Nonrelativistic Research Articles

A relativistic DFT study of small-molecule activation facilitated by actinocenes (An(η8-C8H8)2)

The scarcity and radioactivity of actinides have made it very difficult to study actinocene and other actinide-containing complexes experimentally. Hence, theoretical studies of these complexes can offer significant direction in the enlightenment of difficult-to-obtain experimental data. Keeping in mind, actinocene (An(COT)2, An = Th, Pa, U, Np, Pu, Am, Cm) with D8h symmetry has been investigated in the present study. Under D8h symmetry, the structural parameters of optimized sandwich compounds are found to be in concurrence with the experimental data. This study extensively examines the experimentally characterized actinocene for their capability to activate small molecules (Y = CO, and N2) through relativistic density functional theory (DFT) analysis. After forming a complex with CO, and N2, D8h symmetry of An(COT)2 gets distorted resulting in the bending of both the COT rings. In all the [An(COT)2Y] complexes, a covalent bond was realized between An and Y except [U(COT)2N2], [Np(COT)2N2], and [Pu(COT)2N2], where an ionic bond was observed between An and Y. Furthermore, the experimental inaccessible [An(COT)2Y] complexes were elucidated through thermodynamic computations along with the analyses of geometric, electronic properties and bonding analysis. [Pu(COT)2N2] adducts have the largest contribution of ΔEorb to total ΔEint among all the complexes suggesting that the Pu-N bond is dominated by orbital attractions and shows significant covalency.

Spin polarization in relativistic heavy-ion collisions

Polarization has opened a new physics chapter in relativistic heavy-ion collisions. Since the first prediction and experimental observation of global spin polarization, a lot of progress has been made in understanding its features, both at experimental and theoretical levels. In this paper, we give an overview on the recent advances in this field. The covered topics include a review of measurements of global and local spin polarization of hyperons and the global spin alignment of vector meson’s. We account for the basic theoretical framework to describe spin polarization in a relativistic fluid such as the Quark–Gluon Plasma, including statistical quantum field theory and local thermodynamic equilibrium, spin hydrodynamics, relativistic kinetic theory with spin and coalescence models.

Complexation of trivalent Eu and Am ions with phenanthroline-derived ligands tuned by rotating thiazole/oxazole substituents

The reprocessing of spent nuclear fuels is greatly challenging, as the current separation technique of lanthanide (Ln) and actinide (An) suffers too many difficulties. In this paper, selective ligands of phenanthroline derivatives modified by thiazole/oxazole were designed by relativistic density functional theory calculations. Their complexation of Eu3+ and Am3+ and the mechanism of selective separation were comprehensively examined. The spatial rotation against the CC bond between phenanthroline and thiazole/oxazole has access to six ligands. It is shown that Looo with oxazole substituents and their oxygens being opposite is the best electron donor for metal ions. The results of WBIs and MBO unravel that Am-L bond has more covalency than respective Eu-L bond. From topological analyses, it is found that these metal–ligand bonds are dominated by electrostatic interaction and largely of ionic bond character. Thermodynamically, all ligands prefer binding Eu3+ to Am3+.

Consistent Second-Order Treatment of Spin-Orbit Coupling and Dynamic Correlation in Quasidegenerate N-Electron Valence Perturbation Theory.

We present a formulation and implementation of second-order quasidegenerate N-electron valence perturbation theory (QDNEVPT2) that provides a balanced and accurate description of spin-orbit coupling and dynamic correlation effects in multiconfigurational electronic states. In our approach, the energies and wave functions of electronic states are computed by treating electron repulsion and spin-orbit coupling operators as equal perturbations to the nonrelativistic complete active-space wave functions, and their contributions are incorporated fully up to the second order. The spin-orbit effects are described using the Breit-Pauli (BP) or exact two-component Douglas-Kroll-Hess (DKH) Hamiltonians within spin-orbit mean-field approximation. The resulting second-order methods (BP2- and DKH2-QDNEVPT2) are capable of treating spin-orbit coupling effects in nearly degenerate electronic states by diagonalizing an effective Hamiltonian expanded in a compact non-relativistic basis. For a variety of atoms and small molecules across the entire periodic table, we demonstrate that DKH2-QDNEVPT2 is competitive in accuracy with variational two-component relativistic theories. BP2-QDNEVPT2 shows high accuracy for the second- and third-period elements, but its performance deteriorates for heavier atoms and molecules. We also consider the first-order spin-orbit QDNEVPT2 approximations (BP1- and DKH1-QDNEVPT2), among which DKH1-QDNEVPT2 is reliable but less accurate than DKH2-QDNEVPT2. Both DKH1- and DKH2-QDNEVPT2 hold promise as efficient and accurate electronic structure methods for treating electron correlation and spin-orbit coupling in a variety of applications.

Precessing and periodic timelike orbits and their potential applications in Einsteinian cubic gravity

Einsteinian cubic gravity (ECG) is the most general theory up to cubic order in curvature, which has the same graviton spectrum as the Einstein theory. In this paper, we investigate the geodesic motions of timelike particles around the four dimensional asymptotically flat black holes in ECG, and discuss their potential applications when connecting them with recent observational results. We first explore the effects of the cubic couplings on the marginally bound orbits (MBO), innermost stable circular orbits (ISCO) and on the periodic orbits around the Einsteinian cubic black hole. We find that comparing to Schwarzschild black hole in general relativity, the cubic coupling enhances the energy as well as the angular momentum for all the bound orbits of the particles. Then, we derive the relativistic periastron precessions of the particles and give a preliminary bound on the cubic coupling employing the observational result of the S2 star’s pericenter precession in SgrA*. Finally, after calculating the periodic orbits’ configurations, we preliminarily evaluate the gravitational waveform radiated from several periodic orbits in one complete period of a test object which orbits a supermassive Einsteinian cubic black hole. Our studies could be helpful for us to better understand the gravitational structure of the theory with high curvatures.

Massless Lifshitz field theory for arbitrary z

By using the notion of fractional derivatives, we introduce a class of massless Lifshitz scalar field theory in (1+1)-dimension with an arbitrary anisotropy index z. The Lifshitz scale invariant ground state of the theory is constructed explicitly and takes the form of Rokhsar-Kivelson (RK). We show that there is a continuous family of ground states with degeneracy parameterized by the choice of solution to the equation of motion of an auxiliary classical system. The quantum mechanical path integral establishes a 2d/1d correspondence with the equal time correlation functions of the Lifshitz scalar field theory. We study the entanglement properties of the Lifshitz theory for arbitrary z using the path integral representation. The entanglement measures are expressed in terms of certain cross ratio functions we specify, and satisfy the c-function monotonicity theorems. We also consider the holographic description of the Lifshitz theory. In order to match with the field theory result for the entanglement entropy, we propose a z-dependent radius scale for the Lifshitz background. This relation is consistent with the z-dependent scaling symmetry respected by the Lifshitz vacuum. Furthermore, the time-like entanglement entropy is determined using holography. Our result suggests that there should exist a fundamental definition of time-like entanglement other than employing analytic continuation as performed in relativistic field theory.

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.

Bis(acyl)phosphide Complexes of U(III)/U(IV): A Case of a Hidden Redox-Active Ligand.

The recently reported tris(bis(2,4,6-triisopropylbenzoyl)-phosphide)uranium (UIII(trippBAP)3, 2) complex (Inorg. Chem. 2022, 61 (32), 12508-12517) demonstrated a silent 31P NMR spectrum. This complex was described as a U(III) complex with an organic radical ligand fragment. Moreover, the EPR spectrum of 2 was indicative of an organic radical in the ligand framework complexed to uranium, in contrast to that of UIV(mesBAP)4, 1. Herein, with the help of relativistic density functional theory (DFT) calculations, the electronic structures of 1, 2, and U(mesBAP)3 (4) are examined in an effort to understand the unusual 31P NMR spectrum of 2. Results indicate the reduction of the carbonyl bonds and delocalization of the electrons over the ligands, indicative of U → L backbonding. Additionally, the reduced acyl carbons are found to exist as ketyl radicals [O═C• -] that are responsible for the silent 31P NMR spectra of 2. These findings demonstrate the redox noninnocent nature of BAP- in 2 and 4, causing uranium to exist in a formal oxidation state of +4.

Exploring the bonding and extraction separation effects of N donor ligands with different skeletons on Am(III) and Eu(III)

Designing ligands for effective separation of actinide(III)/lanthanide(III) is one of the key issues in the treatment of spent nuclear fuel. However, due to the chemical similarity of trivalent actinides and lanthanides, their separation faces a great challenge in the reprocessing of spent nuclear fuel. Nitrogen donor extractants are considered as promising reagents for separation of trivalent actinides and lanthanides. To the best of our knowledge, the pre-organized structure of the ligand has a strong influence on the extraction separation capacity. In this work, we designed four N-donor ligands (L1 and L2 with pyridine and bipyridine skeletons, respectively, and L3 and L4 both with phenanthroline skeletons) with different pre-organized structures and investigated their selective extraction for Am(III) and Eu(III) by using scalar relativistic density functional theory (DFT). The absolute minimum ESP values of these ligands and the higher HOMO level suggest that the ligand L2 may have a stronger affinity for Am(III)/Eu(III) ions than other ligands. The three average bond lengths of each complex indicate that the Am(III) and Eu(III) ions have larger bond lengths with N2 atoms than with N1 atoms. Various theoretical approaches have been used to evaluate the properties of the four ligands as well as the coordination structures, bonding properties and thermodynamic properties of the complexes of the four ligands with Am(III) and Eu(III). The WBIs, QTAIM, NBO, DOS and EDA analysis indicate that the metal–ligand bonds are mainly ionic in character, the Am-N bond has more covalency than the Eu-N bond because the Am 5f orbitals are more involved in bonding with ligand than Eu 4f orbitals. According to the extended transition state and natural orbital chemical valence theory (ETS-NOCV) analysis, electrons are obviously transferred from the lone pair of the ligand N atom to the hybrid s, d and f orbitals of the metal ion. The thermodynamic results show that the four ligands can coordinate well with the Am and Eu ions, and also have suitable separation capacity for Am and Eu. Among the four ligands, the L2 and L3 ligands have the strongest coordination ability for metals and the best extraction separation effect for Am and Eu. It can be seen that the bridging skeleton of the ligand and the number of N atoms on the five-membered ring and also different organic solvents have obvious effects on the extraction and separation capacity of the ligand. This study provides a theoretical basis for the efficient separation of Am(III)/Eu(III) by adjusting the preorganization level of ligands, and provides a theoretical basis for the design and screening of ligands by preorganization.

Response to "Comment on 'Theoretical examination of QED Hamiltonian in relativistic molecular orbital theory'" [J. Chem. Phys. 160, 187101 (2024)

Response to "Comment on 'Theoretical examination of QED Hamiltonian in relativistic molecular orbital theory'" [J. Chem. Phys. 160, 187101 (2024)

Comment on "Theoretical examination of QED Hamiltonian in relativistic molecular orbital theory" [J. Chem. Phys. 159, 054105 (2023)

Comment on "Theoretical examination of QED Hamiltonian in relativistic molecular orbital theory" [J. Chem. Phys. 159, 054105 (2023)

Combined Analysis of Neutrino and Antineutrino Charged Current Inclusive Interactions

This paper presents a combined analysis of muon neutrino and antineutrino charged-current cross sections at kinematics of relevance for the T2K, MINERvA and MicroBooNE experiments. We analyze the sum, difference and asymmetry of neutrino versus antineutrino cross sections in order to get a better understanding of the nuclear effects involved in these processes. Nuclear models based on the superscaling behavior and the relativistic mean field theory are applied, covering a wide range of kinematics, from hundreds of MeV to several GeV, and the relevant nuclear regimes, i.e., from quasileastic reactions to deep inelastic scattering processes. The NEUT neutrino-interaction event generator, used in neutrino oscillation experiments, is also applied to the analysis of the quasielastic channel via local Fermi gas and spectral function approaches.

Accretion flows around spinning compact objects in the post-Newtonian regime

We present the structure of a low angular momentum accretion flows around rotating compact objects incorporating relativistic corrections up to the leading post-Newtonian order. To begin with, we formulate the governing post-Newtonian hydrodynamic equations for the mass and energy-momentum flux without imposing any symmetries. However, for the sake of simplicity, we consider the flow to be stationary, axisymmetric, and inviscid. Toward this, we adapt the polytropic equation of state (EoS) and analyze the vertically integrated accretion flow confined to the equatorial plane. It is shown that the spin-orbit effects manifest themselves in the accretion dynamics. In the present analysis, we focus on global transonic accretion solutions, where a subsonic flow enters far away from the compact object and gradually gains radial velocity as it moves inwards. Thus, the flow becomes supersonic after reaching a certain radius, known as the critical point. To better understand the transonic solutions and examine the effect of post-Newtonian corrections, we classify the post-Newtonian equations into semi-relativistic (SR), semi-Newtonian (SN), and non-relativistic (NR) limits and compare the accretion solutions and their corresponding flow variables. With these, we find that SR and SN flow are in good agreement all throughout, although they deviate largely from the NR ones. Interestingly, the density profile seems to follow the profile ρ ∝ r -3/2 in the post-Newtonian regime. The present study has the potential to connect Newtonian and GR descriptions of accretion dynamics.

Tensor-force effects on nuclear matter in relativistic ab initio theory

Tensor-force effects on nuclear matter in relativistic ab initio theory

Evolution of the nuclear spin-orbit splitting explored via the 32Si(d,p)33Si reaction using SOLARIS

The spin-orbit splitting between neutron 1p orbitals at 33Si has been deduced using the single-neutron-adding (d,p) reaction in inverse kinematics with a beam of 32Si, a long-lived radioisotope. Reaction products were analyzed by the newly implemented SOLARIS spectrometer at the reaccelerated-beam facility at the National Superconducting Cyclotron Laboratory. The measurements show reasonable agreement with shell-model calculations that incorporate modern cross-shell interactions, but they contradict the prediction of proton density depletion based on relativistic mean-field theory. The evolution of the neutron 1p-shell orbitals is systematically studied using the present and existing data in the isotonic chains of N=17, 19, and 21. In each case, a smooth decrease in the separation of the 1p3/2-1p1/2 orbitals is seen as the respective p-orbitals approach zero binding, suggesting that the finite nuclear potential strongly influences the evolution of nuclear structure in this region.

Inverse Cosmos

The Big Bang Model is the most widely accepted cosmological model regarding the origin of the universe, resting on two fundamental assumptions: one is Einstein's theory of general relativity, describing the gravitational interaction of matter with space-time, and the other is the cosmological principle, stating that an observer viewing the universe will be faced with homogeneity and isotropy, meaning that the universe has no edge. According to this model, one cannot seek a specific point of origin of the big bang, as this explosion occurred simultaneously throughout the whole universe. Through the evolution of various cosmological models, the Standard Cosmological Model (Lambda-CDM) also assumes that the universe consists of three main components: 1. A cosmological constant associated with dark energy, 2. Cold dark matter, and 3. Ordinary matter. From the perspective of cosmologists, this model provides a general explanation for a wide range of observed phenomena, including the abundance of light elements, cosmic microwave background radiation, and large-scale structures in the universe. However, there still exist aspects of the observed universe that currently pose challenges not explained by the big bang model. In response to these challenges, "T-Consciousness Cosmology" proposes multiple hypotheses, offering not only a new interpretative angle on the behavior and function of the components of the cosmos, but also stating that the latest cosmological models have paradoxes relative to the observations made. T-Consciousness Cosmology asserts that if we accept the prevalent models of cosmology, we are then faced with illogical manifestations of an expanding universe. In this discussion, several reasons are presented under the concept of an "Inverse Cosmos," challenging certain interpretations of the standard cosmological model or the latest big bang model regarding the origin of the cosmos, its geometric shape, and the stages accepted by most cosmologists for cosmic expansion. These challenges include issues such as the Density Obscurity Horizon for Matter and Energy, the Thermal Obscurity Horizon, the Timelessness Horizon, and others.

Dirac-Coulomb-Breit Molecular Mean-Field Exact-Two-Component Relativistic Equation-of-Motion Coupled-Cluster Theory.

We present a relativistic equation-of-motion coupled-cluster with single and double excitation formalism within the exact two-component framework (X2C-EOM-CCSD), where both scalar relativistic effects and spin-orbit coupling are variationally included at the reference level. Three different molecular mean-field treatments of relativistic corrections, including the one-electron, Dirac-Coulomb, and Dirac-Coulomb-Breit Hamiltonian, are considered in this work. Benchmark calculations include atomic excitations and fine-structure splittings arising from spin-orbit coupling. Comparison with experimental values and relativistic time-dependent density functional theory is also carried out. The computation of the oscillator strength using the relativistic X2C-EOM-CCSD approach allows for studies of spin-orbit-driven processes, such as the spontaneous phosphorescence lifetime.

Quasinormal Spectrum of (2+1)$(2+1)$‐Dimensional Asymptotically Flat, dS and AdS Black Holes

AbstractWhile ‐dimensional black holes in the Einstein theory allow for only the anti‐de Sitter (AdS) asymptotic, when the higher curvature correction is tuned on, the asymptotically flat, de Sitter, and AdS cases are included. Here, a detailed study of the stability and quasinormal spectra of the scalar field perturbations around such black holes with all three asymptotics is proposed. Calculations of the frequencies are fulfilled with the help of the 6th order Wentzel–Kramers–Brillouin (WKB) method with Pade approximants, Bernstein polynomial method, and time‐domain integration. Results obtained by all three methods are in a very good agreement in their common range of applicability. When the multipole moment is equal to zero, the purely imaginary, i.e., non‐oscillatory, modes dominate in the spectrum for all types of the asymptotic behavior, while the spectrum at higher resembles that in four‐dimensional spacetime with the corresponding asymptotic.

Continuum Limit of the Green Function in Scaled Affine φ44 Quantum Euclidean Covariant Relativistic Field Theory

Through path integral Monte Carlo computer experiments, we prove that the affine quantization of the φ44-scaled Euclidean covariant relativistic scalar field theory is a valid quantum field theory with a well-defined continuum limit of the one- and two-point functions. Affine quantization leads to a completely satisfactory quantization of field theories in situations involving scaled behavior, leading to an unexpected term, ℏ2/φ2, which arises only in the quantum aspects.