Relativistic Density Research Articles

Dark radiation from the primordial thermal bath in momentum space

Motivated by the stunning projections for future CMB surveys, we evaluate the amount of dark radiation produced in the early Universe by two-body decays or binary scatterings with thermal bath particles via a rigorous analysis in momentum space. We track the evolution of the dark radiation phase space distribution, and we use the asymptotic solution to evaluate the amount of additional relativistic energy density parameterized in terms of an effective number of additional neutrino species ΔN eff. Our approach allows for studying light particles that never reach equilibrium across cosmic history, and to scrutinize the physics of the decoupling when they thermalize instead. We incorporate quantum statistical effects for all the particles involved in the production processes, and we account for the energy exchanged between the visible and invisible sectors. Non-instantaneous decoupling is responsible for spectral distortions in the final distributions, and we quantify how they translate into the corresponding value for ΔN eff. Finally, we undertake a comprehensive comparison between our exact results and approximated methods commonly employed in the existing literature. Remarkably, we find that the difference can be larger than the experimental sensitivity of future observations, justifying the need for a rigorous analysis in momentum space.

Rational Design of Metallylenes for Hydrogenation Reactions

AbstractThe hydrogenation of alkenes, alkynes, carbonyls, and imines by H2‐activated metallylenes (H3C−EH2−L, CELH2; E=Si, Ge, Sn and L=NMe2, PMe2) was studied using relativistic density functional theory at ZORA‐BP86/TZ2P. By means of activation strain and Kohn–Sham molecular orbital analyses, the physical factors underlying the trends in reactivity were identified and quantified. Firstly, the hydrogenation reactivity increases on descending Group 14, that is from silylenes (E=Si) to stannylenes (E=Sn). This reactivity trend originates primarily from a reduced energy required to break the bonds between the Group 14 atom and the hydrogen atoms because the strength of these bonds decreases from Si−H to Ge−H to Sn−H. Secondly, the reactivity decreases as the Group 15 ligand changes from nitrogen to phosphorus (L=NMe2, PMe2) which stems from the trigonal pyramidal PMe2 geometry compared to the trigonal planar NMe2 geometry. The latter can, therefore, effectively engage in stronger orbital interactions with the substrate than the former, due to a more efficient HOMO–LUMO orbital overlap. By combining our insights, we rationally designed an optimally tuned catalyst (Group 14 atom and ligand) considering the overall catalytic cycle involving H2 activation of the metallylene and subsequent hydrogenation.

Evaluation of picture change effects on fractional occupation number states in noble gas atoms

In the two-component relativistic density functional theory, the picture change error (PCE), which originates from insufficient transformation of operators, should be corrected. In this study, we examine the PCE in the fractional occupation number (FON) state based on the spin-free infinite-order two-component Hamiltonian. The PCE for the total and orbital energy changes is estimated with respect to the FON electrons of the highest occupied molecular orbital and 1s core orbital in noble gas atoms. PCE is significant in core orbitals in heavy elements but relatively small in light elements and valence orbitals. The delocalization error, which can be represented by the total energy deviation from the behavior of the exact energy, is overestimated by the lack of picture change correction of the two-electron operator and underestimated by that of the density operator. Corresponding to these results, the PCE influences the value of orbital energies and slope of orbital energy change to FON.

Inquiring 199Hg NMR Parameters by Combining Ab Initio Molecular Dynamics and Relativistic NMR Calculations.

Ab initio molecular dynamics (AIMD) sampling followed by relativistic density functional theory (DFT) 199Hg NMR calculations were performed for Hg organometallic complexes in water, dimethyl sulfoxide, and chloroform. The spin-orbit coupling, a relativistic effect, is a key factor for predicting δ(Hg) and 1J(Hg-C) accurately, in conjunction with a dynamic treatment of the systems. Good agreement between the theoretical and experimental results is reached by adopting implicit (based on a continuum model) and explicit (solvent molecules treated quantum mechanically) solvation models. Broader trends appearing in the experimental data available in the literature are reproduced by the calculations, and therefore, quantum chemistry is able to assist in the assignment and interpretation of 199Hg NMR data. Less pronounced trends, such as changes in the 199Hg chemical shift in different systems with the same atom types bound to Hg, are too weak to be predicted reliably by the current state-of-the-art theoretical methods based on AIMD sampling and relativistic DFT with hybrid functionals for NMR calculations.

Nuclear level density from relativistic density functional theory and combinatorial method

Nuclear level density is calculated with the combinatorial method based on the relativistic density functional theory including pairing correlations. The Strutinsky method is adopted to smooth the total state density in order to refine the prediction at low excitation energy. The impacts of pairing correlations and moments of inertia on the nuclear level density are discussed in detail. Taking Cd112 as an example, it is demonstrated that the nuclear level density based on the relativistic density functional PC-PK1 can reproduce the experimental data at the same level as or even better than the previous approaches.

Paramagnetic Nuclear Magnetic Resonance Shifts for Triplet Systems and Beyond with Modern Relativistic Density Functional Methods.

An efficient framework for the calculation of paramagnetic NMR (pNMR) shifts within exact two-component (X2C) theory and (current-dependent) density functional theory (DFT) up to the class of local hybrid functionals (LHFs) is presented. Generally, pNMR shifts for systems with more than one unpaired electron depend on the orbital shielding contribution and a temperature-dependent term. The latter includes zero-field splitting (ZFS), hyperfine coupling (HFC), and the g-tensor. For consistency, we calculate these three tensors at the same level of theory, i.e., using scalar-relativistic X2C augmented with spin-orbit perturbation theory. Results for pNMR chemical shifts of transition-metal complexes reveal that this X2C-DFT framework can yield good results for both the shifts and the individual tensor contributions of metallocenes and related systems, especially if the HFC constant is large. For small HFC constants, the relative error is often large, and sometimes the sign may be off. 4d and 5d complexes with more complicated structures demonstrate the limitations of a fully DFT-based approach. Additionally, a Co-based complex with a very large ZFS and pronounced multireference character is not well described. Here, a hybrid DFT-multireference framework is necessary for accurate results. Our results show that X2C is sufficient to describe relativistic effects and computationally cheaper than a fully relativistic approach. Thus, it allows use of large basis sets for converged HFCs. Overall, current-dependent meta-generalized gradient approximations and LHFs show some potential; however, the currently available functionals leave a lot to be desired, and the predictive power is limited.

Commencement and Interruption of Relativistic Electron Dropout in the Heart of the Outer Radiation Belt Induced by a Magnetic Cloud Event

AbstractWe analyze and discuss the commencement and interruption of the relativistic electron dropout in the heart of the outer radiation belt (L* = 4–5) induced by a typical magnetic cloud (MC) event. This MC event impinged the Earth’s magnetosphere on 31 October 2012 and caused a moderate geomagnetic storm with a special prolonged initial phase lasting for >13 hr. The relativistic electrons phase space density (PSD) dropout commenced at L* > 5 during the initial phase. The PSD dropout penetrated deep beyond the heart of the radiation belt (reached L* < 4) at the onset of the main phase, while it was partially enhanced with a local PSD maximum around L* = 4.5, thus causing the interruption of the PSD dropout. The dropout became pronounced at L* > ∼4.7 while the local PSD maximum was maintained throughout the main phase. During the recovery phase, the dropout totally disappeared at L* < 5.5 with relativistic electron PSD gradually recovering to pre‐event level or higher. Further investigations on solar wind parameters and plasma waves give evidence that (a) persistent high dynamic pressure and the triggered Ultra‐Low Frequency waves contribute to the dropout of electrons to interplanetary space during the initial phase and the onset of the main phase; (b) local acceleration by chorus waves during the main phase and recovery phase could explain the interruption of the dropout. Our study underlines the persistent high dynamic pressure competing with intense chorus waves in triggering the commencement and interruption of the relativistic electrons PSD dropout in the heart of the outer radiation belt.

Reactivity of Ts and At oxides and oxyhydrides with a gold surface from periodic DFT calculations.

Adsorption energies, Eads, of oxides and oxyhydrides of the superheavy element (SHEs) Ts and of its lighter homologue At on the gold surface are predicted on the basis of relativistic periodic density functional theory calculations via AMS BAND software. The following compounds were considered: MO, MO2, MOO, and MO(OH) (where M = At and Ts). The aim of this study is to support "one-atom-at-a-time" gas-phase chromatography experiments on reactivity/volatility of SHEs. The results obtained indicate that all the molecules investigated should interact fairly strongly with the gold surface, with those of Ts being more reactive than At ones. The similarity in the Eads values of all the considered At compounds would make it challenging to differentiate between them while measuring their adsorption enthalpies, given experimental uncertainty. However, the difference in Eads among Ts compounds is more pronounced, so that one should be able to differentiate between the species.

Uncovering chemical homology of superheavy elements: a close look at astatine.

The fascination with superheavy elements (SHE) spans the nuclear physics, astrophysics, and theoretical chemistry communities. Extreme relativistic effects govern these elements' chemistry and challenge the traditional notion of the periodic law. The experimental quest for SHE critically depends on theoretical predictions of these elements' properties, especially chemical homology, which allows for successful prototypical experiments with more readily available lighter homologues of SHE. This work is a comprehensive quantum-chemical investigation into astatine (At) as a non-intuitive homologue of element 113, nihonium (Nh). Combining relativistic coupled-cluster and density functional theory approaches, we model the behaviour of At and AtOH in thermochromatographic experiments on a pristine gold surface. Insights into the electronic structure of AtOH and NhOH and accurate estimates of At-gold and AtOH-gold adsorption energies rationalise recent experimental findings and justify the use of At as a chemical homologue of Nh for the successful design of future experiments on Nh detection and chemical characterisation.

High-valent actinyl (AnO2; An = U, Np and Pu) complexation with TEtraQuinoline (TEQ) ligand - a DFT study.

A recently synthesised novel macrocycle composed of four quinoline units called TEtraquinoline (TEQ) (J. Am. Chem. Soc., 2023, 145(4), 2609-2618) was reported to exhibit transition metal complexation ability. Meanwhile, there is a growing interest in different binding motifs for radioactive and toxic actinides. In this study, we modelled high-valent actinyl (AnO2)n+, An = U, Np, Pu; n = 1, 2, 3 complexes of TEQ and studied their geometric and electronic properties using scalar relativistic density functional theory (SR-DFT). The calculated results showed that the equatorial An-N and axial AnO bonds were polar bonds with a high degree of covalence, the former being longer than the latter. Natural bond orbital (NBO) analysis of the An-N bond orders decreased from complexes of uranyl to plutonyl and from complexes of heptavalent to pentavalent actinyls. This was due to the localization of the 5f orbital in the heavier actinyl and the high charge on An. The charge analysis showed a ligand-to-metal charge transfer (LMCT) on complexation. It was interesting to observe metal-to-ligand spin delocalization only in the [AnVI/VIIO2L]2+/3+ complexes, where the spin density on An was observed to increase on complexation. Based on the assigned oxidation states, it was observed that the heptavalent neptunyl cation retained its formal high oxidation state on complexation with TEQ. The energetics associated with the formation reaction of all the actinyl-TEQ complexes suggest spontaneity at lower temperatures (i.e., lower than 298.15 K). The energy decomposition analysis (EDA) indicates that the electrostatic energy contributions were predominant in the [AnVO2L]+ complexes, while covalent (orbital) energy contributions were higher in the [AnVIO2L]2+ and [AnVIIO2L]3+ complexes. The extended transition state-natural orbitals for chemical valence (ETS-NOCV) analysis confirmed the prominent covalent character in [AnVIIO2L]3+ over [AnVIO2L]2+ and [AnVO2L]+and the back donation of charges from An to N that stabilizes TEQ.

Stabilization of Diborynes versus Destabilization of Diborenes by Coordination of Lewis Bases: Unravelling the Dichotomy.

We have quantum chemically investigated the boron-boron bonds in B2 , diborynes B2 L2 , and diborenes B2 H2 L2 (L=none, OH2 , NH3 ) using dispersion-corrected relativistic density functional theory at ZORA-BLYP-D3(BJ)/TZ2P. B2 has effectively a single B-B bond provided by two half π bonds, whereas B2 H2 has effectively a double B=B bond provided by two half π bonds and one σ 2p-2p bond. This different electronic structure causes B2 and B2 H2 to react differently to the addition of ligands. Thus, in B2 L2 , electron-donating ligands shorten and strengthen the boron-boron bond whereas, in B2 H2 L2 , they lengthen and weaken the boron-boron bond. The aforementioned variations in boron-boron bond length and strength become more pronounced as the Lewis basicity of the ligands L increases.

Understanding the Retro‐Cope Elimination Reaction of Linear Alkynes

AbstractThe bioorthogonal retro‐Cope elimination reaction of linear alkynes R3C−C≡C−X (R3 = combinations of H, MeO, F; X = H, F, Cl, Br, I) with N,N‐dimethylhydroxylamine was quantum chemically investigated using relativistic density functional theory at ZORA‐BP86/TZ2P. This novel reaction can be tuned through judicious substitution of the alkyne at both the terminal and propargylic position to render second‐order kinetics that rival and out‐compete strain‐promoted variants. Activation strain and quantitative molecular orbital analyses reveal that, both upon terminal or propargylic substitution of propyne, the main effect of substituting H for X is a lowering of the propyne LUMO which stabilizes the HOMO–LUMO interactions and thus the transition state. In the case of terminal substitution with larger halogens (X = Cl, Br, I), a secondary effect interferes: steric repulsion with these larger halogens is absorbed into a longer forming C⋯N bond leading to a more asynchronous reaction accompanied by less (not more) steric Pauli repulsion.

Heterocyclic Ligands with Different N/O Donor Modes for Am(III)/Eu(III) Separation: A Theoretical Perspective.

Excellent "CHON" compatible ligands based on a heterocyclic skeleton for the separation of trivalent actinides [An(III)] from lanthanides [Ln(III)] have been widely explored, the aim being spent nuclear fuel reprocessing. The combination mode of a soft/hard (N/O) donor upon the coordination chemistry of An(III) and Ln(III) should play a vital role with respect to the performance of ligands. As such, in this work, two typical experimentally available phenanthroline-derived tetradentate ligands, CyMe4-BTPhen (L1) and Et-Tol-DAPhen (L4), and two theoretically designed asymmetric tetradentate heterocyclic ligands, L2 and L3, with various N/O donors were investigated using scalar relativistic density functional theory. We have evaluated the electronic structures of L1-L4 and their coordination modes, bonding properties, and extraction reactions with Am(III) and Eu(III). We found that the Am/Eu-N interactions play a more important role in the orbital interactions between the ligand and Am(III)/Eu(III) ions. Compared with those of L1, the coordinated O atoms of L2 and L4 weaken the metal-N bonds. The Am(III)/Eu(III) selectivity follows the order L1 > L2 > L4 based on the change in Gibbs free energy, reflecting the fact that the Am(III)/Eu(III) selectivity of the ligand is affected by the number of coordinated N atoms. In addition, L3 displays the strongest binding ability for Am(III)/Eu(III) ions and the smallest Am(III)/Eu(III) selectivity among the four ligands, due to its structural preorganization. This work clarifies the influence of the number of coordinated N and O atoms of ligands on Am(III)/Eu(III) selectivity, which provides valuable fundamental information for the design of efficient ligands with N and O donors for An(III)/Ln(III) separation.

Tilt-induced charge localisation in phosphide antiperovskite photovoltaics

Antiperovskites are a rich family of compounds with applications in battery cathodes, superconductors, solid-state lighting, and catalysis. Recently, a novel series of antimonide phosphide antiperovskites (A 3SbP, where A = Ca, Sr Ba) were proposed as candidate photovoltaic absorbers due to their ideal band gaps, small effective masses and strong optical absorption. In this work, we explore this series of compounds in more detail using relativistic hybrid density functional theory. We reveal that the proposed cubic structures are dynamically unstable and instead identify a tilted orthorhombic Pnma phase as the ground state. Tilting is shown to induce charge localisation that widens the band gap and increases the effective masses. Despite this, we demonstrate that the predicted maximum photovoltaic efficiencies remain high (24%–31% for 200 nm thin films) by bringing the band gaps into the ideal range for a solar absorber. Finally, we assess the band alignment of the series and suggest hole and electron contact materials for efficient photovoltaic devices.

Tipping the Balance Between the bcc and fcc Phase Within the Alkali and Coinage Metal Groups.

Why the Group 1 elements crystallize in the body-centered cubic (bcc) structure, and the iso-electronic Group 11 elements in the face-centered cubic (fcc) structure, remains a mystery. Here we show that a delicate interplay between many-body effects, vibrational contributions and dispersion interactions obtained from relativistic density functional theory offers an answer to this long-standing controversy. It also sheds light on the Periodic Table of Crystal Structures. A smooth diffusionless transition through cuboidal lattices gives a detailed insight into the bcc→fcc phase transition for the Groups 1 and 11 elements.

Einflüsse auf die Balance zwischen bcc‐ und fcc‐Phasenstabilitäten von Alkali‐ und Münzmetallen

AbstractBisher war es ein Rätsel, weshalb die Elemente der Gruppe 1 in der kubisch‐raumzentrierten (bcc) und die iso‐elektronischen Elemente der Gruppe 11 in der kubisch‐flächenzentrierten Struktur (fcc) kristallisieren. In dieser Untersuchung auf Grundlage von relativistischer Dichtefunktionaltheorie wird demonstriert, wie ein komplexes Zusammenspiel zwischen Mehrteilcheneffekten, Schwingungsenergiebeiträgen und Dispersionswechselwirkungen eine Antwort auf diese langjährige Kontroverse liefert und dabei gleichzeitig zum Verständnis des Periodensystems der Kristallstrukturen beiträgt. Ein sanfter, diffusionloser Übergang durch kuboidale Gitterstrukturen hindurch bietet detaillierte Einblicke in den bcc→fcc Phasenübergang für die Elemente der Gruppen 1 und 11.

Generalized description of neutron star matter with a nucleonic relativistic density functional

Generalized description of neutron star matter with a nucleonic relativistic density functional

Nuclear chiral rotation within Relativistic Configuration-interaction Density functional theory

The Relativistic Configuration-interaction Density functional (ReCD) theory that combines the advantages of large-scale configuration-interaction shell model and relativistic density functional theory is extended to study nuclear chiral rotation. The energy spectra and transition probabilities of the chiral doublet bands are reproduced satisfactorily without any free parameters. By analyzing the probability amplitudes of the wavefunctions, the significant roles of configuration mixing and four quasiparticle states to the chiral doublets are revealed. The evolution from chiral vibration to static chirality is clearly illustrated by the K plot and azimuthal plot. The present investigation provides both microscopic and quantal descriptions for nuclear chirality for the first time and demonstrates the robustness of chiral geometry against the configuration mixing as well as the four quasiparticle states.

Blueshift in Trifurcated Hydrogen Bonds: A Tradeoff between Tetrel Bonding and Steric Repulsion.

We have quantum chemically investigated the origin of the atypical blueshift of the H-C bond stretching frequency in the hydrogen-bonded complex X- •••H3 C-Y (X, Y=F, Cl, Br, I), as compared to the corresponding redshift occurring in Cl- •••H3 N and Cl- •••H3 C-H, using relativistic density functional theory (DFT) at ZORA-BLYP-D3(BJ)/QZ4P. Previously, this blueshift was attributed, among others, to the contraction of the H-C bonds as the H3 C moiety becomes less pyramidal. Herein, we provide quantitative evidence that, instead, the blueshift arises from a direct and strong X- •••C interaction of the HOMO of A- with the backside lobe on carbon of the low-lying C-Y antibonding σ* LUMO of the H3 C-Y fragment. This X- •••C bond, in essence a tetrel bond, pushes the H atoms towards a shorter H-C distance and makes the H3 C moiety more planar. The blueshift may, therefore, serve as a diagnostic for tetrel bonding.

Novel Computational Chemistry Infrastructure for Simulating Astatide in Water: From Basis Sets to Force Fields Using Particle Swarm Optimization.

Using the example of astatine, the heaviest naturally occurring halogen whose isotope At-211 has promising medical applications, we propose a new infrastructure for large-scale computational models of heavy elements with strong relativistic effects. In particular, we focus on developing an accurate force field for At- in water based on reliable relativistic density functional theory (DFT) calculations. To ensure the reliability of such calculations, we design novel basis sets for relativistic DFT, via the particle swarm optimization algorithm to optimize the coefficients of the new basis sets and the polarization-consistent basis set idea's extension to heavy elements to eliminate the basis set error from DFT calculations. The resulting basis sets enable the well-grounded evaluation of relativistic DFT against "gold-standard" CCSD(T) results. Accounting for strong relativistic effects, including spin-orbit interaction, via our redesigned infrastructure, we elucidate a noticeable dissimilarity between At- and I- in halide-water force field parameters, radial distribution functions, diffusion coefficients, and hydration energies. This work establishes the framework for the systematic development of polarization-consistent basis sets for relativistic DFT and accurate force fields for molecular dynamics simulations to be used in large-scale models of complex molecular systems with elements from the bottom of the periodic table, including actinides and even superheavy elements.