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The spin-orbit interaction is quite small compared to electrostatic forces in atoms. Nevertheless, this small interaction can have large consequences. Several examples of the importance of the spin-orbit force in atomic photoionization are presented and explained.
The material α-RuCl 3 , with a two-dimensional Ru honeycomb sublattice, has attracted considerable attention because it may be a realization of the Kitaev quantum spin liquid. Recently, a new honeycomb material, α-RuCl 3 , was prepared under moderately high pressure, and it is stable under ambient conditions. However, different from α-RuCl 3 , α-RuI 3 was reported to be a paramagnetic metal without long-range magnetic order down to 0.35 K. Here, the structural and electronic properties of the quasi-two-dimensional α-RuI 3 are theoretically studied. First, based on first-principles density functional theory calculations, the ABC stacking honeycomb-layer R$\bar{3}$ (No. 148) structure is found to be the most likely stacking order for α-RuI 3 along the c axis. Furthermore, both R$\bar{3}$ and P$\bar{3}$1c are dynamically stable because no imaginary frequency modes were obtained in the phononic dispersion spectrum without Hubbard U. Moreover, the different physical behavior of α-RuI 3 compared to α-RuCl 3 can be understood naturally. The strong hybridization between Ru 4d and I 5p orbitals decreases the “effective” atomic Hubbard repulsion, leading the electrons of RuI3 to be less localized than in RuCl 3 . As a consequence, the effective electronic correlation is reduced from Cl to I, leading to the metallic nature of α-RuI 3 . Based on the DFT+U (Ueff=2 eV) plus spin-orbital coupling, we obtained a spin-orbit Mott insulating behavior for α-RuCl 3 and, with the same procedure, a metallic behavior for α-RuI 3 , in good agreement with experimental results. Furthermore, when introducing large (unrealistic) U eff =6 eV, the spin-orbit Mott gap opens in α-RuI 3 as well, supporting the physical picture we are proposing. Our results provide guidance to experimentalists and theorists working on two-dimensional transition metal tri-iodide layered materials.
We implement and benchmark the frozen core approximation, a technique commonly adopted in electronic structure theory to reduce the computational cost by means of mathematically fixing the chemically inactive core electron states. The accuracy and efficiency of this approach are well controlled by a single parameter, the number of frozen orbitals. Explicit corrections for the frozen core orbitals and the unfrozen valence orbitals are introduced, safeguarding against seemingly minor numerical deviations from the assumed orthonormality conditions of the basis functions. A speedup of over twofold can be achieved for the diagonalization step in all-electron density-functional theory simulations containing heavy elements, without any accuracy degradation in terms of the electron density, total energy, and atomic forces. This is demonstrated in a benchmark study covering 103 materials across the Periodic Table and a large-scale simulation of CsPbBr3 with 2560 atoms. Our study provides a rigorous benchmark of the precision of the frozen core approximation (sub-meV per atom for frozen core orbitals below −200 eV) for a wide range of test cases and for chemical elements ranging from Li to Po. The algorithms discussed here are implemented in the open-source Electronic Structure Infrastructure software package.
The molecular orbital picture plays a fundamental role in analyzing and interpreting the electronic structure of atoms and molecules. Evaluation of molecular orbitals obtained from the Hartree–Fock method and other one-electron Hamiltonian models is routine for quantum-chemical studies. Although these analyses have proven to be useful for identifying different patterns in electronic structure and reactivity, in many cases, the chosen set of orbitals do not incorporate many of the fundamental electron correlation effects needed to accurately describe the atom or molecule under study. This work addresses the question of whether or not the inclusion of electron correlation is essential for the orbital picture by contrasting the differences between canonical Hartree–Fock orbitals and the correlated, normalized Dyson orbitals.
The superstructure of TaTe 2 is examined by total high-energy x-ray scattering and large-scale structure modeling over a broad temperature range. At room temperature, it features double zigzag chains of Ta atoms exhibiting metallic bonding. The chains are sandwiched between planes of weakly interacting Te atoms. Below 170 K, the chains appear broken to “butterflylike” clusters and single zigzag chains of covalently bonded Te atoms emerge while Ta-Te interactions remain largely ionic. This is a rare example of a charge density wave compound stabilized by bonding that is a mix of covalent, ionic, and metallic character giving rise to chemically distinct periodic lattice distortions. We argue that the formation of periodic lattice distortions in the Te sublattice in addition to those in the Ta sublattice favors charge delocalization, which may explain the unusually diminished resistivity and increased magnetic susceptibility exhibited by the low-temperature charge density wave phase of TaTe 2 . The effect may be common for 5d transition metal chalcogenides containing Te because of the extended electronic orbitals of the constituent atoms.
The interplay of lattice, orbital, and charge degrees of freedom in complex oxide materials has hosted a plethora of exotic quantum phases and physical properties. Recent advances in the synthesis of freestanding complex oxide membranes and twisted heterostructures assembled from membranes provide diverse opportunities for discovery using moiré design with local lattice control. To this end, we designed moiré crystals at the coincidence site lattice condition, providing commensurate structure within the moiré supercell arising from the multiatom complex oxide unit cell. We fabricated such twisted bilayers from freestanding SrTiO 3 membranes and used depth-sectioning-based electron microscopic methods to investigate ordered charge states at the moiré interface. By selectively imaging SrTiO 3 atomic planes at different depths through the bilayer, we clearly resolved the moiré periodic structure at the twisted interface and found that it exhibits lattice-dependent charge disproportionation in the local atomic registry within the moiré supercell. Density functional modeling of the twisted oxide interface predicts that these moiré phenomena are accompanied by a two-dimensional flat band that can drive exceptional electronic phases. Our work provides a robust strategy for controlling moiré periodicity in twisted oxides and paves pathways to exploit the extraordinary functionalities via moiré lattice-driven charge-orbital correlation.
The isolation of nucleophilic boron bases has led to a paradigm shift in boron chemistry. Previous studies of the bis(carbene) borylene complexes revealed that these compounds possess strong donor abilities, and their reaction inertness is due to the large steric hindrance between boron reagents and reactant. In the present study, we have theoretically studied the [(N 5 ) 2 BX] 2– and [(N 5 ) 2 B 2 X 2 ] 2– compounds (X = H, F, Cl, Br). Their electronic structures and properties are discussed by using the NBO, LOL, and ELF methods. We found that both π-conjugation and hyperconjugation effects can effectively stabilize the substituted nucleophilic anionic boron compounds [(N 5 ) 2 BX] 2– and [(N 5 ) 2 B 2 X 2 ] 2– . Substituents, especially X = H, stabilize the boron center through highly delocalized π-bonding, involving the formally “empty” in-plane p orbitals of the boron atom. While the halogen substituents have high electron withdrawal ability, leading to systems being less stable, we suggest the borinium anions [(N 5 ) 2 BH] 2– and [(N 5 ) 2 B 2 H 2 ] 2– as possible synthetic targets of novel environmentally friendly catalysts.
In typical carbonyl-containing molecules, bond dissociation events follow initial excitation to $nπ_{C=O}$$^*$ states. However, in acetyl iodide, the iodine atom gives rise to electronic states with mixed $nπ_{C=O}$$^*$ and $nπ_{C–I}$$^*$ character, leading to complex excited-state dynamics, ultimately resulting in dissociation. Using ultrafast extreme ultraviolet (XUV) transient absorption spectroscopy and quantum chemical calculations, we present an investigation of the primary photodissociation dynamics of acetyl iodide via time-resolved spectroscopy of core-to-valence transitions of the I atom after 266 nm excitation. The probed I 4d-to-valence transitions show features that evolve on sub-100-fs time scales, reporting on excited-state wavepacket evolution during dissociation. These features subsequently evolve to yield spectral signatures corresponding to free iodine atoms in their spin–orbit ground and excited states with a branching ratio of 1.1:1 following dissociation of the C–I bond. Calculations of the valence excitation spectrum via equation-of-motion coupled cluster with single and double substitutions (EOM-CCSD) show that initial excited states are of spin-mixed character. From the initially pumped spin-mixed state, we use a combination of time-dependent density functional theory (TDDFT)-driven nonadiabatic ab initio molecular dynamics and EOM-CCSD calculations of the N$_{4,5}$ edge to reveal a sharp inflection point in the transient XUV signal that corresponds to rapid C–I homolysis. Here, by examining the molecular orbitals involved in the core-level excitations at and around this inflection point, we are able to piece together a detailed picture of C–I bond photolysis in which d → σ* transitions give way to d → p excitations as the bond dissociates. We also report theoretical predictions of short-lived, weak 4d → 5d transitions in acetyl iodide, validated by weak bleaching in the experimental transient XUV spectra. This joint experimental–theoretical effort has thus unraveled the detailed electronic structure and dynamics of a strongly spin–orbit coupled system.
Density functional theory calculations are combined with time-resolved photoluminescence experiments to identify the species responsible for reversible trapping of holes following photoexcitation of InP/ZnSe/ZnS core/shell/shell quantum dots (QDs) having excess indium in the shell. Several possible assignments are considered, and a substitutional indium adjacent to a zinc vacancy, In 3+ /V Zn 2- , is found to be the most likely. This assignment is consistent with the observation that trapping occurs only when the QD has excess indium and is supported by experiments showing that the addition of zinc oleate or acetate decreases the extent of trapping, presumably by filling some of the vacancy traps. We also show that addition of alkyl carboxylic acids causes increased trapping, presumably by creation of additional zinc vacancies. The calculations show that either a single In 2+ ion or an In 2+ -In 3+ dimer is much too easily oxidized to form the reversible traps observed experimentally, while In 3+ is far too difficult to oxidize. Additional experimental data on InP/ZnSe/ZnS QDs synthesized in the absence of chloride demonstrates that the reversible traps are not associated with Cl - . Furthermore, a zinc vacancy adjacent to a substitutional indium is calculated to have its highest occupied orbitals about 1 eV above the top of the valence band of bulk ZnSe, in the appropriate energy range to act as reversible traps for quantum confined holes in the InP valence band. The associated orbitals are predominantly composed of p orbitals on the Se atoms adjacent to the Zn vacancy.
Alkylated benzothienobenzothiophenes are an important class of organic semiconductors that exhibit high performance in solution-processed organic field-effect transistors. In this work, we study the near-edge x-ray absorption fine-structure (NEXAFS) spectra of 2,7-didecyl[1]benzothieno[3,2-b][1]benzothiophene (C 10 -BTBT) at both the carbon and sulfur K-edges. Angle-resolved experiments of thin films are performed to characterize the dichroism associated with molecular orientation. First-principles calculations using the density functional theory-based many-body x-ray absorption spectroscopy (MBXAS) method are also performed to correlate the peaks observed and their dichroism with transitions to specific antibonding molecular orbitals. Interestingly, the dichroism of the dominant, lowest energy peak is opposite at the carbon and sulfur K-edges. While the low-energy peak at the carbon K-edge is assigned to carbon 1s → π* transitions with transition dipole moment (TDM) perpendicular to the planar BTBT core, the dominant low energy peak at the sulfur K-edge is assigned to sulfur 1s → σ* transitions with TDM oriented along the long axis of the BTBT core. These differences at the sulfur and carbon K-edges are understood through the MBAXS simulations that find a reordering of the energy of the lowest energy π* and σ* transitions at the sulfur K-edge due to the strong localization of the σ* orbital over the sulfur atom. This work highlights differences in the NEXAFS spectra of organic semiconductors at carbon and sulfur K-edges and provides new insights into peak assignment and x-ray dichroism relevant for studying the molecular orientation of organic semiconductor films.
The valence band maximum (VBM) is an important quantity for semiconductors as it locates the Fermi level relative to the band edge. Accurate measurement of this quantity in near-surface regions of semiconductors by photoemission is a first step toward determining the electronic properties of heterostructures involving these materials. While extrapolating the leading edge of the valence band to the energy axis in photoemission spectra is a widely used way to find the VBM, this method can be ambiguous if the leading edge exhibits multiple slopes. Another way to determine the VBM is to fit the leading edge to an appropriately broadened, cross-section modulated theoretical density of states (DOS). Three kinds of broadening that should be included for maximum accuracy are those due to: (1) finite instrumental resolution, (2) valence hole lifetime, and (3) vibrational excitations. While steps (1) and (2) are straightforward to implement, (3) is more difficult because the appropriate amount of broadening is not known a priori. Here, we demonstrate that explicit inclusion of vibrational broadening using ab initio molecular dynamics facilitates accurate VBM determination for n-SrTiO 3 (001). The total DOS is constructed by summing time-averaged projections at elevated temperature onto s - , p - , and d orbitals for the constituent atoms and modulating with the associated photoemission cross sections. Subsequent convolutions of the total DOS, first with a Gaussian of width equal to the experimental energy resolution and second with a Lorentzian to simulate valence hole lifetime effects, yield line shapes that reproduce the experimental leading edges rather well. The VBM is then given by the energy at which the vibrationally broadened total DOS (prior to the convolutions) goes to zero. The VBMs generated by this method quantitatively agree with those resulting from extrapolating from the middle of the measured leading edge for SrTiO 3 .
The bulk-boundary correspondence in topological crystalline insulators (TCIs) links the topological properties of the bulk to robust observables on the edges, e.g., the existence of robust edge modes or fractional charge. In one dimension, TCIs protected by reflection symmetry have been realized in a variety of systems in which each unit cell has spatially distributed degrees of freedom (SDOF). However, these realizations exhibit sensitivity of the resulting edge modes to variations in edge termination and to the local breaking of the protective spatial symmetries by inhomogeneity. Here we demonstrate topologically protected edge states in a monoatomic, orbital-based TCI that mitigates both of these issues. By collapsing all SDOF within the unit cell to a singular point in space, we eliminate the ambiguity in unit-cell definition and hence remove a prominent source of boundary termination variability. The topological observables are also more tolerant to disorder in the orbital energies. To validate this concept, we experimentally realize a lattice of mechanical resonators where each resonator acts as an “atom” that harbors two key orbital degrees of freedom having opposite reflection parity. Finally, our measurements of this system provide direct visualization of the sp-hybridization between orbital modes that leads to a nontrivial band inversion in the bulk.
A trivalent plutonium–pyrazinyl–tetrazolate complex Na 2 [Pu(Hdtp)(dtp) 2 (H 2 O) 4 ]·9H 2 O (Pu_dtp, H 2 dtp = 2,3-di-1H-tetrazol-5-ylpyrazine) was synthesized through metathesis reaction of plutonium bromide and Na 2 (dtp)·2H 2 O in water. This structure is particularly notable among complexes formed by trivalent f-elements and the dtp 2− ligand in aqueous media. In contrast to other trivalent f-elements, including all Ln 3+ (with the exception of Pm 3+ ) and Cm 3+ , preferentially coordinated with eight water molecules rather than the nitrogen donors of the dtp 2− ligand, Pu 3+ exhibits a distinct affinity for nitrogen coordination. This observation provides strong evidence that the 5f electrons in Pu 3+ are more delocalized than other studied trivalent f-elements. In Pu_dtp, three distinct Pu(III)–N bonds are present: one Pu(III)–N5 from pyrazinyl, one Pu(III)–N4 from the least electronegative nitrogen in the tetrazolate, and three Pu(III)–N1/N2/N3 from the most electronegative nitrogens in the tetrazolate. Experimental Pu(III)–N bond lengths, Wiberg bond indices (WBI), natural localized molecular orbitals (NLMO), quantum theory of atoms in molecules (QTAIM), and energy decomposition analysis (EDA), reveal a covalency trend: Pu(III)–N from the most electronegative nitrogen in tetrazolate > Pu(III)–N from the least electronegative nitrogen in tetrazolate > Pu(III)–N from pyrazinyl. This trend arises from the increased negative charge on the most electronegative nitrogen atoms in the tetrazolate ring, enhancing electrostatic Pu–N1/N2/N3 interactions. These stronger electrostatic interactions lead to shorter bond lengths, thereby enhancing orbital overlap and greater covalency, compared to the less electronegative nitrogen in tetrazolate (Pu–N4) and the neutral pyrazinyl nitrogen (Pu–N5).
Electronic structure analysis is performed to study the properties of several Pb-containing 3 d intermetallics. Our study reveals that binary metastable Co 3 Pb and Fe 3 Pb intermetallic compounds exhibit very attractive intrinsic magnetic properties. We primarily focus on the magnetic anisotropic properties arising from the high spin-orbit coupling of the Pb atom. Decomposing the total anisotropy into intra- and interatomic contributions reveals a significant deviation from single-ion anisotropy model with strong symmetric anisotropic pair interactions present. Furthermore, we consider magnetic properties of ternary Pb-based 3 d intermetallics, which recently have been reported as stable or metastable. Giant magnetic anisotropy is found on Pb atoms in these systems. The origin of such strong anisotropy in La 18 Co 28 Pb 3 appears from two sources: spin-orbit and interelectronic Breit couplings. Additionally, the significance of Breit interaction for magnetic anisotropy in bulk systems is reported. It is expected that Breit coupling-induced anisotropy is dominating in magnetic Pb-based magnets with lower dimensionality including thin films.
A first implementation of analytic gradients for spinor-based relativistic equation-of-motion coupled-cluster singles and doubles method using an exact two-component Hamiltonian augmented with atomic mean-field spin–orbit integrals is reported. To demonstrate its applicability, we present calculations of equilibrium structures and harmonic vibrational frequencies for the electronic ground and excited states of the radium mono-amide molecule (RaNH 2 ) and the radium mono-methoxide molecule (RaOCH 3 ). Spin–orbit coupling is shown to quench Jahn–Teller effects in the first excited state of RaOCH 3 , resulting in a C 3v equilibrium structure. Furthermore, the calculations also show that the radium atoms in these molecules serve as efficient optical cycling centers.
In this work we derived and implemented the calculation of the one-body reduced density matrix for Aufbau suppressed coupled cluster theory, from which excited state natural orbitals and one-body properties, like atomic populations and dipole moments, are obtained. We utilized the natural orbitals to refine the ASCC solution for simple valence and Rydberg systems, exploring the process of repeatedly solving the ASCC equations in successive natural orbital bases to achieve independence from the starting molecular orbitals. For dipole moments in small molecules where high-level comparison data is available, we find that the accuracy of ASCC essentially matches that of linear response and equation-of-motion coupled cluster as long as care is taken to preserve the response's perturbative completeness.
Fe-based superconductors exhibit a diverse interplay between charge, orbital, and magnetic ordering. Variations in atomic geometry affect electron hopping between Fe atoms and the Fermi surface topology, influencing magnetic frustration and the pairing strength through changes of orbital overlap and occupancies. Here, we experimentally demonstrate a systematic approach to realize superconductivity without chemical doping in BaFe 2 As 2 , employing geometric design within an epitaxial heterostructure. We control both tetragonality and orthorhombicity in BaFe 2 As 2 through superlattice engineering, which we experimentally find to induce superconductivity when the As−Fe−As bond angle approaches that in a regular tetrahedron. This approach to superlattice design could lead to insights into low-dimensional superconductivity in Fe-based superconductors.
Accessing coherences is key to fully understand and control ultrafast dynamics of complex quantum systems like molecules. Most photochemical processes are mediated by conical intersections, which generate coherences between electronic states in molecules. We show with accurate calculations performed on gas-phase methyl iodide that electronic coherences of spin-orbit-split states persist in atomic iodine after dissociation. Our simulation predicts a maximum magnitude of vibronic coherence in the molecular regime of 0.75% of the initially photoexcited state population. Upon dissociation, one-third of this coherence magnitude is transferred to a long-lived atomic coherence where vibrational decoherence can no longer occur. To trace these dynamics, we propose a tabletop experimental approach—heterodyned attosecond four-wave-mixing spectroscopy. This technique can temporally resolve small electronic coherence magnitudes and reconstruct the full complex coherence function via phase cycling. Hence, heterodyned attosecond four-wave-mixing spectroscopy leads the way to a complete understanding and optimal control of spin-orbit-coupled electronic states in photochemistry.