Relativistic Electronic Structure Calculations Research Articles

Accelerating Relativistic Exact-Two-Component Density Functional Theory Calculations with Graphical Processing Units.

Numerical integration of the exchange-correlation potential is an inherently parallel problem that can be significantly accelerated by graphical processing units (GPUs). In this Letter, we present the first implementation of GPU-accelerated exchange-correlation potential in the GauXC library for relativistic, 2-component density functional theory. By benchmarking against copper, silver, and gold coinage metal clusters, we demonstrate the speed and efficiency of our implementation, achieving significant speedup compared to CPU-based calculations. One GPU card provides computational power equivalent to roughly 400 CPU cores in the context of this work. The speedup further increases for larger systems, highlighting the potential of our approach for future, more computationally demanding simulations. Our implementation supports arbitrary angular momentum basis functions, enabling the simulation of systems with heavy elements and providing substantial speedup to relativistic electronic structure calculations. This advancement paves the way for more efficient and extensive computational studies in the field of density functional theory.

Nuclear structure and Breit interaction effects in relativistic molecular electronic structure calculations

We examine the effects of nuclear structure and the self-consistent treatment of the Breit interaction on the calculation of properties associated with PT-odd interactions in TlF. We also demonstrate that 99.9999% of the Breit energy in TlF is recovered from the one-centre contributions to the interaction energy in the self-consistent field approximation. The formulation of our electronic structure code, BERTHA, facilitates the evaluation of all one-centre effects using efficient methods borrowed from relativistic atomic physics at negligible computational cost. A further analysis of this behaviour is provided for the homonuclear mean-field system, At, in the Dirac–Hartree–Fock–Breit approximation. For closed-shell systems, a formal analysis of the origin of this behaviour suggests that this computational economy may be of general applicability in relativistic molecular electronic structure theory.

Crystal and electronic structure of the ternary Zintl bismuthide BaLiBi

AbstractReported is the accurate refinement of the structure of the ternary bismuthide BaLiBi, based on single‐crystal X‐ray diffraction data. This compound crystallizes with the ZrBeSi structure type with the space group P63/mmc (no. 194), a=4.9917(6) Å, c=9.079(2) Å, V=195.92(7) Å3 with two formula units per unit cell. In addition to being a colored ternary variant of the AlB2 type, the crystal structure of BaLiBi can be also viewed as a “stuffed” variant of the NiAs structure, where the Bi atoms form a hexagonal close packing, the Ba atoms occupy the octahedral voids in this packing, and the Li atoms are located between adjacent tetrahedral voids on their common triangular faces. In the absence of direct Bi–Bi interactions, the BaLiBi crystal structure rationalized according to the notation (Ba2+)(Li+)(Bi3−), suggesting an electron‐balanced composition, i. e., a Zintl phase. In line with this notation, scalar‐relativistic first‐principle calculations with the LMTO code reveal a semiconducting ground state, with a bandgap of about 0.6 eV. Fully relativistic electronic structure calculations predict a semimetallic ground state.

Radium-containing molecular cations amenable for laser cooling

Recent successful applications of the new experimental technique to measure spectra of radium monofluoride molecules opens great prospects to searching the effects related to “new physics”. Considerable advantages in experiments for search for such effects would be provided by the abilities to trap the working molecules, their laser-coolability and also a variety of nuclear isotopes of elements in the molecule with different nuclear multipole moments.We report ab initio relativistic electronic structure calculations on a series of polyatomic molecular ions containing Ra nuclei and discuss the prospects of laser-coolability of the studied species.

Final-state-resolved mutual neutralization in I+ - I− collisions

We have studied the mutual neutralization reaction of atomic iodine ions (i.e., ${\mathrm{I}}^{+}+{\mathrm{I}}^{\ensuremath{-}}\ensuremath{\rightarrow}\text{I}+\text{I}$) in a cryogenic double electrostatic ion-beam storage-ring apparatus. Our results show that the reaction forms iodine atoms either in the ground-state configuration ($\mathrm{I}(5{p}^{5}\phantom{\rule{0.16em}{0ex}}{}^{2}{P}^{\ensuremath{\circ}})$, \ensuremath{\sim}40%) or with one atom in an electronically excited state ($\mathrm{I}(6s{\phantom{\rule{0.16em}{0ex}}}^{2}[2]$), $\ensuremath{\sim}60%$), with no significant variation over the branching ratios in the studied collision-energy range (0.1--0.8 eV). We estimate the total charge-transfer cross section to be of the order of ${10}^{\ensuremath{-}13}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{2}$ at 0.1 eV collision energy. Ab initio relativistic electronic structure calculations of the potential-energy curves of ${\mathrm{I}}_{2}$ suggest that the reaction takes place at short internuclear distances. The results are discussed in view of their importance for applications in electric thrusters.

Fourier-transform spectroscopy and relativistic electronic structure calculation on the [formula omitted] state of KCs

The Ti:Saphire laser operated within 13800 - 11800 cm−1 range was used to excite the c3Σ+ state of KCs molecule directly from the ground X1Σ+ state. The laser-induced fluorescence (LIF) spectra of the c3Σ+→a3Σ+ transition were recorded with Fourier-transform spectrometer within 8000 to 10000 cm−1 range. Overall 673 rovibronic term values belonging to both e/f-components of the c3Σ+(Ω=1±) state of 39KCs, covering vibrational levels from v = 0 to about 45, and rotational levels J∈[11,149] were determined with the accuracy of about 0.01 cm−1; among them 7 values for 41KCs. The experimental term values with v∈[0,22] were involved in a direct point-wise potential reconstruction for the c3Σ+(Ω=1±) state, which takes into account the Ω-doubling effect caused by the spin-rotational interaction with the nearby c3Σ+(Ω=0−) state. The analysis and interpretation were facilitated by the fully-relativistic coupled cluster calculation of the potential energy curves for the B1Π, c3Σ+, and b3Π states, as well as of spin-forbidden c−X and spin-allowed c−a transition dipole moments; radiative lifetimes and vibronic branching ratios were calculated. A comparison of relative intensity distributions measured in vibrational c→a LIF progressions with their theoretical counterparts unambiguously confirms the vibrational assignment suggested in [J. Szczepkowski, et al., JQSRT, 204, 133–137 (2018)].

Parity-violation effects in the vibrational spectra of CHFClBr and CDFClBr

Relativistic four-component electronic structure calculations at the density functional level have been carried out to describe parity-violation (PV) energy shifts to the total electronic energy for the chiral molecule CHFClBr. An $n$-mode ($n=3,4$) expansion of the complete potential energy surface at the explicitly correlated coupled-cluster level has been used for the vibrational analysis of PV effects for CHFClBr and CDFClBr. The vibrational spectrum and corresponding absolute intensities for fundamental, overtone, and combination band transitions obtained from a variational configuration interaction treatment are in excellent agreement with experimental data and the most accurate so far obtained. The results show that a 3-mode expansion is sufficient for the vibrational analysis. The PV energy shifts for the fundamental, overtone, and combination bands are all in the mHz region. The data provided will be useful for future detection of PV in chiral molecules.

Electronic spectra of ytterbium fluoride from relativistic electronic structure calculations.

We report an investigation of the low-lying excited states of the YbF molecule-a candidate molecule for experimental measurements of the electron electric dipole moment-with 2-component based multi-reference configuration interaction (MRCI), equation of motion coupled cluster (EOM-CCSD) and the extrapolated intermediate Hamiltonian Fock-space coupled cluster (XIHFS-CCSD). Specifically, we address the question of the nature of these low-lying states in terms of configurations containing filled or partially-filled Yb 4f shells. We show that while it does not appear possible to carry out calculations with both kinds of configurations contained in the same active space, reliable information can be extracted from different sectors of Fock space-that is, by performing electron attachment and detachment IHFS-CCSD and EOM-CCSD calculation on the closed-shell YbF+ and YbF− species, respectively. From these calculations we predict Ω = 1/2, 3/2 states, arising from the 4f13σ26s, 4f145d1/6p1, and 4f135d1σ16s configurations to be able to interact as they appear in the same energy range around the ground-state equilibrium geometry. As these states are generated from different sectors of Fock space, they are almost orthogonal and provide complementary descriptions of parts of the excited state manifold. To obtain a comprehensive picture, we introduce a simple adiabatization model to extract energies of interacting Ω = 1/2, 3/2 states that can be compared to experimental observations.

Remarkable low-energy properties of the pseudogapped semimetal Be5Pt

We report measurements and calculations on the properties of the intermetallic compound Be$_5$Pt. High-quality polycrystalline samples show a nearly constant temperature dependence of the electrical resistivity over a wide temperature range. On the other hand, relativistic electronic structure calculations indicate the existence of a narrow pseudogap in the density of states arising from accidental approximate Dirac cones extremely close to the Fermi level. A small true gap of order 3 meV is present at the Fermi level, yet the measured resistivity is nearly constant from low to room temperature. We argue that this unexpected behavior can be understood by a cancellation of the energy dependence of density of states and relaxation time due to disorder, and discuss a model for electronic transport. With applied pressure, the resistivity becomes semiconducting, consistent with theoretical calculations that show that the band gap increases with applied pressure. We further discuss the role of Be inclusions in the samples.

Spin-orbit coupling in periodic systems with broken time-reversal symmetry: Formal and computational aspects

We discuss the treatment of spin-orbit coupling (SOC) in time-reversal-symmetry-broken periodic systems for relativistic electronic structure calculations of materials within the generalized noncollinear Kohn-Sham density functional theory (GKSDFT). We treat SOC self-consistently and express the GKS orbitals in a two-component spinor basis. Crucially, we present a methodology (and its corresponding implementation) for the simultaneous self-consistent treatment of SOC and exact nonlocal Fock exchange operators. The many advantages of the inclusion of nonlocal Fock exchange in the self-consistent treatment of SOC, as practically done in hybrid exchange-correlation functionals, are both formally derived and illustrated through numerical examples: (i) it imparts a local magnetic torque (i.e., the ability of the two-electron potential to locally rotate the magnetization with respect to a starting guess configuration) that is key to converge to the right solution in noncollinear DFT regardless of the initial guess for the magnetization; (ii) because of the local magnetic torque, it improves the rotational invariance of noncollinear formulations of the DFT; (iii) it introduces the dependence on specific pieces of the spinors (i.e., those mapped onto otherwise missing spin blocks of the complex density matrix) into the two-electron potential, which are key to the correct description of the orbital- and spin-current densities and their coupling with the magnetization; and (iv) when space-inversion symmetry is broken, it allows for the full breaking of time-reversal symmetry in momentum space, which would otherwise be constrained by a sum rule linking the electronic band structure at opposite points in the Brillouin zone ($\underline{\mathbf{k}}$ and $\ensuremath{-}\underline{\mathbf{k}}$). The presented methodology is implemented in a developmental version of the public crystal code. Numerical tests are performed on the model system of an infinite radical chain of ${\mathrm{Ge}}_{2}\mathrm{H}$ with both space-inversion and time-reversal symmetries broken, which allows to highlight all the above-mentioned effects.

Gate-Tunable Reversible Rashba-Edelstein Effect in a Few-Layer Graphene/2H-TaS2 Heterostructure at Room Temperature.

We report the observation of current-induced spin polarization, the Rashba-Edelstein effect (REE), and its Onsager reciprocal phenomenon, the spin galvanic effect (SGE), in a few-layer graphene/2H-TaS2 heterostructure at room temperature. Spin-sensitive electrical measurements unveil full spin-polarization reversal by an applied gate voltage. The observed gate-tunable charge-to-spin conversion is explained by the ideal work function mismatch between 2H-TaS2 and graphene, which allows for a strong interface-induced Bychkov-Rashba interaction with a spin-gap reaching 70 meV, while keeping the Dirac nature of the spectrum intact across electron and hole sectors. The reversible electrical generation and control of the nonequilibrium spin polarization vector, not previously observed in a nonmagnetic material, are elegant manifestations of emergent two-dimensional Dirac Fermions with robust spin-helical structure. Our experimental findings, supported by first-principles relativistic electronic structure and transport calculations, demonstrate a route to design low-power spin-logic circuits from layered materials.

Theoretical investigation of quantum confinement on the Rashba effect in ZnO semiconductor nanocrystals

Semiconducting nanocrystals have been the subject of intense research due to the ability to modulate the electronic and magnetic properties by controlling the size of the crystal, introducing dopants, and surface modification. While relatively simple models such as a particle in a sphere can work well to describe moderately sized quantum dots, this approximation becomes less accurate for very small nanocrystals that are strongly confined. In this work, we report all-electron, relativistic ab initio electronic structure calculations for a series of ZnO quantum dots in order to study the modulation of the Rashba effect. The impact and magnitude of spin-orbit coupling and crystalline anisotropy on the fine structure of the band-edge excitonic manifold are discussed.

Accurate nuclear quadrupole moment of ruthenium from the molecular method.

The nuclear electric quadrupole moment (NQM) of ruthenium was reevaluated by means of the molecular method. Therefore, four-component relativistic electronic structure calculations of the electric field gradient at the Ru nucleus in ruthenium monocarbide, which were done with the coupled cluster methodology and carefully augmented large basis sets, were combined with the respective nuclear quadrupole coupling constant from experiments. This provided a recommended NQM value of (425 ± 13) mbarn for 101Ru.

The nature of the chemical bond in UO2

AbstractThe nature of the chemical bond in UO2 was analyzed taking into account the X‐ray photoelectron spectroscopy (XPS) structure parameters of the valence and core electrons, as well as the relativistic discrete variation electronic structure calculation results for this oxide. The ionic/covalent nature of the chemical bond was determined for the UO8 (D4h) cluster, reflecting uranium's close environment in UO2, and the U13O56 and U63O216 clusters, reflecting the bulk of solid uranium dioxide. The bar graph of the theoretical valence band (from 0 to ~35 eV) of XPS spectrum was built such that it was in satisfactory agreement with the experimental spectrum of a UO2 single crystalline thin film. It was shown that unlike the crystal field theory results, the covalence effects in UO2 are significant due to the strong overlap of the U 6p and U 5f atomic orbitals with the ligand orbitals, in addition to the U 6d atomic orbital (AO). A quantitative molecular orbital (MO) scheme for UO2 was built. The contribution of the MO electrons to the chemical bond covalence component was evaluated on the basis of the bond population values. It was found that the electrons of inner valence molecular orbitals (IVMO) weaken the chemical bond formed by the electrons of outer valence molecular orbitals (OVMO) by 32% in UO8 and by 25% in U63O216.

A New Mechanism For XPS Line Broadening: The 2p-XPS of Ti(IV)

There is almost a factor of 2 increase in the full width at half maximum (FWHM) of the main Ti 2p1/2 XPS peak compared to the 2p3/2 in the closed-shell Ti(IV) compounds TiO2 and strontium titanate, STO. Although the spectra of anatase and rutile forms of TiO2 differ slightly from STO, the 2p1/2 broadening over 2p3/2 is very similar. For STO, we show that ascribing this differential broadening to a short 2p1/2 lifetime is unphysical. For STO, rigorous and fully relativistic electronic structure calculations have been carried out for both the initial state and the 2p core-hole states; these calculations include many-body effects as well as the one-body effects of spin–orbit and ligand field splittings. The agreement of the theoretical and measured XPS data for the main 2p1/2 and 2p3/2 peaks indicate that the necessary one- and many-body effects have been included. They show that the broadening is due to the presence of XPS intensity distributed over many unresolved final states for a 2p1/2 core-hole, wherea...

Observation of Out-of-Plane Spin Texture in a SrTiO_{3}(111) Two-Dimensional Electron Gas.

We explore the second order bilinear magnetoelectric resistance (BMER) effect in the d-electron-based two-dimensional electron gas (2DEG) at the SrTiO_{3}(111) surface. We find evidence of a spin-split band structure with the archetypal spin-momentum locking of the Rashba effect for the in-plane component. Under an out-of-plane magnetic field, we find a BMER signal that breaks the sixfold symmetry of the electronic dispersion, which is a fingerprint for the presence of a momentum-dependent out-of-plane spin component. Relativistic electronic structure calculations reproduce this spin texture and indicate that the out-of-plane component is a ubiquitous property of oxide 2DEGs arising from strong crystal field effects. We further show that the BMER response of the SrTiO_{3}(111) 2DEG is tunable and unexpectedly large.

Magnetic moment and magnetic anisotropy of Ge3Mn5 thinfilms on Ge(111) substrate: A density functional study.

Magnetism and magnetic anisotropy energy (MAE) of the Ge3Mn5 bulk, free-standing surface, and Ge3Mn5(001)|Ge(111) thinfilms and superlattice have been systemically investigated by using the relativistic first-principles electronic structure calculations. For Ge3Mn5 adlayers on Ge(111) substrates within Mn1 termination, the direction of magnetization undergoes a transition from in-plane at 1 monolayer (ML) thickness (MAE = -0.50 meV/ML) to out-of-plane beginning at 3 ML thickness (nearly invariant MAE = 0.16 meV/ML). The surficial/interfacial MAE is extracted to be 1.23/-0.54 meV for Mn1-termination; the corresponding value is 0.19/1.03 meV for Mn2/Ge-termination; the interior MAE is averaged to be 0.09 meV per ML. For various Ge3Mn5 systems, the in-plane lattice expansion and/or interlayer distance contraction would enhance the out-of-plane MAE. Our theoretical magnetic moments and MAEs fit well with the experimental measurements. Finally, the origination of MAE is elucidated under the framework of second-order perturbation with the electronic structure analyses.

Enhanced effect of CP -violating nuclear magnetic quadrupole moment in a HfF+ molecule

The ${\mathrm{HfF}}^{+}$ cation is a very promising system to use in the search for the electron electric dipole moment (EDM), and a corresponding experiment is carried out by JILA group [H. Loh, K. C. Cossel, M. C. Grau, K.-K. Ni, E. R. Meyer, J. L. Bohn, J. Ye, and E. A. Cornell, Science 342, 1220 (2013); K.-K. Ni, H. Loh, M. Grau, K. C. Cossel, J. Ye, and E. A. Cornell, J. Mol. Spectrosc. 300, 12 (2014). Here we theoretically investigate the cation to search for another effect which violates time-reversal ($T$) and spatial parity ($P$) symmetries---the nuclear magnetic quadrupole moment (MQM) interaction with electrons. We report an accurate ab initio relativistic electronic structure calculations of the molecular parameter ${W}_{M}=0.494 \frac{{10}^{33}\phantom{\rule{0.16em}{0ex}}\mathrm{Hz}}{e\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{2}}$ that is required to interpret the experimental data in terms of the MQM of the Hf nucleus. For this we have implemented and applied the combined Dirac-Coulomb(-Gaunt) and relativistic effective core potential approaches to treat electron correlation effects from all of the electrons and to take into account high-order correlation effects using the coupled cluster method with single, double, triple and noniterative quadruple cluster amplitudes. We discuss interpretation of the MQM effect in terms of the strength constants of $T,P$-odd nuclear forces, proton and neutron EDMs, the QCD parameter $\ensuremath{\theta}$, and quark chromo-EDMs.

Spectroscopic and theoretical studies of ThCl and ThCl.

The electronic structures of ThCl and ThCl+ have been examined using laser induced fluorescence and two-photon ionization techniques. Rotationally resolved spectra, combined with the predictions from relativistic electronic structure calculations, show that the ground state of the neutral molecule is Th+(7s26d)Cl-, X2Δ3/2. Dispersed fluorescence spectra for ThCl revealed the ground state vibrational levels v = 0-10 and low energy electronic states that also originate from the atomic ion 7s26d configuration. Pulsed field ionization-zero kinetic energy photoelectron spectroscopy established an ionization energy (IE) for ThCl of 51 344(5) cm-1, and the ThCl+ vibrational term energies of the v = 1-3 levels. The zero-point level of the first electronically excited state was found at 949(2) cm-1. Comparisons with high-level theoretical results indicate that the ground and excited states are Th2+(7s6d)Cl- X3Δ1 and Th2+(7s2)Cl- Σ+1, respectively. Relativistic coupled cluster composite thermochemistry calculations yielded an IE within 1.2 kcal/mol of experiment and a bond dissociation energy (118.3 kcal/mol) in perfect agreement with previous experiments.

Spectroscopic and theoretical studies of the low-lying states of BaO(+).

The BaO(+) cation is of interest from the perspectives of electronic structure and the potential for cooling to ultra-cold temperatures. Spectroscopic data for the ion have been obtained using a two-color photoionization technique. The ionization energy for BaO was found to be 6.8123(3) eV. The ground state of BaO(+) was identified as X(2)Σ(+), and both vibrational and rotational constants were determined. Vibrationally resolved spectra were recorded for A(2)Π, the first electronically excited state. These data yielded the term energy, vibrational frequency, and the spin-orbit interaction constant. Relativistic electronic structure calculations were carried out using multi-reference configuration interaction (MRCI), coupled cluster and density functional theory methods. Transition moments for the pure vibrational and A(2)Π-X(2)Σ(+) transitions were predicted using the MRCI method.