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Around half of the Earth's soil organic carbon (SOC) is presently stored in the Northern Hemisphere permafrost region. In polar permafrost regions, low temperatures particularly inhibit both the production and biodegradation of organic matter. Under such conditions, abiotic factors such as mesoclimate, pedogenic substrate or altitude are thought to be more important for soil development than biological factors. In Antarctica, biological factors are generally underestimated in soil development due to the rare occurrence of higher plants and the short time since deglaciation. In this study, we aim to assess the relationship between SOC and other soil properties related to the pedogenic factors or properties. Nine plots were investigated along the altitudinal gradient from 10 to 320 m in the deglaciated area of James Ross Island (Ulu Peninsula) using a parallel tea-bag decomposition experiment. SOC contents showed a positive correlation with the content of easily extractable glomalin-related soil protein (EE-GRSP; Spearman r=0.733, P=0.031) and the soil buffering capacity (expressed as ΔpH; Spearman r=0.817, P=0.011). The soil-available P was negatively correlated with altitude (Spearman r=-0.711, P=0.032), and the exchangeable Mg was negatively correlated with the rock fragment content (Spearman r=-0.683, P=0.050). No correlation was found between the available mineral nutrients (P, K, Ca and Mg) and SOC or GRSP. This may be a consequence of the inhibition of biologically mediated nutrient cycling in the soil. Therefore, the main factor influencing nutrient availability in these soils does not seem to the biotic environment; rather, the main impact appears to stem from the abiotic environment influencing the mesoclimate (altitude) or the level of weathering (rock content). Incubation in tea bags for 45 d resulted in the consumption and translocation of more labile polyphenolic and water-extractable organic matter, along with changes in the C content (increase of up to +0.53 % or decrease of up to −1.31 % C) and a decrease in the C:N ratio (from 12.5 to 7.1–10.2), probably due to microbial respiration and an increase in the abundance of nitrogen-binding microorganisms. Our findings suggest that one of the main variables influencing the SOC/GRSP content is not the altitude or coarse-fraction content (for which a correlation with SOC/GRSP was not found); rather, we suspect effects from other factors that are difficult to quantify, such as the availability of liquid water.

A potential effect of adjuvants/wetting agents added to the spray mixture on the water stability of soil aggregates (WSA) in agricultural soil was studied. Nine sites were chosen in the Czech Republic. Each site was mapped using representative soil pits (depth min. 1.3 m). A total of 54 mixed samples were collected from topsoil horizons on the selected sites. The samples were exposed to the action of four different types of wetting agents (organosilicone wetting agent; methyl ester of rapeseed oil; mixture of methyl ester palmitic and oleic acids; isodecyl alcohol ethoxylate), which are the most common wetting agents used in agriculture in the Czech Republic. WSA was determined before and after the addition of wetting agents (WA). Initial WSA values were at the same level in a majority of sampling points. Two sites were an exception, on which Haplic Luvisols and Relictistagnic Fluvisols occurred. These soil types featured the lowest WSA values. After the addition of WA across the sampling points, average WSA values exhibited a demonstrable trend: WSA of control sample (without the WA application) was at all times higher than in samples with the addition of WA. If the measured WSA values are compared in terms of overall means, it is evident that the control variant always exhibited the highest WSA value (on average 44.04 %) and the variants with the application of WA showed always WSA values lower by min. 16 %. The worst effect on WSA was that of wetting agents whose basic component was methyl ester of rapeseed. These wetting agents caused a decrease in WSA by more than 50 %. All soil samples were also analysed for basic soil parameters (glomalin, oxidizable carbon – Cox, pH, Na, P, Ca, K, Mg) in order to determine their potential influence on aggregate stability and to possibly eliminate the negative impact of WA. In this respect, only a significant influence of Cox content on WSA was recorded, which positively correlated with the stability of soil aggregates.

Time-resolved photoemission spectroscopy is the key technique to probe the real-time nonequilibrium dynamics of electronic states. Theoretical predictions of the time dependent spectral function for realistic systems is however, a challenge. Employing the Kadanoff-Baym equations to find this quantity results in a cubic scaling in the total number of time steps, quickly becoming prohibitive and often fail quantitatively and even qualitatively. In comparison, mean-field methods have more favorable numerical scaling both in the number of time steps and in the complexity associated with the cost of evolving for a single time step, however they miss key spectral properties such as emergent spectral features. Here we present a scheme that allows for the inclusion of dynamical correlations to the spectral function while maintaining the same scaling in the number of time steps as for mean-field approaches, while capturing the emergent physics. Further, the scheme can be efficiently implemented on top of equilibrium real-time many-body perturbation theory schemes and codes. We see excellent agreement with exact results for test systems. Furthermore, we exemplify the method on a periodic system and demonstrate clear evidence that our proposed scheme produces complex spectral features including excitonic band replicas, features that are not observed using static mean-field approaches.

Twisted bilayers host many emergent phenomena in which the electronic excitations (quasiparticles, QPs) are closely intertwined with the local stacking order. By inspecting twisted hexagonal boron nitride (t-hBN), we show that nonlocal long-range interactions in large twisted systems cannot be reliably described by the local (high-symmetry) stacking and that the band gap variation (typically associated with the moiré excitonic potential) shows multiple minima with variable depth depending on the twist angle. We investigate twist angles of 2.45°, 2.88°, 3.48°, and 5.09° using the GW approximation together with stochastic compression to analyze the QP state interactions. We find that band-edge QP hybridization is suppressed for intermediate angles that exhibit two distinct local minima in the moiré potential (at AA region and saddle point (SP)) which become degenerate for the largest system (2.45°).

Legal regulation, whether we want it or not, plays a role in protecting and promoting individual and public health. This also applies to legislation involving vaccination, especially compulsory vaccination. It is appropriate that legislation should not create barriers to the provision of health care. Where there is legal ambiguity, problems can arise that make the provision of health care more difficult, as we have seen, for example, in the context of the COVID pandemic. Furthermore, in the case of compulsory vaccination, there is a conflict between fundamental rights and freedoms. On the one hand, the right to the protection of personal freedom and bodily integrity, and on the other, the right to life and health. Most compulsory vaccinations concern children. As far as adult vaccination is concerned, this mainly includes compulsory vaccination of medical and social staff caring for patients and operating at biological risk, as well as patient groups also at risk of serious infectious disease. For these reasons, it is essential that the legislation is such that it does not impose a burden where it is not necessary and, on the contrary, allows for optimal protection of persons at biological risk.

Regarding the vaccination of children, it can be said that there are basically three vaccination policies in the world, one of which is usually used in particular country depending on the national legislation. These are the mandatory vaccination policy, mandatory vaccination policy for school entry and recommended vaccination policy. The mandatory vaccination policy and the mandatory vaccination policy for school entry face obstacles consisting of conflicts between fundamental human rights and freedoms. This is, for example, a conflict between the right to health and the right to life on the one hand and the right to protect the inviolability of the person and body integrity or the right to personal freedom, freedom of movement, residence, etc., on the other. Another issue is the right to undisrupted school attendance, based on both compulsory schooling and the right to education. This article looks at different approaches to the vaccination of children in different countries. It provides an illustrative comparison of approaches to vaccination of children in selected countries. It is obvious that the essential problems with organizing and ensuring the vaccination of children are and will be associated with the indicated conflicts of fundamental human rights. It is therefore necessary to search and try to find the optimal policy for undergoing the necessary vaccinations and thereby creating herd immunity, of course for those infectious diseases where this is possible. These efforts are necessary for sufficiently effective protection of individual and public health.

Calculations of excited states in the Green's function formalism often invokes the diagonal approximation, in which the quasiparticle states are taken from a mean-field calculation. In this paper, we extend the stochastic approaches applied in the many-body perturbation theory and overcome this limitation for large systems in which we are interested in a small subset of states. We separate the problem into a core subspace whose coupling to the remainder of the system environment is stochastically sampled. This method is exemplified on computing hole injection energies into CO 2 on an extended gold surface with nearly 3000 electrons. We find that in the extended system the size of the problem can be compressed up to 95% using stochastic sampling. This result provides a way forward for self-consistent stochastic methods and determination of Dyson orbitals in large systems.

The vertex function (Γ) 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 nonlocal exchange interaction. The direct Γ correction to the self-energy is further updated by adjusting the rescaling factor in a self-consistent post-processing cycle. 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.

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 Å, and this pattern is independent of the type of solvent environment. The 9 Å 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.

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 σ-π orbitals) compared with other schemes. However, when applied to giant nanoscale systems, the orbital localization suffers from a large computational cost overhead if 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 work space and sequentially exhausts the entire orbital space until the convergence of the localization functional. It tackles systems with ∼10000 electrons within 0.5 h 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 an 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.

The buffering capacity of the soil is a very important property of the soil, which determines the ability of the soil to resist external influences, especially changes in pH and thus create good living conditions for plants and microorganisms in the soil. The buffering capacity thus significantly contributes to maintaining the health and quality of the soil. Buffering capacity is an important indicator of soil quality, because it is related to the overall condition of the soil ecosystem and other soil properties. The goal of this paper is to determine the effect of applying different soil amendments on the soils, 10 years after application. We compared the effect of 6 different treatments in closed plots: Natural conditions (N = control); Bare soil (B); Straw mulching (S); Pine mulch (P); TerraCottem hydroabsorbent polymers (H); Prescribed burn (F); and Sewage sludge (M). Our results have shown that the application of different amedments leads to an effect on the plowing capacity of the soil. While in the case of the control variant (Natural conditions, N) the buffering capacity of the soil was measured at 144.93 ± 0.25, the addition of different amendments decreased the buffering capacity in the following order: Bare soil (B) 142.73±0.21 > TerraCotem hydroaborbent polymer (H) 142.23±.15 > Pine mulch (P) 140.40±0.30, Prescribed burn (F) 138.20±0.30, Sludge (S) 127.47±0.15. In the case of all variants, these are statistically significant differences (p ≤ 0.05). Thus, soil amendments have been shown to have a statistically significant effect on soil buffering capacity., Competing Interests: The authors have declared that no competing interests exist.

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 containing up to 1000 electrons representing the solvated systems are inexpensive and require ≤1000 central processing unit hrs. We find that the coupling with the environment accounts for ∼40% 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 quasiparticle 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.

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. The 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 method. We critically compare these results to calculations with the many-body perturbation theory, based on the GW and vertex corrected GWΓ approaches. The latter explicitly accounts for two-QP quantum interactions, which have often been neglected. We demonstrate that for molecular systems, the vertex correction universally improves the theoretical spectra, and it is crucial for the accurate prediction of QPs as well as capturing the rich satellite structures of high-energy excitations. GWΓ 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.

We present two new developments for computing excited state energies within the GW approximation. First, calculations of the Green's function and the screened Coulomb interaction are decomposed into two parts: one is deterministic, while the other relies on stochastic sampling. Second, this separation allows constructing a subspace self-energy, which contains dynamic correlation from only a particular (spatial or energetic) region of interest. The methodology is exemplified on large-scale simulations of nitrogen-vacancy states in a periodic hBN monolayer and hBN-graphene heterostructure. We demonstrate that the deterministic embedding of strongly localized states significantly reduces statistical errors, and the computational cost decreases by more than an order of magnitude. The computed subspace self-energy unveils how interfacial couplings affect electronic correlations and identifies contributions to excited-state lifetimes. While the embedding is necessary for the proper treatment of impurity states, the decomposition yields new physical insight into quantum phenomena in heterogeneous systems.

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.

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 0 W 0 , G 0 W 0 tc , and G 0 W 0 tc Γ X . All three methods are formulated in the time domain, and the latter two incorporate nonlocal vertex corrections. In the case of G 0 W 0 tc Γ 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 of the 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.

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.

Objectives: This paper describes and comments on contemporary legislation concerning prevention of epidemics caused by contaminated drinking water from public water supplies in the Czech Republic., Methods: Suggestions are made for removing existing legislative shortcomings, clarifying diction of existing laws and expanding sanctions and penalties for health injury caused by providers and operators of public drinking water., Results: The author reflects on improving legislation concerning the compensation of victims of contaminated water with reference to the aftermath of a local epidemic in the Dejvice District of Prague., Conclusion: The issues raised should be addressed since better legislation can significantly contribute to the limitation of water-borne epidemics and their consequences.

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 GW self-consistency approach, labeled here Δ ¯ G W 0 , can be trivially implemented at zero additional cost for large scale one-shot G 0 W 0 calculations. The method significantly improves one-shot G 0 W 0 and for large systems is very accurate. Δ ¯ G W 0 is similar in spirit to ev GW 0 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 ¯ G W 0 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 G 0 W 0 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 ¯ G W 0 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 ev GW 0 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 ev GW 0 quite well and both methods are in good agreement with the experiment.

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., (Copyright © 2018 The Author(s). Published by Elsevier Inc. All rights reserved.)

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.

Objectives: This article describes and comments on contemporary legal regulations concerning the supply of medicines during pandemics in terms of public procurement., Methods: Suggestions are made for removing existing legislative shortcomings, clarifying the diction of existing laws or rendering precision to legal regulation of public procurement given purchases of medicines during periods of imminent threats of pandemics and duration of pandemics., Results: The author reflects on improving legislation concerning the lack of clarity and the doubts concerning the contemporary legal order of the Czech Republic, with reference to speeding up and simplifying public procurement procedures for incident-free purchases of necessary medicines in time of pandemic crisis situation and then effectively supporting the struggle against any pandemic infection., Conclusion: The issues raised should be addressed since better legislation can significantly contribute to the containment of pandemics and their consequences for individual and public health., (Copyright© by the National Institute of Public Health, Prague 2018.)

Symmetry breaking has been recently observed in the endofullerenes M@C 60 (M = H 2 , HF, H 2 O), manifesting in the splittings of the three-fold degenerate ground states of the endohedral ortho-H 2 , ortho-H 2 O 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 C 60 is considered, comprised of the central C 60 molecule surrounded by twelve nearest-neighbor (NN) C 60 molecules. The fullerenes have either P (major) or H (minor) orientational orderings, and are assumed to be rigid with I h symmetry. Only the central C 60 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 C 60 molecules and that on M inside the central C 60 give rise to the symmetry breaking responsible for the measured level splittings. Using this model, the M@C 60 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@C 60 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.

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.

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 length. Moreover, we find that 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.

In exact density functional theory, 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 cannot 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.