Self-consistent GW Calculations Research Articles

Insulating behaviour in room temperature rhombohedral LiNiO2 cathodes is driven by dynamic correlation

Abstract Inspired by the experimental finding of a paramagnetic insulating state in rhombohedral LiNiO2, a lithium-ion battery cathode of great interest, we calculate the electronic, magnetic, and optical properties of LiNiO2 employing a range of single-particle and many-body methods. Within density-functional theory (DFT) using the generalized-gradient approximation (GGA), meta-GGA, and hybrid functionals, we obtain a ferromagnetic half-metallic ground state for rhombohedral LiNiO2, as has been seen previously. Self-consistent GW calculations including self-interaction corrections beyond DFT for various flavours show an electronic band gap albeit with a small quasiparticle peak at the Fermi energy. Moving beyond this, room temperature state-of-the-art dynamical mean-field theory (DMFT) calculations on rhombohedral LiNiO2 show for the first time a gap of combined Mott and charge-transfer character. The paramagnetic insulating state has a band gap of ~0.6 eV, in excellent agreement with experiments and is in sharp contrast to DFT calculations that require the presence of an extra structural symmetry breaking in the form of Jahn–Teller distortions to open a gap. We observe Ni to be in a +2 state in a d 8L configuration, with a charge-transfer ligand hole in O p, and identify the ligand hole state from the DMFT DOS. We further show that whereas DFT shows the presence of an unphysical metallic Drude peak in the optical absorption spectra, DMFT calculations capture the correct form of the optical absorption spectra, and have an excellent match with the calculated band gap as well. Our results clarify that at room temperature, it is the charge transfer gap with a Mott character that causes rhombohedral LiNiO2’s insulating nature; a structural distortion is not required.

A Similarity Renormalization Group Approach to Green's Function Methods.

The family of Green's function methods based on the GW approximation has gained popularity in the electronic structure theory thanks to its accuracy in weakly correlated systems combined with its cost-effectiveness. Despite this, self-consistent versions still pose challenges in terms of convergence. A recent study [Monino and Loos J. Chem. Phys. 2022, 156, 231101.] has linked these convergence issues to the intruder-state problem. In this work, a perturbative analysis of the similarity renormalization group (SRG) approach is performed on Green's function methods. The SRG formalism enables us to derive, from first-principles, the expression of a naturally static and Hermitian form of the self-energy that can be employed in quasiparticle self-consistent GW (qsGW) calculations. The resulting SRG-based regularized self-energy significantly accelerates the convergence of qsGW calculations, slightly improves the overall accuracy, and is straightforward to implement in existing code.

Broken-symmetry self-consistent GW approach: Degree of spin contamination and evaluation of effective exchange couplings in solid antiferromagnets

We adopt a broken-symmetry strategy for evaluating effective magnetic constants J within the fully self-consistent GW method. To understand the degree of spin contamination present in broken-symmetry periodic solutions, we propose several extensive quantities demonstrating that the unrestricted self-consistent GW preserves the broken-symmetry character of the unrestricted Hartree-Fock solutions. The extracted J are close to the ones obtained from multireference wave-function calculations. In this paper, we establish a robust computational procedure for finding magnetic coupling constants from self-consistent GW calculations and apply it to solid antiferromagnetic nickel and manganese oxides.

Unphysical discontinuities, intruder states and regularization in GW methods.

By recasting the non-linear frequency-dependent GW quasiparticle equation into a linear eigenvalue problem, we explain the appearance of multiple solutions and unphysical discontinuities in various physical quantities computed within the GW approximation. Considering the GW self-energy as an effective Hamiltonian, it is shown that these issues are key signatures of strong correlation in the (N ± 1)-electron states and can be directly related to the intruder state problem. A simple and efficient regularization procedure inspired by the similarity renormalization group is proposed to avoid such issues and speed up the convergence of partially self-consistent GW calculations.

Experimental determination of the valence band offsets of ZnGeN2 and (ZnGe)0.94Ga0.12N2 with GaN

A predicted type-II staggered band alignment with an approximately 1.4 eV valence band offset at the ZnGeN2/GaN heterointerface has inspired novel band-engineered III-N/ZnGeN2 heterostructure-based device designs for applications in high performance optoelectronics. We report on the determination of the valence band offset between metalorganic chemical vapor deposition grown (ZnGe)1−x Ga2x N2, for x = 0 and 0.06, and GaN using x-ray photoemission spectroscopy. The valence band of ZnGeN2 was found to lie 1.45–1.65 eV above that of GaN. This result agrees well with the value predicted by first-principles density functional theory calculations using the local density approximation for the potential profile and quasiparticle self-consistent GW calculations of the band edge states relative to the potential. For (ZnGe)0.94Ga0.12N2 the value was determined to be 1.29 eV, ∼10%–20% lower than that of ZnGeN2. The experimental determination of the large band offset between ZnGeN2 and GaN provides promising alternative solutions to address challenges faced with pure III-nitride-based structures and devices.

Effects of the van der Waals Interactions on Structural and Electronic Properties of CH3NH3(Pb,Sn)(I,Br,Cl)3 Halide Perovskites.

In hybrid perovskite materials like CH3NH3PbI3, methylammonium (MA) lead iodide (MAPI), the orientation of the MA+ cations and their ordering can significantly affect the structure of the inorganic framework. Although the states near the band edges are known to be primarily derived from the Pb and halogen orbitals rather than from the organic ion, the latter may have an indirect effect through their impact on the structural relaxation. In this work, we investigate both the structural relaxation effects of the inorganic framework in response to the MA+ orientation and their impact on the electronic structure near the band edges. Calculations are performed for MA(Pb,Sn)X3 with (X = I, Br, and Cl) materials for both Pb- and Sn-based compounds. The work focuses on the high-temperature α-phase, which is nominally cubic if averaged over all possible MA orientations and in which no alternating rotations of the octahedral occur, so that the unit cell is the smallest possible. The effects of van der Waals (vdW) corrections to density functional theory on the structural relaxation are investigated. Our results reveal that the vdW interactions between the MA+ cation and the inorganic framework can strongly affect the optimized orientation and position of the molecule and the resulting distortion of the inorganic framework. Consequently, it also affects the electronic properties of the materials and specifically can change the band structure from direct to indirect band gaps. The robustness of this result is studied by comparing hybrid functional calculations and quasiparticle self-consistent GW calculations as well as spin–orbit coupling.

Relativistic correction scheme for core-level binding energies from GW.

We present a relativistic correction scheme to improve the accuracy of 1s core-level binding energies calculated from Green's function theory in the GW approximation, which does not add computational overhead. An element-specific corrective term is derived as the difference between the 1s eigenvalues obtained from the self-consistent solutions to the non- or scalar-relativistic Kohn-Sham equations and the four-component Dirac-Kohn-Sham equations for a free neutral atom. We examine the dependence of this corrective term on the molecular environment and the amount of exact exchange in hybrid exchange-correlation functionals. This corrective term is then added as a perturbation to the quasiparticle energies from partially self-consistent and single-shot GW calculations. We show that this element-specific relativistic correction, when applied to a previously reported benchmark set of 65 core-state excitations [D. Golze et al., J. Phys. Chem. Lett. 11, 1840-1847 (2020)], reduces the mean absolute error (MAE) with respect to the experiment from 0.55 eV to 0.30 eV and eliminates the species dependence of the MAE, which otherwise increases with the atomic number. The relativistic corrections also reduce the species dependence for the optimal amount of exact exchange in the hybrid functional used as a starting point for the single-shot G0W0 calculations. Our correction scheme can be transferred to other methods, which we demonstrate for the delta self-consistent field (ΔSCF) approach based on density functional theory.

Optical properties of organosilicon compounds containing sigma-electron delocalization by quasiparticle self-consistent GW calculations.

We investigate theoretically the electronic and optical absorption properties of two sub-classes of oligosilanes: (i) Si(CH3)4, Si4(CH3)8, and Si8(CH3)8 that contain Si dot, ring and cage, respectively, and exhibit typical SiC and SiSi bonds; and (ii) persilastaffanes Si7H6(CH3)6 and Si12H6(CH3)12, which contain extended delocalized σ-electrons in SiSi bonds over three-dimensional Si frameworks. Our modeling is performed within the GW approach up to the partially self-consistent GW0 approximation, which is more adequate for reliably predicting the optical band gaps of materials. We examine how the optical properties of these organosilicon compounds depend on their size, geometric features, and Si/C composition. Our results indicate that the present methodology offers a viable way of describing the optical excitations of tailored functional Si-C-based clusters and molecular optical tags with potential use as efficient light absorbers/emitters in molecular optical devices.

Nonempirical hybrid functionals for band gaps of inorganic metal-halide perovskites

Nonempirical hybrid functionals are investigated for band-gap predictions of inorganic metal-halide perovskites belonging to the class CsBX3, with B = Ge, Sn, Pb and X = Cl, Br, I. We consider both global and range-separated hybrid functionals and determine the parameters through two different schemes. The first scheme is based on the static screening response of the material and thus yields dielectric-dependent hybrid functionals. The second scheme defines the hybrid functionals through the enforcement of Koopmans' condition for localized defect states. We also carry out quasiparticle self-consistent GW calculations with vertex corrections to establish state-of-the-art references. For the investigated class of materials, dielectric-dependent functionals and those fulfilling Koopmans' condition yield band gaps of comparable accuracy (similar to 0.2 eV), but the former only require calculations for the primitive unit cell and are less subject to the specifics of the material.

Heteroatom-doped derivatives of cyclopentadithiophene–benzothiadiazole. quasiparticle study

A list of cyclopentadithiophene–benzothiadiazole derivatives has been investigated within ab intio approaches. Self-consistent GW calculations were performed to determine electronic properties. Macroscopic dielectric function including excitonic effects was evaluated within the Bethe-Salpeter approach. We also obtained charge contributions of each atom states to define the impact of heteroatomic changes.

Nearest-neighbor sp3d5s* tight-binding parameters based on the hybrid quasi-particle self-consistent GW method verified by modeling of type-II superlattices

We report determination of parameters in the nearest-neighbor sp3d5s* tight-binding (TB) model for nine binary compound semiconductors which consist of Al, Ga, or In and of P, As, or Sb based on the hybrid quasi-particle self-consistent GW (QSGW) calculations. We have used the determination parameters to calculated band structures and related properties of the compounds in the bulk phase relevant to mid-infrared applications and of the type-II (InAs)/(GaSb) superlattices. For the type-II (InAs)/(GaSb) superlattices with various superlattice periods, good agreement with photoluminescence measurements on the band gaps has been confirmed. Furthermore, two aspects of the band gap properties from other calculations have been reproduced: the band gap energies rising up to some superlattice periods and shrinking beyond them asymptotically. In both the bulk phase and the superlattices, erroneous flat valence bands have appeared within the nearest-neighbor sp3s* TB model. The present TB model has been eliminated these artifacts, potential obstacles to design advanced superlattices.

Anharmonicity and Disorder in the Black Phases of Cesium Lead Iodide Used for Stable Inorganic Perovskite Solar Cells.

Hybrid organic-inorganic perovskites emerged as a new generation of absorber materials for high-efficiency low-cost solar cells in 2009. Very recently, fully inorganic perovskite quantum dots also led to promising efficiencies, making them a potentially stable and efficient alternative to their hybrid cousins. Currently, the record efficiency is obtained with CsPbI3, whose crystallographical characterization is still limited. Here, we show through high-resolution in situ synchrotron XRD measurements that CsPbI3 can be undercooled below its transition temperature and temporarily maintained in its perovskite structure down to room temperature, stabilizing a metastable perovskite polytype (black γ-phase) crucial for photovoltaic applications. Our analysis of the structural phase transitions reveals a highly anisotropic evolution of the individual lattice parameters versus temperature. Structural, vibrational, and electronic properties of all the experimentally observed black phases are further inspected based on several theoretical approaches. Whereas the black γ-phase is shown to behave harmonically around equilibrium, for the tetragonal phase, density functional theory reveals the same anharmonic behavior, with a Brillouin zone-centered double-well instability, as for the cubic phase. Using total energy and vibrational entropy calculations, we highlight the competition between all the low-temperature phases of CsPbI3 (γ, δ, β) and show that avoiding the order-disorder entropy term arising from double-well instabilities is key to preventing the formation of the yellow perovskitoid phase. A symmetry-based tight-binding model, validated by self-consistent GW calculations including spin-orbit coupling, affords further insight into their electronic properties, with evidence of Rashba effect for both cubic and tetragonal phases when using the symmetry-breaking structures obtained through frozen phonon calculations.

Nearest-neighbor sp3s* tight-binding parameters based on the hybrid quasi-particle self-consistent GW method verified by modeling of type-II superlattices

We report the determination of parameters for the nearest-neighbor sp3s* tight-binding (TB) model for GaP, GaAs, GaSb, InP, InAs, and InSb at 0, 77, and 300 K based on the hybrid quasi-particle self-consistent GW (QSGW) calculation and their application to a type II (InAs)/(GaSb) superlattice. The effects of finite temperature have been incorporated empirically by adjusting the parameter for blending the exchange-correlation terms of the pure QSGW method and local density approximation, in addition to the usage of experimental lattice parameters. As expected, the TB band gap shrinks with temperature and asymptotically with superlattice period when it is large. In addition, a bell curve in the band gap in the case of small superlattice period and slight and remarkable anisotropy in effective masses of electron and hole, both predicted by the hybrid QSGW method, respectively, are reproduced.

Electronic structures of rutile (011)(2 × 1) surfaces: A many-body perturbation theory study.

Using the GW method within many-body perturbation theory, we investigate the electronic properties of the rutile (011) surfaces with different reconstruction patterns. We find that keeping the Ti:O ratio on the reconstructedsurface to 1:2 enlarges the bandgap of the rutile (011) surface to ca. 4.0 eV. Increasing the content of O atoms in the surface can turn rutile into a semi-metal. For some surfaces, it is important to apply self-consistent GW calculation to get the correct charge distributions for the frontier orbitals, which are relevant to the photocatalytic behavior of TiO2.

Quasiparticle self-consistent GW band structure of β-Ga2O3 and the anisotropy of the absorption onset

Quasiparticle self-consistent GW calculations are presented for the band structure of β-Ga2O3, including a lattice polarization correction of the screened Coulomb interaction W. It is found that this correction is of the order of 0.5 eV. When an estimated zero-point motion correction is also included, the direct gap is found to be 4.8 ± 0.1 eV in good agreement with experiment. The indirect gap is found to be 0.1 eV smaller. The origin of the anisotropy of the absorption edge is interpreted in terms of selection rules and the symmetry labeling of the bands at Γ.

Abinitio Electronic Structure of Liquid Water.

Self-consistent GW calculations with efficient vertex corrections are employed to determine the electronic structure of liquid water. Nuclear quantum effects are taken into account through abinitio path-integral molecular dynamics simulations. We reveal a sizable band-gap renormalization of up to 0.7eV due to hydrogen-bond quantum fluctuations. Our calculations lead to a band gap of 8.9eV, in accord with the experimental estimate. We further resolve the ambiguities in the band-edge positions of liquid water. The valence-band maximum and the conduction-band minimum are found at -9.4 and -0.5 eV with respect to the vacuum level, respectively.

Ab Initio Study of the Dynamical Si–O Bond Breaking Event in α-Quartz**Supported by the National Natural Science Foundation of China under Grant Nos 10744048 and 11202032, and the Defense Industrial Technology Development Program of China under Grant No B1520132013.

The Si–O bond breaking event in the α-quartz at the first triplet (T1) excitation state is studied by using ab initio molecular dynamics (AIMD) and nudged elastic band calculations. A meta-stable non-bridging oxygen hole center and E′ center (NBOHC-E′) is observed in the AIMD which consists of a broken Si–O bond with a Si–O distance of 2.54 Å. By disallowing the re-bonding of the Si and O atoms, another defect configuration (III-Si/V-Si) is obtained and validated to be stable at both ground and excitation states. The NBOHC-E′ is found to present on the minimal energy pathway of the initial to III-Si/V-Si transition, showing that the generating of the NBOHC-E′ is an important step of the excitation induced structure defect. The energy barriers to produce the NBOHC-E′ and III-Si/V-Si defects are calculated to be 1.19 and 1.28 eV, respectively. The electronic structures of the two defects are calculated by the self-consistent GW calculations and the results show a clear electron transition from the bonding orbital to the non-bonding orbital.

Towards improved exact exchange functionals relying onGWquasiparticle methods for parametrization

We use fully self-consistent GW calculations on diamond and silicon carbide to reparametrize the Heyd-Scuseria-Ernzerhof exact exchange density functional for use in band structure calculations of semiconductors and insulators. We show that the thus modified functional is able to calculate the band structure of bulk Si, Ge, GaAs, and CdTe with good quantitative accuracy at a significantly reduced computational cost as compared to GW methods. We discuss the limitations of this functional in low-dimensions by calculating the band structures of single-layer hexagonal BN and MoS$_{2}$, and by demonstrating that the diameter scaling of curvature induced band gaps in single-walled carbon nanotubes is still physically incorrect using our functional; we consider possible remedies to this problem.

Accurate band gaps of extended systems via efficient vertex corrections inGW

We propose the use of an approximate bootstrap exchange-correlation kernel to account for vertex corrections in self-consistent GW calculations. We show that the approximate kernel gives accurate band gaps for a variety of extended systems, including simple sp semiconductors, wide band-gap insulators, and transition-metal compounds with either closed or open d shells. The accuracy is comparable with that obtained via the solution of the Bethe-Salpeter equation but only at a fraction of the computational cost.

Benchmarking the Bethe-Salpeter Formalism on a Standard Organic Molecular Set.

We perform benchmark calculations of the Bethe–Salpeter vertical excitation energies for the set of 28 molecules constituting the well-known Thiel’s set, complemented by a series of small molecules representative of the dye chemistry field. We show that Bethe–Salpeter calculations based on a molecular orbital energy spectrum obtained with non-self-consistent G0W0 calculations starting from semilocal DFT functionals dramatically underestimate the transition energies. Starting from the popular PBE0 hybrid functional significantly improves the results even though this leads to an average −0.59 eV redshift compared to reference calculations for Thiel’s set. It is shown, however, that a simple self-consistent scheme at the GW level, with an update of the quasiparticle energies, not only leads to a much better agreement with reference values, but also significantly reduces the impact of the starting DFT functional. On average, the Bethe–Salpeter scheme based on self-consistent GW calculations comes close to the best time-dependent DFT calculations with the PBE0 functional with a 0.98 correlation coefficient and a 0.18 (0.25) eV mean absolute deviation compared to TD-PBE0 (theoretical best estimates) with a tendency to be red-shifted. We also observe that TD-DFT and the standard adiabatic Bethe–Salpeter implementation may differ significantly for states implying a large multiple excitation character.