Electronic structure calculations with GPAW: a real-space implementation of the projector augmented-wave method

Mechanism of Electron-Beam Manipulation of Single-Dopant Atoms in Silicon

The precise positioning of dopant atoms within bulk crystal lattices could enable novel applications in areas including solid-state sensing and quantum computation. Established scanning probe techniques are capable tools for the manipulation of surface atoms, but at a disadvantage due to their need to bring a physical tip into contact with the sample. This has prompted interest in electron-beam techniques, followed by the first proof-of-principle experiment of bismuth dopant manipulation in crystalline silicon. Here, we use first-principles modeling to discover a novel indirect exchange mechanism that allows electron impacts to non-destructively move dopants with atomic precision within the silicon lattice. However, this mechanism only works for the two heaviest group V donors with split-vacancy configurations, Bi and Sb. We verify our model by directly imaging these configurations for Bi and by demonstrating that the promising nuclear spin qubit Sb can be manipulated using a focused electron beam.

[Pt2Cu34(PET)22Cl4]2-: An Atomically Precise, 10-Electron PtCu Bimetal Nanocluster with a Direct Pt-Pt Bond

Heteroatom-doped metal nanoclusters (NCs) are highly desirable to gain fundamental insights into the effect of doping on the electronic structure and catalytic properties. Unfortunately, their controlled synthesis is highly challenging when the metal atomic sizes are largely different (e.g., Cu and Pt). Here, we design a metal-exchange strategy that enables simultaneous doping and resizing of NCs. Specifically, [Pt₂Cu₃₄(PET)₂₂Cl₄]^2- NC, the first example of a Pt-doped Cu NC, is synthesized by utilizing the unique reactivity of [Cu₃₂(PET)₂₄Cl₂H₈]^2- NC with Pt⁴⁺ ions. The single-crystal X-ray structure reveals that two directly bonded Pt atoms occupy the two centers of an unusually interpenetrating, incomplete biicosahedron core (Pt₂Cu₁₈), which is stabilized by a Cu₁₆(PET)₂₂Cl₄ shell. The molecular structure and composition of the NC are validated by combined experimental and theoretical results. Electronic structure calculations, using the density functional theory, show that the Pt₂Cu₃₄ NC is a 10-electron superatom. The computed absorption spectrum matches well with the measured data and allows for assignment of the absorption peaks. The calculations also rationalize energetics for ligand exchange observed in the mass spectrometry data. The synergistic effects induced by Pt doping are found to enhance the catalytic activity of Cu NCs by ∼300-fold in silane to silanol conversion under mild conditions. Furthermore, our synthetic strategy has potential to produce Ni-, Pd-, and Au-doped Cu NCs, which will open new avenues to uncover their molecular structures and catalytic properties.

A mechanochromic donor-acceptor torsional spring

Mechanochromic polymers are intriguing materials that allow to sense force of specimens under load. Most mechanochromic systems rely on covalent bond scission and hence are two-state systems with optically distinct "on" and "off" states where correlating force with wavelength is usually not possible. Translating force of different magnitude with gradually different wavelength of absorption or emission would open up new possibilities to map and understand force distributions in polymeric materials. Here, we present a mechanochromic donor-acceptor (DA) torsional spring that undergoes force-induced planarization during uniaxial elongation leading to red-shifted absorption and emission spectra. The DA spring is based on ortho-substituted diketopyrrolopyrrole (o-DPP). Covalent incorporation of o-DPP into a rigid yet ductile polyphenylene matrix allows to transduce sufficiently large stress to the DA spring. The mechanically induced deflection from equilibrium geometry of the DA spring is theoretically predicted, in agreement with experiments, and is fully reversible upon stress release.

Method for Calculating Excited Electronic States Using Density Functionals and Direct Orbital Optimization with Real Space Grid or Plane-Wave Basis Set

A direct orbital optimization method is presented for density functional calculations of excited electronic states using either a real space grid or a plane-wave basis set. The method is variational, provides atomic forces in the excited states, and can be applied to Kohn-Sham (KS) functionals as well as orbital-density-dependent (ODD) functionals including explicit self-interaction correction. The implementation for KS functionals involves two nested loops: (1) An inner loop for finding a stationary point in a subspace spanned by the occupied and a few virtual orbitals corresponding to the excited state; (2) an outer loop for minimizing the energy in a tangential direction in the space of the orbitals. For ODD functionals, a third loop is used to find the unitary transformation that minimizes the energy functional among occupied orbitals only. Combined with the maximum overlap method, the algorithm converges in challenging cases where conventional self-consistent field algorithms tend to fail. The benchmark tests presented include two charge-transfer excitations in nitrobenzene and an excitation of CO to degenerate π* orbitals where the importance of complex orbitals is illustrated. The application of this method to several metal-to-ligand charge-transfer and metal-centered excited states of an Fe^II photosensitizer complex is described, and the results are compared to reported experimental estimates. This method is also used to study the effect of the Perdew-Zunger self-interaction correction on valence and Rydberg excited states of several molecules, both singlet and triplet states, and the performance compared to semilocal and hybrid functionals.

Ultrafast Adsorbate Excitation Probed with Subpicosecond-Resolution X-Ray Absorption Spectroscopy

We use a pump-probe scheme to measure the time evolution of the C K-edge x-ray absorption spectrum from CO/Ru(0001) after excitation by an ultrashort high-intensity optical laser pulse. Because of the short duration of the x-ray probe pulse and precise control of the pulse delay, the excitation-induced dynamics during the first picosecond after the pump can be resolved with unprecedented time resolution. By comparing with density functional theory spectrum calculations, we find high excitation of the internal stretch and frustrated rotation modes occurring within 200 fs of laser excitation, as well as thermalization of the system in the picosecond regime. The ∼100  fs initial excitation of these CO vibrational modes is not readily rationalized by traditional theories of nonadiabatic coupling of adsorbates to metal surfaces, e.g., electronic frictions based on first order electron-phonon coupling or transient population of adsorbate resonances. We suggest that coupling of the adsorbate to nonthermalized electron-hole pairs is responsible for the ultrafast initial excitation of the modes.

Understanding Superatomic Ag Nanohydrides

Bulk Ag hydrides are extremely challenging to make even at very high pressures, but they may become stable as the particle size shrinks to the nanometer regime. Here, the formation and electronic structure of Ag nanohydrides are investigated from a superatomic perspective by density functional theory. It is found that as the coverage increases, adsorption energy of hydrogen atoms on Ag₃₈ cluster to form Ag₃₈ H_{2 n} nanohydride (n is from 1 to 15) can be energetically favorable with respect to bare Ag₃₈ and H₂ . Furthermore, the adsorbed hydrogen atoms contribute their 1s electrons to the superatom electron count and behave as a metal instead of a ligand. The electronic structure of the silver nanohydrides follows the superatomic complex model, leading to magic or relatively more stable compositions such as Ag₃₈ H₂ , Ag₃₈ H₂₀ , and Ag₃₈ H₃₀ , which correspond to 40-electron, 58-electron, and 68-electron shell closings, respectively. Angular momentum analyses of the superatomic orbitals suggest a convoluted interaction of geometry, symmetry, and orbital splitting.

Interferometric 4D-STEM for Lattice Distortion and Interlayer Spacing Measurements of Bilayer and Trilayer 2D Materials

Van der Waals materials composed of stacks of individual atomic layers have attracted considerable attention due to their exotic electronic properties that can be altered by, e.g., manipulating the twist angle of bilayer materials or the stacking sequence of trilayer materials. To fully understand and control the unique properties of these few-layer materials, a technique that can provide information about their local in-plane structural deformations, twist direction, and out-of-plane structure is needed. In principle, interference in overlap regions of Bragg disks originating from separate layers of a material encodes 3D information about the relative positions of atoms in the corresponding layers. Here, an interferometric 4D scanning transmission electron microscopy technique is described that utilizes this phenomenon to extract precise structural information from few-layer materials with nm-scale resolution. It is demonstrated how this technique enables measurement of local pm-scale in-plane lattice distortions as well as twist direction and average interlayer spacings in bilayer and trilayer graphene, and therefore provides a means to better understand the interplay between electronic properties and precise structural arrangements of few-layer 2D materials.

Design Rules for Selecting Fluorinated Linear Organic Solvents for Li Metal Batteries

Fluorinated linear organic solvents have great potential in improving the safety and lifetime of next-generation Li metal batteries. However, this group of solvents is underexplored. Here, we investigate the molecular and interfacial reactivity properties of seven partially and fully fluorinated linear carbonates designed based on conventional solvents. Using density functional theory, we find the highest occupied molecular orbital levels decrease with increasing substitution of the fluorinated functional groups, implying that fluorination, to a first approximation, improves the stability toward high voltage cathodes. On the basis of the simulated decomposition mechanisms and statistical analyses, we find that a fluorinated linear carbonate with partial fluorination at the methyl component is more accessible in terms of degradation and LiF nascence formation, leading to a potentially LiF-rich solid electrolyte interphase (SEI). The molecular design concepts and the computational techniques presented are transferable to ester and ether systems, facilitating the navigation in a large chemical design space.

Influence of a Cu-zirconia interface structure on CO2 adsorption and activation

CO₂ adsorption and activation on a catalyst are key elementary steps for CO₂ conversion to various valuable products. In the present computational study, we screened different Cu-ZrO₂ interface structures and analyzed the influence of the interface structure on CO₂ binding strength using density functional theory calculations. Our results demonstrate that a Cu nanorod favors one position on both tetragonal and monoclinic ZrO₂ surfaces, where the bottom Cu atoms are placed close to the lattice oxygens. In agreement with previous calculations, we find that CO₂ prefers a bent bidentate configuration at the Cu-ZrO₂ interface and the molecule is clearly activated being negatively charged. Straining of the Cu nanorod influences CO₂ adsorption energy but does not change the preferred nanorod position on zirconia. Altogether, our results highlight that CO₂ adsorption and activation depend sensitively on the chemical composition and atomic structure of the interface used in the calculations. This structure sensitivity may potentially impact further catalytic steps and the overall computed reactivity profile.

Correlation-driven phenomena in periodic molecular systems from variational two-electron reduced density matrix theory

Correlation-driven phenomena in molecular periodic systems are challenging to predict computationally not only because such systems are periodically infinite but also because they are typically strongly correlated. Here, we generalize the variational two-electron reduced density matrix (2-RDM) theory to compute the energies and properties of strongly correlated periodic systems. The 2-RDM of the unit cell is directly computed subject to necessary N-representability conditions such that the unit-cell 2-RDM represents at least one N-electron density matrix. Two canonical but non-trivial systems, periodic metallic hydrogen chains and periodic acenes, are treated to demonstrate the methodology. We show that while single-reference correlation theories do not capture the strong (static) correlation effects in either of these molecular systems, the periodic variational 2-RDM theory predicts the Mott metal-to-insulator transition in the hydrogen chains and the length-dependent polyradical formation in acenes. For both hydrogen chains and acenes, the periodic calculations are compared with previous non-periodic calculations with the results showing a significant change in energies and increase in the electron correlation from the periodic boundary conditions. The 2-RDM theory, which allows for much larger active spaces than are traditionally possible, is applicable to studying correlation-driven phenomena in general periodic molecular solids and materials.

Phonoritons as Hybridized Exciton-Photon-Phonon Excitations in a Monolayer h-BN Optical Cavity

A phonoriton is an elementary excitation that is predicted to emerge from hybridization between exciton, phonon, and photon. Besides the intriguing many-particle structure, phonoritons are of interest as they could serve as functional nodes in devices that utilize electronic, phononic, and photonic elements for energy conversion and thermal transport applications. Although phonoritons are predicted to emerge in an excitonic medium under intense electromagnetic wave irradiation, the stringent condition for their existence has eluded direct observation in solids. In particular, on-resonance, intense pumping schemes have been proposed, but excessive photoexcitation of carriers prevents optical detection. Here, we theoretically predict the appearance of phonoritonic features in monolayer hexagonal boron nitride (h-BN) embedded in an optical cavity. The coherent superposition nature of phonoriton states is evidenced by the hybridization of exciton-polariton branches with phonon replicas that is tunable by the cavity-matter coupling strength. This finding simultaneously provides an experimental pathway for observing the predicted phonoritons and opens a new avenue for tuning materials properties.

Cubic aromaticity in ligand-stabilized doped Au superatoms

The magnetic response of valence electrons in doped gold-based M@Au₈L₈ ^q superatoms (M = Pd, Pt, Ag, Au, Cd, Hg, Ir, and Rh; L = PPh₃; and q = 0, +1, +2) is studied by calculating the gauge including magnetically induced currents (GIMIC) in the framework of the auxiliary density functional theory. The studied systems include 24 different combinations of the dopant, total cluster charge, and cluster structure (cubic-like or oblate). The magnetically induced currents (both diatropic and paratropic) are shown to be sensitive to the atomic structure of clusters, the number of superatomic electrons, and the chemical nature of the dopant metal. Among the cubic-like structures, the strongest aromaticity is observed in Pd- and Pt-doped M@Au₈L₈ ⁰ clusters. Interestingly, Pd- and Pt-doping increases the aromaticity as compared to a similar all-gold eight-electron system Au₉L₈ ⁺¹. With the recent implementation of the GIMIC in the deMon2k code, we investigated the aromaticity in the cubic and butterfly-like M@Au₈ core structures, doped with a single M atom from periods 5 and 6 of groups IX-XII. Surprisingly, the doping with Pd and Pt in the cubic structure increases the aromaticity compared to the pure Au case not only near the central atom but encompassing the whole metallic core, following the aromatic trend Pd > Pt > Au. These doped (Pd, Pt)@Au₈ nanoclusters show a closed shell 1S²1P⁶ superatom electronic structure corresponding to the cubic aromaticity rule 6n + 2.

The abTEM code: transmission electron microscopy from first principles

Simulation of transmission electron microscopy (TEM) images or diffraction patterns is often required to interpret experimental data. Since nuclear cores dominate electron scattering, the scattering potential is typically described using the independent atom model, which completely neglects valence bonding and its effect on the transmitting electrons. As instrumentation has advanced, new measurements have revealed subtle details of the scattering potential that were previously not accessible to experiment. We have created an open-source simulation code designed to meet these demands by integrating the ability to calculate the potential via density functional theory (DFT) with a flexible modular software design. abTEM can simulate most standard imaging modes and incorporates the latest algorithmic developments. The development of new techniques requires a program that is accessible to domain experts without extensive programming experience. abTEM is written purely in Python and designed for easy modification and extension. The effective use of modern open-source libraries makes the performance of abTEM highly competitive with existing optimized codes on both CPUs and GPUs and allows us to leverage an extensive ecosystem of libraries, such as the Atomic Simulation Environment and the DFT code GPAW. abTEM is designed to work in an interactive Python notebook, creating a seamless and reproducible workflow from defining an atomic structure, calculating molecular dynamics (MD) and electrostatic potentials, to the analysis of results, all in a single, easy-to-read document.  This article provides ongoing documentation of abTEM development. In this first version, we show use cases for hexagonal boron nitride, where valence bonding can be detected, a 4D-STEM simulation of molybdenum disulfide including ptychographic phase reconstruction, a comparison of MD and frozen phonon modeling for convergent-beam electron diffraction of a 2.6-million-atom silicon system, and a performance comparison of our fast implementation of the PRISM algorithm for a decahedral 20000-atom gold nanoparticle.

The abTEM code: transmission electron microscopy from first principles

Simulation of transmission electron microscopy (TEM) images or diffraction patterns is often required to interpret experimental data. Since nuclear cores dominate electron scattering, the scattering potential is typically described using the independent atom model, which completely neglects valence bonding and its effect on the transmitting electrons. As instrumentation has advanced, new measurements have revealed subtle details of the scattering potential that were previously not accessible to experiment. We have created an open-source simulation code designed to meet these demands by integrating the ability to calculate the potential via density functional theory (DFT) with a flexible modular software design. abTEM can simulate most standard imaging modes and incorporates the latest algorithmic developments. The development of new techniques requires a program that is accessible to domain experts without extensive programming experience. abTEM is written purely in Python and designed for easy modification and extension. The effective use of modern open-source libraries makes the performance of abTEM highly competitive with existing optimized codes on both CPUs and GPUs and allows us to leverage an extensive ecosystem of libraries, such as the Atomic Simulation Environment and the DFT code GPAW. abTEM is designed to work in an interactive Python notebook, creating a seamless and reproducible workflow from defining an atomic structure, calculating molecular dynamics (MD) and electrostatic potentials, to the analysis of results, all in a single, easy-to-read document.  This article provides ongoing documentation of abTEM development. In this first version, we show use cases for hexagonal boron nitride, where valence bonding can be detected, a 4D-STEM simulation of molybdenum disulfide including ptychographic phase reconstruction, a comparison of MD and frozen phonon modeling for convergent-beam electron diffraction of a 2.6-million-atom silicon system, and a performance comparison of our fast implementation of the PRISM algorithm for a decahedral 20000-atom gold nanoparticle.

Unveiling Adatoms in On-Surface Reactions: Combining Scanning Probe Microscopy with van't Hoff Plots

Scanning probe microscopy has become an essential tool to not only study pristine surfaces but also on-surface reactions and molecular self-assembly. Nonetheless, due to inherent limitations, some atoms or (parts of) molecules are either not imaged or cannot be unambiguously identified. Herein, we discuss the arrangement of two different nonplanar molecular assemblies of para-hexaphenyl-dicarbonitrile (Ph₆(CN)₂) on Au(111) based on a combined theoretical and experimental approach. For deposition of Ph₆(CN)₂ on Au(111) kept at room temperature, a rhombic nanoporous network stabilized by a combination of hydrogen bonding and antiparallel dipolar coupling is formed. Annealing at 575 K resulted in an irreversible thermal transformation into a hexagonal nanoporous network stabilized by native gold adatoms. However, the Au adatoms could neither be unequivocally identified by scanning tunneling microscopy nor by noncontact atomic force microscopy. By combining van't Hoff plots derived from our scanning probe images with our density functional theory calculations, we were able to confirm the presence of the elusive Au adatoms in the hexagonal molecular network.

Combining density functional theory with macroscopic QED for quantum light-matter interactions in 2D materials

A quantitative and predictive theory of quantum light-matter interactions in ultra thin materials involves several fundamental challenges. Any realistic model must simultaneously account for the ultra-confined plasmonic modes and their quantization in the presence of losses, while describing the electronic states from first principles. Herein we develop such a framework by combining density functional theory (DFT) with macroscopic quantum electrodynamics, which we use to show Purcell enhancements reaching 10⁷ for intersubband transitions in few-layer transition metal dichalcogenides sandwiched between graphene and a perfect conductor. The general validity of our methodology allows us to put several common approximation paradigms to quantitative test, namely the dipole-approximation, the use of 1D quantum well model wave functions, and the Fermi's Golden rule. The analysis shows that the choice of wave functions is of particular importance. Our work lays the foundation for practical ab initio-based quantum treatments of light-matter interactions in realistic nanostructured materials.

Ultrafast X-ray scattering offers a structural view of excited-state charge transfer

Intramolecular charge transfer and the associated changes in molecular structure in N,N'-dimethylpiperazine are tracked using femtosecond gas-phase X-ray scattering. The molecules are optically excited to the 3p state at 200 nm. Following rapid relaxation to the 3s state, distinct charge-localized and charge-delocalized species related by charge transfer are observed. The experiment determines the molecular structure of the two species, with the redistribution of electron density accounted for by a scattering correction factor. The initially dominant charge-localized state has a weakened carbon-carbon bond and reorients one methyl group compared with the ground state. Subsequent charge transfer to the charge-delocalized state elongates the carbon-carbon bond further, creating an extended 1.634 Å bond, and also reorients the second methyl group. At the same time, the bond lengths between the nitrogen and the ring-carbon atoms contract from an average of 1.505 to 1.465 Å. The experiment determines the overall charge transfer time constant for approaching the equilibrium between charge-localized and charge-delocalized species to 3.0 ps.

Mn Dimer Can Be Described Accurately with Density Functional Calculations When Self-Interaction Correction Is Applied

Qualitatively incorrect results are obtained for the Mn dimer in density functional theory calculations using the generalized gradient approximation (GGA), and similar results are obtained from local density and meta-GGA functionals. The coupling is predicted to be ferromagnetic rather than antiferromagnetic, and the bond between the atoms is predicted to be an order of magnitude too strong and approximately an Ångstrøm too short. Explicit, self-interaction correction (SIC) applied to a commonly used GGA energy functional, however, provides close agreement with both experimental data and high-level, multireference wave function calculations. These results show that the failure is not due to a strong correlation but rather the single electron self-interaction that is necessarily introduced in estimates of the classical Coulomb and exchange-correlation energy when only the total electron density is used as the input. The corrected functional depends explicitly on the orbital densities and can, therefore, avoid the introduction of a self-Coulomb interaction. The error arises because of an overstabilization of bonding d-states in the minority spin channel resulting from an overestimate of the d-electron self-interaction in the semilocal exchange-correlation functionals. Since the computational effort in the SIC calculations scales with the system size in the same way as for regular semilocal functional calculations, this approach provides a way to calculate properties of Mn nanoclusters as well as biomolecules and extended solids, where Mn dimers and larger cluster are present, while multireference wave function calculations can only be applied to small systems.

What Atomic Positions Determines Reactivity of a Surface? Long-Range, Directional Ligand Effects in Metallic Alloys

Ligand and strain effects can tune the adsorption energy of key reaction intermediates on a catalyst surface to speed up rate-limiting steps of the reaction. As novel fields like high-entropy alloys emerge, understanding these effects on the atomic structure level is paramount: What atoms near the binding site determine the reactivity of the alloy surface? By statistical analysis of 2000 density functional theory calculations and subsequent host/guest calculations, it is shown that three atomic positions in the third layer of an fcc(111) metallic structure fourth-nearest to the adsorption site display significantly increased influence on reactivity over any second or third nearest atomic positions. Subsequently observed in multiple facets and host metals, the effect cannot be explained simply through the d-band model or a valence configuration model but rather by favorable directions of interaction determined by lattice geometry and the valence difference between host and guest elements. These results advance the general understanding of how the electronic interaction of different elements affect adsorbate-surface interactions and will contribute to design principles for rational catalyst discovery of better, more stable and energy efficient catalysts to be employed in energy conversion, fuel cell technologies, and industrial processes.

Magnetically induced currents and aromaticity in ligand-stabilized Au and AuPt superatoms

Understanding magnetically induced currents (MICs) in aromatic or metallic nanostructures is crucial for interpreting local magnetic shielding and NMR data. Direct measurements of the induced currents have been successful only in a few planar molecules but their indirect effects are seen in NMR shifts of probe nuclei. Here, we have implemented a numerically efficient method to calculate gauge-including MICs in the formalism of auxiliary density functional theory. We analyze the currents in two experimentally synthesized gold-based, hydrogen-containing ligand-stabilized nanoclusters [HAu₉(PPh₃)₈]²⁺ and [PtHAu₈(PPh₃)₈]⁺. Both clusters have a similar octet configuration of Au(6s)-derived delocalized "superatomic" electrons. Surprisingly, Pt-doping in gold increases the diatropic response of the superatomic electrons to an external magnetic field and enhances the aromaticity of [PtHAu₈(PPh₃)₈]⁺. This is manifested by a stronger shielding of the hydrogen proton in the metal core of the cluster as compared to [HAu₉(PPh₃)₈]²⁺, causing a significant upfield shift in agreement with experimental proton NMR data measured for these two clusters. Our method allows the determination of local magnetic shielding properties for any component in large 3D nanostructures, opening the door for detailed interpretation of complex NMR spectra.

Dynamics & Spectroscopy with Neutrons-Recent Developments & Emerging Opportunities

This work provides an up-to-date overview of recent developments in neutron spectroscopic techniques and associated computational tools to interrogate the structural properties and dynamical behavior of complex and disordered materials, with a focus on those of a soft and polymeric nature. These have and continue to pave the way for new scientific opportunities simply thought unthinkable not so long ago, and have particularly benefited from advances in high-resolution, broadband techniques spanning energy transfers from the meV to the eV. Topical areas include the identification and robust assignment of low-energy modes underpinning functionality in soft solids and supramolecular frameworks, or the quantification in the laboratory of hitherto unexplored nuclear quantum effects dictating thermodynamic properties. In addition to novel classes of materials, we also discuss recent discoveries around water and its phase diagram, which continue to surprise us. All throughout, emphasis is placed on linking these ongoing and exciting experimental and computational developments to specific scientific questions in the context of the discovery of new materials for sustainable technologies.

Electronic excitation in graphene under single-particle irradiation

Single-particle irradiation is a typical condition in space applications, which could be detrimental for electronic devices through processes such as single-event upset or latch-up. For functional devices made of few-atom-thick monolayers that are entirely exposed to the environment, the irradiation effects could be manifested through localized or delocalized electronic excitation, in addition to lattice defect creation. In this work, we explore the single-H irradiation effects on bare or coated graphene monolayers. Real-time time-dependent density functional theory-based first-principles calculation results elucidate the evolution of charge densities in the composite system, showing notable charge excitation but negligible charge deposition. A hexagonal boron nitride coating layer does not protect graphene from these processes. Principal component analysis demonstrates the dominance of localized excitation accompanied by nuclear motion, bond distortion and vibration, as well as a minor contribution from delocalized plasmonic excitation. The significance of coupled electron-ion dynamics in modulating the irradiation processes is identified from comparative studies on the spatial and temporal patterns of excitation for unconstrained and constrained lattices. The stopping power or energy deposition is also calculated, quantifying the dissipative nature of charge density excitation. This study offers fundamental understandings of the single-particle irradiation effects on optoelectronic devices constructed from low-dimensional materials, and inspires unconventional techniques to excite the electrons and ions in a controllable way.

First-principles calculations of hybrid inorganic-organic interfaces: from state-of-the-art to best practice

The computational characterization of inorganic-organic hybrid interfaces is arguably one of the technically most challenging applications of density functional theory. Due to the fundamentally different electronic properties of the inorganic and the organic components of a hybrid interface, the proper choice of the electronic structure method, of the algorithms to solve these methods, and of the parameters that enter these algorithms is highly non-trivial. In fact, computational choices that work well for one of the components often perform poorly for the other. As a consequence, default settings for one materials class are typically inadequate for the hybrid system, which makes calculations employing such settings inefficient and sometimes even prone to erroneous results. To address this issue, we discuss how to choose appropriate atomistic representations for the system under investigation, we highlight the role of the exchange-correlation functional and the van der Waals correction employed in the calculation and we provide tips and tricks how to efficiently converge the self-consistent field cycle and to obtain accurate geometries. We particularly focus on potentially unexpected pitfalls and the errors they incur. As a summary, we provide a list of best practice rules for interface simulations that should especially serve as a useful starting point for less experienced users and newcomers to the field.

ab initio description of bonding for transmission electron microscopy

The simulation of transmission electron microscopy (TEM) images or diffraction patterns is often required to interpret their contrast and extract specimen features. This is especially true for high-resolution phase-contrast imaging of materials, but electron scattering simulations based on atomistic models are widely used in materials science and structural biology. Since electron scattering is dominated by the nuclear cores, the scattering potential is typically described by the widely applied independent atom model. This approximation is fast and fairly accurate, especially for scanning TEM (STEM) annular dark-field contrast, but it completely neglects valence bonding and its effect on the transmitting electrons. However, an emerging trend in electron microscopy is to use new instrumentation and methods to extract the maximum amount of information from each electron. This is evident in the increasing popularity of techniques such as 4D-STEM combined with ptychography in materials science, and cryogenic microcrystal electron diffraction in structural biology, where subtle differences in the scattering potential may be both measurable and contain additional insights. Thus, there is increasing interest in electron scattering simulations based on electrostatic potentials obtained from first principles, mainly via density functional theory, which was previously mainly required for holography. In this Review, we discuss the motivation and basis for these developments, survey the pioneering work that has been published thus far, and give our outlook for the future. We argue that a physically better justified ab initio description of the scattering potential is both useful and viable for an increasing number of systems, and we expect such simulations to steadily gain in popularity and importance.

Real-time time-dependent density functional theory implementation of electronic circular dichroism applied to nanoscale metal-organic clusters

Electronic circular dichroism (ECD) is a powerful spectroscopy method for investigating chiral properties at the molecular level. ECD calculations with the commonly used linear-response time-dependent density functional theory (LR-TDDFT) framework can be prohibitively costly for large systems. To alleviate this problem, we present here an ECD implementation within the projector augmented-wave method in a real-time-propagation TDDFT framework in the open-source GPAW code. Our implementation supports both local atomic basis sets and real-space finite-difference representations of wave functions. We benchmark our implementation against an existing LR-TDDFT implementation in GPAW for small chiral molecules. We then demonstrate the efficiency of our local atomic basis set implementation for a large hybrid nanocluster and discuss the chiroptical properties of the cluster.

Improved band gaps and structural properties from Wannier-Fermi-Löwdin self-interaction corrections for periodic systems

The accurate prediction of band gaps and structural properties in periodic systems continues to be one of the central goals of electronic structure theory. However, band gaps obtained from popular exchange-correlation (XC) functionals (such as LDA and PBE) are severely underestimated partly due to the spurious self-interaction error (SIE) inherent to these functionals. In this work, we present a new formulation and implementation of Wannier function-derived Fermi-Löwdin (WFL) orbitals for correcting the SIE in periodic systems. Since our approach utilizes a variational minimization of the self-interaction energy with respect to the Wannier charge centers (WCC), it is computationally more efficient than the HSE hybrid functional and other self-interaction corrections that require a large number of transformation matrix elements. Calculations on several (17 in total) prototypical molecular solids, semiconductors, and wide-bandgap materials show that our WFL self-interaction correction approach gives better band gaps and bulk moduli compared to semilocal functionals, largely due to the partial removal of self-interaction errors.

Oxygen adsorption on (100) surfaces in Fe-Cr alloys

The adsorption of oxygen on bcc Fe–Cr(100) surfaces with two different alloy concentrations is studied using ab initio density functional calculations. Atomic-scale analysis of oxygen–surface interactions is indispensable for obtaining a comprehensive understanding of macroscopic surface oxidation processes. Up to two chromium atoms are inserted into the first two surface layers. Atomic geometries, energies and electronic properties are investigated. A hollow site is found to be the preferred adsorption site over bridge and on-top sites. Chromium atoms in the surface and subsurface layers are found to significantly affect the adsorption properties of neighbouring iron atoms. Seventy-one different adsorption geometries are studied, and the corresponding adsorption energies are calculated. Estimates for the main diffusion barriers from the hollow adsorption site are given. Whether the change in the oxygen affinity of iron atoms can be related to the chromium-induced charge transfer between the surface atoms is discussed. The possibility to utilize the presented theoretical results in related experimental research and in developing semiclassical potentials for simulating the oxidation of Fe–Cr alloys is addressed.

Electronic and optical properties of fluorinated graphene within many-body Green's function framework

In this article, a systematic examination of the electronic and optical properties of partially fluorinated graphene is presented. In order to capture a large variety of fluorination degrees and configurations, different sizes of the supercell combining with various degrees of fluorination are considered. On top of periodic density functional theory, the G₀W₀ method and the G₀W₀Γ method within many-body Green's function framework are employed. Including the description of electron-hole interactions, the optical spectra based on the Bethe-Salpeter equation are calculated. Two-sided fluorination with compact fluorination arrangements is energetically most favorable. The fluorination degree has a determined impact on the bandgap value in the system, while the fluorination pattern strongly influences the characteristics of the bands in the electronic structures. Depending on the polarization of the applied electromagnetic field, the optical absorption spectra of the same structure could vary significantly. These interesting results suggest the potential applications of partially fluorinated graphene as optoelectronic materials.

Role of Chiral Two-Body Currents in ^{6}Li Magnetic Properties in Light of a New Precision Measurement with the Relative Self-Absorption Technique

A direct measurement of the decay width of the excited 0_{1}^{+} state of ^{6}Li using the relative self-absorption technique is reported. Our value of Γ_{γ,0_{1}^{+}→1_{1}^{+}}=8.17(14)_{stat.}(11)_{syst.}  eV provides sufficiently low experimental uncertainties to test modern theories of nuclear forces. The corresponding transition rate is compared to the results of ab initio calculations based on chiral effective field theory that take into account contributions to the magnetic dipole operator beyond leading order. This enables a precision test of the impact of two-body currents that enter at next-to-leading order.

Dipolar coupling of nanoparticle-molecule assemblies: An efficient approach for studying strong coupling

Strong light-matter interactions facilitate not only emerging applications in quantum and non-linear optics but also modifications of properties of materials. In particular, the latter possibility has spurred the development of advanced theoretical techniques that can accurately capture both quantum optical and quantum chemical degrees of freedom. These methods are, however, computationally very demanding, which limits their application range. Here, we demonstrate that the optical spectra of nanoparticle-molecule assemblies, including strong coupling effects, can be predicted with good accuracy using a subsystem approach, in which the response functions of different units are coupled only at the dipolar level. We demonstrate this approach by comparison with previous time-dependent density functional theory calculations for fully coupled systems of Al nanoparticles and benzene molecules. While the present study only considers few-particle systems, the approach can be readily extended to much larger systems and to include explicit optical-cavity modes.

Fast 3D-lithium-ion diffusion and high electronic conductivity of Li2MnSiO4 surfaces for rechargeable lithium-ion batteries

High theoretical capacity, high thermal stability, the low cost of production, abundance, and environmental friendliness are among the potential attractiveness of Li2MnSiO4 as a positive electrode (cathode) material for rechargeable lithium-ion batteries. However, the experimental results indicated poor electrochemical performance in its bulk phase due to high intrinsic charge transfer resistance and capacity fading during cycling, which limit its large-scale commercial applications. Herein, we explore the surface stability and various lithium-ion diffusion pathways of Li2MnSiO4 surfaces using the density functional theory (DFT) framework. Results revealed that the stability of selected surfaces is in the following order: (210) > (001) > (010) > (100). Moreover, the Wulff-constructed equilibrium shape revealed that the Li2MnSiO4 (001) surface is the most predominant facet, and thus, preferentially exposed to electrochemical activities. The Hubbard-corrected DFT (DFT + U, with U = 3 eV) results indicated that the bulk insulator with a wide band gap (E g = 3.42 eV) changed into narrow electronic (E g = 0.6 eV) when it comes to the Li2MnSiO4 (001) surface. Moreover, the nudged elastic band analysis shows that surface diffusion along the (001) channel was found to be unlimited and fast in all three dimensions with more than 12-order-of-magnitude enhancements compared with the bulk system. These findings suggest that the capacity limitation and poor electrochemical performance that arise from limited electronic and ionic conductivity in the bulk system could be remarkably improved on the surfaces of the Li2MnSiO4 cathode material for rechargeable lithium-ion batteries.

Ultrafast Carrier and Lattice Dynamics in Plasmonic Nanocrystalline Copper Sulfide Films

Excited carrier dynamics in plasmonic nanostructures determines many important optical properties such as nonlinear optical response and photocatalytic activity. Here it is shown that mesoscopic plasmonic covellite nanocrystals with low free-carrier concentration exhibit a much faster carrier relaxation than in traditional plasmonic materials. A nonequilibrium hot-carrier population thermalizes within first 20 fs after photoexcitation. A decreased thermalization time in nanocrystals compared to a bulk covellite is consistent with the reduced Coulomb screening in ultrathin films. The subsequent relaxation of thermalized, equilibrium electron gas is faster than in traditional plasmonic metals due to the lower carrier concentration and agrees well with that in a bulk covellite showing no evidence of quantum confinement or hot-hole trapping at the surface states. The excitation of coherent optical phonon modes in a covellite is also demonstrated, revealing coherent lattice dynamics in plasmonic materials, which until now was mainly limited to dielectrics, semiconductors, and semimetals. These findings show advantages of this new mesoscopic plasmonic material for active control of optical processes.

Engineering Cationic Sulfur-Doped Co3O4 Architectures with Exposing High-Reactive (112) Facets for Photoelectrocatalytic Water Purification

Promoting the generation of intermediate active species (superoxide radical (^•O₂^-)) is an important and challenging task for water purification by photoelectrocatalytic (PEC) oxidation. Herein, we have constructed hierarchical cationic sulfur-doped Co₃O₄ architectures with controllable morphology and highly exposed reactive facets by introducing l-cysteine as a capping reagent and sulfur resource via a one-step hydrothermal reaction. The as-obtained cationic sulfur (1.8 mmol l-cysteine) source doped Co₃O₄ (SC-1.8) architectures with highly exposed (112) facets exhibited superior PEC activities and long-term stability (∼25,000 s) in 1.0 mol·L^-1 sulfuric acid for an accelerated reactive brilliant blue KN-R degradation test. Our experimental and theoretical results confirmed that the superior PEC performance of the SC-1.8 architectures could be ascribed the following factors: (1) the highly exposed reactive (112) facets of SC-1.8 promoted carrier transport and diffusion during the PEC process and facilitated separating the electron/hole pairs and producing the predominant active species (^•O₂^-) compared with currently used other electrodes. (2) Cationic sulfur doped on the lattice of Co₃O₄ can narrow the band gap to extend the photoadsorption range and improve the lifetime of ^•O₂^- to enhance the PEC efficiency. This work not only proves that the SC-1.8 architectures with highly exposed (112) facets are a promising PEC catalyst due to increasing the electron transport and the lifetime of active species but also presents a new strategy for constructing an active PEC catalyst.

Anomalous plasmons in a two-dimensional Dirac nodal-line Lieb lattice

Plasmons in two-dimensional (2D) Dirac materials feature an interesting regime with a tunable frequency, and long propagating length and lifetime, but are rarely achieved in the visible light regime. Using a tight-binding (TB) model in combination with first-principles calculations, we investigated plasmon modes in a 2D Lieb lattice with a Dirac nodal-line electronic structure. In contrast to conventional 2D plasmons, anomalous plasmons in the Lieb lattice exhibit the unique features of a carrier-density-independent frequency, being Landau-damping free in a wide-range of wave vectors, a high frequency, and high subwavelength confinement. Remarkably, by using first-principles calculations, we proposed a candidate material, 2D Be₂C monolayer, to achieve these interesting plasmon properties. The plasmons in the Be₂C monolayer can survive up to the visible frequency region and propagate to large momentum transfer that has rarely been reported. The anomalous plasmons revealed in the Lieb lattice offer a promising platform for the study of 2D plasmons as well as the design of 2D plasmonic materials.

Intrinsic Defects in MoS2 Grown by Pulsed Laser Deposition: From Monolayers to Bilayers

Pulsed laser deposition (PLD) can be considered a powerful method for the growth of two-dimensional (2D) transition-metal dichalcogenides (TMDs) into van der Waals heterostructures. However, despite significant progress, the defects in 2D TMDs grown by PLD remain largely unknown and yet to be explored. Here, we combine atomic resolution images and first-principles calculations to reveal the atomic structure of defects, grains, and grain boundaries in mono- and bilayer MoS₂ grown by PLD. We find that sulfur vacancies and Mo_S antisites are the predominant point defects in 2D MoS₂. We predict that the aforementioned point defects are thermodynamically favorable under a Mo-rich/S-poor environment. The MoS₂ monolayers are polycrystalline and feature nanometer size grains connected by a high density of grain boundaries. In particular, the coalescence of nanometer grains results in the formation of 180° mirror twin boundaries consisting of distinct 4- and 8-membered rings. We show that PLD synthesis of bilayer MoS₂ results in various structural symmetries, including AA' and AB, but also turbostratic with characteristic moiré patterns. Moreover, we report on the experimental demonstration of an electron beam-driven transition between the AB and AA' stacking orientations in bilayer MoS₂. These results provide a detailed insight into the atomic structure of monolayer MoS₂ and the role of the grain boundaries on the growth of bilayer MoS₂, which has importance for future applications in optoelectronics.

Cu2ZnSbS4: A Thioantimonate(V) with Remarkably Strong Covalent Sb-S Bonding

A new member to the A₂^IB^IIC^IVX₄ compound family, Cu₂ZnSbS₄, was synthesized successfully using ball milling and postannealing in H₂S-atmosphere. For comparative purposes, Cu₃SbS₄ was additionally prepared using the same synthetic approach. As is common for A₂^IB^IIC^IVX₄ compounds, Cu₂ZnSbS₄ crystallizes isostructural to Cu₃SbS₄ in the stannite-type structure in space group I42m. Both antimony sulfides contain monovalent diamagnetic copper and are characterized by substantial covalent bonding. This is consistent with the ¹²¹Sb isomer shifts occurring for the Mössbauer spectra of Cu₂ZnSbS₄ (-7.71 mm s^-1) and Cu₃SbS₄ (-7.68 mm s^-1) which fall in the region of covalently bonded Sb(V) compounds. These spectroscopic results are supported by electronic structure calculations.

Density Functional Theory Study of Optical and Electronic Properties of (TiO2)n=5,8,68 Clusters for Application in Solar Cells

A range of solution-processed organic and hybrid organic−inorganic solar cells, such as dye-sensitized and bulk heterojunction organic solar cells have been intensely developed recently. TiO₂ is widely employed as electron transporting material in nanostructured TiO₂ perovskite-sensitized solar cells and semiconductor in dye-sensitized solar cells. Understanding the optical and electronic mechanisms that govern charge separation, transport and recombination in these devices will enhance their current conversion efficiencies under illumination to sunlight. In this work, density functional theory with Perdew-Burke Ernzerhof (PBE) functional approach was used to explore the optical and electronic properties of three modeled TiO₂ brookite clusters, (TiO₂)_n=5,8,68. The simulated optical absorption spectra for (TiO₂)₅ and (TiO₂)₈ clusters show excitation around 200–400 nm, with (TiO₂)₈ cluster showing higher absorbance than the corresponding (TiO₂)₅ cluster. The density of states and the projected density of states of the clusters were computed using Grid-base Projector Augmented Wave (GPAW) and PBE exchange correlation functional in a bid to further understand their electronic structure. The density of states spectra reveal surface valence and conduction bands separated by a band gap of 1.10, 2.31, and 1.37 eV for (TiO₂)₅, (TiO₂)₈, and (TiO₂)₆₈ clusters, respectively. Adsorption of croconate dyes onto the cluster shifted the absorption peaks to higher wavelengths.

Field Effect and Local Gating in Nitrogen-Terminated Nanopores (NtNP) and Nanogaps (NtNG) in Graphene

Functionalization of electrodes is a wide-used strategy in various applications ranging from single-molecule sensing and protein sequencing, to ion trapping, to desalination. We demonstrate, employing non-equilibrium Green's function formalism combined with density functional theory, that single-species (N, H, S, Cl, F) termination of graphene nanogap electrodes results in a strong in-gap electrostatic field, induced by species-dependent dipoles formed at the electrode ends. Consequently, the field increases or decreases electronic transport through a molecule (benzene) placed in the nanogap by shifting molecular levels by almost 2 eV in respect to the electrode Fermi level via a field effect akin to the one used for field-effect transistors. We also observed the local gating in graphene nanopores terminated with different single-species atoms. Nitrogen-terminated nanogaps (NtNGs) and nanopores (NtNPs) show the strongest effect. The in-gap potential can be transformed from a plateau-like to a saddle-like shape by tailoring NtNG and NtNP size and termination type. In particular, the saddle-like potential is applicable in single-ion trapping and desalination devices.

Magnetic and Electronic Properties of Heavy Lanthanides (Gd, Tb, Dy, Er, Ho, Tm)

Rare earth metals (REM) occupy a special and important place in our lives. This became especially noticeable during the rapid development of industry in the industrial era of the twentieth century. The tendency of development of the rare-earth metals market certainly remains in the XXI century. According to experts estimates the industry demand for chemical compounds based on them will tend to grow during the nearest years until it reaches the market balance. At the same time, the practical use of high-purity rare-earth metals requires the most accurate understanding of the physical properties of metals, especially magnetic ones. Despite a certain decline in interest in the study of high-purity REM single crystals during the last decade, a number of scientific groups (Ames Lab, Lomonosov Moscow State University (MSU), Baikov Institute of Metallurgy and Materials Science Russian Academy of Science (RAS)) are still conducting high-purity studies on high-purity metal samples. The present article is a combination of a review work covering the analysis of the main works devoted to the study of heavy REMs from gadolinium to thulium, as well as original results obtained at MSU. The paper considers the electronic properties of metals in terms of calculating the density of states, analyzes the regularities of the magnetic phase diagrams of metals, gives the original dependences of the Neel temperature and tricritical temperatures for Gd, Tb, Dy, Er, Ho, Tm, and also introduces a phenomenological parameter that would serve as an indicator of the phase transformation in heavy REMs.

Electronic structure and transport properties of coupled CdS/ZnSe quantum dots

Electronic structure and transport characteristics of coupled CdS and ZnSe quantum dots are studied using density functional theory and non equilibrium Greens function method respectively. Our investigations show that in these novel coupled dots, the Frontier occupied and unoccupied molecular orbitals are spatially located in two different parts, thereby indicating the possibility of asymmetry in electronic transport. We have calculated electronic transport through the coupled quantum dot by varying the coupling strength between the individual quantum dots in the limits of weak and strong coupling. Calculations reveal asymmetric current vs voltage curves in both the limits indicating the rectifying properties of the coupled quantum dots. Additionally we discuss the possibility to tune the switching behavior of the coupled dots by different gate geometries.

Engineering Dielectric Screening for Potential-well Arrays of Excitons in 2D Materials

Tailoring of the band gap in semiconductors is essential for the development of novel devices. In standard semiconductors, this modulation is generally achieved through highly energetic ion implantation. In two-dimensional (2D) materials, the photophysical properties are strongly sensitive to the surrounding dielectric environment presenting novel opportunities through van der Waals heterostructures encompassing atomically thin high-κ dielectrics. Here, we demonstrate a giant tuning of the exciton binding energy of the monolayer WSe₂ as a function of the dielectric environment. Upon increasing the average dielectric constant from 2.4 to 15, the exciton binding energy is reduced by as much as 300 meV in ambient conditions. The experimentally determined exciton binding energies are in excellent agreement with the theoretical values predicted from a Mott-Wannier exciton model with parameters derived from first-principles calculations. Finally, we show how texturing of the dielectric environment can be used to realize potential-well arrays for excitons in 2D materials, which is a first step toward exciton metamaterials.

Dynamics of weak interactions in the ligand layer of meta-mercaptobenzoic acid protected gold nanoclusters Au68(m-MBA)32 and Au144(m-MBA)40

Atomically precise metal nanoclusters, stabilized and functionalized by organic ligands, are emerging nanomaterials with potential applications in plasmonics, nano-electronics, bio-imaging, nanocatalysis, and as therapeutic agents or drug carriers in nanomedicine. The ligand layer has an important role in modifying the physico-chemical properties of the clusters and in defining the interactions between the clusters and the environment. While this role is well recognized from a great deal of experimental studies, there is very little theoretical information on dynamical processes within the layer itself. Here, we have performed extensive molecular dynamics simulations, with forces calculated from the density functional theory, to investigate thermal stability and dynamics of the ligand layer of the meta-mercaptobenzoic acid (m-MBA) protected Au68 and Au144 nanoclusters, which are the first two gold nanoclusters structurally solved to atomic precision by electron microscopy [Azubel et al., Science, 2014, 345, 909 and ACS Nano, 2017, 11, 11866]. We visualize and analyze dynamics of three distinct non-covalent interactions, viz., ligand-ligand hydrogen bonding, metal-ligand O[double bond, length as m-dash]C-OHAu interaction, and metal-ligand Ph(π)Au interaction. We discuss their relevance for defining, at the same time, the dynamic stability and reactivity of the cluster. These interactions promote the possibility of ligand addition reactions for bio-functionalization or allow the protected cluster to act as a catalyst where active sites are dynamically accessible inside the ligand layer.