Density-functional theory for f-electron systems: the α-γ phase transition in cerium

Analytical Forces for the Optimized Effective Potential Calculations

The optimized effective potential (OEP) equation is an ill-conditioned linear system when using finite basis sets. Without any special treatment, the obtained exchange-correlation (XC) potential may have unphysical oscillations. One way to alleviate this problem is to regularize the solutions; however, a regularized XC potential is not the exact solution to the OEP equation. As a result, the system's energy is no longer variational against the Kohn-Sham (KS) potential, and the analytical forces cannot be derived from the Hellmann-Feynman theorem. In this work, we develop a robust and nearly black-box OEP method to ensure that the system's energy is variational against the KS potential. The basic idea is to add a penalty function that regularizes the XC potential to the energy functional. Analytical forces can then be derived based on the Hellmann-Feynman theorem. Another key result is that the impact of the regularization can be much reduced by regularizing the difference between the XC potential and an approximate XC potential rather than regularizing the XC potential. Numerical tests show that forces and the energy differences between systems are not sensitive to the regularization coefficient, which indicates that in practice accurate structural and electronic properties can be obtained without extrapolating the regularization coefficient to zero. We expect this new method to be found useful for calculations that employ advanced, orbital-based functionals, especially for applications that require efficient force calculations.

New Insights on the Electronic-Structural Interplay in LaPdSb and CePdSb Intermetallic Compounds

Multifunctional physical properties are usually a consequence of a rich electronic-structural interplay. To advance our understanding in this direction, we reinvestigate the structural properties of the LaPdSb and CePdSb intermetallic compounds using single-crystal neutron and X-ray diffraction. We establish that both compounds can be described by the non-centrosymmetric space group P6₃mc, where the Pd/Sb planes are puckered and show ionic order rather than ionic disorder as was previously proposed. In particular, at 300 K, the (h, k, 10)-layer contains diffuse scattering features consistent with the Pd/Sb puckered layers. The experimental results are further rationalized within the framework of DFT and DFT+ embedded DMFT methods, which confirm that a puckered structure is energetically more favorable. We also find strong correspondence between puckering strength and band topology. Namely, strong puckering removes the bands and, consequently, the Fermi surface pockets at the M point. In addition, the Pd-d band character is reduced with puckering strength. Thus, these calculations provide further insights into the microscopic origin of the puckering, especially the correspondence between the band's character, Fermi surfaces, and the strength of the puckering.

γ-αphase transition of elemental cerium metal

The isostructuralγ-αphase transition in elemental cerium has been the subject of many experimental and theoretical studies over almost the past century without a universally agreed upon mechanism. Here, we report the results of an extensive study of electronic and magnetic structures,f-electron number, entanglement entropy, and elastic properties of cerium in the GGA +Uframework. We have found that almost all changes in the studied quantities mimic their behavior in the phase transition and could be related to the symmetry of the 4foccupation and the small change in HubbardUnear a critical value.

Interpretations of ground-state symmetry breaking and strong correlation in wavefunction and density functional theories

Strong correlations within a symmetry-unbroken ground-state wavefunction can show up in approximate density functional theory as symmetry-broken spin densities or total densities, which are sometimes observable. They can arise from soft modes of fluctuations (sometimes collective excitations) such as spin-density or charge-density waves at nonzero wavevector. In this sense, an approximate density functional for exchange and correlation that breaks symmetry can be more revealing (albeit less accurate) than an exact functional that does not. The examples discussed here include the stretched H2 molecule, antiferromagnetic solids, and the static charge-density wave/Wigner crystal phase of a low-density jellium. Time-dependent density functional theory is used to show quantitatively that the static charge-density wave is a soft plasmon. More precisely, the frequency of a related density fluctuation drops to zero, as found from the frequency moments of the spectral function, calculated from a recent constraint-based wavevector- and frequency-dependent jellium exchange-correlation kernel.

Lanthanide contraction regulates the HER activity of iron triad intermetallics in alkaline media

In this work, we have systematically investigated the HER activity of the RE₂Co₁₇ (RE = Y, Pr, Gd, Tb, Ho and Er) series and revealed that their HER activities are highly correlated with the averaged Co-Co bond length of each compound. The HER performance follows the order of Gd₂Co₁₇ > Tb₂Co₁₇ > Pr₂Co₁₇ > Y₂Co₁₇ > Ho₂Co₁₇ > Er₂Co₁₇. This suggests that the unique feature of rare-earth metals, lanthanide contraction, can effectively alter the interatomic spacing and impact the corresponding HER activity. Additionally, Gd₂Fe₁₇ and Gd₂Ni₁₇ with different d electron density in the system were synthesized and comparison of their HER efficiencies is also discussed. Gd₂Ni₁₇ demonstrates the highest HER efficiency among all samples, and it only requires an overpotential (η) of 44 mV to acquire a current density of 10 mA cm^-2. The theoretical calculation offers a clue that the H adsorption energy (GH_ad) for H atoms on Ni is lower than that on Co and Fe due to the high electron population in the antibonding state of the Ni atom. This well explains the origin of the synergistic effect for the high electrocatalytic HER of these iron triad intermetallics.

Probing Cerium 4f States across the Volume Collapse Transition by X-ray Raman Scattering

Understanding the volume collapse phenomena in rare-earth materials remains an important challenge due to a lack of information on 4f electronic structures at different pressures. Here, we report the first high-pressure inelastic X-ray scattering measurement on elemental cerium (Ce) metal. By overcoming the ultralow signal issue in the X-ray measurement at the Ce N_4,5-edge, we observe the changes of unoccupied 4f states across the volume collapse transition around 0.8 GPa. To help resolve the longstanding debate on the Anderson-Kondo and Mott-Hubbard models, we further compare the experiments with extended multiplet calculations that treat both screening channels on equal footing. The results indicate that a modest change in the 4f-5d Kondo coupling can well describe the spectral redistribution across the volume collapse, whereas the hybridization between neighboring atoms in the Hubbard model appears to play a minor role. Our study helps to constrain the theoretical models and opens a promising new route for systematic investigation of volume collapse phenomena in rare-earth materials.

The GW Compendium: A Practical Guide to Theoretical Photoemission Spectroscopy

The GW approximation in electronic structure theory has become a widespread tool for predicting electronic excitations in chemical compounds and materials. In the realm of theoretical spectroscopy, the GW method provides access to charged excitations as measured in direct or inverse photoemission spectroscopy. The number of GW calculations in the past two decades has exploded with increased computing power and modern codes. The success of GW can be attributed to many factors: favorable scaling with respect to system size, a formal interpretation for charged excitation energies, the importance of dynamical screening in real systems, and its practical combination with other theories. In this review, we provide an overview of these formal and practical considerations. We expand, in detail, on the choices presented to the scientist performing GW calculations for the first time. We also give an introduction to the many-body theory behind GW, a review of modern applications like molecules and surfaces, and a perspective on methods which go beyond conventional GW calculations. This review addresses chemists, physicists and material scientists with an interest in theoretical spectroscopy. It is intended for newcomers to GW calculations but can also serve as an alternative perspective for experts and an up-to-date source of computational techniques.

Revealing the Nature of Antiferroquadrupolar Ordering in Cerium Hexaboride: CeB_{6}

The cerium hexaboride (CeB_{6}) f-electron compound displays a rich array of low-temperature magnetic phenomena, including a "magnetically hidden" order, identified as multipolar in origin via advanced x-ray scattering. From first-principles electronic-structure results, we find that the antiferroquadrupolar (AFQ) ordering in CeB_{6} arises from crystal-field splitting and yields a band structure in agreement with experiments. With interactions of p electrons between Ce and B_{6} being small, the electronic state of CeB_{6} is suitably described as Ce(4f^{1})^{3+}(e^{-})(B_{6})^{2-}. The AFQ state of orbital spins is caused by an exchange interaction induced through spin-orbit interaction, which also splits the J=5/2 state into a Γ_{8} ground state and a Γ_{7} excited state. Within the smallest antiferromagnetic (AFM) (111) configuration, an orbital-ordered AFQ state appears during charge self-consistency, and it supports the appearance of a "hidden" order. Hydrostatic pressure (either applied or chemically induced) stabilizes the AFM (AFQ) states over a ferromagnetic one, as observed at low temperatures.

Electronic correlations in cerium's high-pressure phases

Under high pressure, cerium exhibits three distinct phases, namely [Formula: see text], [Formula: see text], and ϵ-cerium. It is unclear whether the 4f electronic correlations will play a vital role in these phases or not. By utilizing the combination of traditional density functional theory and single-site dynamical mean-field theory, we tried to calculate the electronic structures of cerium's high-pressure phases. Their momentum-resolved spectral functions, total and 4f partial density of states, local self-energy functions, and 4f electronic configurations were exhaustively studied. The calculated results show that the correlated 4f bands strongly hybridize with the conducting spd bands around the Fermi level. The Matsubara self-energy functions exhibit Fermi-liquid like characteristic in the low-frequency regime. In addition, the fluctuations among the 4f atomic eigenstates are somewhat prominent (especially for the ϵ phase), which lead to slight modification of the 4f occupancy. It is suggested that the 4f electrons in these phases tend to be itinerant.

Directly patching high-level exchange-correlation potential based on fully determined optimized effective potentials

The key element in Kohn-Sham (KS) density functional theory is the exchange-correlation (XC) potential. We recently proposed the exchange-correlation potential patching (XCPP) method with the aim of directly constructing high-level XC potential in a large system by patching the locally computed, high-level XC potentials throughout the system. In this work, we investigate the patching of the exact exchange (EXX) and the random phase approximation (RPA) correlation potentials. A major challenge of XCPP is that a cluster's XC potential, obtained by solving the optimized effective potential equation, is only determined up to an unknown constant. Without fully determining the clusters' XC potentials, the patched system's XC potential is "uneven" in the real space and may cause non-physical results. Here, we developed a simple method to determine this unknown constant. The performance of XCPP-RPA is investigated on three one-dimensional systems: H₂₀, H₁₀Li₈, and the stretching of the H₁₉-H bond. We investigated two definitions of EXX: (i) the definition based on the adiabatic connection and fluctuation dissipation theorem (ACFDT) and (ii) the Hartree-Fock (HF) definition. With ACFDT-type EXX, effective error cancellations were observed between the patched EXX and the patched RPA correlation potentials. Such error cancellations were absent for the HF-type EXX, which was attributed to the fact that for systems with fractional occupation numbers, the integral of the HF-type EXX hole is not -1. The KS spectra and band gaps from XCPP agree reasonably well with the benchmarks as we make the clusters large.

Towards a First-Principles Determination of Effective Coulomb Interactions in Correlated Electron Materials: Role of Intershell Interactions

The determination of the effective Coulomb interactions to be used in low-energy Hamiltonians for materials with strong electronic correlations remains one of the bottlenecks for parameter-free electronic structure calculations. We propose and benchmark a scheme for determining the effective local Coulomb interactions for charge-transfer oxides and related compounds. Intershell interactions between electrons in the correlated shell and ligand orbitals are taken into account in an effective manner, leading to a reduction of the effective local interactions on the correlated shell. Our scheme resolves inconsistencies in the determination of effective interactions as obtained by standard methods for a wide range of materials, and allows for a conceptual understanding of the relation of cluster model and dynamical mean field-based electronic structure calculations.

Phase dependent structural and electronic properties of lanthanum orthophosphate (LaPO4)

We study the phase-dependent structural and electronic properties of bulk LaPO4, using density functional theory (DFT). The applicability of conventional semi-local and hybrid functionals in predicting structural and electronic properties of monoclinic and hexagonal LaPO4 is evaluated by comparing results to available experimental data. The monoclinic LaPO4 was found to be more stable than the hexagonal phase in ambient conditions with a small energy difference, suggesting a possibility of a phase transition. Both the phases in the bulk form are found to be diamagnetic with indirect energy gaps. These results are consistent with available experimental results. In the monoclinic phase, the hybrid functionals predict indirect band gap at about 8 eV. Furthermore, the calculated indirect-direct transition energy offset (ΔE) in the hexagonal phase was three times lower than the monoclinic phase. Our calculations based on hybrid functionals also reveal that the states near the conduction band edge in the hexagonal LaPO4 are strongly hybridized between La and PO4 states. By analyzing the band dispersion around the band edges, we show that the hexagonal phase has lighter electron effective mass, as compared to the monoclinic phase. With a larger energy gap, smaller ΔE, and smaller electron effective mass, the hexagonal LaPO4 might be a promising candidate material as an n-type transparent oxide.

First-principles study of relative stability of rutile and anatase TiO2 using the random phase approximation

By considering high-order correlations using the random phase approximation, rutile is correctly predicted to be more stable than anatase.

New developments in micro-X-ray diffraction and X-ray absorption spectroscopy for high-pressure research at 16-BM-D at the Advanced Photon Source

The monochromator and focusing mirrors of the 16-BM-D beamline, which is dedicated to high-pressure research with micro-X-ray diffraction (micro-XRD) and X-ray absorption near edge structure (XANES) (6-45 keV) spectroscopy, have been recently upgraded. Monochromatic X-rays are selected by a Si (111) double-crystal monochromator operated in an artificial channel-cut mode and focused to 5 μm × 5 μm (FWHM) by table-top Kirkpatrick-Baez type mirrors located near the sample stage. The typical X-ray flux is ∼5 × 10(8) photons/s at 30 keV. The instrumental resolution, Δq/qmax, reaches to 2 × 10(-3) and is tunable through adjustments of the detector distance and X-ray energy. The setup is stable and reproducible, which allows versatile application to various types of experiments including resistive heating and cryogenic cooling as well as ambient temperature compression. Transmission XANES is readily combined with micro-XRD utilizing the fixed-exit feature of the monochromator, which allows combined XRD-XANES measurements at a given sample condition.

Cerium; crystal structure and position in the periodic table

The properties of the cerium metal have intrigued physicists and chemists for many decades. In particular a lot of attention has been directed towards its high pressure behavior, where an isostructural volume collapse (γ phase → α phase) has been observed. Two main models of the electronic aspect of this transformation have been proposed; one where the 4f electron undergoes a change from being localized into an itinerant metallic state, and one where the focus is on the interaction between the 4f electron and the conduction electrons, often referred to as the Kondo volume collapse model. However, over the years it has been repeatedly questioned whether the cerium collapse really is isostructural. Most recently, detailed experiments have been able to remove this worrisome uncertainty. Therefore the isostructural aspect of the α-γ transition has now to be seriously addressed in the theoretical modeling, something which has been very much neglected. A study of this fundamental characteristic of the cerium volume collapse is made in present paper and we show that the localized ⇌ delocalized 4f electron picture provides an adequate description of this unique behavior. This agreement makes it possible to suggest that an appropriate crossroad position for cerium in The Periodic Table.

γ-α isostructural transition in cerium

We present zero-temperature first-principles calculations of elemental cerium and we compute its pressure-volume phase diagram within a theoretical framework able to describe simultaneously both the α and the γ phases. A surprising result revealed by our study is the presence of a clear signature of the transition at zero temperature and that this signature can be observed if and only if the spin-orbit coupling is taken into account. Our calculations indicate that the transition line in the pressure-temperature phase diagram of this material has a low-T critical point at negative pressures, placed very close to zero temperature. This suggests that cerium is very close to being "quantum critical," in agreement with recent experiments.