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We introduce three developments within the stochastic many-body perturbation theory: efficient evaluation of off-diagonal self-energy terms, construction of Dyson orbitals, and stochastic constrained random phase approximation. The stochastic approaches readily handle systems with thousands of atoms. We use them to explore the electronic states of twisted bilayer graphene (tBLG) characterized by giant unit cells and correlated electronic states. We document the formation of electron localization under compression; weakly correlated states are merely shifted in energy. We demonstrate how to efficiently downfold the correlated subspace on a model Hamiltonian with a screened frequency-dependent two-body interaction. For the 6° tBLG system, the onsite interactions are between 200 and 300 meV under compression. The Dyson orbitals exhibit spatial distribution similar to the mean-field single-particle states. Under pressure, the electron-electron interactions increase in the localized states; however, the dynamical screening does not fully balance the dominant bare Coulomb interaction.

Molecular excitations in the liquid-phase environment are renormalized by the surrounding solvent molecules. Herein, we employ the GW approximation to investigate the solvation effects on the ionization energy of phenol in various solvent environments. The electronic effects differ by up to 0.4 eV among the five investigated solvents. This difference depends on both the macroscopic solvent polarizability and the spatial decay of the solvation effects. The latter is probed by separating the electronic subspace and the GW correlation self-energy into fragments. The fragment correlation energy decays with increasing intermolecular distance and vanishes at ~9 angstroms, and this pattern is independent of the type of solvent environment. The 9 angstrom cutoff defines an effective interacting volume within which the ionization energy shift per solvent molecule is proportional to the macroscopic solvent polarizability. Finally, we propose a simple model for computing the ionization energies of molecules in an arbitrary solvent environment.

Within many-body perturbation theory, Hedin's formalism offers a systematic way to iteratively compute the self-energy $\Sigma$ of any interacting system, provided one can evaluate the interaction vertex $\Gamma$ exactly. This is however impossible in general, for it involves the functional derivative of $\Sigma$ with respect to the Green's function. Here, we analyze the structure of this derivative, splitting it into four contributions and outlining the type of quasiparticle interactions that each of them generate. Moreover we show how, in the implementation of self-consistency, the action of these contributions can be classified into two: a quantitative renormalization of previously included interaction terms, and the inclusion of qualitatively novel interaction terms through successive functional derivatives of $\Gamma$ itself, neglected until now. Implementing this latter type of self-consistency can extend the validity of Hedin's equations towards the high interaction limit, as we show in the example of the Hubbard dimer. Our analysis also provides a unifying perspective on the perturbation theory landscape, showing how the T-matrix approach is completely contained in Hedin's formalism., Comment: Main manuscript: 6 pages, 3 figures. SI: 15 pages, 3 figures

The vertex function ($\Gamma$) within the Green's function formalism encapsulates information about all higher-order electron-electron interaction beyond those mediated by density fluctuations. Herein, we present an efficient approach that embeds vertex corrections in the one-shot $GW$ correlation self-energy for isolated and periodic systems. The vertex-corrected self-energy is constructed through the proposed separation-propagation-recombination procedure: the electronic Hilbert space is separated into an active space and its orthogonal complement denoted as the "rest"; the active component is propagated by a space-specific effective Hamiltonian different from the rest. The vertex corrections are introduced by a rescaled time-dependent non-local exchange interaction. The direct $\Gamma$ correction to the self-energy is further updated by adjusting the rescaling factor in a self-consistent post-processing circle. Our embedding method is tested mainly on donor-acceptor charge-transfer systems. The embedded vertex effects consistently and significantly correct the quasiparticle energies of the gap-edge states. The fundamental gap is generally improved by 1-3 eV upon the one-shot $GW$ approximation. Furthermore, we provide an outlook for applications of (embedded) vertex corrections in calculations of extended solids.

Wannier functions have become a powerful tool in the electronic structure calculations of extended systems. The generalized Pipek-Mezey Wannier functions exhibit appealing characteristics (e.g., reaching an optimal localization and the separation of the $\sigma$-$\pi$ orbitals) when compared with other schemes. However, when applied to giant nanoscale systems, the orbital localization suffers from a large computational cost overhead when one is interested in localized states in a small fragment of the system. Herein we present a swift, efficient, and robust approach for obtaining regionally localized orbitals of a subsystem within the generalized Pipek-Mezey scheme. The proposed algorithm introduces a reduced workspace and sequentially exhausts the entire orbital space until the convergence of the localization functional. It tackles systems with $\sim$10000 electrons within 0.5 hours with no loss in localization quality compared to the traditional approach. Regionally localized orbitals with a higher extent of localization are obtained via judiciously extending the subsystem's size. Exemplifying on large bulk and a 4-nm wide slab of diamond with NV$^-$ center, we demonstrate the methodology and discuss how the choice of the localization region affects the excitation energy of the defect. Furthermore, we show how the sequential algorithm is easily extended to stochastic methodologies that do not provide individual single-particle eigenstates. It is thus a promising tool to obtain regionally localized states for solving the electronic structure problems of a subsystem embedded in giant condensed systems., Comment: 36 pages, 7 figures, 2 tables

New stochastic approaches for the computation of electronic excitations are developed within the many-body perturbation theory. Three approximations to the electronic self-energy are considered: $G_0W_0$, $G_0W_0^tc$, and $G_0W_0^{tc}\Gamma_x$. All three methods are formulated in the time domain and the latter two incorporate non-local vertex corrections. In case of $G_0W_0^{tc}\Gamma_x$, the vertex corrections are included both in the screened Coulomb interaction and in the expression for the self-energy. The implementation of the three approximations is verified by comparison to deterministic results for a set of small molecules. The performance fully stochastic implementation is tested on acene molecules, C$_{60}$ and PC$_{60}$BM. The vertex correction appears crucial for the description of unoccupied states. Unlike conventional (deterministic) approaches, all three stochastic methods scale linearly with the number of electrons., Comment: 18 pages, 5 figures

Accurate predictions of charge excitation energies of molecules in the disordered condensed phase are central to the chemical reactivity, stability, and optoelectronic properties of molecules and critically depend on the specific environment. Herein, we develop a stochastic GW method for calculating these charge excitation energies. The approach employs maximally localized electronic states to define the electronic subspace of a molecule and the rest of the system, both of which are randomly sampled. We test the method on three solute-solvent systems: phenol, thymine, and phenylalanine in water. The results are in excellent agreement with the previous high-level calculations and available experimental data. The stochastic calculations for supercells representing the solvated systems are inexpensive and require $\sim 1000$ CPU$\cdot$hrs. We find that the coupling with the environment accounts for $\sim40\%$ of the total correlation energy. The solvent-to-solute feedback mechanism incorporated in the molecular correlation term causes up to 0.6 eV destabilization of the QP energy. Simulated photo-emission spectra exhibit red shifts, state-degeneracy lifting, and lifetime shortening. Our method provides an efficient approach for an accurate study of excitations of large molecules in realistic condensed phase environments., 9 pages, 4 figures

Photo-emission spectroscopy directly probes individual electronic states, ranging from single excitations to high-energy satellites, which simultaneously represent multiple quasiparticles (QPs) and encode information about electronic correlation. First-principles description of the spectra requires an efficient and accurate treatment of all many-body effects. This is especially challenging for inner valence excitations where the single QP picture breaks down. Here, we provide the full valence spectra of small closed-shell molecules, exploring the independent and interacting quasiparticle regimes, computed with the fully-correlated adaptive sampling configuration interaction (ASCI) method. We critically compare these results to calculations with the many-body perturbation theory, based on the $GW$ and vertex corrected $GW\Gamma$ approaches. The latter explicitly accounts for two-QP quantum interactions, which have been often neglected. We demonstrate that for molecular systems, the vertex correction universally improves the theoretical spectra, and it is crucial for accurate prediction of QPs as well as capturing the rich satellite structures of high-energy excitations. $GW\Gamma$ offers a unified description across all relevant energy scales. Our results suggest that the multi-QP regime corresponds to dynamical correlations, which can be described via perturbation theory., Comment: 14 pages, 3 figures, plus SI

The performance of organic semiconductor devices is linked to highly ordered nanostructures of self-assembled molecules and polymers. Many-body perturbation theory is employed to study the excited states in bulk copolymers. The results show that acceptors in the polymer scaffold introduce a, hitherto unrecognized, conduction impurity band that leads to electron localization. The donor states are responsible for the formation of conjugated bands, which are only mildly perturbed by the presence of the acceptors. Along the polymer axis, the nonlocal electronic correlations among copolymer strands hinder efficient band transport, which is, however, strongly enhanced across individual chains. Holes are most effectively transported along the π-π stacking, while electrons in the impurity band follow the edge-to-edge directions. The copolymers exhibit regions with inverted transport polarity, in which electrons and holes are efficiently transported in mutually orthogonal directions.

Summary: Neutral zinc alkoxide complexes show high activity toward the ring-opening polymerization of cyclic esters and carbonates, to generate biodegradable plastics applicable in several areas. Herein, we use a ferrocene-chelating heteroscorpionate complex in redox-switchable polymerization reactions, and we show that it is a moderately active catalyst for the ring-opening polymerization of L-lactide, ɛ-caprolactone, trimethylene carbonate, and δ-valerolactone. Uniquely for this type of catalyst, the oxidized complex has a similar polymerization activity as the corresponding reduced compound, but displays significantly different rates of reaction in the case of trimethylene carbonate and δ-valerolactone. Investigations of the oxidized compound suggest the presence of an organic radical rather than an Fe(III) complex. Electronic structure and density functional theory (DFT) calculations were performed to support the proposed electronic states of the catalytic complex and to help explain the observed reactivity differences. The catalyst was also compared with a monomeric phenoxide complex to show the influence of the phosphine-zinc interaction on catalytic properties. : Chemistry; Inorganic Chemistry; Catalysis; Polymer Chemistry Subject Areas: Chemistry, Inorganic Chemistry, Catalysis, Polymer Chemistry

One of the outstanding puzzles in the photoelectron spectroscopy of water anion clusters, which serve as precursors to the hydrated electron, is that the excess electron has multiple vertical detachment energies (VDEs), with different groups seeing different distributions of VDEs. We have studied the photoelectron spectroscopy of water cluster anions using simulation techniques designed to mimic the different ways that water cluster anions are produced experimentally. Our simulations take advantage of density functional theory-based Born-Oppenheimer molecular dynamics with an optimally tuned range-separated hybrid functional that is shown to give outstanding accuracy for calculating electron binding energies for this system. We find that our simulations are able to accurately reproduce the experimentally observed VDEs for cluster anions of different sizes, with different VDE distributions observed depending on how the water cluster anions are prepared. For cluster anion sizes up to 20 water molecules, we see that the excess electron always resides on the surface of the cluster and that the different discrete VDEs result from the discrete number of hydrogen bonds made to the electron by water molecules on the surface. Clusters that are less thermally equilibrated have surface waters that tend to make single H-bonds to the electron, resulting in lower VDEs, while clusters that are more thermally equilibrated have surface waters that prefer to make two H-bonds to the electron, resulting in higher VDEs.

Quasiparticle (QP) excitations are extremely important for understanding and predicting charge transfer and transport in molecules, nanostructures, and extended systems. Since density functional theory (DFT) within the Kohn-Sham (KS) formulation does not provide reliable QP energies, many-body perturbation techniques such as the GW approximation are essential. The main practical drawback of GW implementations is the high computational scaling with system size, prohibiting its use in extended, open boundary systems with many dozens of electrons or more. Recently, a stochastic formulation of GW (sGW) was presented (Phys. Rev. Lett. 2014, 113, 076402) with a near-linear-scaling complexity, illustrated for a series of silicon nanocrystals reaching systems of more than 3000 electrons. This advance provides a route for many-body calculations on very large systems that were impossible with previous approaches. While earlier we have shown the gentle scaling of sGW, its accuracy was not extensively demonstrated. Therefore, we show that this new sGW approach is very accurate by calculating the ionization energies of a group of sufficiently small molecules where a comparison to other GW codes is still possible. Using a set of 10 such molecules, we demonstrate that sGW provides reliable vertical ionization energies in close agreement with benchmark deterministic GW results (J. Chem. Theory Comput, 2015, 11, 5665), with mean (absolute) deviation of 0.05 and 0.09 eV. For completeness, we also provide a detailed review of the sGW theory and numerical implementation.

We report structural properties and diffusivity of liquid Fe0.96O0.04 over a density range of 5.421–11.620 g cm−3, corresponding to pressures of 0–330 GPa and 2200–5500 K, using first-principles molecular dynamics. We predict a change in compression mechanism near 8 g cm−3. At lower density, Fe and O coordinations increase from ~10 to ~13 and ~3 to ~6, respectively, the average Fe–O distance increases from ~1.81 A to ~1.88 A, and the Fe–Fe distance remains essentially constant. Calculated oxygen diffusivities, DO, remain constant over the corresponding pressure range, consistent with experiments. For larger densities, interatomic distances and diffusion rates for both species decrease monotonically. Oxygen coordination reaches a maximum of ~8.5 at ~9.4 g cm−3, indicating a local B2 packing for Fe around O under conditions of the Earth's core. The pressure-induced structural evolution provides an explanation for a previously reported change in pressure dependence of oxygen solubility in liquid iron.

Chemical diffusion rates of Si and Cr in liquid iron have been measured over the P – T range of 1–18 GPa and 1873–2428 K. The experiments were performed using a multi-anvil apparatus with diffusion couples comprised of pure iron and iron alloy placed end to end in a vertical orientation. In order to extend our dataset to the Earth’s core–mantle boundary and to compare experimental data with theoretical diffusion rates calculated under laboratory-accessible conditions, we have also performed first principles molecular dynamic simulations (FP-MD) and calculated self-diffusion coefficients and activation parameters for Si, Cr, and Fe diffusion in liquid Fe, Fe 0.92 Si 0.08 and Fe 0.92 Cr 0.08 compositions over the P – T range of 1 bar–135 GPa and 2200–5500 K. Over the entire range of pressures and temperatures studied using both methods, diffusion coefficients are described well using an exponential function of the homologous temperature relation, D = D h exp(− gT h ), where T h = T m / T , T m is the melting temperature at the pressure of interest and g and D h are constants. Our findings indicate constant diffusivities of approximately 4 × 10 −9 m 2 s −1 for Si and Cr and 5 × 10 −9 m 2 s −1 for Fe along the melting curve from ambient to core pressures in all liquid compositions studied, with an increase of ∼0.8 log units at T = 2 T m . Differences between experimental data and computational results are less than 0.1 log units. Structural properties of liquid iron alloys analyzed using partial radial distribution functions (RDFs) show the average distance between two Fe atoms, r Fe–Fe , is identical to that of r Fe–Si and r Fe–Cr over the entire P – T range of study, which supports that the diffusion of Si and Cr (and thus likely other species of similar atomic radii) occurs via direct substitution with Fe. Diffusion coefficients and interatomic distances used to calculate liquid viscosities via the Stokes–Einstein relation yield constant viscosity along the melting curve of ∼6 mPa s for liquid Fe, ∼7 mPa s for liquid Fe 0.92 Cr 0.08 , and ∼8 mPa s for liquid Fe 0.92 Si 0.08 , with a decrease of ∼0.8 log units at T = 2 T m . The data can also be reproduced within P – T conditions. Verification of a homologous temperature dependence of diffusion in liquid metals, as well as the excellent agreement between experimental results and FP-MD simulations, provides a new and simple framework for interpreting and modeling mass transport processes of liquid iron alloys in all planetary bodies regardless of size. Our results are used to evaluate the kinetics of metal–silicate chemical equilibration during core formation and diffusivity contrasts across a solid–liquid metal interface, i.e. at the inner core boundary.

Nonmonotonic bending-induced changes of fundamental band gaps and quasiparticle energies are observed for realistic nanoscale phosphorene nanosheets. Calculations using stochastic many-body perturbation theory (sGW) show that even slight curvature causes significant changes in the electronic properties. For small bending radii (< 4 nm) the band-gap changes from direct to indirect. The response of phosphorene to deformation is strongly anisotropic (different for zig-zag vs. armchair bending) due to an interplay of exchange and correlation effects. Overall, our results show that fundamental band gaps of phosphorene sheets can be manipulated by as much as 0.7 eV depending on the bending direction., 23 pages, 5 figures, 3 tables

We develop a stochastic approach to time-dependent density functional theory with optimally tuned range-separated hybrids containing nonlocal exchange, for calculating optical spectra. The attractive electron-hole interaction, which leads to the formation of excitons, is included through a time-dependent linear-response technique with a nonlocal exchange interaction which is computed very efficiently through a stochastic scheme. The method is inexpensive and scales quadratically with the number of electrons, at almost the same (low) cost of time dependent Kohn-Sham with local functionals. Our results are in excellent agreement with experimental data, and the efficiency of the approach is demonstrated on large finite phosphorene sheets containing up to 1958 valence electrons.

Splittings of the translation–rotation (TR) eigenstates of the solid light-molecule endofullerenes M@C60 (M = H2, H2O, HF) attributed to the symmetry breaking have been observed in the infrared (IR) and inelastic neutron scattering spectra of these species in the past couple of years. In a recent paper [Felker et al., Phys. Chem. Chem. Phys., 2017, 19, 31274], we established that the electrostatic, quadrupolar interaction between the guest molecule M and the twelve nearest-neighbor C60 cages of the solid is the main source of the symmetry breaking. The splittings of the three-fold degenerate ground states of the endohedral ortho-H2, ortho-H2O and the j = 1 level of HF calculated using this model were found to be in excellent agreement with the experimental results. Utilizing the same electrostatic model, this theoretical study investigates the effects of the symmetry breaking on the excited TR eigenstates of the three species, and how they manifest in their simulated low-temperature (5–6 K) near-IR (NIR) and far-IR (FIR) spectra. The TR eigenstates are calculated variationally for both the major P and minor H crystal orientations. For the H orientation, the calculated splittings of all of the TR levels of these species are less than 0.1 cm−1. For the dominant P orientation, the splittings vary strongly depending on the character of the excitations involved. In all of the species, the splittings of the higher rotationally excited levels are comparable in magnitude to those for the j = 1 levels. For the levels corresponding to purely translational excitations, the calculated splittings are about an order of magnitude smaller than those of the purely rotational eigenstates. Based on the computed TR eigenstates, the low-temperature NIR (for M = H2) and FIR (for M = HF and H2O) spectra are simulated for both the P and H orientations, and also combined as their weighted sum (0.15H + 0.85P). The weighted sum spectra computed for M = H2 and HF match quantitatively the corresponding measured spectra, while for M = H2O, the weighted sum FIR spectrum predicts features that can potentially be observed experimentally.

We show that a rigid scissors-like

Absorption cross-section spectra for gold nanoparticles were calculated using fully quantum Stochastic Density Functional Theory and a classical Finite-Difference Time Domain (FDTD) Maxwell solver. Spectral shifts were monitored as a function of size (1.3-3.1 nm) and shape (octahedron, cubeoctahedron, and truncated cube). Even though the classical approach is forced to fit the quantum TDDFT at 3.1nm, at smaller sizes there is a significant deviation as the classical theory is unable to account for peak splitting and spectral blue shifts even after quantum spectral corrections. We attribute the failure of classical methods at predicting these features to quantum effects and low density of states in small nanoparticles. Classically, plasmon resonances are modeled as collective conduction electron excitations, but at small nanoparticle size these excitations transition to few or even individual conductive electron excitations, as indicated by our results.

Splittings of the translation-rotation (TR) eigenstates of the solid light-molecule endofullerenes M@C60 (M = H2, H2O, HF) attributed to the symmetry breaking have been observed in the infrared (IR) and inelastic neutron scattering spectra of these species in the past couple of years. In a recent paper [Felker et al., Phys. Chem. Chem. Phys., 2017, 19, 31274], we established that the electrostatic, quadrupolar interaction between the guest molecule M and the twelve nearest-neighbor C60 cages of the solid is the main source of the symmetry breaking. The splittings of the three-fold degenerate ground states of the endohedral ortho-H2, ortho-H2O and the j = 1 level of HF calculated using this model were found to be in excellent agreement with the experimental results. Utilizing the same electrostatic model, this theoretical study investigates the effects of the symmetry breaking on the excited TR eigenstates of the three species, and how they manifest in their simulated low-temperature (5-6 K) near-IR (NIR) and far-IR (FIR) spectra. The TR eigenstates are calculated variationally for both the major P and minor H crystal orientations. For the H orientation, the calculated splittings of all of the TR levels of these species are less than 0.1 cm-1. For the dominant P orientation, the splittings vary strongly depending on the character of the excitations involved. In all of the species, the splittings of the higher rotationally excited levels are comparable in magnitude to those for the j = 1 levels. For the levels corresponding to purely translational excitations, the calculated splittings are about an order of magnitude smaller than those of the purely rotational eigenstates. Based on the computed TR eigenstates, the low-temperature NIR (for M = H2) and FIR (for M = HF and H2O) spectra are simulated for both the P and H orientations, and also combined as their weighted sum (0.15H + 0.85P). The weighted sum spectra computed for M = H2 and HF match quantitatively the corresponding measured spectra, while for M = H2O, the weighted sum FIR spectrum predicts features that can potentially be observed experimentally.

We introduce the concept of sparse stochastic compression, an efficient stochastic sampling of any general function. The technique uses sparse stochastic orbitals (SSOs), short vectors that sample a small number of space points. As a first demonstration, SSOs are applied in conjunction with simple direct projection to accelerate our recent stochastic $GW$ technique; the new developments enable accurate prediction of ${G}_{0}{W}_{0}$ quasiparticle energies and gaps for systems with up to ${N}_{e}g10,000$ electrons, with small statistical errors of $\ifmmode\pm\else\textpm\fi{}0.05\phantom{\rule{0.28em}{0ex}}\mathrm{eV}$ and using less than 2000 core CPU hours. Overall, stochastic $GW$ scales now linearly (and often sublinearly) with ${N}_{e}.$

A stochastic cumulant GW method is presented, allowing us to map the evolution of photoemission spectra, quasiparticle energies, lifetimes and emergence of collective excitations from molecules to bulk-like systems with up to thousands of valence electrons, including Si nanocrystals and nanoplatelet. The quasiparticle energies rise due to their coupling with collective shake-up (plasmon) excitations, and this coupling leads to significant spectral weight loss (up to 50% for the low energy states), shortening the lifetimes and shifting the spectral features to lower energy by as much as 0.6 eV. Such features are common to all the systems studied irrespective of their size and shape. For small and low dimensional systems the surface plasmon resonances affect the frequency of the collective excitation and position of the satellites., Comment: 6 pages, 4 figures

Symmetry breaking has been recently observed in the endofullerenes M@C

Symmetry breaking has been recently observed in the endofullerenes M@C60 (M = H2, HF, H2O), manifesting in the splittings of the three-fold degenerate ground states of the endohedral ortho-H2, ortho-H2O and the j = 1 level of HF. The nature of the interaction causing the symmetry breaking is established in this study. A fragment of the solid C60 is considered, comprised of the central C60 molecule surrounded by twelve nearest-neighbor (NN) C60 molecules. The fullerenes have either P (major) or H (minor) orientational orderings, and are assumed to be rigid with Ih symmetry. Only the central C60 is occupied by the guest molecule M, while the NN fullerenes are all empty. The key proposition of the study is that the electrostatic interactions between the charge densities on the NN C60 molecules and that on M inside the central C60 give rise to the symmetry breaking responsible for the measured level splittings. Using this model, the M@C60 level splittings of interest are calculated variationally and using perturbation theory, for both the P and H orientations. Those obtained for the dominant P orientation are in excellent agreement with the experimental results, with respect to the splitting magnitudes and patterns, for all three M@C60 systems considered, pointing strongly to the quadrupolar M–NN interactions as the main cause of the symmetry breaking. The level splittings calculated for the H orientation are about 30 times smaller than the ones in the P orientation.

Permingeatite from a new occurrence, the Přibram uranium-base metal ore district (central Bohemia, Czech Republic), has been studied in detail. Its occurrence is similar to the type occurrence in Předbořice (Czech Republic). Based on electron microprobe analysis, the empirical formula of the studied permingeatite (mean of 10 point analyses, based on Sb + Cu + Fe + Se + S = 8 apfu ) is Cu 3.00 (Sb 0.99 Fe 0.04 ) ∑1.03 (Se 3.74 S 0.23 ) ∑3.97 . The unit-cell parameters refined from powder X-ray diffraction data are a 5.6323(2) A, c 11.2354(7) A, with V 356.41(2) A 3 (for space group I 4 ¯ 2 m ). The Se-S substitution is characteristic for the permingeatite from Přibram, in contrast to permingeatite from Předbořice, where the As-Sb substitution dominates. Regarding substitution trends, only two, Sb-As and S-Se, play a role in the luzonite group minerals. The only other element (as documented by the present study) which enters the structure of the luzonite-group minerals in considerable concentrations is Fe. Raman spectroscopy was used to characterize vibrational properties of the luzonite group of minerals. The dominant feature in the Raman spectra of the studied minerals is a suite of spectral bands that corresponds to the stretching and bending vibrations of tetrahedral XY 4 ( X = As/Sb; Y = S/Se) groups. Intrinsic shifts in observed energies for distinct studied minerals are connected with different elemental compositions of the tetrahedral groups. The reflectance data obtained from the studied permingeatite are close to the published data, but more significant differences were found, particularly in the areas of 420–500 nm and about 640 nm. The studied association was formed, based on the presence of umangite, at temperatures below 112 °C.

We show that a rigid scissors-like GW self-consistency approach, labeled here Δ¯GW0, can be trivially implemented at zero additional cost for large scale one-shot G0W0 calculations. The method significantly improves one-shot G0W0 and for large systems is very accurate. Δ¯GW0 is similar in spirit to evGW0 where the self-consistency is only applied on the eigenvalues entering Green’s function, while both W and the eigenvectors of Green’s function are held fixed. Δ¯GW0 further assumes that the shift of the eigenvalues is rigid scissors-like so that all occupied states are shifted by the same amount and analogously for all the unoccupied states. We show that this results in a trivial modification of the time-dependent G0W0 self-energy, enabling an a posteriori self-consistency cycle. The method is applicable for our recent stochastic-GW approach, thereby enabling self-consistent calculations for giant systems with thousands of electrons. The accuracy of Δ¯GW0 increases with the system size. For molecules, it is up to 0.4-0.5 eV away from coupled-cluster single double triple (CCSD(T)), but for tetracene and hexacene, it matches the ionization energies from both CCSD(T) and evGW0 to better than 0.05 eV. For solids, as exemplified here by periodic supercells of semiconductors and insulators with 6192 valence electrons, the method matches evGW0 quite well and both methods are in good agreement with the experiment.We show that a rigid scissors-like GW self-consistency approach, labeled here Δ¯GW0, can be trivially implemented at zero additional cost for large scale one-shot G0W0 calculations. The method significantly improves one-shot G0W0 and for large systems is very accurate. Δ¯GW0 is similar in spirit to evGW0 where the self-consistency is only applied on the eigenvalues entering Green’s function, while both W and the eigenvectors of Green’s function are held fixed. Δ¯GW0 further assumes that the shift of the eigenvalues is rigid scissors-like so that all occupied states are shifted by the same amount and analogously for all the unoccupied states. We show that this results in a trivial modification of the time-dependent G0W0 self-energy, enabling an a posteriori self-consistency cycle. The method is applicable for our recent stochastic-GW approach, thereby enabling self-consistent calculations for giant systems with thousands of electrons. The accuracy of Δ¯GW0 increases with the system size. For molecules, it ...

UO 2 SO 4 ·2.5H 2 O is monoclinic, space group P 2 1 / c (No. 14), unit-cell parameters of a = 6.7260(1)A, b = 12.4210(2)A, c = 16.8270(3)A, β = 90.781(1)° with unit-cell volume V = 1405.66(4)A 3 , Z = 8, D calc = 3.84 g/cm 3 . Two distinct uranium atoms, present as uranyl (UO 2 ) 2+ , forming uranyl pentagonal bipyramids, two distinct sulfur atoms, forming sulfate tetrahedra and 17 oxygen atoms are present in the asymmetric part of its unit-cell. Two of oxygen atoms are water molecules bonded to the uranyl cation and one is water molecule bonded only by hydrogen-bonding. Crystal structure was refined fully anisotropically. Vibration modes of each molecular unit in Raman and infrared spectra were tentatively assigned and discussed, regarding refined structure. Inferred U–O lengths and hydrogen bond lengths are consistent with the crystal structure refinement.

Potarite, ideally PdHg, is reported in the literature to have compositions varying from PdHg or Pd(Hg,Au) to Pd3Hg2. Such a Pd3Hg2 phase is unknown in the synthetic Pd–Hg binary system. For the first time, Pd–Hg grains recovered from the historical Bom Sucesso alluvium, regarded as the type locality of Pd, are shown to consist of arborescent and lamellar intergrowths of two intermetallic compounds, compositionally close to empirical Pd(Hg,Au), i.e. auriferous potarite, and (Pd,Au)3Hg2. The Pd–Hg–Au grains have a rim of palladiferous Pt. The otherwise sharp Pd–Hg–Au intergrowths become diffuse at the contact with the palladiferous Pt rim. Both the Pd–Hg–Au compounds and the palladiferous Pt rim did not diffract using the electron-backscattered diffraction (EBSD) and powder X-ray microdiffraction techniques, indicating that they are poorly crystalline. Their poor crystallinity and the diffuse zone between the Pd–Hg–Au core and the Pt-rich overgrowth are suggestive of electrochemical metal precipitation from dilute solutions within the alluvium.

In exact density functional theory (DFT) the total ground-state energy is a series of linear segments between integer electron points, a condition known as "piecewise linearity". Deviation from this condition is indicative of poor predictive capabilities for electronic structure, in particular of ionization energies, fundamental gaps, and charge transfer. In this article, we take a new look at the deviation from linearity (i.e., curvature) in the solid-state limit by considering two different ways of approaching it: a large finite system of increasing size and a crystal represented by an increasingly large reference cell with periodic boundary conditions. We show that the curvature approaches vanishing values in both limits, even for functionals which yield poor predictions of electronic structure, and therefore can not be used as a diagnostic or constructive tool in solids. We find that the approach towards zero curvature is different in each of the two limits, owing to the presence of a compensating background charge in the periodic case. Based on these findings, we present a new criterion for functional construction and evaluation, derived from the size-dependence of the curvature, along with a practical method for evaluating this criterion. For large finite systems we further show that the curvature is dominated by the self-interaction of the highest occupied eigenstate. These findings are illustrated by computational studies of various solids, semiconductor nanocrystals, and long alkane chains., 12 pages, 5 figures

Charge carrier localization in extended atomic systems has been described previously as being driven by disorder, point defects or distortions of the ionic lattice. Here we show for the first time by means of first-principles computations that charge carriers can spontaneously localize due to a purely electronic effect in otherwise perfectly ordered structures. Optimally-tuned range-separated density functional theory and many-body perturbation calculations within the GW approximation reveal that in trans-polyacetylene and polythiophene the hole density localizes on a length scale of several nanometers. This is due to exchange-induced translational symmetry breaking of the charge density. Ionization potentials, optical absorption peaks, excitonic binding energies and the optimally-tuned range parameter itself all become independent of polymer length as it exceeds the critical localization scale. Moreover, lattice disorder and the formation of a polaron result from the charge localization in contrast to the traditional view that lattice distortions precede charge localization. Our results can explain experimental findings that polarons in conjugated polymers form instantaneously after exposure to ultrafast light pulses., Comment: 5 pages, 4 figures

A recently published generalized gradient approximation functional within density functional theory (DFT) has shown, in a few paradigm tests, an improved KS orbital description over standard (semi) local approximations. The characteristic feature of this functional is an enhancement factor that diverges like s ln(s) for large reduced density gradients s which leads to unusual properties. We explore the improved orbital description of this functional more thoroughly by computing the electronic band structure, band gaps, and the optical dielectric constants in semiconductors, Mott insulators, and ionic crystals. Compared to standard semilocal functionals, we observe improvement in both the band gaps and the optical dielectric constants. In particular, the results are similar to those obtained with orbital functionals or by perturbation theory methods in that it opens band gaps in systems described as metallic by standard (semi) local density functionals, e. g., Ge, alpha-Sn, and CdO. Funding Agencies|Deutsche Forschungsgemeinschaft (DFG) [STE1105/8-1, SFB840, B1]; Swedish Research Council [621-2011-4249]; VR

We performed first-principles calculations to obtain values of electrical ($\ensuremath{\sigma}$) and thermal conductivity ($\ensuremath{\kappa}$) for compressed aluminum liquid at temperatures and pressures up to 8000 K and 110 GPa. To do this we apply the Kubo-Greenwood formula via density functional perturbation theory to phase trajectories generated using first-principles molecular dynamics. Our results are consistent with measurements at low pressures, and indicate that electronic transport coefficients $\ensuremath{\sigma}$ and $\ensuremath{\kappa}$ increase under compression; with increasing temperature $\ensuremath{\sigma}$ decreases and $\ensuremath{\kappa}$ increases. Behavior in response to compression and heating are explained in terms of changes in occupation of conduction bands by thermally excited electrons. Based on the frequency dependence of $\ensuremath{\sigma}$, we further show that liquid aluminum is well described by the Drude picture over a wide range of conditions, confirming its free-electron nature. At high $P$ and $T$, our computed $\ensuremath{\sigma}$ and $\ensuremath{\kappa}$ yield Lorenz numbers up to 7$%$ lower than the theoretical value, indicating that the Wiedemann-Franz law remains approximately satisfied at extreme conditions. Using an electronically simple metal such as liquid Al as a guide to the behavior of more complex metals, we infer that present extrapolation-based estimates of $\ensuremath{\sigma}$ and $\ensuremath{\kappa}$ for the Earth's outer core may be 3--4 times too low.

Earth’s magnetic field is sustained by magnetohydrodynamic convection within the metallic liquid core. In a thermally advecting core, the fraction of heat available to drive the geodynamo is reduced by heat conducted along the core geotherm, which depends sensitively on the thermal conductivity of liquid iron and its alloys with candidate light elements. The thermal conductivity for Earth’s core is very poorly constrained, with current estimates based on a set of scaling relations that were not previously tested at high pressures. We perform first-principles electronic structure computations to determine the thermal conductivity and electrical resistivity for Fe, Fe–Si, and Fe–O liquid alloys. Computed resistivity agrees very well with existing shock compression measurements and shows strong dependence on light element concentration and type. Thermal conductivity at pressure and temperature conditions characteristic of Earth’s core is higher than previous extrapolations. Conductive heat flux near the core–mantle boundary is comparable to estimates of the total heat flux from the core but decreases with depth, so that thermally driven flow would be constrained to greater depths in the absence of an inner core.

The tribosphenic molar is a dental apomorphy of mammals and the molar type from which all derived types originated. Its enamel coat is expected to be ancestral: a thin, evenly distributed layer of radial prismatic enamel. In the bat Myotis myotis, we reinvestigated the 3D architecture of the dental enamel using serial sectioning combined with scanning electron microscopy analyses, biometrics of enamel prisms and crystallites, and X-ray diffraction. We found distinct heterotopies in enamel thickness (thick enamel on the convex sides of the crests, thin on the concave ones), angularity of enamel prisms, and in distribution of particular enamel types (prismatic, interprismatic, aprismatic) and demonstrated structural relations of these heterotopies to the cusp and crest organization of the tribosphenic molar. X-ray diffraction demonstrated that the crystallites composing the enamel are actually the aggregates of much smaller primary crystallites. The differences among particular enamel types in degree of crystallite aggregation and the variation in structural microstrain of the primary crystallites (depending upon the duration and the mechanical context of mineralization) represent factors not fully understood as yet that may contribute to the complexity of enamel microarchitecture in a significant way.