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The goal of this lecture is to cover the basics of atomic electrons: Definitions of shells, subshells, and orbitals; Max number of electrons per subshell; Order of filling shells; The Periodic Table and electron configuration; and Covalent and Ionic Bonding.
Density-functional theory (DFT) is employed to investigate the thermodynamic and ground-state properties of bulk uranium tri-iodide, UI3. The theory is fully relativistic and electron correlations, beyond the DFT and generalized gradient approximation, are addressed with orbital polarization. The electronic structure indicates anti-ferromagnetism, in agreement with neutron diffraction, with band gaps and a non-metallic system. Furthermore, the formation energy, atomic volume, crystal structure, and heat capacity are calculated in reasonable agreement with experiments, whereas for the elastic constants experimental data are unavailable for comparison. The thermodynamical properties are modeled within a quasi-harmonic approximation and the heat capacity and Gibbs free energy as functions of temperature agree with available calculation of phase diagram (CALPHAD) thermodynamic assessment of the experimental data.
Experimental and theoretical studies disagree on the energetics of methane adsorption on carbon materials. However, this information is critical for the rational design and optimization of the structure and composition of adsorbents for natural gas storage. The delicate nature of dispersion interactions, polarization of both the adsorbent and the adsorbate, interplay between H-bonding and tetrel bonding, and induced dipole/Coulomb interactions inherent to methane physisorption require computational treatment at the highest possible level of theory. In this study, we employed the smallest reasonable computational model, a maquette of porous carbon surfaces with a central site for substitution and methane binding. The most accurate predictions of methane adsorption energetics were achieved by electron-correlated molecular orbital theory CCSD(T) and hybrid density functional theory MN15 calculations employing a saturated, all-electron basis set. Here, the characteristic geometry of methane adsorption on a carbon surface (“lander approach”) arises due to bonding interactions of the adsorbent π-system with the proximal H–C bonds of methane, in addition to tetrel bonding between the antibonding orbital of the distal C–H bond and the central atom of the maquette (C, B, or N). The polarization of the electron density, structural deformations, and the comprehensive energetic analysis clearly indicate a ∼3 kJ mol –1 preference for methane binding on the N-substituted maquette. The B-substituted maquette showed a comparable or lower binding energy than the unsubstituted, pure C model, depending on the level of theory employed. The calculated thermodynamic results indicate a strategy for incorporating electron-enriched substitutions (e.g., N) into carbon materials as a way to increase methane storage capacity over electron-deficient (e.g., B) modifications. The thermochemical analysis was revised for establishing a conceptual agreement between the experimental isosteric heat of adsorption and the binding enthalpies from statistical thermodynamics principles.
The magnetic susceptibility of NO x -loaded RE-DOBDC (rare earth (RE): Y, Eu, Tb, Yb; DOBDC: 2,5-dihydroxyterephthalic acid) metal–organic frameworks (MOFs) is unique to the MOF metal center. RE-DOBDC samples were synthesized, activated, and subsequently exposed to humid NO x . Each NO x -loaded MOF was characterized by powder X-ray diffraction, and the magnetic characteristics were probed by using a VersaLab vibrating sample magnetometer (VSM). Lanthanide-containing RE-DOBDC (Eu, Tb, Yb) are paramagnetic with a reduction in paramagnetism upon adsorption of NO x . Y-DOBDC has a diamagnetic moment with a slight reduction upon adsorption of NO x . The magnetic susceptibility of the MOF is determined by the magnetism imparted by the framework metal center. The electronic population of orbitals contributes to determining the extent of magnetism and change with NO x (electron acceptor) adsorption. Eu-DOBDC results in the largest mass magnetization change upon adsorption of NO x due to more available unpaired f electrons. Experimental changes in magnetic moment were supported by density functional theory (DFT) simulations of NO x adsorbed in lanthanide Eu-DOBDC and transition metal Y-DOBDC MOFs.
Density functional theory (DFT) and electron propagator theory (EPT) calculations were performed to study ground and excited electronic structures of alkali-metal (M) coordinated 9-crown-3, 24-crown-8, [2.1.1]cryptand, o-Me 2 -1.1.1, and 3 6 Adamanzane complexes. Each complex bears an expanded electron in the periphery and occupies diffuse 1p-, 1d-, 1f-type molecular orbitals (or superatomic 1P, 1D, 1F orbitals) in excited electronic states. The calculated superatomic shell model of the M(9-crown-3) 2 is 1S, 1P, 1D, 1F, 2S, 2P, 2D, 1G and it is held by all other complexes up to the studied 1F level. Due to the highly diffuse nature of the electron, the ionization energies of these complexes are significantly lower (1.6–2.0 eV) and hence these complexes belong to the superalkali category. Further, the ab initio EPT ionization energy and the excitation energies of the Li(9-crown-3) 2 were used to evaluate DFT errors associated with a series of exchange correlation functionals that span multiple rungs of Jacob's ladder (i.e., GGA, meta-GGA, global GGA hybrid, meta-GGA hybrid, range-separated hybrid, double-hybrid). Among these, the best performing functional is the range-separated hybrid CAM-B3LYP and the errors are within 6% of high-level ab initio EPT results. The accuracy of CAM-B3LYP is indeed transferable to similar complexes and hence the findings are expected to accelerate the progression of studies of Rydberg-type systems.
An alternative formulation of the non-orthogonal molecular orbital model of electronic structure theory is developed based on the expansion of the inverse molecular orbital overlap matrix. From this model, a hierarchy of ab initio fragment-based quantum chemistry methods, referred to as the nth-order expanded non-orthogonal molecular orbital methods, are developed using a minimal number of approximations, each of which is frequently employed in intermolecular interaction theory. These novel methods are compared to existing fragment-based quantum chemistry methods, and the implications of those significant differences, where they exist, between the methods developed herein and those already existing methods are examined in detail. Computational complexities and theoretical scaling are also analyzed and discussed. Future extensions for the hierarchy of methods, to account for additional intrafragment and interfragment interactions, are outlined.
We calculate the elastic production of dijets from electron collisions with a longitudinally polarized proton target at small values of the Bjorken x variable. Building on the pioneering proposals of Hatta [Gluon orbital angular momentum at small- x , .] and Bhattacharya [Signature of the gluon orbital angular momentum, ., Probing the quark orbital angular momentum at electron-ion colliders using exclusive π 0 production, ., and Exploring orbital angular momentum and spin-orbit correlation for gluons at the Electron-Ion Collider, .] for measuring the quark and gluon orbital angular momentum (OAM) distributions, our focus is on both the longitudinal double spin asymmetry (DSA) and longitudinal single spin asymmetry (SSA). We compute the numerators of these asymmetries in the small- x formalism of the light-cone operator treatment. Utilizing the small- x expressions for the OAM distributions derived earlier in Kovchegov and Manley [Orbital angular momentum at small x revisited, .], we demonstrate that the DSA provides a robust probe for both the quark and gluon OAM distributions within the proton. In contrast, we find that while the SSA is also sensitive to the OAM distributions, extraction of the latter from the SSA would require new developments in small- x theory and phenomenology, and is probably not feasible at this point in time. These findings highlight the potential of DSA measurements in elastic dijet production at the future Electron-Ion Collider to provide the first-ever direct access to the quark and gluon OAM distributions at small x , paving the way for new insights into the proton spin puzzle. Published by the American Physical Society 2025
Spin-orbit-coupled Mott iridates show great similarity with parent compounds of superconducting cuprates, attracting extensive research interest especially for their electron-doped states. However, previous experiments have been largely limited within a small doping range due to the absence of effective dopants, and therefore the electron-doped phase diagram remains elusive. Here, an ionic-liquid-gating-induced protonation method is utilized to achieve electron-doping into a 5d Mott-insulator built with a SrIrO 3 /SrTiO 3 superlattice (SL), and a systematic mapping of its electron-doped phase diagram is achieved with the evolution of the iridium valence state from 4+ to 3+, equivalent to doping of one electron per iridium ion. Along increasing doping level, the parent Mott-insulator is first turned into a localized metallic state with gradually suppressed magnetic ordering, and then further evolves into a nonmagnetic band insulating state. This work forms an important step forward for the study of electron-doped Mott iridate systems, and the strategy of manipulating the band filling in an artificially designed SL structure can be readily extended into other systems with more exotic states to explore.
The electronic structure of surfaces and interfaces plays a key role in the properties of quantum devices. Here, we study the electronic structure of realistic Al/InAs/Al heterojunctions using a combination of density functional theory with hybrid functionals and state-of-the-art quasiparticle G W (QSGW) calculations. We find a good agreement between QSGW calculations and hybrid functional calculations, which themselves compare favorably well with angle-resolved photoemission spectroscopy experiments. Our paper confirms the need for well-controlled quality of the interfaces to obtain the needed properties of InAs/Al heterojunctions. A detailed analysis of the effects of spin-orbit coupling on the spin splitting of the electronic states shows a linear scaling in k space, related to the two-dimensional nature of some interface states. The good agreement by QSGW and hybrid functional calculations opens the door towards trustable use of an effective approximation to QSGW for studying very large heterojunctions. Published by the American Physical Society 2024
The Jahn–Teller effect, in which electronic configurations with energetically degenerate orbitals induce lattice distortions to lift this degeneracy, has a key role in many symmetry-lowering crystal deformations. Lattices of Jahn–Teller ions can induce a cooperative distortion, as exemplified by LaMnO 3 . Although many examples occur in octahedrally or tetrahedrally coordinated transition metal oxides due to their high orbital degeneracy, this effect has yet to be manifested for square-planar anion coordination, as found in infinite-layer copper, nickel, iron and manganese oxides. Here, for this work, we synthesize single-crystal CaCoO 2 thin films by topotactic reduction of the brownmillerite CaCoO 2.5 phase. We observe a markedly distorted infinite-layer structure, with ångström-scale displacements of the cations from their high-symmetry positions. This can be understood to originate from the Jahn–Teller degeneracy of the d xz and d yz orbitals in the d 7 electronic configuration along with substantial ligand–transition metal mixing. A complex pattern of distortions arises in a $2\sqrt2$ x $2\sqrt2$ x $1$ tetragonal supercell, reflecting the competition between an ordered Jahn–Teller effect on the CoO 2 sublattice and the geometric frustration of the associated displacements of the Ca sublattice, which are strongly coupled in the absence of apical oxygen. As a result of this competition, the CaCoO 2 structure forms an extended two-in–two-out type of Co distortion following ‘ice rules’.
Spin relaxation and decoherence is at the heart of spintronics and spin-based quantum information science. Currently, theoretical approaches that can accurately predict spin relaxation of general solids including necessary scattering pathways and are capable of nanosecond to millisecond simulation time are urgently needed. We present a first-principles real-time density-matrix approach based on Lindblad dynamics to simulate ultrafast spin dynamics for general solid-state systems. Through the complete first-principles descriptions of pump, probe, and scattering processes including electron-phonon, electron-impurity, and electron-electron scatterings with self-consistent electronic spin-orbit couplings, our method can directly simulate the ultrafast pump-probe measurements for coupled spin and electron dynamics over nanoseconds at any temperatures and doping levels. We first apply this method to a prototypical system GaAs and obtain excellent agreement with experiments. We found that the relative contributions of different scattering mechanisms and phonon modes differ considerably between spin and carrier relaxation processes. In sharp contrast to previous work based on model Hamiltonians, we point out that the electron-electron scattering is negligible at room temperature but becomes dominant at low temperatures for spin relaxation in n-type GaAs. We further examine ultrafast dynamics in novel spin-valleytronic materials: monolayer and bilayer WSe 2 with realistic defects. We find that spin relaxation is highly sensitive to local symmetry and chemical bonds around defects. For the bilayer WSe 2 , we identify the scattering pathways in ultrafast dynamics and determine relevant dynamical properties, essential to its utilization of unique spin-valley-layer locking effects. In conclusion, our work provides a predictive computational platform for spin dynamics in solids, which has potential for designing new materials ideal for spintronics and quantum information technology.
Flat electronic bands are expected to show proportionally enhanced electron correlations, which may generate a plethora of novel quantum phases and unusual low-energy excitations. They are increasingly being pursued in d-electron-based systems with crystalline lattices that feature destructive electronic interference, where they are often topological. Such flat bands, though, are generically located far away from the Fermi energy, which limits their capacity to partake in the low-energy physics. Here we show that electron correlations produce emergent flat bands that are pinned to the Fermi energy. We demonstrate this effect within a Hubbard model, in the regime described by Wannier orbitals where an effective Kondo description arises through orbital-selective Mott correlations. Moreover, the correlation effect cooperates with symmetry constraints to produce a topological Kondo semimetal. Our results motivate a novel design principle for Weyl Kondo semimetals in a new setting, viz.d-electron-based materials on suitable crystal lattices, and uncover interconnections among seemingly disparate systems that may inspire fresh understandings and realizations of correlated topological effects in quantum materials and beyond.
HgTe is a versatile topological material and has enabled the realization of a variety of topological states, including two- and three-dimensional (3D) topological insulators and topological semimetals. Nevertheless, a quantitative understanding of its electronic structure remains challenging, in particular, due to coupling of the Te $5p$-derived valence electrons to Hg $5d$ core states at shallow binding energy. Here, we present a joint experimental and theoretical study of the electronic structure in strained HgTe(001) films in the 3D topological-insulator regime, based on angle-resolved photoelectron spectroscopy and density functional theory. The results establish detailed agreement in terms of: (i) electronic band dispersions and orbital symmetries, (ii) surface and bulk contributions to the electronic structure, and (iii) the importance of Hg $5d$ states in the valence-band formation. Supported by theory, our experiments directly image the paradigmatic band inversion in HgTe, underlying its nontrivial band topology.
Abstract Kagome lattice hosts a plethora of quantum states arising from the interplay of topology, spin-orbit coupling, and electron correlations. Here, we report symmetry-breaking electronic orders tunable by an applied magnetic field in a model Kagome magnet FeSn consisting of alternating stacks of two-dimensional Fe 3 Sn Kagome and Sn 2 honeycomb layers. On the Fe 3 Sn layer terminated FeSn thin films epitaxially grown on SrTiO 3 (111) substrates, we observe trimerization of the Kagome lattice using scanning tunneling microscopy/spectroscopy, breaking its six-fold rotational symmetry while preserving the translational symmetry. Such a trimerized Kagome lattice shows an energy-dependent contrast reversal in dI/dV maps, which is significantly enhanced by bound states induced by Sn vacancy defects. This trimerized Kagome lattice also exhibits stripe modulations that are energy-dependent and tunable by an applied in-plane magnetic field, indicating symmetry-breaking nematicity from the entangled magnetic and charge degrees of freedom in antiferromagnet FeSn.
While the main thrust of quantum computing research in materials science is to accurately measure the classically intractable electron correlation effects due to Coulomb repulsion, designing optimal quantum algorithms for simpler problems with well-understood solutions is a useful tactic to advance our quantum “toolbox”. With this in mind, we consider the quantum calculation of a periodic system’s single-electron band structure over a path through reciprocal space. Previous efforts have used the Variational Quantum Eigensolver algorithm to solve the energy of each band, which involves numerically optimizing the parameters of a variational quantum circuit to minimize a cost function, constructed as the expectation value of a Hamiltonian operator. Traditionally, a unique Hamiltonian operator is constructed for each k-point, so that many cost functions, each with their own parameter space, must be optimized to generate a single band. Similarly, calculating higher bands than the first has traditionally involved modifying the cost function with additional overlap terms to ensure higher-energy eigenstates are orthogonal to those of lower bands. In this paper, we adopt a direct space approach, using a novel hybrid first/second-quantized qubit mapping which allows us to construct a single Hamiltonian, and a single cost-function, suitable for solving the entire electronic band structure. In contrast to previous approaches, the k-point and the band index are selected by additional parameters in our quantum circuit, rather than through modifications to the cost function. The result is a technically and conceptually simpler approach to band structure calculations on a quantum computer. Moreover, we expect that the tools developed herein will motivate new strategies for tackling highly-correlated materials beyond the grasp of classical computing.
Magnetoresistance (MR) at a fixed field can demonstrate a non-monotonic temperature dependence—an anomaly—in many systems, including low-dimensional chalcogenides, spin- and charge-density-wave metals, and topological semimetals. These systems are often low-carrier-density compensated metals, and the physics are expected to be quasi-classical. Nevertheless, the MR anomaly also exists in the highly conductive metals Cr, Mo, and W for both linear and quadratic field dependence, with their non-saturation attributed to either open orbit or electron-hole compensation. We argue that quantum transport across sharp Fermi surface arcs, but not necessarily the full cyclotron orbit, governs this MR anomaly, thereby accounting for the profound effects of disorder. In Cr, an overlay exists between three temperature dependences: MR at a constant high field, linear MR at a low field, and Shubnikov-de Haas (SdH) oscillations of the smallest orbit. In Mo, the MR anomaly extends beyond the temperature of its SdH oscillations but disappears before Kohler’s scaling reemerges.
Reduction of the cobalt(II) chloride complex, Ph 2 B( t BuIm) 2 Co(THF)Cl (1) in the presence of t BuN≡C affords the diamagnetic, square planar cobalt(I) complex Ph 2 B( t BuIm) 2 Co(C≡N t Bu) 2 (2). This is a rare example of a 16-electron cobalt(I) complex that is structurally related to square planar noble metal complexes. Accordingly, the electronic structure of 2, as calculated by DFT, reveals that the HOMO is largely d z 2 in character. Complex 2 is readily oxidized to its cobalt(II) congener [Ph 2 B( t BuIm) 2 Co(C=N t Bu) 2 ]BPh 4 (3-BPh 4 ), whose EPR spectral parameters are characteristic of low-spin d 7 with an unpaired electron in an orbital of d z 2 parentage. Further, this is also consistent with the results of DFT calculations. Despite its 16-electron configuration and the d z 2 parentage of the HOMO, the only tractable reactions of 2 involve one electron oxidation to afford 3.
Developing controlled platforms for plasmon-driven chemistry is of great importance in catalytic reactions at the nanoscale. We report anion radical formation for five bipyridyl complexes of varying degrees of electron affinity utilizing optically fo-cused intraband (594 nm) and interband (532 nm) pump excitation of single gold nanoparticles. The surface-enhanced Raman scattering (SERS) of anion radicals for the five non-resonant adsorbed molecules 2,2’-bipyridine (22BPY), 4,4’-bipyridine (44BPY), trans-1,2-bis(4-pyridyl)ethylene (BPE), 1,2-bis(4-pyridyl)acetylene (BPA), and 1,2-bis(4-pyridyl)ethane (BPEt) were detected using localized surface-plasmon resonance (LSPR) excitation with 785 nm. The electron affinity of the five bipyridyl complexes were determined using electrochemistry. Molecules with low electron affinity experienced high-er instances of radical anion formation under a plasmon-coupled intraband electron transfer excitation (594 nm) whereas molecules with high electron affinity showed a preference for anion radical formation under direct interband electron trans-fer excitation (532 nm). The lowest unoccupied molecular orbital (LUMO) energy levels for low electron affinity surface-bound molecules (22BPY, BPEt) are on average ~0.43 eV higher for high electron affinity surface-bound molecules (BPA, BPE, 44BPY) as calculated using time-dependent density functional theory, elucidating the importance of plasmon coupling to energy levels that facilitate charge transfer pathways. We also show the ability to ‘activate’ high vs low electron affinity single nanoparticles with the choice of pump excitation wavelength. The findings show the complex interplay between molecular electron affinity, orbital overlap with the density of states of the plasmonic metal, and excitation energetics of the pump laser wavelength. Potential applications of this work include enhanced control over molecular scale catalysis, biosensor design, and solar energy capture.