GW Approximation Research Articles

Advancing DFT predictions in Cu-chalcogenides with full-yet-shallow 3d-orbitals: Meta-GGA plus Hubbard-like U correction.

The technologically important Cu-chalcogenides, such as Cu2Se and CuInSe2, usually have relatively small band gaps. Achieving a reliable yet efficient description of the electronic properties has proven to be quite challenging for the popular exchange-correlation functionals of density functional theory, primarily due to the involvement of full-yet-shallow Cu-3d orbitals. In this study, we evaluate the applicability of several meta-generalized gradient approximation (GGA) functionals that have been recently developed. We find that the r2SCAN (regularized-restored strongly constrained and appropriately normed) functional significantly improves upon conventional local density approximation and GGA in terms of geometry and electronic band structure; however, there is still a notable discrepancy with experimental results due to the remaining delocalization error. This error is mitigated by combining r2SCAN with a Hubbard-like U correction applied to the Cu-3d orbitals. For predicting band gaps, both the TASK functional and the mBJ potential, when combined with the U correction, demonstrate similar accuracies with a mean absolute error of 0.17-0.19eV. This accuracy is lower than that achieved with the many-body Hedin's GW approximation method but more accurate than that of hybrid functionals. Moreover, the r2SCAN+U approach well reproduces the phonon dispersion in CuInSe2, revealing a neglected computational problem in previous reports. We conclude that the meta-GGA+U approach represents a significant advancement by striking a balance between reliability and computational effort, and further efforts are still required to describe the Cu-3d orbitals more accurately.

Embedded Many‐Body Green's Function Methods for Electronic Excitations in Complex Molecular Systems

ABSTRACTMany‐body Green's function theory in the GW approximation with the Bethe–Salpeter equation (BSE) provides a powerful framework for the first‐principles calculations of single‐particle and electron–hole excitations in perfect crystals and molecules alike. Application to complex molecular systems, for example, solvated dyes, molecular aggregates, thin films, interfaces, or macromolecules, is particularly challenging as they contain a prohibitively large number of atoms. Exploiting the often localized nature of excitation in such disordered systems, several methods have recently been developed in which GW‐BSE is applied to a smaller, tractable region of interest that is embedded into an environment described with a lower‐level method. Here, we review the various strategies proposed for such embedded many‐body Green's functions approaches, including quantum–quantum and quantum–classical embeddings, and focus in particular on how they include environment screening effects either intrinsically in the screened Coulomb interaction in the GW and BSE steps or via extrinsic electrostatic couplings.

Optical Gaps of Ionic Materials from GW/BSE-in-DFT and CC2-in-DFT.

This work presents a density functional theory (DFT)-based embedding technique for the calculation of optical gaps in ionic solids. The approach partitions the supercell of the ionic solid and embeds a small molecule-like cluster in a periodic environment using a cluster-in-periodic embedding method. The environment is treated with DFT, and its influence on the cluster is captured by a DFT-based embedding potential. The optical gap is estimated as the lowest singlet excitation energy of the embedded cluster, obtained using a wave function theory method: second-order approximate coupled-cluster singles and doubles (CC2), and a many-body perturbation theory method: GW approximation combined with the Bethe-Salpeter equation (GW/BSE). The calculated excitation energies are benchmarked against the periodic GW/BSE values, equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) results, and experiments. Both CC2-in-DFT and GW/BSE-in-DFT deliver excitation energies that are in good agreement with experimental values for several ionic solids (MgO, CaO, LiF, NaF, KF, and LiCl) while incurring negligible computational costs. Notably, GW/BSE-in-DFT exhibits remarkable accuracy with a mean absolute error (MAE) of just 0.38 eV with respect to experiments, demonstrating the effectiveness of the embedding strategy. In addition, the versatility of the method is highlighted by investigating the optical gap of a 2D MgCl2 system and the excitation energy of an oxygen vacancy in MgO, with results in good agreement with reported values.

Valence photoelectron spectra of aminobenzoic acid molecules: a combined theoretical and experimental study

Abstract The valence photoelectron spectra (PES) of gas-phase aminobenzoic acids (meta-, ortho- and para-isomers) were measured using synchrotron radiation and calculated from first principles using Density Functional Theory (DFT) with popular hybrid exchange-correlation functionals and many-body perturbation theory using the perturbative one-shot (G0W0) and eigenvalue self-consistent (GnW0) approaches within the GW approximation. The vibrational structures and line shapes found in the PES were modeled using Time-Dependent DFT. Theory can reproduce the experimental results very well. The photoelectron-photoion coincidence spectra of the ortho- and para-isomers were also measured. They reveal interesting differences in the fragmentation patterns and the influence of metastable states at the onset of fragmentation.

Discovery of novel silicon allotropes with optimized band gaps to enhance solar cell efficiency through evolutionary algorithms and machine learning

In the pursuit of advancing solar energy technologies, this study presents 20 direct and quasi-direct band gap silicon crystalline semiconductors that satisfy the Shockley-Queisser limit, a benchmark for solar cell efficiency. Employing two evolutionary algorithm-based searches, we optimize structures and calculate fitness function using the DFTB method and Gaussian approximation potential. Following the preselection of structures based on energy considerations, we further optimize them using PBEsol DFT. Subsequently, we screen the structures based on their band gap, employing a DFTB method tailored for band gap calculation of silicon crystals. To ensure accurate band gap determination, we employ HSE and GW methods. To validate the structural stability, we employ phonon analysis via linear regression algorithm applied to PBEsol DFT data. Significantly, the structures unveiled in this study are of great importance due to their proven stability from both mechanical and dynamic perspectives. Furthermore, the ductility and low density of certain structures enhance their potential application. We examine the optical properties by studying the imaginary part of the dielectric function by solving the Bethe–Salpeter Equation on top of GW approximation. By calculating the SLME, we achieve an efficiency of 32.7% for Si22 at a thickness of 500 nm. Moreover, the study harnesses various machine learning algorithms to develop a predictive model for the band gap energy of these silicon structures. Input data for machine learning models are derived from structural MBTR and SOAP descriptors, as well as DFT outputs. Notably, the results reveal that features extracted from DFT outperform the MBTR and SOAP descriptors.

Excitonic and optoelectronic investigations of bromide-chloride mixed vacancy-ordered double tellurium perovskite systems

Metal-halide perovskites, including vacancy-ordered double perovskites, are versatile semiconductors with applications in photovoltaics and sensors. Here we explore the structural stability, electronic and optical properties of Cs2Te(Br1-xClx)6 series using first-principles-based on density functional theory and state-of-the-art many-body perturbation theory. Our study reveals consistent energy levels across different crystal structures obtained by varying Cl concentrations, indicating uniform structural stability. By employing hybrid density functional theory with spin-orbit coupling, we analyze the effect of Cl-site substitutions on electronic and optical properties. We observe a quasi-linear relationship between band gap and Cl concentration in Cs2Te(Br1-xClx)6 compositions, with alloying resulting in a redshift in the optical absorption coefficient. Moreover, we explore electron-hole interactions using the GW approximation and Bethe−Salpeter equation, revealing exciton binding energies and dark-bright splitting. Remarkably, exciton binding energies, reaching up to 930 meV, can be finely tuned through substitutional engineering. Finally, we investigate the thermoelectric properties of the Br/Cl mixed halide double perovskites, suggesting promising prospects for their application as thermoelectric materials.

First-Principles Studies of the Electronic and Optical Properties of Two-Dimensional Arsenic-Phosphorus (2D As-P) Compounds.

In this work, we propose the construction of a two-dimensional system based on the stable phases previously reported for the 2D arsenic and phosphorus compounds, with hexagonal and orthorhombic symmetries. Therefore, we have modeled one hexagonal and three possible orthorhombic structures. To ensure the dynamical stability, we performed phonon spectra calculations for each system. We found that all phases are dynamically stable. To ensure the thermodynamic and mechanical stabilities, we have calculated cohesive energies and elastic constants. Our results show that the criteria for the stabilities are all fulfilled. For these stable structures, we computed the electronic and optical properties from first-principles studies based on density functional theory. The computation of electronic band gaps was performed by using the GW approximation to overcome the underestimation of the results obtained from standard DFT approaches. To study the optical properties, we have computed the dielectric function imaginary part within the BSE approach, which takes into account the excitonic effects and allows us to calculate the exciton binding energies of each system. The study was complemented by the computation of the absorption coefficient. From our calculations, it can be established that the 2D As-P systems are good candidates for several technological applications.

Ab Initio calculations of Low-Energy Quasiparticle Lifetimes in Bilayer Graphene

Motivated by recent experimental resultswe calculate from first-principles the lifetime of low-energy quasiparticles in bilayer graphene (BLG). We take into account the scattering rate arising from electron-electron interactions within the GW approximation for the electron self-energy and consider several p-type doping levels ranging from 0 to ~ 2.4x1012 holes/cm2. In the undoped case we find that the average inverse lifetime scales linearly with energy away from the charge neutrality point, with values in good agreement with experiments. The decay rate is approximately three times larger than in monolayer graphene, a consequence of the enhanced screening in BLG.In the doped case, the dependence of the inverse lifetime on quasiparticle energy acquires a non-linear component due to the opening of an additional decay channel mediated by acoustic plasmons.This work was supported by the LDRD program at Sandia National Laboratories (SNL). SNL is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA0003525.The views expressed in the article do not necessarily represent the views of the U.S. Department of Energy or the United States Government.

Excited‐State Dynamics and Optical Properties of Silica Under Ultrafast Laser Irradiation

AbstractExcited by intense infrared ultrafast light pulses, a wide bandgap material undergoes nonlinear ionization, generating a high density of free electrons in conduction states. As a result, the electronic band structure is critically modified and the bandgap shrinks. This induces rapid changes in optical properties, dramatically affecting the absorption spectrum during light coupling to the dielectric surface or during nonlinear propagation inside the bulk. This study analyzes the structural behavior and the modification of the optical properties of laser‐excited silica glass at the molecular cluster level through first‐principles simulations. Employing density functional theory and the GW approximations for band structure under nonequilibrium conditions, alongside the Bethe–Salpeter equation, the dynamics of the optical properties of fused silica are comprehensively explored. The behavior of excited fused silica in a wide photon energy range (from a few to 20 eV) is thus predicted. Laser‐induced electron excitation triggers a redistribution of charges between oxygen and silicon atoms, accompanied by a significant increase in electronic pressure, local atomic structure rearrangement, and material expansion. Molecular dynamics simulations offer a temporal perspective on the excited state dynamics, unveiling the intricate interplay between electronic and atomic effects on bandgap evolution. The analysis sheds light on excitonic resonances, intraband and interband transitions in fused silica under ultrafast laser irradiation, providing valuable insights into its excited state behavior and optical properties.

BSE@GW Prediction of Charge Transfer Exciton in Molecular Complexes: Assessment of Self-Energy and Exchange-Correlation Dependence.

The Bethe-Salpeter equation using the GW approximation to the self-energy (BSE@GW) is a computationally attractive method for studying electronic excitation from first principles within the many-body Green's function theory framework. We examine its dependence on the underlying exchange-correlation (XC) approximation as well as on the GW approximation for predicting the charge transfer exciton formation at representative type-II interfaces between molecular systems of tetrachloro-1,2-benzoquinone (TCBQ) and acene derivatives. For the XC approximation, we consider several widely used generalized gradient approximation (GGA) and hybrid GGA functionals. For the GW self-energy approximation, we examine the recently proposed renormalized singles approach by Yang and coauthors [J. Phys. Chem. Lett. 2019, 10 (3), 447-452; J. Chem. Theory Comput. 2022, 18, 7570-7585] in addition to other commonly employed approximated GW schemes. We demonstrate a reliable prediction of the charge transfer exciton within the BSE@GW level of theory.

Classical and quantum theory of fluctuations for many‐particle systems out of equilibrium

AbstractCorrelated classical and quantum many‐particle systems out of equilibrium are of high interest in many fields, including dense plasmas, correlated solids, and ultracold atoms. Accurate theoretical description of these systems is challenging both, conceptionally and with respect to computational resources. While for classical systems, in principle, exact simulations are possible via molecular dynamics, this is not the case for quantum systems. Alternatively, one can use many‐particle approaches such as hydrodynamics, kinetic theory, or nonequilibrium Green functions (NEGF). However, NEGF exhibit a very unfavorable cubic scaling of the CPU time with the number of time steps. An alternative is the G1–G2 scheme [N. Schlünzen et al., Phys. Rev. Lett. 124, 076601 (2020)] which allows for NEGF simulations with time linear scaling, however, at the cost of large memory consumption. The reason is the need to store the two‐particle correlation function. This problem can be overcome for a number of approximations by reformulating the kinetic equations in terms of fluctuations – an approach that was developed, for classical systems, by Yu.L. Klimontovich [JETP 33, 982 (1957)]. Here, we present an overview of his ideas and extend them to quantum systems. In particular, we demonstrate that this quantum fluctuations approach can reproduce the nonequilibrium GW approximation [E. Schroedter et al., Cond. Matt. Phys. 25, 23401 (2022)] promising high accuracy at low computational cost which arises from an effective semiclassical stochastic sampling procedure. We also demonstrate how to extend the approach to the two‐time exchange‐correlation functions and the density response properties. [E. Schroedter et al., Phys. Rev. B 108, 205109 (2023)]. The results are equivalent to the Bethe–Salpeter equation for the two‐time exchange‐correlation function when the generalized Kadanoff‐Baym ansatz with Hartree‐Fock propagators is applied [E. Schroedter and M. Bonitz, phys. stat. sol. (b) 2024, 2300564].

Beyond Electrons: Correlation and Self-Energy in Multicomponent Density Functional Theory.

Post-Kohn-Sham methods are used to evaluate the ground-state correlation energy and the orbital self-energy of systems consisting of multiple flavors of different fermions. Starting from multicomponent density functional theory, suitable ways to arrive at the corresponding multicomponent random-phase approximation and the multicomponent Green's function approximation, including relativistic effects, are outlined. Given the importance of both of this methods in the development of modern Kohn-Sham density functional approximations, this work will provide a foundation to design advanced multicomponent density functional approximations. Additionally, the quasiparticle energies are needed to study light-matter interactions with the Bethe-Salpeter equation.

Strange metal to insulator transitions in the lowest Landau level

We study the microscopic model of electrons in the partially-filled lowest Landau level interacting via the Coulomb potential by the diagrammatic theory within the GW approximation. In a wide range of filling fractions and temperatures, we find a homogeneous non-Fermi liquid (nFL) state similar to that found in the Sachdev-Ye-Kitaev (SYK) model, with logarithmic corrections to the anomalous dimension. In addition, the phase diagram is qualitatively similar to that of SYK: a first-order transition terminating at a critical end-point separates the nFL phase from a band insulator that corresponds to the fully filled Landau level. This critical point, as well as that of the SYK model—whose critical exponents we determine more precisely—are shown to both belong to the Van der Waals universality class. The possibility of a charge density wave (CDW) instability is also investigated, and we find the homogeneous nFL state to extend down to the ground state for fillings 0.2≲ν≲0.8, while a CDW appears outside this range of fillings at sufficiently low temperatures. Our results suggest that the SYK-like nFL state should be a generic feature of the partially filled lowest Landau level at intermediate temperatures. Published by the American Physical Society 2024

Electronic Couplings and Conversion Dynamics between Localized and Charge Transfer Excitations from Many-Body Green's Functions Theory.

We investigate the determination of electronic coupling between localized excitations (LEs) and charge-transfer (CT) excitations based on many-body Green's functions theory in the GW approximation with the Bethe-Salpeter equation (GW-BSE). Using a small molecule dimer system, we first study the influence of different diabatization methods, as well as different model choices within GW-BSE, such as the self-energy models or different levels of self-consistency, and find that these choices affect the LE-CT couplings only minimally. We then consider a large-scale low-donor morphology formed from rubrene and fullerene and evaluate the LE-CT couplings based on coupled GW-BSE-molecular mechanics calculations. For these disordered systems of bulky molecules, we observe differences in the couplings based on the Edmiston-Ruedenberg diabatization compared to the more approximate Generalize Mulliken-Hush and fragment charge difference diabatization formalisms. In a kinetic model for the conversion between LE and CT states, these differences affect the details of state populations in an intermediate time scale but not the final populations.

Computational Discovery of Intermolecular Singlet Fission Materials Using Many-Body Perturbation Theory.

Intermolecular singlet fission (SF) is the conversion of a photogenerated singlet exciton into two triplet excitons residing on different molecules. SF has the potential to enhance the conversion efficiency of solar cells by harvesting two charge carriers from one high-energy photon, whose surplus energy would otherwise be lost to heat. The development of commercial SF-augmented modules is hindered by the limited selection of molecular crystals that exhibit intermolecular SF in the solid state. Computational exploration may accelerate the discovery of new SF materials. The GW approximation and Bethe-Salpeter equation (GW+BSE) within the framework of many-body perturbation theory is the current state-of-the-art method for calculating the excited-state properties of molecular crystals with periodic boundary conditions. In this Review, we discuss the usage of GW+BSE to assess candidate SF materials as well as its combination with low-cost physical or machine learned models in materials discovery workflows. We demonstrate three successful strategies for the discovery of new SF materials: (i) functionalization of known materials to tune their properties, (ii) finding potential polymorphs with improved crystal packing, and (iii) exploring new classes of materials. In addition, three new candidate SF materials are proposed here, which have not been published previously.

Significant improvement in structural, electronic, optical and thermoelectric properties of PdTe2 in bulk and monolayer phase: A G0W0+BSE approach

Using first principles calculations structural, electronic, thermoelectric and optical properties of PdTe2 in bulk and monolayer were investigated. The calculated lattice parameters with different exchange correlation functionals show that the results obtained with addition of van der Waals corrections (vdW-DFC09x) are very well matched with the results obtained experimental. For correct prediction of electronic band gap, G0W0 approximation is used and the calculated band structure reveal that PdTe2 in bulk form has metallic nature as attained in experimental studies. In addition, the electronic band gap results with G0W0 approximation depicted that PdTe2 in monolayer phase is a semiconductor material with a direct band gap of 1.12 eV. The optical spectra have been calculated via many-body perturbation theory (MBPT) by solving Bethe-Salpeter equation (BSE) (G0W0+BSE). Ultimately, the results of optical spectra demonstrated that PdTe2 in monolayer phase has strong optical absorption within visible light wavelengths than the bulk phase which is good for solar cell applications. Thermoelectric (TE) properties of PdTe2 in bulk and monolayer structures have been studied using BoltzTraP code. The TE properties calculations indicated that better performance can be obtained by reducing the dimensionality of materials. The figure of merit was found to be above unity for monolayer phase. This paper successfully exploited the enhancement of the figure of merit values with the monolayer structure of PdTe2 material.

Two-dimensional monolayer BiSnO3: a novel wide-band-gap semiconductor with high stability and strong ultraviolet absorption

The exploration of two-dimensional (2D) wide-band-gap semiconductors (WBGSs) holds significant scientific and technological importance in the field of condensed matter physics and is actively being pursued in optoelectronic research. In this study, we present the discovery of a novel WBGS, namely monolayer BiSnO3, using first-principles calculations in conjunction with the quasi-particle G0W0 approximation. Our calculations confirm that monolayer BiSnO3 exhibits moderate cleavage energy, positive phonon modes, mechanical resilience, and high temperature resistance (up to 1000 K), which demonstrate its structural stability, flexibility, and potential for experimental realization. Furthermore, band-structure calculations reveal that monolayer BiSnO3 is a typical WBGS material with a band-gap energy (E g) of 3.61 eV and possesses a unique quasi-direct electronic feature due to its quasi-flat valence band. The highest occupied valence flat-band originates from the electronic hybridization between Bi-6p and O-2p states, which are in close proximity to the Fermi level. Remarkably, monolayer BiSnO3 exhibits a high absorption capacity for ultraviolet light spanning the UVA to UVC regions, displaying optical isotropy absorption and an unusual excitonic effect. These intriguing structural and electronic properties establish monolayer BiSnO3 as a promising candidate for the development of new multi-function-integrated electronic and optoelectronic devices in the emerging field of 2D WBGSs.

AB-G0W0: A practical G0W0 method without frequency integration based on an auxiliary boson expansion.

Common G0W0 implementations rely on numerical or analytical frequency integration to determine the G0W0 self-energy, which results in a variety of practical complications. Recently, we have demonstrated an exact connection between the G0W0 approximation and equation-of-motion quantum chemistry approaches [J. Tölle and G. Kin-Lic Chan, J. Chem. Phys. 158, 124123 (2023)]. Based on this connection, we propose a new method to determine G0W0 quasiparticle energies, which completely avoids frequency integration and its associated problems. To achieve this, we make use of an auxiliary boson (AB) expansion. We name the new approach AB-G0W0 and demonstrate its practical applicability in a range of molecular problems.

Fully Dynamic G3W2 Self-Energy for Finite Systems: Formulas and Benchmark.

Over the years, Hedin's GW self-energy has been proven to be a rather accurate and simple approximation to evaluate electronic quasiparticle energies in solids and in molecules. Attempts to improve over the simple GW approximation, the so-called vertex corrections, have been constantly proposed in the literature. Here, we derive, analyze, and benchmark the complete second-order term in the screened Coulomb interaction W for finite systems. This self-energy named G3W2 contains all the possible time orderings that combine 3 Green's functions G and 2 dynamic W. We present the analytic formula and its imaginary frequency counterpart, with the latter allowing us to treat larger molecules. The accuracy of the G3W2 self-energy is evaluated on well-established benchmarks (GW100, Acceptor 24, and Core 65) for valence and core quasiparticle energies. Its link with the simpler static approximation, named SOSEX for static screened second-order exchange, is analyzed, which leads us to propose a more consistent approximation named 2SOSEX. In the end, we find that neither the G3W2 self-energy nor any of the investigated approximations to it improve over one-shot G0W0 with a good starting point. Only quasi-particle self-consistent GW HOMO energies are slightly improved by addition of the G3W2 self-energy correction. We show that this is due to the self-consistent update of the screened Coulomb interaction, leading to an overall sign change of the vertex correction to the frontier quasiparticle energies.

Efficient Full-Frequency GW Calculations Using a Lanczos Method.

The GW approximation is widely used for reliable and accurate modeling of single-particle excitations. It also serves as a starting point for many theoretical methods, such as its use in the Bethe-Salpeter equation (BSE) and dynamical mean-field theory. However, full-frequency GW calculations for large systems with hundreds of atoms remain computationally challenging, even after years of efforts to reduce the prefactor and improve scaling. We propose a method that reformulates the correlation part of the GW self-energy as a resolvent of a Hermitian matrix, which can be efficiently and accurately computed using the standard Lanczos method. This method enables full-frequency GW calculations of material systems with a few hundred atoms on a single computing workstation. We further demonstrate the efficiency of the method by calculating the defect-state energies of silicon quantum dots with diameters up to 4nm and nearly 2,000 silicon atoms using only 20 computational nodes.