Relativistic Method Research Articles

Theoretical investigation of iodine plasma through detailed electron impact excitation cross-section calculations and collisional-radiative model analysis

Abstract In the present study, we consider the electron impact excitation of neutral iodine and its application in developing a collisional-radiative model for plasma diagnostics of iodine plasma. Electron impact excitation cross- sections are calculated using fully relativistic distorted wave theory. The required atomic structure calculations for iodine are carried out using the relativistic multi-configuration Dirac-Fock method. The excitation energies obtained are reported and compared with values from the NIST database. The electron impact excitation cross-sections are calculated from the ground (5p5 2P3/2) and first- excited state (5p5 2P1/2) to the several upper fine structure levels. Our cross- section results align well with previous studies, reported by Ambalampitiya et al. [Atoms, 9, 103, 2021] using the Breit-Pauli B-spline R-matrix method. Further calculated cross-section results are incorporated into the collisional-radiative model. Our model also includes electron impact ionization, de-excitation, three- body recombination, and radiative decay. We validate our model using emission spectra from inductively coupled iodine plasma. For this purpose, we used the recorded intensities for the emission lines, 486.23 nm, 511.92 nm, 523.45 nm, 589.40 nm, and 608.24 nm are compared with those obtained from our model to calculate electron temperature and electron density of the iodine plasma.

Relativistic treatment of hole alignment in noble gas atoms

The development in attosecond physics allows for unprecedented control of atoms and molecules in the time domain. Here, ultrashort pulses are used to prepare atomic ions in specific magnetic states, which may be important for controlling charge migration in molecules. Our work fills the knowledge gap of relativistic hole alignment prepared by femtosecond and attosecond pulses. The research focuses on optimizing the central frequency and duration of pulses to exploit specific spectral features, such as Fano profiles, Cooper minima, and giant resonances. Simulations are performed using the Relativistic Time-Dependent Configuration-Interaction Singles method. Ultrafast hole alignment with large ratios (on the order of one hundred) is observed in the outer-shell hole of argon. An even larger alignment (on the order of one thousand) is observed in the inner-shell hole of xenon.

Unified Implementation of Relativistic Wave Function Methods: 4C-iCIPT2 as a Showcase.

In parallel to the unified construction of relativistic Hamiltonians based solely on physical arguments (J. Chem. Phys. 2024, 160, 084111), a unified implementation of relativistic wave function methods is achieved here via programming techniques (e.g., template metaprogramming and polymorphism in C++). That is, once the code for constructing the Hamiltonian matrix is made ready, all the rest can be generated automatically from existing templates used for the nonrelativistic counterparts. This is facilitated by decomposing a second-quantized relativistic Hamiltonian into diagrams that are topologically the same as those required for computing the basic coupling coefficients between spin-free configuration state functions (CSF). Moreover, both time reversal and binary double point group symmetries can readily be incorporated into molecular integrals and Hamiltonian matrix elements. The latter can first be evaluated in the space of (randomly selected) spin-dependent determinants and then transformed to that of spin-dependent CSFs, thanks to simple relations in between. As a showcase, we consider here the no-pair four-component relativistic iterative configuration interaction with selection and perturbation correction (4C-iCIPT2), which is a natural extension of the spin-free iCIPT2 (J. Chem. Theory Comput. 2021, 17, 949), and can provide near-exact numerical results within the manifold of positive energy states (PES), as demonstrated by numerical examples.

Second order Rayleigh–Schrödinger perturbation theory for the Grasp2018 package: Core–core correlations

GRASP package is based on the relativistic configuration interaction in which accurate calculations, accounting for valence, valence–valence, core–valence, core and core–core electron correlations, often rely on massive CSF expansions. This paper presents a further development of the method based on the second-order perturbation theory for finding the most important CSFs that have the greatest influence on the core–valence, core and core–core correlations. This method is based on a combination of the relativistic configuration interaction method and the stationary second-order Rayleigh–Schrödinger many-body perturbation theory in an irreducible tensorial form [G. Gaigalas, P. Rynkun, and L. Kitovienė, Second-order Rayleigh–Schrödinger perturbation theory for the GRASP2018 package: Core–valence correlations, Lith. J. Phys. 64(1), 20–39 (2024), https://doi.org/10.3952/physics.2024.64.1.3, and G. Gaigalas, P. Rynkun, and L. Kitovienė, Second-order Rayleigh–Schrödinger perturbation theory for the GRASP2018 package: Core correlations, Lith. J. Phys. 64(2), 73–81 (2024), https://doi.org/10.3952/physics.2024.64.2.1]. In this extension, the perturbation theory takes into account electron core–valence, core and core–core correlations, where an atom or ion has any number of valence electrons, for calculation of energy spectra and other properties. Meanwhile, the rest of the correlations are taken into account in a traditional way. This allows a significant reduction of the space of the configuration state function for complex atoms and ions. We also demonstrate how this method works for calculations of the energy structure and E1 transition properties of Fe XV ion.

Cross sections for electron scattering from atomic gallium

Abstract The relativistic convergent close-coupling method was applied to calculate cross sections for electron scattering on atomic gallium. The integrated and momentum-transfer cross sections for elastic scattering are presented from the 4 s 2 4 p 4P 1 / 2 , 3 / 2 electronic states for incident energies between 0.03 eV and 1000 eV. Integrated excitation cross sections are also presented from these initial states to the 4 s 2 4 [ d , f ] , 4 s 2 5 [ s , p , d ] , 4 s 2 6 [ s , p ] and 4 s 2 7 s manifolds, as well as cross sections for excitation of the 4 s 2 4 p 2P 1 / 2 state to the 4 s 2 4 p 2P 3 / 2 state. Estimates were presented for the total single ionisation cross section and total cross section for scattering on gallium in the 4 s 2 4 p 2P 1 / 2 , 3 / 2 states, including direct ionisation from the 4p, 4s and 3d electrons, and excitation-autoionisation contributions from the 4s and 3d electrons. The estimated total single ionisation cross section was found to agree well with existing experimental data.

Atomic Data for Astrophysically Important Spectral Lines of Singly Ionized Nitrogen

Nitrogen lines are widely observed in astrophysical spectra and provide important diagnostics for plasma properties. In this work, we present extended calculations for accurate energy levels, electric dipole radiative transition parameters, and lifetimes for the lowest 102 states of the 2s 22p 2, 2s2p 3, 2s2p 23s, 2s 22p{n 1 l, n 2 d, 4f}(n 1 = 3–5, l = s, p, n 2 = 3, 4), and 2p 4 configurations of N ii within the framework of the fully relativistic multiconfiguration Dirac–Hartree–Fock and relativistic configuration interaction methods. These data are useful for modeling astrophysical spectra, for example, for nitrogen abundance determinations in early B-type stars, and for studying the compositions and plasma properties of H ii regions and planetary nebulae. Our computed transition parameters are compared with available experimental and theoretical data. The accuracy of the calculations is also assessed via a statistical analysis of the differences between the transition rates in the Babushkin and Coulomb gauges and by consideration of cancellation factors. In this way, 201 of the 1656 transitions computed in this work are estimated to be from accurate to better than 3%, corresponding to an accuracy class of A.

Fully relativistic energies, transition properties, and lifetimes of lithium-like germanium

Abstract Employing two fully relativistic methods, the multi-reference configuration Dirac–Hartree–Fock (MCDHF) method and the relativistic many-body perturbation theory (RMBPT) method, we report energies and lifetime values for the lowest 35 energy levels of the (1s2)nl configurations (where the principal quantum number n = 2–6 and the angular quantum number l = 0, …, n–1) of lithium-like germanium (Ge XXX), as well as complete data on the transition wavelengths, radiative rates, absorption oscillator strengths, and line strengths between the levels. Both the allowed (E1) and forbidden (magnetic dipole M1, magnetic quadrupole M2, and electric quadrupole E2) ones are reported. The results from the two methods are consistent with each other and align well with previous accurate experimental and theoretical findings. We assess the overall accuracies of present RMBPT results to be likely the most precise ones to date. The present fully relativistic results should be helpful for soft x-ray laser research, spectral line identification, plasma modeling and diagnosing. The datasets presented in this paper are openly available at https://doi.org/10.57760/sciencedb.j00113.00135.

State Interaction for Relativistic Four-Component Methods: Choose the Right Zeroth-Order Hamiltonian for Late-Row Elements.

We present several schemes based on the spin-separation of the Dirac-Coulomb-Breit Hamiltonian for the perturbative treatment of relativistic four-component Hamiltonians within the state interaction framework. While state interaction approaches traditionally use zeroth-order scalar-relativistic states, we develop augmented zeroth-order Hamiltonians with increasing accuracy and investigate convergence to the variational limit as a function of the choice of zeroth-order Hamiltonian. The state interaction schemes developed in this work are benchmarked using ground-state fine-structure splitting of late-row atoms and diatomic hyrides. Although the scalar-relativistic zeroth-order Hamiltonian exhibits significant errors in ground-state fine-structure splitting, the predictive accuracy can be improved by augmenting the zeroth-order Hamiltonian with one- and two-electron vector-relativistic operators (e.g., spin-orbit, spin-spin, orbit-orbit). This work lays the theoretical foundation for the development of low-scaling, high-accuracy perturbative relativistic methods suitable for late-row elements.

Estimating the mass-to-distance ratio for a set of megamaser AGN black holes by employing a general relativistic method

Context. Motivated by the recent achievements of a full general relativistic method in determining black hole (BH) parameters, we continue to estimate the mass-to-distance ratio of the supermassive BHs hosted at the core of the active galactic nuclei (AGNs) of the megamaser galaxies NGC 1320, NGC 1194, NGC 5495, and Mrk 1029. Aims. Our aim is to study the properties of super massive BHs at the centers of the selected AGNs by using a full general relativistic method that allows us to address the potential detection of relativistic effects within such astrophysical systems. Methods. In order to perform statistical estimations with publicly available observational data, we used a general relativistic model that describes BH rotation curves and further employed a Bayesian fitting method. Results. We estimated the mass-to-distance ratio of the aforementioned BHs, their position and the recessional redshifts of the host galaxies produced by both peculiar motion and cosmological expansion of the Universe. Finally, we calculated the gravitational redshift of the closest maser to the BH for each AGN. This gravitational redshift is a general relativistic effect produced by the gravitational field of the BH properly included in the modelling.

High-accuracy optical clocks with sensitivity to the fine-structure constant variation based on Sm[formula omitted]

We identify two metastable excited states in Sm10+ highly charged ion as candidates for high accuracy optical clocks. Several atomic properties relevant to optical clock development are calculated using relativistic many-body methods. This includes energy levels, transition amplitudes, lifetimes, scalar polarizabilities, black body radiation shift, and the sensitivity to the fine structure constant variation. We found that the clock transitions are not sensitive to perturbation, e.g., relative black body radiation shifts are ∼10−19. The enhancement factor for the α variation is ∼ 0.8 for one clock transition and ∼ 16 for another.

Absolute emission height determination of the radio emission components of PSR B2111+46 at multiple bands by relativistic phase shift method

Absolute emission height determination of the radio emission components of PSR B2111+46 at multiple bands by relativistic phase shift method

Toward Accurate Spin-Orbit Splittings from Relativistic Multireference Electronic Structure Theory.

Most nonrelativistic electron correlation methods can be adapted to account for relativistic effects, as long as the relativistic molecular spinor integrals are available, from either a four-, two-, or one-component mean-field calculation. However, relativistic multireference correlation methods remain a relatively unexplored area, with mixed evidence regarding the improvements brought by perturbative treatments. We report, for the first time, the implementation of state-averaged four-component relativistic multireference perturbation theories to second and third order based on the driven similarity renormalization group (DSRG). With our methods, named 4c-SA-DSRG-MRPT2 and 3, we find that the dynamical correlation included on top of 4c-CASSCF references can significantly improve the spin-orbit splittings in p-block elements and potential energy surfaces when compared to 4c-CASSCF and 4c-CASPT2 results. We further show that 4c-DSRG-MRPT2 and 3 are applicable to these systems over a wide range of the flow parameter, with systematic improvement from second to third order in terms of both improved error statistics and reduced sensitivity with respect to the flow parameter.

Electronic structure and resonant inelastic x-ray scattering in Ca3Ru2O7

We have investigated the electronic structure of the transition metal oxide Ca3Ru2O7 within density-functional theory using the generalized gradient approximation while considering strong Coulomb correlations in the framework of the fully relativistic spin-polarized Dirac linear muffin-tin orbital band structure method. Ca3Ru2O7 can be classified as a Mott insulator since it was expected to be metallic from band structure calculations. We found that the magnetic ground state of Ca3Ru2O7 possesses an AFM−b magnetic structure with the Ru spin moments ordered antiferromagnetically along the b axis. We have investigated the resonant inelastic x-ray scattering (RIXS) spectra at the Ru and Ca K, L3, and M3 edges as well as at the OK edge. The experimentally measured RIXS spectrum of Ca3Ru2O7 at the Ru L3 edge possesses a sharp feature ≤2eV corresponding to transitions within the Ru t2g levels. The excitation located from 2 to 4 eV is due to t2g→ eg transitions. The third wide structure situated at 4.5−11eV appears due to transitions between the Ru 4dO states derived from the tails of oxygen 2p states and eg and t2g states. The RIXS spectra at the Ru L3 and M3 edges are quite similar. However, the corresponding RIXS spectra at the Ca site are quite different from each other due to the significant difference in the widths of core levels. The RIXS spectrum at the OK edge consists of three major inelastic excitations. We found that the first two low energy features ≤2.5eV are due to interband transitions between occupied and empty Ot2g states which appear due to the strong hybridization between oxygen 2p and Ru t2g states in close vicinity to the Fermi level. The next major peak between 2.5 and 8 eV reflects interband transitions from occupied O2p to empty Ot2g states. A wide energy interval between 4 and 11 eV is occupied by rather weak O2p→Oeg transitions. Published by the American Physical Society 2024

Performance of density-functional-theory and random-phase-approximation methods on the study of transition-metal clusters: the Tan clusters as an example

Recently developed density-functional-theory (DFT) and random-phase-approximation (RPA) methods are used to study competing isomers of some negatively charged Ta clusters, namely Ta12 - and Ta10 -, in an attempt to find a suitable strategy towards accurate studies of transition-metal clusters based on DFT. Also the neutral and cationic forms Ta12 (0,+) of the twelve-atom cluster are studied. The results are compared with experimental information obtained by several methods that differ in the property under study and the total electric charge of the clusters. We find that a careful choice of the density functional, the use of relativistic two-component methods, eventually in combination with all-electron basis sets, and the application of RPA-type methods, may all be necessary steps for a good assessment. Such an assessment should be made in relation to several experimental properties as much as possible.

Schwarzschild black hole and redshift rapidity: a new approach towards measuring cosmic distances

Motivated by recent achievements of a full general relativistic method in estimating the mass-to-distance ratio of supermassive black holes hosted at the core of active galactic nuclei, we introduce the new concept redshift rapidity in order to express the Schwarzschild black hole mass and its distance from the Earth just in terms of observational quantities. The redshift rapidity is also an observable relativistic invariant that represents the evolution of the frequency shift with respect to proper time in the Schwarzschild spacetime. We extract concise and elegant analytic formulas that allow us to disentangle mass and distance to black holes in the Schwarzschild background and estimate these parameters separately. This procedure is performed in a completely general relativistic way with the aim of improving the precision in measuring cosmic distances to astrophysical compact objects. Our exact formulas are valid on the midline and close to the line of sight, having direct astrophysical applications for megamaser systems, whereas the general relations can be employed in black hole parameter estimation studies. We also computed the frequency shift and the redshift rapidity for emitter eccentric orbits and calculated their relative error with respect to their numerical exact value for different eccentricities.

On the geometry dependence of the nuclear magnetic resonance chemical shift of mercury in thiolate complexes: A relativistic density functional theory study.

Thiolate containing mercury(II) complexes of the general formula [Hg(SR) ] have been of great interest since the toxicity of mercury was recognized. 199Hg nuclear magnetic resonance spectroscopy (NMR) is a powerful tool for characterization of mercury complexes. In this work, the Hg shielding constants in a series of [Hg(SR) ] complexes are therefore investigated computationally with particular emphasis on their geometry dependence. Geometry optimizations and NMR chemical shift calculations are performed at the density functional theory (DFT) level with both the zeroth-order regular approximation (ZORA) and four-component relativistic methods. The four exchange-correlation (XC) functionals PBE0, PBE, B3LYP, and BLYP are used in combination with either Dyall's Gaussian-type (GTO) or Slater-type orbitals (STOs) basis sets. Comparing ZORA and four-component calculations, one observes that the calculated shielding constants for a given molecular geometry have a constant difference of 1070 ppm. This confirms that ZORA is an acceptable relativistic method to compute NMR chemical shifts. The combinations of four-component/PBE0/v3z and ZORA/PBE0/QZ4P are applied to explore the geometry dependence of the isotropic shielding. For a given coordination number, the distance between mercury and sulfur is the key factor affecting the shielding constant, while changes in bond and dihedral angles and even different side groups have relatively little impact.

Relativistic Quantum Chemical Investigation of Actinide Covalency Measured by Electron Paramagnetic Resonance Spectroscopy.

We investigate actinide covalency effects in two [AnCptt3] (An = Th, U) complexes recently studied with pulsed electron paramagnetic resonance spectroscopy, using the Hyperion package to obtain relativistic hyperfine coupling constants from relativistic multiconfigurational wave functions. 1H and 13C HYSCORE simulations using the computed parameters show excellent agreement with the experimental data, highlighting the accuracy of modern relativistic ab initio methods. The extent of covalency indicated from the calculations on [ThCptt3] is in agreement with the original report based on traditional spectral fitting methods, while the covalency in [UCptt3] is found to be previously overestimated. The latter is due to the paramagnetic spin-orbit effect that arises naturally in a relativistic theory of hyperfine coupling and yet was not accounted for in the original study, thus highlighting the necessity of relativistic approaches for the interpretation of magnetic resonance data pertaining to actinides.

Theoretical investigation of energy levels and transitions for Ce iii with applications to kilonova spectra

ABSTRACT Doubly ionized cerium (Ce2+) is one of the most important ions to understand the kilonova spectra. In particular, near-infrared (NIR) transitions of Ce iii between the ground (5p6 4f2) and first excited (5p6 4f 5d) configurations are responsible for the absorption features around 14 500 Å. However, there is no dedicated theoretical studies to provide accurate transition probabilities for these transitions. We present energy levels of the ground and first excited configurations and transition data between them for Ce iii. Calculations are performed using the grasp2018 package, which is based on the multiconfiguration Dirac–Hartree–Fock and relativistic configuration interaction methods. Compared with the energy levels in the NIST data base (Kramida et al. 2024), our calculations reach the accuracy with the root-mean-square (rms) of 2732 or 1404 cm−1 (excluding one highest level) for ground configuration, and rms of 618 cm−1 for the first excited configuration. We extensively study the line strengths and find that the Babushkin gauge provides the more accurate values. By using the calculated gf values, we show that the NIR spectral features of kilonova can be explained by the Ce iii lines.

Relativistic configuration-interaction calculations on K α X-ray satellites of medium-charge Be-like ions

This study puts forward a calculation of the transitions of 1s2s22p 1P1−1s22s2 1S0 and 1s2s22p 3P1−1s22s2 1S0 for Be-like ions (Z = 6–30) using the multiconfiguration Dirac-Hartree–Fock (MCDHF) and relativistic configuration interaction methods. The computational results include transition wavelengths, transition probabilities, line strengths, and weighted oscillator strengths. The calculations also consider the contributions of the Breit interaction and quantum electrodynamics corrections (QED) to these levels. The results show that the contribution of the Breit interaction, self-energy, and vacuum polarization increase rapidly with increasing nuclear charge for certain configurations. The present calculated values are in good agreement with previous theoretical and experimental results, with errors better than 0.3%. A V/A L comparisons demonstrate the reliability of the data.

Interoperable workflows by exchanging grid-based data between quantum-chemical program packages.

Quantum-chemical subsystem and embedding methods require complex workflows that may involve multiple quantum-chemical program packages. Moreover, such workflows require the exchange of voluminous data that go beyond simple quantities, such as molecular structures and energies. Here, we describe our approach for addressing this interoperability challenge by exchanging electron densities and embedding potentials as grid-based data. We describe the approach that we have implemented to this end in a dedicated code, PyEmbed, currently part of a Python scripting framework. We discuss how it has facilitated the development of quantum-chemical subsystem and embedding methods and highlight several applications that have been enabled by PyEmbed, including wave-function theory (WFT) in density-functional theory (DFT) embedding schemes mixing non-relativistic and relativistic electronic structure methods, real-time time-dependent DFT-in-DFT approaches, the density-based many-body expansion, and workflows including real-space data analysis and visualization. Our approach demonstrates, in particular, the merits of exchanging (complex) grid-based data and, in general, the potential of modular software development in quantum chemistry, which hinges upon libraries that facilitate interoperability.