Semicore Electrons Research Articles

Origin of competing charge density waves in kagome metal ScV6Sn6

Understanding competing charge density wave (CDW) orders in the bilayer kagome metal ScV6Sn6 remains challenging. Experimentally, upon cooling, short-range order with wave vector q2=(13,13,12)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{{{\\bf{q}}}}}_{2}=(\\frac{1}{3},\\frac{1}{3},\\frac{1}{2})$$\\end{document} forms, which is subsequently suppressed by the condensation of long-range q3=(13,13,13)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{{{\\bf{q}}}}}_{3}=(\\frac{1}{3},\\frac{1}{3},\\frac{1}{3})$$\\end{document} CDW order at lower temperature. Theoretically, however, the q2 CDW is predicted as the ground state, leaving the CDW mechanism elusive. Here, using anharmonic phonon-phonon calculations combined with density functional theory, we predict a temperature-driven structural phase transitions from the high-temperature pristine phase to the q2 CDW, followed by the low-temperature q3 CDW, explaining experimental observations. We demonstrate that semi-core electron states stabilize the q3 CDW over the q2 CDW. Furthermore, we find that the out-of-plane lattice parameter controls the competing CDWs, motivating us to propose compressive bi-axial strain as an experimental protocol to stabilize the q2 CDW. Finally, we suggest Ge or Pb doping at the Sn site as another potential avenue to control CDW instabilities. Our work provides a full theory of CDWs in ScV6Sn6, rationalizing experimental observations and resolving earlier discrepancies between theory and experiment.

Pseudopotential Bethe-Salpeter calculations for shallow-core x-ray absorption near-edge structures: Excitonic effects in α−Al2O3

We present an ab initio description of optical and shallow-core x-ray absorption spectroscopies in a unified formalism based on the pseudopotential plane-wave method at the level of the Bethe-Salpeter equation (BSE) within Green's functions theory. We show that norm-conserving pseudopotentials are reliable and accurate not only for valence, but also for semicore electron excitations. In order to validate our approach, we compare BSE absorption spectra obtained with two different codes: the pseudopotential-based code EXC and the all-electron full-potential code Exciting. We take corundum $\alpha$-Al$_2$O$_3$ as an example, being a prototypical material that presents strong electron-hole interactions for both valence and core electron excitations. We analyze in detail the optical absorption spectrum as well as the Al L$_1$ and L$_{2,3}$ edges in terms of anisotropy, crystal local fields, interference and excitonic effects. We perform a thorough inspection of the origin and localization of the lowest-energy excitons, and conclude highlighting the purely electronic character off the pre-edge of L$_1$ and the dichroic nature of the optical and L$_{23}$ spectra.

Electronic stopping power in titanium for proton and helium ions from first-principle calculations

The energy loss rate from energetic proton and helium ions to electrons of a transition metal titanium (Ti) is studied using real-time time-dependent density functional theory. Nonequilibrium simulations with and without semicore electrons explicitly included in describing the electronic structure of target atoms are performed to understand their involvement in the dissipation mechanism. It is found that the low-lying $3s$ and $3p$ semicore excitations play significant roles in determining the profile of the stopping curve around and above the stopping maximum. Additionally, we investigate the effect of impact geometry on electronic stopping. An important conclusion is that although off-channeling geometry, which makes possible the strong interaction with tightly bound electrons, indeed improves the amplitude of the stopping curve, especially for the regime around the stopping maximum, it does not shift the position of the stopping maximum. Our results about the relation between effective charge and electronic stopping are in qualitative agreement with the linear response theory.

Effects of semicore electrons on stopping power in helium-irradiated aluminum nanosheets.

The stopping power of energetic He ions traversing an Al film is studied by combining the time-dependent density-functional theory method with molecular dynamics simulations. We investigated the dependence of the semicore electron excitation of the Al film on the projectile's trajectory and its charge state. Our results show that for the off-channeling trajectories the semicore electrons contribute significantly to the stopping power of the Al film as the He+ ion velocity exceeds 1.0 a.u, and in contrast, it is negligible for the channeling trajectories. Most importantly, we found two unexpected effects of semicore electrons on the stopping power in helium-irradiated aluminum nanosheets, i.e., (1) the semicore electrons can contribute to the energy loss for both high and low energy projectiles under the off-channeling trajectory; (2) as the projectile velocity increases from 0.4 a.u. to 2.0 a.u. although semicore electron excitation (including transition in the target, ionization away from the target and transfer to the projectile ion) of the target atom is gradually inhibited, the influence of semicore electrons on valence electron excitation is gradually enhanced. Our finding allows us to gain new insights into the stopping of ions in metals.

First-principles study of the electronic stopping power of indium for protons and He ions

The electronic stopping power of protons and He ions traveling along the channeling and off-channeling trajectories in indium is reported based on time-dependent density functional theory combined with Ehrenfest molecular dynamics simulations. We provided an intuitive description of the electronic stopping power for a wide range of ion energies, and revealed the microcosmic excitation mechanism of the semicore $4d$ electrons of In. The velocity-proportional electronic stopping power and the kink velocity which is due to $4d$-electron excitation are reproduced in the low-energy regime. Because the $5s5p$ valence electrons are uniformly distributed in indium, the electronic excitation of valence electrons via Coulomb scattering is independent of the impact parameter in the investigated velocity range. On the contrary, due to the highly localized nature of semicore electrons, the excitation of $4d$ electrons increases significantly with decreasing of the impact parameter, which suggests that it is triggered by direct ion-electron collision. Our calculated stopping power is in quantitative agreement with the experimental data up to the stopping maximum, and showed that the stopping power obtained from the off-channeling geometry is greatly improved in comparison with the channeling results. Finally, we examined the extent to which the linear response theory is applicable to describe the electronic stopping power by quantifying the velocity dependence of the mean steady-state charge of protons and $\ensuremath{\alpha}$ particles and the effective charge state for $\ensuremath{\alpha}$ particles, and it is found that the linear response theory can be used to predict the stopping power in a wider energy range if the mean steady-state charge is used instead of assuming fully ionized charges.

First-principles study of semicore electron excitation in the electronic energy loss of ZnO for protons

The electronic stopping power of zinc oxide for protons is presented over a wide range of velocities by using real-time time-dependent density functional theory. We calculated the electronic stopping power of energetic protons for both channeling and off-channeling trajectories, and revealed the microcosmic mechanism of semicore $3d$-electron excitation in ZnO. In the low-energy regime, the stopping power obtained from channeling geometry is in a quantitative agreement with the measured data, which reproduced not only the experimental threshold velocity of the stopping power, but also the deviation from velocity-proportional electronic stopping power which is considered to be caused by excitation of the tightly bound $3d$ electrons. In the high-energy regime, we examined the impact parameter dependence of semicore $3d$-electron excitation of ZnO, and showed that the stopping power obtained from off-channeling geometry greatly improves the simulation results in comparison with the channeling results. We also demonstrated that the electronic energy loss of protons is not only related to the number of electrons excited, but also associated with the energy distribution of excited electrons and holes after collisions.

Aluminum Hugoniot from model calculations including semicore electrons based on density functional theory

We present a method to obtain Hugoniot from model calculations based on density functional theory, and apply the method to aluminum Hugoniot. Technological advances have extended the experimental research of high energy density physics, and call for quantitative theoretical analysis. However, direct computation of Hugoniot from density functional theory is very difficult. We propose two step calculations of Hugoniot from density functional theory. The first step is molecular dynamics simulations with an ambient temperature for electrons. The second step is total energy calculations of a crystal with desired high temperatures for electrons and with the ambient temperature for electrons. We treated the semicore 2s and 2p electrons of aluminum as valence electrons only for the total energy calculations of the aluminum crystal. The aluminum Hugoniot from our model calculations is in excellent agreement with available experimental data and the previous density functional theory calculations in the literature.

Hybrid functional analysis of planar metal-organic frameworks

The electronic energy band structure and optical properties of the planar metal-organic frameworks, namely M-HAB and M3[HITP] (M = Ni, Cu; HAB = hexaaminobenzene; HITP = hexaiminotriphenylene) were investigated in this work using two hybrid exchange-correlation functionals. The materials studied here contain nickel and copper, 3d electrons of which should be considered as strongly correlated subsystem. These semi-core electrons are treated here by means of the hybrid HSE06 and PBE0 functionals. We have found that Ni-HAB and Cu-HAB are metals, whereas Ni3[HITP]2 and Cu3[HITP]2 are degenerate p-type semiconductors.

Stability and bonding nature of clathrate H cages in a near-room-temperature superconductor LaH10

Lanthanum hydride (${\mathrm{LaH}}_{10}$) with a sodalitelike clathrate structure was experimentally synthesized to exhibit a near-room-temperature superconductivity under megabar pressures. Based on first-principles density-functional theory calculations, we reveal that the metal framework of La atoms has excess electrons at interstitial regions. Such anionic electrons are easily captured to form a stable clathrate structure of H cages. We thus propose that the charge transfer from La to H atoms is mostly driven by the electride property of the La framework. Furthermore, the interaction between La atom and H cage induces a delocalization of La $5p$ semicore states to hybridize with the H $1s$ state. Consequently, the bonding nature of ${\mathrm{LaH}}_{10}$ is characterized as a mixture of ionic and covalent bonding between La atom and H cage. Our findings demonstrate that anionic and semicore electrons play important roles in stabilizing clathrate H cages in ${\mathrm{LaH}}_{10}$, which can be broadly applicable to other compressed rare-earth hydrides with clathrate structures.

Modified Becke-Johnson calculations using norm-conserving pseudopotential plane-wave approach: Systematic analysis

The modified Becke-Johnson potential for exchange and local density approximation for correlation (mBJLDA) approach is proved to provide a highly improved description of the bandgap. This work presents the results of a systematic investigation of the mBJLDA electronic band structure calculations using the norm-conserving pseudopotential (PP) approach, as implemented in the ABINIT code. The considered systems represent different classes of semiconductors and insulators. Moreover, all-electron (AE) mBJLDA potential and screened hybrid functional YS-PBE0 calculations are also performed for comparison purposes. We show that the mBJLDA@PP bandgaps obtained using typical PP's (i.e., valence and semicore electrons are allowed to relax) are generally speaking smaller than that of the mBJLDA@AE approach. This artifact cannot be attributed to a small “c” parameter of the mBJLDA, since we found that this parameter is quite insensitive to the adopted computational method. Interestingly, the number of electrons treated as valence, especially for the cations, can be used as an extra adjustable parameter to improve the mBJLDA@PP bandgaps. In particular, the best agreement with the mBJLDA@AE bandgaps is obtained by including the outer core p electrons as valence. The optimal PP's for mBJLDA@PP calculations are transferable. A similar agreement is also achieved for the binding energies of the semicore d electrons (in the IIB-VI and IIIB-V compounds), upper valence bandwidths and electron effective masses. Sound explanations of the mBJLDA@PP results for the considered electronic structure properties are provided.

Covalent vs Charge-Shift Nature of the Metal-Metal Bond in Transition Metal Complexes: A Unified Understanding.

We present here a general conceptualization of the nature of metal-metal (M-M) bonding in transition-metal (TM) complexes across the periods of TM elements, by use of ab initio valence-bond theory. The calculations reveal a dual-trend: For M-M bonds in groups 7 and 9, the 3d-series forms charge-shift bonds (CSB), while upon moving down to the 5d-series, the bonds become gradually covalent. In contrast, M-M bonds of metals having filled d-orbitals (groups 11 and 12) behave oppositely; initially the M-M bond is covalent, but upon moving down the Periodic Table, the CSB character increases. These trends originate in the radial-distribution-functions of the atomic orbitals, which determine the compactness of the valence-orbitals vis-à-vis the filled semicore orbitals. Key factors that gauge this compactness are the presence/absence of a radial-node in the valence-orbital and relativistic contraction/expansion of the valence/semicore orbitals. Whenever these orbital-types are spatially coincident, the covalent bond-pairing is weakened by Pauli-repulsion with the semicore electrons, and CSB takes over. Thus, for groups 3-10, which possess (n - 1)s2(n - 1)p6 semicores, this spatial-coincidence is maximal at the 3d-transition-metals which consequently form charge-shift M-M bonds. However, in groups 11 and 12, the relativistic effects maximize spatial-coincidence in the third series, wherein the 5d10 core approaches the valence 6s orbital, and the respective Pauli repulsion generates M-M bonds with CSB character. These considerations create a generalized paradigm for M-M bonding in the transition-elements periods, and Pauli repulsion emerges as the factor that unifies CSB over the periods of main-group and transition elements.

Excitation effect of d electrons on the electronic energy loss of energetic protons colliding with a Zn atom

By using a nonequilibrium approach based on real-time time-dependent density-functional theory combined with molecular dynamics simulations, the effects of $d$-electron excitation on the electronic energy loss of energetic protons colliding with atomic zinc target are studied. The results show that the semicore electrons play a crucial role in the electronic energy loss in an extended energy range. In the low-energy regime, the electronic energy loss displays the threshold effect before it is proportional to velocity, which is explained by the quantization of the energy levels of zinc atom, and the charge transfer contributes greatly to the electronic energy loss, especially at 0.1 a.u. In addition, due to the electron resonance excitation, the number of excited electrons and charge transfer is significantly increased at the velocity thresholds for electron excitation. In the high-energy regime, the electronic energy loss is greatly enhanced as the the impact parameter decreases, which is ascribed to the excitation of $3d$ electrons. We also calculated the stopping cross section for energetic protons colliding with atomic zinc, which is in a good agreement with the experimental values in both low- and high-velocity regimes.

Stoichiometry, band alignment, and electronic structure of Eu2O3 thin films studied by direct and inverse photoemission: A reevaluation of the electronic band structure

The electronic structure of Eu sesquioxide (Eu2O3) presents a significant challenge to the electronic structure theory due to the presence of correlated Eu semicore 4f electrons. The bandgap values do not agree between computational methods, and even experimentally, there are discrepancies between reports. Eu2O3 was grown epitaxially in a thin film form on n-type GaN (0001) by molecular beam epitaxy. The film was analyzed using UV and x-ray photoemission spectroscopies as well as inverse photoelectron spectroscopy in order to characterize both occupied and unoccupied states. Signatures of Eu2+ are detected after annealing in UHV or after exposure to air, which can be removed by subsequent O2 annealing. The sample reduction is shown to strongly affect the electronic structure. The bandgap of 4.3 eV, electron affinity of 2.2 eV, and band alignment to the substrate with a valence band offset of 0.2 eV for a stoichiometric Eu2O3 film were extracted from the measurements of the occupied and unoccupied electronic states. The electronic structure is interpreted in view of recent theoretical models, and the energy band alignment across the Eu2O3/GaN interface is discussed.

Real-Space Based Benchmark of G0W0 Calculations on GW100: Effects of Semicore Orbitals and Orbital Reordering.

Using an implementation based on real-space wave functions, we perform G0W0 calculations of the HOMO and LUMO energies of molecules and atoms in the GW100 set. Our main conclusions are as follows: (1) Different implementations of the G0W0 approximation show much better agreements for HOMO (highest occupied molecular orbital) energies than for LUMO (lowest unoccupied molecular orbital) energies. The mean absolute differences between the results calculated with different pseudopotential codes range from 100 to 200 meV. For delocalized LUMOs, all-electron codes that use local orbital basis tend to predict much higher energies than those calculated with plane-wave basis or real-space methods. (2) The effects of semicore electrons in pseudopotentials can explain some of the large discrepancies between results calculated with different GW implementations. For molecules or atoms that include I, Xe, and Ga, pseudopotential-based calculations that exclude semicore electrons produce results that agree better with all-electron calculations. For polar molecules such as NaCl and BrK, however, it is necessary to include semicore electrons for alkaline metal elements to get correct LUMO energies. (3) More than 20 molecules show rearrangement of the order between LUMO (or HOMO) with other orbitals due to GW corrections. Such orbitals that switch order with LUMO are unbound and delocalized in space. The predicted LUMO GW levels (or electron affinity) can be corrected by 2.0 eV if we consider the rearrangement of orbitals in GW calculations. In all, our work clarifies some of the discrepancies between different GW codes and sets a benchmark for real-space implementations of the G0W0 approximation.

Role of Valence and Semicore Electron Correlation on Spin Gaps in Fe(II)-Porphyrins.

The role of valence and semicore correlation in differentially stabilizing the intermediate spin state of Fe(II)-porphyrins is analyzed. For CASSCF treatments of valence correlation, a (32,34) active space containing metal 3d, d′ orbitals and the entire π system of the porphyrin is necessary to stabilize the intermediate spin state. Semicore correlation provides a minor (−1.6 kcal/mol) but quantitatively significant correction. Accounting for valence, semicore, and correlation beyond the active space enlarges the (3Eg–5A1g) spin gap to −5.7 kcal/mol.

A new generation of effective core potentials from correlated calculations: 3d transition metal series.

Recently, we have introduced a new generation of effective core potentials (ECPs) designed for accurate correlated calculations but equally useful for a broad variety of approaches. The guiding principle has been the isospectrality of all-electron and ECP Hamiltonians for a subset of valence many-body states using correlated, nearly-exact calculations. Here we present such ECPs for the 3d transition series Sc to Zn with Ne-core, i.e., with semi-core 3s and 3p electrons in the valence space. Besides genuine many-body accuracy, the operators are simple, being represented by a few gaussians per symmetry channel with resulting potentials that are bounded everywhere. The transferability is checked on selected molecular systems over a range of geometries. The ECPs show a high overall accuracy with valence spectral discrepancies typically ≈0.01-0.02 eV or better. They also reproduce binding curves of hydride and oxide molecules typically within 0.02-0.03 eV deviations over the full non-dissociation range of interatomic distances.

Discerning Chemical Pressure amidst Weak Potentials: Vibrational Modes and Dumbbell/Atom Substitution in Intermetallic Aluminides.

The space requirements of atoms are generally regarded as key constraints in the structures, reactivity, and physical properties of chemical systems. However, the empirical nature of such considerations renders the elucidation of these size effects with first-principles calculations challenging. DFT-chemical pressure (DFT-CP) analysis, in which the output of DFT calculations is used to construct maps of the local pressures acting between atoms due to lattice constraints, is one productive approach to extracting the role of atomic size in the crystal structures of materials. While in principle this method should be applicable to any system for which DFT is deemed an appropriate treatment, so far it has worked most successfully when semicore electrons are included in the valence set of each atom to supply an explicit repulsive response to compression. In this Article, we address this limiting factor, using as model systems intermetallics based on aluminum, a key component in many structurally interesting phases that is not amenable to modeling with a semicore pseudopotential. Beginning with the Laves phase CaAl2, we illustrate the difficulties of creating a CP scheme that reflects the compound's phonon band structure with the original method due to minimal core responses on the Al atoms. These deficiencies are resolved through a spatial mapping of three energetic terms that were previously treated as homogeneous background effects: the Ewald, Eα, and nonlocal pseudopotential components. When charge transfer is factored into the integration scheme, CP schemes consistent with the phonon band structure are obtainable for CaAl2, regardless of whether Ca is modeled with a semicore or valence-only pseudopotential. Finally, we demonstrate the utility of the revised method through its application to the La3Al11 structure, which is shown to soothe CPs that would be encountered in a hypothetical BaAl4-type parent phase through the substitution of selected Al2 pairs with single Al atoms. La3Al11 then emerges as an example of a more general phenomenon, CP-driven substitutions of simple motifs.

Relativistic quasiparticle band structures of Mg2Si, Mg2Ge, and Mg2Sn: Consistent parameterization and prediction of Seebeck coefficients

We apply density functional and many-body perturbation theory calculations to consistently determine and parameterize the relativistic quasiparticle band structures of Mg2Si, Mg2Ge, and Mg2Sn, and predict the Seebeck coefficient as a function of doping and temperature. The quasiparticle band gaps, including spin-orbit coupling effects, are determined to be 0.728 eV, 0.555 eV, and 0.142 eV for Mg2Si, Mg2Ge, and Mg2Sn, respectively. The inclusion of the semicore electrons of Mg, Ge, and Sn in the valence is found to be important for the accurate determination of the band gaps of Mg2Ge and Mg2Sn. We also developed a Luttinger-Kohn Hamiltonian and determined a set of band parameters to model the near-edge relativistic quasiparticle band structure consistently for all three compounds that can be applied for thermoelectric device simulations. Our calculated values for the Seebeck coefficient of all three compounds are in good agreement with the available experimental data for a broad range of temperatures and carrier concentrations. Our results indicate that quasiparticle corrections are necessary for the accurate determination of Seebeck coefficients at high temperatures at which bipolar transport becomes important.

Convergence of calculated dislocation core structures in hexagonal close packed titanium

The core structure of -type screw dislocations in hexagonal close packed titanium is investigated computationally using periodic supercells with quadrupolar configurations in combination with density functional theory (DFT) and a modified embedded atom method (MEAM) classical potential. Two arrangements of the quadrupolar supercell configurations are examined, and within each arrangement two initial dislocation positions are compared. (Meta)stable pyramidal and prismatic dislocation core structures exist within both DFT and MEAM methods, and the relaxed structure from a given configuration resulting from our anisotropic elasticity theory solution depends only on the assumed initial dislocation positions. Within DFT we find the ground state core structure to be spread on the pyramidal plane. We find that it is necessary to include the semi-core 3p electrons as valence states in the DFT calculations in order to converge the ground state dislocation core configuration and difference in energy between structures. In terms of k-point sampling, it is found that at least a k-point mesh is necessary to converge the dislocation core structure for a supercell one Burgers vector deep. Use of higher k-point densities or inclusion of additional semi-core electronic states as valence electrons results in the same core structure. With the MEAM potential considered in this work, we find the ground state core configuration to be spread predominantly on the prismatic plane, in contrast with the DFT results.

The importance of inner-shell electronic structure for enhancing the EUV absorption of photoresist materials.

In order to increase computation power and efficiency, the semiconductor industry continually strives to reduce the size of features written using lithographic techniques. The planned switch to a shorter wavelength extreme ultraviolet (EUV) source presents a challenge for the associated photoresists, which in their current manifestation show much poorer photoabsorption cross sections for the same dose. Here we consider the critical role that an inner-shell electronic structure might play in enhancing photoabsorption cross sections, which one can control by the choice of substituent elements in the photoresist. In order to increase the EUV sensitivity of current photoresists, it is critical to consider the inner-shell atomic structure of the elements that compose the materials. We validate this hypothesis using a series of halogenated organic molecules, which all have similar valence structures, but differ in the character of their semi-core and deep valence levels. Using various implementations of time-dependent density functional theory, the absorption cross sections are computed for the model systems of CH3X, X = H, OH, F, Cl, Br, I, as well as a representative polymer fragment: 2-methyl-phenol and its halogenated analogues. Iodine has a particularly high cross section in the EUV range, which is due to delayed absorption by its 4d electrons. The computational results are compared to standard database values and experimental data when available. Generally we find that the states that dominate the EUV oscillator strength are generated by excitations of deep valence or semi-core electrons, which are primarily atomic-like and relatively insensitive to the specific molecular structure.