Relativistic Electronic Structure Research Articles

Finite-order method to calculate approximate density matrices in the Fock-space multireference coupled cluster theory

An efficient approach to calculate approximate pure-state and transition reduced density matrices in the framework of the multireference relativistic Fock-space coupled cluster (FS CC) theory is proposed. The method is based on the effective operator formalism and consists of the direct substitution of the FS CC Ansatz for a wave operator into the effective operator expression with the subsequent truncation of expansion at the terms quadratic in cluster amplitudes. The final density matrix is defined by active-space density matrices of different ranks ‘dressed’ with contributions from cluster operators. The method gives a connected expression for pure-state density matrices, provided that the intermediate normalisation condition is fulfilled. Moreover, under some additional assumptions, the connectivity can also be ensured for calculated transition property matrix elements and natural transition spinors. The developed technique allows for fast and accurate calculations of one-particle reduced density matrices for a wide range of electronic states. A pilot application of the new technique to construct averaged atomic natural orbital (ANO) basis sets for fully relativistic electronic structure calculations is presented.

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.

Temperature Dependence of Relativistic Valence Band Splitting Induced by an Altermagnetic Phase Transition.

Altermagnetic (AM) materials exhibit non-relativistic, momentum-dependent spin-split states, ushering in new opportunities for spin electronic devices. While the characteristics of spin-splitting are documented within the framework of the non-relativistic spin group symmetry, there is limited exploration of the inclusion of relativistic symmetry and its impact on the emergence of a novel spin-splitting in the band structure. This study delves into the intricate relativistic electronic structure of an AM material, α-MnTe. Employing temperature-dependent angle-resolved photoelectron spectroscopy across the AM phase transition, the emergence of a relativistic valence band splitting concurrent with the establishment of magnetic order is elucidated. This discovery is validated through disordered local moment calculations, modeling the influence of magnetic order on the electronic structure and confirming the magnetic origin of the observed splitting. The temperature-dependent splitting is ascribed to the advent of relativistic spin-splitting resulting from the strengthening of AM order in α-MnTe as the temperature decreases. This sheds light on a previously unexplored facet of this intriguing material.

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.

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.

Relativistic resolution-of-the-identity with Cholesky integral decomposition.

In this study, we present an efficient integral decomposition approach called the restricted-kinetic-balance resolution-of-the-identity (RKB-RI) algorithm, which utilizes a tunable RI method based on the Cholesky integral decomposition for in-core relativistic quantum chemistry calculations. The RKB-RI algorithm incorporates the restricted-kinetic-balance condition and offers a versatile framework for accurate computations. Notably, the Cholesky integral decomposition is employed not only to approximate symmetric large-component electron repulsion integrals but also those involving small-component basis functions. In addition to comprehensive error analysis, we investigate crucial conditions, such as the kinetic balance condition and variational stability, which underlie the applicability of Dirac relativistic electronic structure theory. We compare the computational cost of the RKB-RI approach with the full in-core method to assess its efficiency. To evaluate the accuracy and reliability of the RKB-RI method proposed in this work, we employ actinyl oxides as benchmark systems, leveraging their properties for validation purposes. This investigation provides valuable insights into the capabilities and performance of the RKB-RI algorithm and establishes its potential as a powerful tool in the field of relativistic quantum chemistry.

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.

LIBGRPP: A Library for the Evaluation of Molecular Integrals of the Generalized Relativistic Pseudopotential Operator over Gaussian Functions

Generalized relativistic pseudopotentials (GRPP) of atomic cores implying the use of different potentials for atomic electronic shells with different principal quantum numbers give rise to accurate and reliable relativistic electronic structure models of atoms, molecules, clusters, and solids. These models readily incorporate the effects of Breit electron–electron interactions and one-loop quantum electrodynamics effects. Here, we report the computational procedure for evaluating one-electron integrals of GRPP over contracted Gaussian functions. This procedure was implemented in a library of routines named LIBGRPP, which can be integrated into existing quantum chemistry software, thus enabling the application of various methods to solve the many-electron problem with GRPPs. Pilot applications to electronic transitions in the ThO and UO2 molecules using the new library and intermediate-Hamiltonian Fock space relativistic coupled cluster method are presented. Deviations of excitation energies obtained within the GRPP approach from their all-electron Dirac–Coulomb–Gaunt counterparts do not exceed 50 cm−1 for the 31 lowest-energy states of ThO and 110 cm−1 for the 79 states of UO2. The results clearly demonstrate that rather economical tiny-core GRPP models can exceed in accuracy relativistic all-electron models defined by Dirac–Coulomb and Dirac–Coulomb–Gaunt Hamiltonians.

Relativistic electronic structure and photovoltaic performance of K2CsSb

We identify K2CsSb as a potential photovoltaic absorber by considering it's optoelectronic properties and maximum theoretical power conversion efficiency.

Solvent effects in four-component relativistic electronic structure theory based on the reference interaction-site model.

A combined method of the Dirac-Hartree-Fock (DHF) method and the reference interaction-site model (RISM) theory is reported; this is the initial implementation of the coupling of the four-component relativistic electronic structure theory and an integral equation theory of molecular liquids. In the method, the DHF and RISM equations are solved self-consistently, and therefore the electronic structure of the solute, including relativistic effects, and the solvation structure are determined simultaneously. The formulation is constructed based on the variational principle with respect to the Helmholtz energy, and analytic free energy gradients are also derived using the variational property. The method is applied to the iodine ion (I- ), methyl iodide (CH3 I), and hydrogen chalcogenide (H2 X, where X=O-Po) in aqueous solutions, and the electronic structures of the solutes, as well as the solvation free energies and their component analysis, solvent distributions, and solute-solvent interactions, are discussed.

GRASP: The Future?

The theoretical foundations of relativistic electronic structure theory within quantum electrodynamics (QED) and the computational basis of the atomic structure code GRASP are briefly surveyed. A class of four-component basis set is introduced, which we denote the CKG-spinor set, that enforces the charge-conjugation symmetry of the Dirac equation. This formalism has been implemented using the Gaussian function technology that is routinely used in computational quantum chemistry, including in our relativistic molecular structure code, BERTHA. We demonstrate that, unlike the kinetically matched two-component basis sets that are widely employed in relativistic quantum chemistry, the CKG-spinor basis is able to reproduce the well-known eigenvalue spectrum of point-nuclear hydrogenic systems to high accuracy for all atomic symmetry types. Calculations are reported of third- and higher-order vacuum polarization effects in hydrogenic systems using the CKG-spinor set. These results reveal that Gaussian basis set expansions are able to calculate accurately these QED effects without recourse to the apparatus of regularization and in agreement with existing methods. An approach to the evaluation of the electron self-energy is outlined that extends our earlier work using partial-wave expansions in QED. Combined with the treatment of vacuum polarization effects described in this article, these basis set methods suggest the development of a comprehensive ab initio approach to the calculation of radiative and QED effects in future versions of the GRASP code.

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.

Emergent quasi-two-dimensional electron gas betweenLi1±xNbO3andLaAlO3and its prospectively switchable magnetism

Oxide interfaces between insulating perovskites can provide a two-dimensional electron gas (2DEG), which was observed initially beneath polar $\mathrm{La}\mathrm{Al}{\mathrm{O}}_{3}$ (LAO) grown on $\mathrm{Ti}{\mathrm{O}}_{2}$-terminated $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_{3}$(001). Here, we suggest to use a solid electrolyte $\mathrm{Li}\mathrm{Nb}{\mathrm{O}}_{3}$ (LiNO) instead of $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_{3}$ to create in LAO/LiNO a robustly switchable and magnetic quasi 2DEG (q2DEG). This prospective phenomenon is achieved by charging and discharging lithium niobate while its $n\ensuremath{\rightarrow}p$ doping induces the alteration of magnetic order in LAO/LiNO and, thus, the spin degrees of freedom in q2DEG. On the basis of ab initio calculations and starting from the defectless and insulating LAO/LiNO superlattice, we demonstrate that either a ferromagnetic q2DEG or weakly magnetic quasi-2D hole gas emerge there due to the presence of excessive electrons or holes, respectively. These defects were simulated by one extra Li and a lithium vacancy in LiNO. By varying the $\mathrm{Li}\mathrm{Nb}{\mathrm{O}}_{3}$ thicknesses up to 18 formula units, we found that (i) the spatial extent of q2DEG is 1.5 nm along the stacking direction and that (ii) the dopant position at the Al-terminated interface is energetically preferable by more than 0.5 eV compared to the deep layers. In the context of the advanced design of q2DEG, the out-of-plane electric polarization, which intrinsically appears in multiferroic LAO/LiNO, allows to switch externally the electric-field dependence of the Rashba effect. Moreover, the in-plane charge current via q2DEG may generate there a transverse spin density due to the Rashba-Edelstein effect. We discuss this scenario using the relativistic electronic structures and locally projected density of states which differ remarkably in $\mathrm{L}\mathrm{A}\mathrm{O}/{\mathrm{Li}}_{1+x}\mathrm{N}\mathrm{O}$ and $\mathrm{L}\mathrm{A}\mathrm{O}/{\mathrm{Li}}_{1\ensuremath{-}x}\mathrm{N}\mathrm{O}$.

Quantifying Spin-Mixed States in Ferromagnets.

We quantify the presence of spin-mixed states in ferromagnetic 3D transition metals by precise measurement of the orbital moment. While central to phenomena such as Elliot-Yafet scattering, quantification of the spin-mixing parameter has hitherto been confined to theoretical calculations. We demonstrate that this information is also available by experimental means. Comparison of ferromagnetic resonance spectroscopy with x-ray magnetic circular dichroism results show that Kittel's original derivation of the spectroscopic g factor requires modification, to include spin mixing of valence band states. Our results are supported by abinitio relativistic electronic structure theory.

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.

Colossal anomalous Nernst effect in a correlated noncentrosymmetric kagome ferromagnet.

The transverse voltage generated by a temperature gradient in a perpendicularly applied magnetic field, termed the Nernst effect, has promise for thermoelectric applications and for probing electronic structure. In magnetic materials, an anomalous Nernst effect (ANE) is possible in a zero magnetic field. We report a colossal ANE in the ferromagnetic metal UCo0.8Ru0.2Al, reaching 23 microvolts per kelvin. Uranium's 5f electrons provide strong electronic correlations that lead to narrow bands, a known route to producing a large thermoelectric response. In addition, uranium's strong spin-orbit coupling produces an intrinsic transverse response in this material due to the Berry curvature associated with the relativistic electronic structure. Theoretical calculations show that in UCo0.8Ru0.2Al at least 148 Weyl nodes, and two nodal lines, exist within 60 millielectron volt of the Fermi level. This work demonstrates that magnetic actinide materials can host strong Nernst and Hall responses due to their combined correlated and topological nature.

Large magnetic anisotropy in an OsIr dimer anchored in defective graphene

Single-atom magnets represent the ultimate limit of magnetic data storage. The identification of substrates that anchor atom-sized magnets firmly and, thus, prevent their diffusion and large magnetic anisotropy has been at the centre of intense research efforts for a long time. Using density functional theory we show the binding of transition metal (TM) atoms in defect sites in the graphene lattice: single vacancy and double vacancy, both pristine and decorated by pyridinic nitrogen atoms, are energetically more favourable than away from the centre of defects, which could be used for engineering the position of TMs with atomic precision. Relativistic calculations revealed magnetic anisotropy energy (MAE) of ∼10 meV for Ir@NSV with an easy axis parallel to the graphene plane. MAE can be remarkably boosted to 50 meV for OsIr@NSV with the easy axis perpendicular to the graphene plane, which paves the way to the storage density of ∼490 Tb/inch2 with the blocking temperature of 14 K assuming the relaxation time of 10 years. Magnetic anisotropy is discussed based on the relativistic electronic structures. The influence of an orbital-dependent on-site Coulomb repulsion U and a non-local correlation functional optB86b-vdW on MAE is also discussed.

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.