Implementation and Validation of Fully Relativistic GW Calculations: Spin–Orbit Coupling in Molecules, Nanocrystals, and Solids

Challenges with relativistic GW calculations in solids and molecules

For molecules and solids containing heavy elements, accurate electronic-structure calculations require accounting not only for electronic correlations but also for relativistic effects. In molecules, relativity can lead to severe changes in the ground-state description. In solids, the interplay between both correlation and relativity can change the stability of phases or it can lead to an emergence of completely new phases. Traditionally, the simplest illustration of relativistic effects can be done either by including pseudopotentials in non-relativistic calculations or alternatively by employing large all-electron basis sets in relativistic methods. By analyzing different electronic properties (band structure, equilibrium lattice constant and bulk modulus) in semiconductors and insulators, we show that capturing the interplay of relativity and electron correlation can be rather challenging in Green's function methods. For molecular problems with heavy elements, we also observe that similar problems persist. We trace these challenges to three major problems: deficiencies in pseudopotential treatment as applied to Green's function methods, the scarcity of accurate and compact all-electron basis sets that can be converged with respect to the basis-set size, and linear dependencies arising in all-electron basis sets, particularly when employing Gaussian orbitals. Our analysis provides detailed insight into these problems and opens a discussion about potential approaches to mitigate them.

Uncertainty Quantification of Linear Scaling, Machine Learning, and Density Functional Theory Derived Thermodynamics for the Catalytic Partial Oxidation of Methane on Rhodium

Accurate and complete microkinetic models (MKMs) are powerful for anticipating the behavior of complex chemical systems at different operating conditions. In heterogeneous catalysis, they can be further used for the rapid development and screening of new catalysts. Density functional theory (DFT) is often used to calculate the parameters used in MKMs with relatively high fidelity. However, given the high cost of DFT calculations for adsorbates in heterogeneous catalysis, linear scaling relations (LSRs) and machine learning (ML) models were developed to give rapid estimates of the parameters in MKM. Regardless of the method, few studies have attempted to quantify the uncertainty in catalytic MKMs, as the uncertainties are often orders of magnitude larger than those for gas phase models. This study explores uncertainty quantification and Bayesian Parameter Estimation for thermodynamic parameters calculated by DFT, LSRs, and GemNet-OC, a ML model developed under the Open Catalyst Project. A model for catalytic partial oxidation of methane (CPOX) on Rhodium was chosen as a case study, in which the model's thermodynamic parameters and their associated uncertainties were determined using DFT, LSR, and GemNet-OC. Markov Chain Monte Carlo coupled with Ensemble Slice Sampling was used to sample the highest probability density (HPD) region of the posterior and determine the maximum of the a posteriori (MAP) for each thermodynamic parameter included. The optimized microkinetic models for each of the three estimation methods had quite similar mechanisms and agreed well with the experimental data for gas phase mole fractions. Exploration of the HPD region of the posterior further revealed that adsorbed hydroxide and oxygen likely bind on facets other than Rhodium 111. The demonstrated workflow addresses the issue of inaccuracies arising from the integration of data from multiple sources by considering both experimental and computational uncertainties, and further reveals information about the active site that would not have been discovered without considering the posterior.

Blue-Light-Excitable Red-Emitting Organic Antimony Halides as a Reversible Humidity Sensor

Zero-dimensional organic antimony halides have attracted significant attention recently due to their structural variety, tunable optical properties, and high luminescence efficiency. Here, a new series of antimony bromide hybrid structures with seesaw [SbBr4] and pyramidal [SbBr5] geometries are reported with low band gaps and blue-light excited red emissions. Their luminescence is attributed to self-trapped excitons with a broadband emission of a large Stokes shift. Their photoluminescence signal is sensitive to water molecules, with a reversible positive correlation in a relative humidity range of 30-90%, enabling them as potential materials for real-time, self-consistent humidity sensors.

Electronic Structure and Surface Chemistry of BaZrS3 Perovskite Powder and Sputtered Thin Film

Chalcogenide perovskites exhibit optoelectronic properties that position them as potential materials in the field of photovoltaics. We report a detailed investigation into the electronic structure and chemical properties of polycrystalline BaZrS3 perovskite powder by X-ray photoelectron spectroscopy, complemented by an analysis of its long- and short-range geometric structures using X-ray diffraction and X-ray absorption spectroscopy. The results obtained for the powdered BaZrS3 are compared to similar measurements on a sputtered polycrystalline BaZrS3 thin film prepared through rapid thermal processing. While bulk characterization confirms the good quality of the powder, depth-profiling achieved by photoelectron spectroscopy utilizing Al Kα (1.487 keV) and Ga Kα (9.25 keV) radiations shows that, regardless of the fabrication method, the oxidation effects extend beyond 10 nm from the sample surface, with zirconium oxides specifically distributing deeper than the oxidized sulfur species. A hard X-ray photoelectron spectroscopy study on the powder and thin film detects signals with minimal contamination contributions and allows for the determination of the valence band maximum position with respect to the Fermi level. Based on these measurements, we establish a correlation between the experimental valence band spectra and the theoretical density of states derived from density functional theory calculations, thereby discerning the orbital constituents involved. Our analysis provides an improved understanding of the electronic structure of BaZrS3 developed through different synthesis protocols by linking it to material geometry, surface chemistry, and the nature of doping. This methodology can thus be adapted for describing electronic structures of chalcogenide perovskite semiconductors in general, a knowledge that is significant for interface engineering and, consequently, for device integration.

Identification of Semiconductor Nanocrystals with Bright Ground-State Excitons

While semiconductor nanocrystals provide versatile fluorescent materials for light-emitting devices, their brightness suffers from the "dark exciton"─an optically inactive electronic state into which nanocrystals relax before emitting. Recently, a theoretical mechanism, the Rashba effect, was discovered that can overcome this limitation by inverting the lowest-lying levels and creating a bright excitonic ground state. However, no methodology is available to systematically identify materials that exhibit this inversion, hindering the development of superbright nanocrystals and their devices. Here, based on a detailed understanding of the Rashba mechanism, we demonstrate a procedure that reveals previously unknown "bright-exciton" nanocrystals. We first define physical criteria to reduce over 500,000 known solids to 173 targets. Higher-level first-principles calculations then refine this list to 28 candidates. From these, we select five with high oscillator strength and develop effective-mass models to determine the nature of their lowest excitonic state. We confirm that four of the five solids yield bright ground-state excitons in nanocrystals. Thus, our results provide a badly needed roadmap for experimental investigation of bright-exciton nanomaterials.

Biaxial Tensile Strain Enhances Electron Mobility of Monolayer Transition Metal Dichalcogenides

Strain engineering can modulate the properties of two-dimensional (2D) semiconductors for electronic and optoelectronic applications. Recent theory and experiments have found that uniaxial tensile strain can improve the electron mobility of monolayer MoS2, a 2D semiconductor, but the effects of biaxial strain on charge transport are not well characterized in 2D semiconductors. Here, we use biaxial tensile strain on flexible substrates to probe electron transport in monolayer WS2 and MoS2 transistors. This approach experimentally achieves ∼2× higher on-state current and mobility with ∼0.3% applied biaxial strain in WS2, the highest mobility improvement at the lowest strain reported to date. We also examine the mechanisms behind this improvement through density functional theory simulations, concluding that the enhancement is primarily due to reduced intervalley electron-phonon scattering. These results underscore the role of strain engineering in 2D semiconductors for flexible electronics, sensors, integrated circuits, and other optoelectronic applications.

Lithiation Induced Phases in 1T'-MoTe2 Nanoflakes

Multiple polytypes of MoTe2 with distinct structures and intriguing electronic properties can be accessed by various physical and chemical approaches. Here, we report electrochemical lithium (Li) intercalation into 1T'-MoTe2 nanoflakes, leading to the discovery of two previously unreported lithiated phases. Distinguished by their structural differences from the pristine 1T' phase, these distinct phases were characterized using in situ polarization Raman spectroscopy and in situ single-crystal X-ray diffraction. The lithiated phases exhibit increasing resistivity with decreasing temperature, and their carrier densities are two to 4 orders of magnitude smaller than the metallic 1T' phase, as probed through in situ Hall measurements. The discovery of these gapped phases in initially metallic 1T'-MoTe2 underscores electrochemical intercalation as a potent tool for tuning the phase stability and electron density in two-dimensional (2D) materials.

Relativistic Fully Self-Consistent GW for Molecules: Total Energies and Ionization Potentials

The fully self-consistent GW (scGW) method with an iterative solution of the Dyson equation provides a consistent approach for describing the ground and excited states without any dependence on the mean-field reference. In this work, we present a relativistic version of scGW for molecules containing heavy elements using the exact two-component (X2C) Coulomb approximation. We benchmark SOC-81 data set containing closed shell heavy elements for the first ionization potential using the fully self-consistent GW as well as one-shot GW. The self-consistent GW provides superior results compared to G0W0 with PBE reference and comparable results to G0W0 with PBE0 while also removing the starting point dependence. The photoelectron spectra obtained at the X2C level demonstrate very good agreement with the experimental spectra. We also observe that scGW provides very good estimation of ionization potential for the inner d-shell orbitals. Additionally, using the well-conserved total energy, we investigate the equilibrium bond length and harmonic frequencies of a few halogen dimers using scGW. Overall, our findings demonstrate the applicability of the fully self-consistent GW method for accurate ionization potential, photoelectron spectra, and total energies in finite systems with heavy elements with a reasonable computational scaling.

Quantum fluctuations lead to glassy electron dynamics in the good metal regime of electron doped KTaO3

One of the central challenges in condensed matter physics is to comprehend systems that have strong disorder and strong interactions. In the strongly localized regime, their subtle competition leads to glassy electron dynamics which ceases to exist well before the insulator-to-metal transition is approached as a function of doping. Here, we report on the discovery of glassy electron dynamics deep inside the good metal regime of an electron-doped quantum paraelectric system: KTaO3. We reveal that upon excitation of electrons from defect states to the conduction band, the excess injected carriers in the conduction band relax in a stretched exponential manner with a large relaxation time, and the system evinces simple aging phenomena-a telltale sign of glassy dynamics. Most significantly, we observe a critical slowing down of carrier dynamics below 35 K, concomitant with the onset of quantum paraelectricity in the undoped KTaO3. Our combined investigation using second harmonic generation technique, density functional theory and phenomenological modeling demonstrates quantum fluctuation-stabilized soft polar modes as the impetus for the glassy behavior. This study addresses one of the most fundamental questions regarding the potential promotion of glassiness by quantum fluctuations and opens a route for exploring glassy dynamics of electrons in a well-delocalized regime.

Static versus dynamically polarizable environments within the many-body GW formalism

Continuum- or discrete-polarizable models for the study of optoelectronic processes in embedded subsystems rely mostly on the restriction of the surrounding electronic dielectric response to its low frequency limit. Such a description hinges on the assumption that the electrons in the surrounding medium react instantaneously to any excitation in the central subsystem, thus treating the environment in the adiabatic limit. Exploiting a recently developed embedded GW formalism with an environment described at the fully ab initio level, we assess the merits of the adiabatic limit with respect to an environment where the full dynamics of the dielectric response are considered. Furthermore, we show how to properly take the static limit of the environment's susceptibility by introducing the so-called Coulomb-hole and screened-exchange contributions to the reaction field. As a first application, we consider a C60 molecule at the surface of a C60 crystal, namely, a case where the dynamics of the embedded and embedding subsystems are similar. The common adiabatic assumption, when properly treated, generates errors below 10% on the polarization energy associated with frontier energy levels and associated energy gaps. Finally, we consider a water molecule inside a metallic nanotube, the worst case for the environment's adiabatic limit. The error on the gap polarization energy remains below 10%, even though the error on the frontier orbital polarization energies can reach a few tenths of an electronvolt.

Large exchange-driven intrinsic circular dichroism of a chiral 2D hybrid perovskite

In two-dimensional chiral metal-halide perovskites, chiral organic spacers endow structural and optical chirality to the metal-halide sublattice, enabling exquisite control of light, charge, and electron spin. The chiroptical properties of metal-halide perovskites have been measured by transmissive circular dichroism spectroscopy, which necessitates thin-film samples. Here, by developing a reflection-based approach, we characterize the intrinsic, circular polarization-dependent complex refractive index for a prototypical two-dimensional chiral lead-bromide perovskite and report large circular dichroism for single crystals. Comparison with ab initio theory reveals the large circular dichroism arises from the inorganic sublattice rather than the chiral ligand and is an excitonic phenomenon driven by electron-hole exchange interactions, which breaks the degeneracy of transitions between Rashba-Dresselhaus-split bands, resulting in a Cotton effect. Our study suggests that previous data for spin-coated films largely underestimate the optical chirality and provides quantitative insights into the intrinsic optical properties of chiral perovskites for chiroptical and spintronic applications.

Point Defect Limited Carrier Mobility in 2D Transition Metal Dichalcogenides

2D transition metal dichalcogenide (MX2) semiconductors are promising candidates for electronic and optoelectronic applications. However, they have relatively low charge carrier mobility at room temperature. Defects are important scattering sources, while their quantitative roles remain unclear. Here we employ first-principles methods to accurately calculate the scatterings by different types of defects (chalcogen vacancies, antisites, and oxygen substitutes) and the resulting carrier mobilities for various MX2 (M = Mo/W and X = S/Se). We find that for the same X, WX2 always has a higher mobility than MoX2, regardless of defect type and carrier type. Further analyses attribute this to the universally weaker electron-defect coupling in WX2. Moreover, we find filling the chalcogen vacancy with O always improves the mobility, while filling by a metal atom decreases the mobility except for WSe2. Finally, we identify the critical defect concentrations where the defect- and phonon-limited mobilities cross, providing guidelines for experimental optimization.

Field-free deterministic switching of all-van der Waals spin-orbit torque system above room temperature

Two-dimensional van der Waals (vdW) magnetic materials hold promise for the development of high-density, energy-efficient spintronic devices for memory and computation. Recent breakthroughs in material discoveries and spin-orbit torque control of vdW ferromagnets have opened a path for integration of vdW magnets in commercial spintronic devices. However, a solution for field-free electric control of perpendicular magnetic anisotropy (PMA) vdW magnets at room temperatures, essential for building compact and thermally stable spintronic devices, is still missing. Here, we report a solution for the field-free, deterministic, and nonvolatile switching of a PMA vdW ferromagnet, Fe3GaTe2, above room temperature (up to 320 K). We use the unconventional out-of-plane anti-damping torque from an adjacent WTe2 layer to enable such switching with a low current density of 2.23 × 106 A cm-2. This study exemplifies the efficacy of low-symmetry vdW materials for spin-orbit torque control of vdW ferromagnets and provides an all-vdW solution for the next generation of scalable and energy-efficient spintronic devices.

Quantum Dots in Transition Metal Dichalcogenides Induced by Atomic-Scale Deformations

Single-photon emission from monolayer transition metal dichalcogenides requires the existence of localized, atom-like states within the extended material. Here, we predict from first-principles the existence of quantum dots around atomic-scale protrusions, which result from substrate roughness or particles trapped between layers. Using density functional theory, we find such deformations to give rise to local membrane stretching and curvature, which lead to the emergence of gap states. Having enhanced outer-surface localization, they are prone to mixing with states pertaining to chalcogen vacancies and adsorbates. If the deformation is sharp, the conduction band minimum furthermore assumes atomic and valley-mixed character, potentially enabling quantum light emission. When such structural defects are arranged in an array, the new states couple to form energetically separated sub-bands, holding promise for intriguing superlattice dynamics. All of the observed features are shown to be closely linked to elastic, deformation-induced intra- and intervalley scattering processes.

Relativistic effects and pressure-induced phase transition in CsAu

Cesium auride (CsAu) is an intriguing compound formed by two metals that, upon reacting, exhibits properties of an ionic salt. In this study, we employ computer simulations to explore the influence of relativistic effects on the structure and some physical properties of CsAu, as well as on a potential pressure-induced structural phase transition, the effect of high pressures on its electronic gap, and the possible transition to a conducting state. We have found that including relativistic effects reduces the lattice parameter of CsAu and brings its volumetric properties closer to the trend observed in alkali halides. It also enhances the charge transfer from cesium to gold, resulting in a difference of up to 0.15e, at ambient pressure, between non-relativistic and fully relativistic calculations. Additionally, upon increasing pressure, in the absence of intervening structural phase transitions, the closing of CsAu's band gap is expected at approximately 31.5 GPa. The inclusion of relativistic effects stabilizes the CsAu Pm3̄m structure and shifts the transition pressure to a possible high-pressure P4/mmm phase from 2 GPa (non-relativistic calculation) to 14 GPa (fully-relativistic calculation). Both the Pm3̄m and P4/mmm structures become dynamically unstable around 15 GPa, thus suggesting that the tetragonal structure may be an intermediate state towards a truly stable high-pressure CsAu phase.

Excitons in metal-halide perovskites from first-principles many-body perturbation theory

Metal-halide perovskites are a structurally, chemically, and electronically diverse class of semiconductors with applications ranging from photovoltaics to radiation detectors and sensors. Understanding neutral electron-hole excitations (excitons) is key for predicting and improving the efficiency of energy-conversion processes in these materials. First-principles calculations have played an important role in this context, allowing for a detailed insight into the formation of excitons in many different types of perovskites. Such calculations have demonstrated that excitons in some perovskites significantly deviate from canonical models due to the chemical and structural heterogeneity of these materials. In this Perspective, I provide an overview of calculations of excitons in metal-halide perovskites using Green's function-based many-body perturbation theory in the GW + Bethe-Salpeter equation approach, the prevalent method for calculating excitons in extended solids. This approach readily considers anisotropic electronic structures and dielectric screening present in many perovskites and important effects, such as spin-orbit coupling. I will show that despite this progress, the complex and diverse electronic structure of these materials and its intricate coupling to pronounced and anharmonic structural dynamics pose challenges that are currently not fully addressed within the GW + Bethe-Salpeter equation approach. I hope that this Perspective serves as an inspiration for further exploring the rich landscape of excitons in metal-halide perovskites and other complex semiconductors and for method development addressing unresolved challenges in the field.

Two-Component GW Calculations: Cubic Scaling Implementation and Comparison of Vertex-Corrected and Partially Self-Consistent GW Variants

We report an all-electron, atomic orbital (AO)-based, two-component (2C) implementation of the GW approximation (GWA) for closed-shell molecules. Our algorithm is based on the space-time formulation of the GWA and uses analytical continuation (AC) of the self-energy, and pair-atomic density fitting (PADF) to switch between AO and auxiliary basis. By calculating the dynamical contribution to the GW self-energy at a quasi-one-component level, our 2C-GW algorithm is only about a factor of 2-3 slower than in the scalar relativistic case. Additionally, we present a 2C implementation of the simplest vertex correction to the self-energy, the statically screened G3W2 correction. Comparison of first ionization potentials (IPs) of a set of 67 molecules with heavy elements (a subset of the SOC81 set) calculated with our implementation against results from the WEST code reveals mean absolute deviations (MAD) of around 70 meV for G0W0@PBE and G0W0@PBE0. We check the accuracy of our AC treatment by comparison to full-frequency GW calculations, which shows that in the absence of multisolution cases, the errors due to AC are only minor. This implies that the main sources of the observed deviations between both implementations are the different single-particle bases and the pseudopotential approximation in the WEST code. Finally, we assess the performance of some (partially self-consistent) variants of the GWA for the calculation of first IPs by comparison to vertical experimental reference values. G0W0@PBE0 (25% exact exchange) and G0W0@BHLYP (50% exact exchange) perform best with mean absolute deviations (MAD) of about 200 meV. Explicit treatment of spin-orbit effects at the 2C level is crucial for systematic agreement with experiment. On the other hand, eigenvalue-only self-consistent GW (evGW) and quasi-particle self-consistent GW (qsGW) significantly overestimate the IPs. Perturbative G3W2 corrections increase the IPs and therefore improve the agreement with experiment in cases where G0W0 alone underestimates the IPs. With a MAD of only 140 meV, 2C-G0W0@PBE0 + G3W2 is in best agreement with the experimental reference values.

Stabilizing tetramethylammonium lead iodide perovskite and exploring its electronic and optical absorption for solar cell absorber application

Modeling perovskites as solar cell absorbers has become popular due to the breakthrough of methylammonium lead iodide (CH3NH3PbI3). In this study, we modeled a tetramethylammonium lead iodide (CH3)4NPbI3 structure. We further confirmed the stability of the structure by determining the phonon dispersion using density functional perturbation theory. We calculated the spin-orbit and non-spin-orbit coupling-based electronic structure using the Perdew-Burke-Ernzerhof exchange-correlation functional within the generalized gradient approximation of the density functional theory and the self-consistent GW quasiparticle methods. Similarly, the absorption spectra were calculated from the real and imaginary parts of the dielectric tensor obtained from solving the Bethe-Salpeter equation using the GW quasiparticle database. The solar cell absorber spectroscopic limited maximum efficiency was calculated at 293.15 K. The self-consistent GW method without spin-orbit coupling reported bandgaps of 2.63 eV and 2.89 eV for GW0 and GW methods, respectively, in agreement with experimental reports. The phonon dispersion showed positive phonon modes across the high symmetry point, which attest to its thermodynamic stability. The absorption coefficient on the order of 105 was reported along the ultraviolet region. The standard limited maximum efficiency between 7% and 12% was recorded at 293.15 K between 0.01 and 100 μm absorber thicknesses. The thermodynamic stability, high absorption coefficient, and low transmittance indicated exciting prospects for a non-transparent (CH3)4NPbI3 solar cell absorber.

Robust relativistic many-body Green's function based approaches for assessing core ionized and excited states

A two-component contour deformation (CD) based GW method that employs frequency sampling to drastically reduce the computational effort when assessing quasiparticle states far away from the Fermi level is outlined. Compared to the canonical CD-GW method, computational scaling is reduced by an order of magnitude without sacrificing accuracy. This allows for an efficient calculation of core ionization energies. The improved computational efficiency is used to provide benchmarks for core ionized states, comparing the performance of 15 density functional approximations as Kohn-Sham starting points for GW calculations on a set of 65 core ionization energies of 32 small molecules. Contrary to valence states, GW calculations on core states prefer functionals with only a moderate amount of Hartree-Fock exchange. Moreover, modern ab initio local hybrid functionals are also shown to provide excellent generalized Kohn-Sham references for core GW calculations. Furthermore, the core-valence separated Bethe-Salpeter equation (CVS-BSE) is outlined. CVS-BSE is a convenient tool to probe core excited states. The latter is tested on a set of 40 core excitations of eight small inorganic molecules. Results from the CVS-BSE method for excitation energies and the corresponding absorption cross sections are found to be in excellent agreement with those of reference damped response BSE calculations.

Surface asymmetry induced turn-overed lifetime of acoustic phonons in monolayer MoSSe

Recent successful growth of asymmetric transition metal dichalcogenides via accurate manipulation of different chalcogen atoms in top and bottom surfaces demonstrates exotic electronic and chemical properties in such Janus systems. Within the framework of density functional perturbation theory, anharmonic phonon properties of monolayer Janus MoSSe sheet are explored. By considering three-phonons scattering, out-of-plane flexural acoustic (ZA) mode tends to undergo a stronger phonon scattering than transverse acoustic (TA) mode and the longitudinal acoustic (LA) mode with phonon lifetime of ZA (1.0 ps) < LA (23.8 ps) < TA (25.8 ps). This is sharply different from the symmetric MoS₂ where flexural ZA mode has the weakest anharmonicity and is least scattered. Moreover, utilizing non-equilibrium Green function method, ballistic thermal conductance at room temperature is found to be around 0.11 nWK^-1nm^-2, lower than that of MoS₂. Our work highlights intriguing phononic properties of such MoSSe Janus layers associated with asymmetric surfaces.

Practical Post-Kohn-Sham Methods for Time-Reversal Symmetry Breaking References

The applicability of reduced scaling algorithms based on auxiliary subspace methods for the correlation energy from the random phase approximation (RPA) as well as the correlation part of the self-energy obtained from the GW method is outlined for time-reversal symmetry breaking Kohn-Sham (KS) references. The updated algorithms allow for an efficient evaluation of RPA energies and GW quasiparticle energies for molecular systems with KS references that break time-reversal symmetry. The latter occur, for example, in magnetic fields. Furthermore, KS references for relativistic open-shell molecules also break time-reversal symmetry due to the single determinant ansatz used. Errors of the updated reduced-scaling algorithms are shown to be negligible compared to reference implementations, while the overall computational scaling is reduced by 2 orders of magnitude. Ionization energies obtained from the GW approximation are shown to be robust even for the electronically complicated group of trivalent lanthanoid ions. Starting from GW quasiparticle energies, it is subsequently shown that light-matter interactions of these systems can be calculated using the Bethe-Salpeter equation (BSE). Using the combined GW-BSE method, the absorption and emission spectra of a molecular europium(III) complex can be obtained including spin-orbit coupling.

Unidirectional Rashba spin splitting in single layer WS2(1-x)Se2xalloy

Atomically thin two-dimensional (2D) layered semiconductors such as transition metal dichalcogenides have attracted considerable attention due to their tunable band gap, intriguing spin-valley physics, piezoelectric effects and potential device applications. Here we study the electronic properties of a single layer WS_1.4Se_0.6alloys. The electronic structure of this alloy, explored using angle resolved photoemission spectroscopy, shows a clear valence band structure anisotropy characterized by two paraboloids shifted in one direction of thek-space by a constant in-plane vector. This band splitting is a signature of a unidirectional Rashba spin splitting with a related giant Rashba parameter of 2.8 ± 0.7 eV Å. The combination of angle resolved photoemission spectroscopy with piezo force microscopy highlights the link between this giant unidirectional Rashba spin splitting and an in-plane polarization present in the alloy. These peculiar anisotropic properties of the WS_1.4Se_0.6alloy can be related to local atomic orders induced during the growth process due the different size and electronegativity between S and Se atoms. This distorted crystal structure combined to the observed macroscopic tensile strain, as evidenced by photoluminescence, displays electric dipoles with a strong in-plane component, as shown by piezoelectric microscopy. The interplay between semiconducting properties, in-plane spontaneous polarization and giant out-of-plane Rashba spin-splitting in this 2D material has potential for a wide range of applications in next-generation electronics, piezotronics and spintronics devices.

Density Functional Theory Plus Dynamical Mean Field Theory within the Framework of Linear Combination of Numerical Atomic Orbitals: Formulation and Benchmarks

The combination of density functional theory with dynamical mean-field theory (DFT+DMFT) has become a powerful first-principles approach to tackle strongly correlated materials in condensed matter physics. The wide use of this approach relies on robust and easy-to-use implementations, and its implementation in various numerical frameworks will increase its applicability on the one hand and help crosscheck the validity of the obtained results on the other. In this work, we develop a formalism within the linear combination of numerical atomic orbital (NAO) basis set framework, which allows for merging of NAO-based DFT codes with DMFT quantum impurity solvers. The formalism is implemented by interfacing two NAO-based DFT codes with three DMFT impurity solvers, and its validity is testified by benchmark calculations for a wide range of strongly correlated materials, including 3d transition metal compounds, lanthanides, and actinides. Our work not only enables DFT+DMFT calculations using popular and rapidly developing NAO-based DFT code packages but also facilitates the combination of more advanced beyond-DFT methodologies available in these codes with the DMFT machinery.

GPU Acceleration of Large-Scale Full-Frequency GW Calculations

Many-body perturbation theory is a powerful method to simulate electronic excitations in molecules and materials starting from the output of density functional theory calculations. By implementing the theory efficiently so as to run at scale on the latest leadership high-performance computing systems it is possible to extend the scope of GW calculations. We present a GPU acceleration study of the full-frequency GW method as implemented in the WEST code. Excellent performance is achieved through the use of (i) optimized GPU libraries, e.g., cuFFT and cuBLAS, (ii) a hierarchical parallelization strategy that minimizes CPU-CPU, CPU-GPU, and GPU-GPU data transfer operations, (iii) nonblocking MPI communications that overlap with GPU computations, and (iv) mixed precision in selected portions of the code. A series of performance benchmarks has been carried out on leadership high-performance computing systems, showing a substantial speedup of the GPU-accelerated version of WEST with respect to its CPU version. Good strong and weak scaling is demonstrated using up to 25 920 GPUs. Finally, we showcase the capability of the GPU version of WEST for large-scale, full-frequency GW calculations of realistic systems, e.g., a nanostructure, an interface, and a defect, comprising up to 10 368 valence electrons.

Quantum embedding theories to simulate condensed systems on quantum computers

Quantum computers hold promise to improve the efficiency of quantum simulations of materials and to enable the investigation of systems and properties that are more complex than tractable at present on classical architectures. Here, we discuss computational frameworks to carry out electronic structure calculations of solids on noisy intermediate-scale quantum computers using embedding theories, and we give examples for a specific class of materials, that is, solid materials hosting spin defects. These are promising systems to build future quantum technologies, such as quantum computers, quantum sensors and quantum communication devices. Although quantum simulations on quantum architectures are in their infancy, promising results for realistic systems appear to be within reach.

Band Alignment Engineering by Twist Angle and Composition Modulation for Heterobilayer

Atomically thin monolayer semiconducting transition metal dichalcogenides (TMDs), exhibiting direct band gap and strong light-matter interaction, are promising for optoelectronic devices. However, an efficient band alignment engineering method is required to further broaden their practical applications as versatile optoelectronics. In this work, the band alignment of two vertically stacked monolayer TMDs using the chemical vapor deposition (CVD) method is effectively tuned by two strategies: 1) formulating the compositions of MoS_2(1-x) Se_2x alloys, and 2) varying the twist angles of the stacked heterobilayer structures. Photoluminescence (PL) results combined with density functional theory (DFT) calculation show that by changing the alloy composition, a continuously tunable band alignment and a transition of type II-type I-type II band alignment of TMD heterobilayer is achieved. Moreover, only at moderate (10°-50°) twist angles, a PL enhancement of 28%-110% caused by the type I alignment is observed, indicating that the twist angle is coupled with the global band structure of heterobilayer. A heterojunction device made with MoS_0.76 Se_1.24 /WS₂ of 14° displays a significantly high photoresponsivity (55.9 A W^-1 ), large detectivity (1.07 × 10¹⁰ Jones), and high external quantum efficiency (135%). These findings provide engineering tools for heterostructure design for their application in optoelectronic devices.

Screening of Excitons by Organic Cations in Quasi-Two-Dimensional Organic-Inorganic Lead-Halide Perovskites

Interlayer organic cations in quasi-two-dimensional halide perovskites are a versatile tuning vehicle for the optoelectronic properties of these complex systems, but chemical intuition for this design route is yet to be established. Here, we use density functional theory, the GW approximation, and the Bethe-Salpeter equation approach to understand the contribution of the organic cation to the quasiparticle band gap and exciton binding energy of layered perovskites. We show that organic cations in quasi-two-dimensional perovskites contribute significantly to the dielectric screening in these systems, countering quantum confinement effects on the quasiparticle band gap and the exciton binding energy. Using a simple electrostatics model inspired by parallel-plate capacitors, we decouple the organic cation and inorganic layer contributions to the effective dielectric constants and show that dielectric properties of layered perovskites are broadly tunable via the interlayer cation, providing a direct means of tuning photophysical properties for a variety of applications.

DFT+U within the framework of linear combination of numerical atomic orbitals

We present a formulation and implementation of the density functional theory (DFT)+U method within the framework of linear combination of numerical atomic orbitals (NAO). Our implementation not only enables single-point total energy and electronic-structure calculations but also provides access to atomic forces and cell stresses, hence allowing for full structure relaxations of periodic systems. Furthermore, our implementation allows one to deal with non-collinear spin texture, with the spin-orbit coupling (SOC) effect treated self-consistently. The key aspect behind our implementation is a suitable definition of the correlated subspace when multiple atomic orbitals with the same angular momentum are used, and this is addressed via the "Mulliken charge projector" constructed in terms of the first (most localized) atomic orbital within the d/f angular momentum channel. The important Hubbard U and Hund J parameters can be estimated from a screened Coulomb potential of the Yukawa type, with the screening parameter either chosen semi-empirically or determined from the Thomas-Fermi screening model. Benchmark calculations are performed for four late transition metal monoxide bulk systems, i.e., MnO, FeO, CoO, and NiO, and for the 5d-electron compounds IrO₂. For the former type of systems, we check the performance of our DFT+U implementation for calculating bandgaps, magnetic moments, electronic band structures, as well as forces and stresses; for the latter, the efficacy of our DFT+U+SOC implementation is assessed. Systematic comparisons with available experimental results, especially with the results from other implementation schemes, are carried out, which demonstrate the validity of our NAO-based DFT+U formalism and implementation.

Improved proton-transfer barriers with van der Waals density functionals: Role of repulsive non-local correlation

Proton-transfer (PT) between organic complexes is a common and important biochemical process. Unfortunately, PT energy barriers are difficult to accurately predict using density functional theory (DFT); in particular, using the generalized gradient approximation (GGA) tends to underestimate PT barriers. Moreover, PT typically occurs in environments where dispersion forces contribute to the cohesion of the system; thus, a suitable exchange-correlation functional should accurately describe both dispersion forces and PT barriers. This paper provides benchmark results for the PT barriers of several density functionals including several variants of the van der Waals density functional (vdW-DF).The benchmark set comprises small organic molecules with inter- and intra-molecular PT. The results show that replacing GGA correlation with a fully non-local vdW-DF correlation increases the PT barriers, making it closer to the quantum chemical reference values.In contrast, including non-local correlations with the Vydrov-Voorhis (VV) method or dispersion-corrections at the DFT-D3 or the Tkatchenko-Scheffler (TS) levelhas barely any impact on the PT barriers.Hybrid functionals also increase and improve the energies,resulting in excellent performance of hybrid versions of the van der Waals density functionals vdW-DF-cx and vdW-DF2-B86R. For the formic acid dimer PT system, we analyzed the GGA exchange and non-local correlation contributions. The analysis shows that the repulsive part of the non-local correlation kernel plays a key role in the PT energy barriers predicted with vdW-DF.

Bridging the gap between atomically thin semiconductors and metal leads

Electrically interfacing atomically thin transition metal dichalcogenide semiconductors (TMDSCs) with metal leads is challenging because of undesired interface barriers, which have drastically constrained the electrical performance of TMDSC devices for exploring their unconventional physical properties and realizing potential electronic applications. Here we demonstrate a strategy to achieve nearly barrier-free electrical contacts with few-layer TMDSCs by engineering interfacial bonding distortion. The carrier-injection efficiency of such electrical junction is substantially increased with robust ohmic behaviors from room to cryogenic temperatures. The performance enhancements of TMDSC field-effect transistors are well reflected by the low contact resistance (down to 90 Ωµm in MoS₂, towards the quantum limit), the high field-effect mobility (up to 358,000 cm²V^-1s^-1 in WSe₂), and the prominent transport characteristics at cryogenic temperatures. This method also offers possibilities of the local manipulation of atomic structures and electronic properties for TMDSC device design.

Multipole polaron in the devil's staircase of CeSb

Rare-earth intermetallic compounds exhibit rich phenomena induced by the interplay between localized f orbitals and conduction electrons. However, since the energy scale of the crystal-electric-field splitting is only a few millielectronvolts, the nature of the mobile electrons accompanied by collective crystal-electric-field excitations has not been unveiled. Here, we examine the low-energy electronic structures of CeSb through the anomalous magnetostructural transitions below the Néel temperature, ~17 K, termed the 'devil's staircase', using laser angle-resolved photoemission, Raman and neutron scattering spectroscopies. We report another type of electron-boson coupling between mobile electrons and quadrupole crystal-electric-field excitations of the 4f orbitals, which renormalizes the Sb 5p band prominently, yielding a kink at a very low energy (~7 meV). This coupling strength is strong and exhibits anomalous step-like enhancement during the devil's staircase transition, unveiling a new type of quasiparticle, named the 'multipole polaron', comprising a mobile electron dressed with a cloud of the quadrupole crystal-electric-field polarization.

Light-Tunable Charge Density Wave Orders in MoTe_{2} and WTe_{2} Single Layers

By using constrained density functional theory modeling, we demonstrate that ultrafast optical pumping unveils hidden charge orders in group VI monolayer transition metal ditellurides. We show that irradiation of the insulating 2H phases stabilizes multiple transient charge density wave orders with light-tunable distortion, periodicity, electronic structure, and band gap. Moreover, optical pumping of the semimetallic 1T^{'} phases generates a transient charge ordered metallic phase composed of 2D diamond clusters. For each transient phase we identify the critical fluence at which it is observed and the specific optical and Raman fingerprints to directly compare with future ultrafast pump-probe experiments. Our work demonstrates that it is possible to stabilize charge density waves even in insulating 2D transition metal dichalcogenides by ultrafast irradiation.

Role of topological surface states and mirror symmetry in topological crystalline insulator SnTe as an efficient electrocatalyst

The surface orientation dependence on the hydrogen evolution reaction (HER) performance of topological crystalline insulator (TCI) SnTe thin films is studied. Their intrinsic activities are determined by linear sweep voltammetry and cyclic voltammetry measurements. It is found that SnTe (001) and (111) surfaces exhibit intrinsic activities significantly larger than the (211) surface. Density functional theory calculations reveal that pure (001) and (111) surfaces are not good electrocatalysts, while those with Sn vacancies or partially oxidized surfaces, with the latter as evidenced by X-ray photoelectron spectroscopy, have high activity. The calculated overall performance of the (001) and (111) surfaces with robust topological surface states (TSSs) is better than that of the lowly symmetric (211) surface with fragile or without TSSs, which is further supported by their measured weak antilocalization strength. The high HER activity of SnTe (001) and (111) is attributed to the enhanced charge transfer between H atoms and TSSs. We also address the effect of possible surface facets and the contrast of the HER activity of the available active sites among the three samples. Our study demonstrates that the TSSs and mirror symmetry of TCIs expedite their HER activity.

First-principles study on the electronic and optical properties of Bi2WO6

Photocatalytic materials attract continued scientific interest due to their possible application in energy harvesting. These applications critically rely on efficient photon absorption and exciton physics, which are governed by the underlying electronic structure. We report the electronic properties and optical response of the Bi₂WO₆ bulk photocatalyst using first-principle methods. The density functional theory DFT-computed electronic band gap is corrected by including Hubbard potentials for W-5d and O-2p orbitals, and one of the most advanced methods, Quasi-Particle (QP) GW at different levels, with semi-core states of Bi (5s and 5p) and W (4f), carefully taken into account in GW calculations. The perplexing nature of band character of Bi₂WO₆ is examined, and it comes out to be direct at PBE level without SOC. However, it shows indirect nature at GW level or when Spin–Orbit Coupling (SOC) is turned on even at PBE level. The optical response of the material system is computed within independent-particle approximation (IPA), taking into account local field effects and employing the time-dependent DFT (TDDFT) method. Bethe–Salpeter equation (BSE) is used to capture the excitonic effect, and the results of these approximations are compared with the experimental data. Our first-principle calculations results indicate that electron–hole interaction significantly modifies optical absorption of Bi₂WO₆, thereby verifying the reported experimental observations.

The nature of the band gap obtained from SOC and QP corrections changes to indirect. The semi-core states of Bi have been proved to be crucial in the GW calculations. Optical absorption from BSE, including SOC best matches the experimental data.

Phase transition and topological transistors based on monolayer Na3Bi nanoribbons

Recently, a topological-to-trivial insulator quantum-phase transition induced by an electric field has been experimentally reported in monolayer (ML) and bilayer (BL) Na₃Bi. A narrow ML/BL Na₃Bi nanoribbon is necessary to fabricate a high-performance topological transistor. By using the density functional theory method, we found that wider ML Na₃Bi nanoribbons (>7 nm) are topological insulators, featured by insulating bulk states and dissipationless metallic edge states. However, a bandgap is opened for extremely narrow ML Na₃Bi nanoribbons (<4 nm) due to the quantum confinement effect, and its size increases with the decrease in width. In the topological insulating ML Na₃Bi nanoribbons, a bandgap is opened in the metallic edge states under an external displacement electric field, with strength (∼1.0 V Å^-1) much smaller than the reopened displacement electric field in ML Na₃Bi (3 V Å^-1). An ultrashort ML Na₃Bi zigzag nanoribbon topological transistor switched by the electrical field was calculated using first-principles quantum transport simulation. It shows an on/off current/conductance ratio of 4-71 and a large on-state current of 1090 μA μm^-1. Therefore, a proof of the concept of topological transistors is presented.

Phonon Screening of Excitons in Semiconductors: Halide Perovskites and Beyond

The ab initio Bethe-Salpeter equation (BSE) approach, an established method for the study of excitons in materials, is typically solved in a limit where only static screening from electrons is captured. Here, we generalize this framework to include dynamical screening from phonons at lowest order in the electron-phonon interaction. We apply this generalized BSE approach to a series of inorganic lead halide perovskites, CsPbX_{3}, with X=Cl, Br, and I. We find that inclusion of screening from phonons significantly reduces the computed exciton binding energies of these systems. By deriving a simple expression for phonon screening effects, we reveal general trends for their importance in semiconductors and insulators, based on a hydrogenic exciton model. We demonstrate that the magnitude of the phonon screening correction in isotropic materials can be reliably predicted using four material specific parameters: the reduced effective mass, static and optical dielectric constants, and frequency of the most strongly coupled longitudinal-optical phonon mode. This framework helps to elucidate the importance of phonon screening and its relation to excitonic properties in a broad class of semiconductors.

Calculation of Berry curvature using non-orthogonal atomic orbitals

We present a derivation of the full formula to calculate the Berry curvature on non-orthogonal numerical atomic orbital (NAO) bases. Because usually, the number of NAOs is larger than that of the Wannier bases, we use a orbital contraction method to reduce the basis sizes, which can greatly improve the calculation efficiency without significantly reducing the calculation accuracy. We benchmark the formula by calculating the Berry curvature of ferroelectric BaTiO₃and bcc Fe, as well as the anomalous Hall conductivity for Fe. The results are in excellent agreement with the finite-difference and previous results in the literature. We find that there are corrections terms to the Kubo formula of the Berry curvature. For the full NAO base, the differences between the two methods are negligibly small, but for the reduced bases sets, the correction terms become larger, which may not be neglected in some cases. The formula developed in this work can readily be applied to the non-orthogonal generalized Wannier functions.

When band convergence is not beneficial for thermoelectrics

Band convergence is considered a clear benefit to thermoelectric performance because it increases the charge carrier concentration for a given Fermi level, which typically enhances charge conductivity while preserving the Seebeck coefficient. However, this advantage hinges on the assumption that interband scattering of carriers is weak or insignificant. With first-principles treatment of electron-phonon scattering in the CaMg2Sb2-CaZn2Sb2 Zintl system and full Heusler Sr2SbAu, we demonstrate that the benefit of band convergence can be intrinsically negated by interband scattering depending on the manner in which bands converge. In the Zintl alloy, band convergence does not improve weighted mobility or the density-of-states effective mass. We trace the underlying reason to the fact that the bands converge at a one k-point, which induces strong interband scattering of both the deformation-potential and the polar-optical kinds. The case contrasts with band convergence at distant k-points (as in the full Heusler), which better preserves the single-band scattering behavior thereby successfully leading to improved performance. Therefore, we suggest that band convergence as thermoelectric design principle is best suited to cases in which it occurs at distant k-points.

Materials Design and Optimization for Next-Generation Solar Cell and Light-Emitting Technologies

We review some of the most potent directions in the design of materials for next-generation solar cell and light-emitting technologies that go beyond traditional solid-state inorganic semiconductor-based devices, from both the experimental and computational standpoints. We focus on selected recent conceptual advances in tackling issues which are expected to significantly impact applied literature in the coming years. Specifically, we consider solution processability, design of dopant-free charge transport materials, two-dimensional conjugated polymeric semiconductors, and colloidal quantum dot assemblies in the fields of experimental synthesis, characterization, and device fabrication. Key modeling issues that we consider are calculations of optical properties and of effects of aggregation, including recent advances in methods beyond linear-response time-dependent density functional theory and recent insights into the effects of correlation when going beyond the single-particle ansatz as well as in the context of modeling of thermally activated fluorescence.

Cubic-Scaling All-Electron GW Calculations with a Separable Density-Fitting Space-Time Approach

We present an implementation of the GW space-time approach that allows cubic-scaling all-electron calculations with standard Gaussian basis sets without exploiting any localization or sparsity considerations. The independent-electron susceptibility is constructed in a time representation over a nonuniform distribution of real-space locations {r_k} optimized within a separable resolution-of-the-identity framework to reproduce standard Coulomb-fitting calculations with meV accuracy. The compactness of the obtained {r_k} distribution leads to a crossover with the standard Coulomb-fitting scheme for system sizes below a few hundred electrons. The needed analytic continuation follows a recent approach that requires the continuation of the screened Coulomb potential rather than the much more structured self-energy. The present scheme is benchmarked over large molecular sets, and scaling properties are demonstrated on a family of defected hexagonal boron-nitride flakes containing up to 6000 electrons.

Gate-controlled BCS-BEC crossover in a two-dimensional superconductor

Bardeen-Cooper-Schrieffer (BCS) superfluidity and Bose-Einstein condensation (BEC) are the two extreme limits of the ground state of the paired fermion systems. We report crossover behavior from the BCS limit to the BEC limit realized by varying carrier density in a two-dimensional superconductor, electron-doped zirconium nitride chloride. The phase diagram, established by simultaneous measurements of resistivity and tunneling spectra under ionic gating, demonstrates a pseudogap phase in the low-doping regime. The ratio of the superconducting transition temperature and Fermi temperature in the low-carrier density limit is consistent with the theoretical upper bound expected in the BCS-BEC crossover regime. These results indicate that the gate-doped semiconductor provides an ideal platform for the two-dimensional BCS-BEC crossover without added complexities present in other solid-state systems.

Determining the Structure-Property Relationships of Quasi-Two-Dimensional Semiconductor Nanoplatelets

We report a theoretical study of CdSe nanoplatelets aimed at identifying the main factors determining their photophysical properties. Using atomic configurations optimized with density functional theory calculations, we computed quasiparticle and exciton binding energies of nanoplatelets with two to seven monolayers. We employed many body perturbation theory at the GW level and solved the Bethe-Salpeter equation to obtain absorption spectra and excitonic properties. Our results, which agree well with recent experiments, were then used to design a model that allows us to disentangle the effects of quantum confinement, strain induced by passivating ligands, and dielectric environment on the electronic properties of nanoplatelets. We found that, for the model to accurately reproduce our first principle results, it is critical to account for surface stress and consider a finite potential barrier and energy-dependent effective masses when describing quantum confinement. Our findings call into question previous assumptions on the validity of an infinite barrier to describe carrier confinement in nanoplatelets, suggesting that it may be possible to optimize interfacial charge transfer and extraction by appropriately choosing passivating ligands. The model developed here is generalizable to core-shell platelets and enables the description of system sizes not yet directly treatable by first-principles calculations.

Machine learning dielectric screening for the simulation of excited state properties of molecules and materials

Accurate and efficient calculations of absorption spectra of molecules and materials are essential for the understanding and rational design of broad classes of systems. Solving the Bethe-Salpeter equation (BSE) for electron-hole pairs usually yields accurate predictions of absorption spectra, but it is computationally expensive, especially if thermal averages of spectra computed for multiple configurations are required. We present a method based on machine learning to evaluate a key quantity entering the definition of absorption spectra: the dielectric screening. We show that our approach yields a model for the screening that is transferable between multiple configurations sampled during first principles molecular dynamics simulations; hence it leads to a substantial improvement in the efficiency of calculations of finite temperature spectra. We obtained computational gains of one to two orders of magnitude for systems with 50 to 500 atoms, including liquids, solids, nanostructures, and solid/liquid interfaces. Importantly, the models of dielectric screening derived here may be used not only in the solution of the BSE but also in developing functionals for time-dependent density functional theory (TDDFT) calculations of homogeneous and heterogeneous systems. Overall, our work provides a strategy to combine machine learning with electronic structure calculations to accelerate first principles simulations of excited-state properties.

Quantum Information and Algorithms for Correlated Quantum Matter

Discoveries in quantum materials, which are characterized by the strongly quantum-mechanical nature of electrons and atoms, have revealed exotic properties that arise from correlations. It is the promise of quantum materials for quantum information science superimposed with the potential of new computational quantum algorithms to discover new quantum materials that inspires this Review. We anticipate that quantum materials to be discovered and developed in the next years will transform the areas of quantum information processing including communication, storage, and computing. Simultaneously, efforts toward developing new quantum algorithmic approaches for quantum simulation and advanced calculation methods for many-body quantum systems enable major advances toward functional quantum materials and their deployment. The advent of quantum computing brings new possibilities for eliminating the exponential complexity that has stymied simulation of correlated quantum systems on high-performance classical computers. Here, we review new algorithms and computational approaches to predict and understand the behavior of correlated quantum matter. The strongly interdisciplinary nature of the topics covered necessitates a common language to integrate ideas from these fields. We aim to provide this common language while weaving together fields across electronic structure theory, quantum electrodynamics, algorithm design, and open quantum systems. Our Review is timely in presenting the state-of-the-art in the field toward algorithms with nonexponential complexity for correlated quantum matter with applications in grand-challenge problems. Looking to the future, at the intersection of quantum information science and algorithms for correlated quantum matter, we envision seminal advances in predicting many-body quantum states and describing excitonic quantum matter and large-scale entangled states, a better understanding of high-temperature superconductivity, and quantifying open quantum system dynamics.

Low-Order Scaling G0W0 by Pair Atomic Density Fitting

We derive a low-scaling G0W0 algorithm for molecules using pair atomic density fitting (PADF) and an imaginary time representation of the Green's function and describe its implementation in the Slater type orbital (STO)-based Amsterdam density functional (ADF) electronic structure code. We demonstrate the scalability of our algorithm on a series of water clusters with up to 432 atoms and 7776 basis functions and observe asymptotic quadratic scaling with realistic threshold qualities controlling distance effects and basis sets of triple-ζ (TZ) plus double polarization quality. Also owing to a very small prefactor, a G0W0 calculation for the largest of these clusters takes only 240 CPU hours with these settings. We assess the accuracy of our algorithm for HOMO and LUMO energies in the GW100 database. With errors of 0.24 eV for HOMO energies on the quadruple-ζ level, our implementation is less accurate than canonical all-electron implementations using the larger def2-QZVP GTO-type basis set. Apart from basis set errors, this is related to the well-known shortcomings of the GW space-time method using analytical continuation techniques as well as to numerical issues of the PADF approach of accurately representing diffuse atomic orbital (AO) products. We speculate that these difficulties might be overcome by using optimized auxiliary fit sets with more diffuse functions of higher angular momenta. Despite these shortcomings, for subsets of medium and large molecules from the GW5000 database, the error of our approach using basis sets of TZ and augmented double-ζ (DZ) quality is decreasing with system size. On the augmented DZ level, we reproduce canonical, complete basis set limit extrapolated reference values with an accuracy of 80 meV on average for a set of 20 large organic molecules. We anticipate our algorithm, in its current form, to be very useful in the study of single-particle properties of large organic systems such as chromophores and acceptor molecules.

Influence of Electronic Structure Modeling and Junction Structure on First-Principles Chiral Induced Spin Selectivity

We have carried out a comprehensive study of the influence of electronic structure modeling and junction structure description on the first-principles calculation of the spin polarization in molecular junctions caused by the chiral induced spin selectivity (CISS) effect. We explore the limits and the sensitivity to modeling decisions of a Landauer/Green's function/two-component density functional theory approach to CISS. We find that although the CISS effect is entirely attributed in the literature to molecular spin filtering, spin-orbit coupling being partially inherited from the metal electrodes plays an important role in our calculations on ideal carbon helices, even though this effect cannot explain the experimental conductance results. Its magnitude depends considerably on the shape, size, and material of the metal clusters modeling the electrodes. Also, a pronounced dependence on the specific description of exchange interaction and spin-orbit coupling is manifest in our approach. This is important because the interplay between exchange effects and spin-orbit coupling may play an important role in the description of the junction magnetic response. Our calculations are relevant for the whole field of spin-polarized electron transport and electron transfer, because there is still an open discussion in the literature about the detailed underlying mechanism and the magnitude of physical parameters that need to be included to achieve a consistent description of the CISS effect: seemingly good quantitative agreement between simulation and the experiment can be caused by error compensation, because spin polarization as contained in a Landauer/Green's function/two-component density functional theory approach depends strongly on computational and structural parameters.

First-principles studies of strongly correlated states in defect spin qubits in diamond

Using a recently developed quantum embedding theory, we present first-principles calculations of strongly correlated states of spin defects in diamond. Using this theory, effective Hamiltonians are constructed, which can be solved by classical and quantum computers; the latter promise a much more favorable scaling as a function of system size than the former. In particular, we report a study on the neutral group-IV vacancy complexes in diamond, and we discuss their strongly correlated spin-singlet and spin-triplet excited states. Our results provide valuable predictions for experiments aimed at optical manipulation of these defects for quantum information technology applications.

Improving the efficiency of G0W0 calculations with approximate spectral decompositions of dielectric matrices

Recently, it was shown that the calculation of quasiparticle energies using the G₀W₀ approximation can be performed without computing explicitly any virtual electronic states, by expanding the Green function and screened Coulomb interaction in terms of the eigenstates of the static dielectric matrix. Avoiding the evaluation of virtual electronic states leads to improved efficiency and ease of convergence of G₀W₀ calculations. Here, we propose a further improvement of the efficiency of these calculations, based on an approximation of density-density response functions of molecules and solids. The approximation relies on the calculation of a subset of eigenvectors of the dielectric matrix using the kinetic operator instead of the full Hamiltonian, and it does not lead to any substantial loss of accuracy for the quasiparticle energies. The computational savings introduced by this approximation depend on the system, and they become more substantial as the number of electrons increases.