBE exchange-correlation functional combined with a numerical double-ζ plus polarization (DNP) basis set as implemented in DMol3. To include the relativistic effects of core electrons of Zn atoms, DFT-semicore pseudopotentials were adopted. The DFT + D scheme proposed by Grimme was used to involve weak dispersion interactions within the DFT calculations. The reaction energy paths were generated by the minimum energy path calculations using the NEB method.

Accretion tori around rotating neutron stars I. Structure, shape, and size

We present a full general relativistic analytic solution for a radiation-pressure-supported equilibrium fluid torus orbiting a rotating neutron star (NS). We applied previously developed analytical methods that include the effects of both the NS's angular momentum and quadrupole moment in the Hartle-Thorne geometry. The structure, size, and shape of the torus are explored, with a particular focus on the critically thick solution -- the cusp tori. For the astrophysically relevant range of NS parameters, we examined how our findings differ from those obtained for the Schwarzschild space-time. The solutions for rotating stars display signatures of an interplay between relativistic and Newtonian effects where the impact of the NS angular momentum and quadrupole moment are almost counterbalanced at a given radius. Nevertheless, the space-time parameters still strongly influence the size of tori, which can be shown in a coordinate-independent way. Finally, we discuss the importance of the size of the central NS which determines whether or not a surrounding torus exists. We provide a set of tools in a Wolfram Mathematica code, which establishes a basis for further investigation of the impact of the NSs’ super-dense matter equation of state on the spectral and temporal behaviour of accretion tori.

Overlooked effects of wavefront reception with or without speed limit, from aberration to time measurement

A general approach to wavefront reception applicable to any type of wave allows to point out some overlooked aspects and ignored consequences of established theories. The Doppler and aberration effects of electromagnetic waves, the cosmological redshift and the measurement of durations are all perceptual phenomena, and as such require the use of reception rather than Lorentz-transformed coordinates, since perceived durations relate proper to proper durations whereas the famous time dilation of special relativity relates proper to improper durations. Taking this subtlety into account rehabilitates the controversial Poincaré ellipsoid whose polar equation is just the relativistic Doppler effect. The application of this approach to the Galilean case whose transformed and received wavefronts are homothetic, reveals new aberration relations and the existence of a transverse Doppler effect very similar, in proportion to the respective wave velocities, to the relativistic one, thus forbidding in practice the test of his theory proposed by Einstein. The reasons for the long persistence of a classical angular Doppler formula divorced from wavefront reception are discussed, one of them ironically being the theory of special relativity.

Relativity and the Magnitude of Velocities

In modern physics, relativity is primarily understood through the framework of Einstein’s theory. According to the special theory of relativity (STR), Galilean relativity serves as a very accurate approximation at low velocities, where ‘relativistic effects’ can be neglected. However, at high velocities, these effects become significant and are accurately described by STR. This paper challenges this understanding, arguing that the opposite is true. In Galilean relativity, the relativity of time is substantial and cannot be ignored. Thus, relative time is more negligible in STR than in Galilean relativity. By comparing Galilean relativity and STR through physical, mathematical, and specific examples, two conclusions are drawn: first, the current categorization of relativity theories based on velocity magnitude is artificial and inaccurate; second, the relativity of time can be ignored in special relativity, while it remains significant and cannot be overlooked in Galilean relativity.

Apsidal motion and TESS light curves of three southern close eccentric eclipsing binaries: GM Nor, V397 Pup, and PT Vel

The study of apsidal motion in eccentric eclipsing binaries provides an important observational test of theoretical models of stellar structure and evolution. New ground-based and space-based photometric data have been obtained and archival spectroscopic measurements were used in this study of three detached early-type and southern-hemisphere eccentric eclipsing binaries GM Nor (P = 1d​​.88, e = 0.05), V397 Pup (3d​​.00, 0.30), and PT Vel (1d​​.80, 0.12). Their TESS observations in several sectors have also been included and the corresponding light curves were solved using the PHOEBE code. As a result, new accurate photoelectric times of minimum light have been obtained. The newly completed O − C diagrams were analyzed using all reliable timings found in the literature and calculated using the TESS light curves. New or improved values for the elements of apsidal motion were obtained. Using ESO archive spectroscopy, for V397 Pup, the precise absolute parameters were newly derived: M1 = 3.076(35) M⊙, M2 = 2.306(35) M⊙, and R1 = 2.711(55) R⊙, R2 = 1.680(55) R⊙. For PT Vel the absolute dimensions were improved: M1 = 2.204(25) M⊙, M2 = 1.638(25) M⊙, and R1 = 2.108(30) R⊙, R2 = 1.605(30) R⊙. For GM Nor, the less accurate absolute parameters based on the light curve analysis were evaluated: M1 = 1.94(15) M⊙, M2 = 1.84(14) M⊙, and R1 = 2.27(20) R⊙, R2 = 2.25(20) R⊙. We found more precise and relatively short periods of apsidal motion of about 80, 335, and 160 years, along with the corresponding internal structure constants, log k2, –2.524, –2.361, and –2.563, for GM Nor, V397 Pup, and PT Vel, respectively. Relativistic effects are small but not negligible, making up to 10% of the total apsidal motion rate in all systems. No marks of the presence of the third body were revealed in the light curves, on the O − C diagrams, or in the reduced spectra of the eccentric systems studied here.

On acoustic solitary waves in a multispecies degenerate relativistic magnetized plasma using physics informed neural networks

In this paper, we investigate the nonlinear electrostatic wave propagation in a two-dimensional magnetized plasma. The plasma consists of electron and positron components with relativistic degeneracy and stationary ions for neutralizing its background. Using the basic equations for this type of plasma in combination with the reductive perturbation method, we derived the Zakharov–Kuznetsov equation using the Lorentz transformation stretching method (LT). For the first time, we compared the results of the Galilean transformation stretching method (GT) and the LT method to investigate the effect of plasma parameters, such as the relativistic degeneracy parameter of electron particles (re0), the density ratio of ion to electrons (δ), and the normalized electron cyclotron (Ωe), on the amplitude and width of the wave solutions. The plasma parameters used in this research are representative of compact astrophysical objects. Numerical results showed that the amplitude of wave solutions obtained by the LT method is smaller than the GT method, but the width is greater. We provide a physical explanation for these differences. Furthermore, we present a physics-informed neural network (PINN) approach to directly recover the intrinsic nonlinear dynamics from spatiotemporal data. The PINN model uses a deep neural network constrained by the governing equations to learn the optimal parameters, with the aim of enhancing the predictive capabilities of the system. The results of this study provide valuable insight into the propagation of nonlinear waves in white dwarfs, where relativistic effects are significant. These findings could substantially advance the development of emerging machine learning applications in astrophysics.

Toward Accurate Ab Initio Ground-State Potential Energy and Electric Dipole Moment Functions of Carbon Monoxide.

Accurate potential energy and electric dipole moment functions of the CO molecule in its ground electronic state X1Σ+ have been obtained using the single-reference coupled-cluster approach, up to the CCSDTQP level of approximation, in conjunction with the augmented core-valence correlation-consistent basis sets, aug-cc-pCVnZ, up to octuple-zeta quality. The scalar relativistic, adiabatic, and nonadiabatic effects were discussed. The ab initio predicted functions were compared with their experimentally derived counterparts.