Quasiparticle Energy Calculations Research Articles

GW with hybrid functionals for large molecular systems

A low-cost approach for stochastically sampling static exchange during time-dependent Hartree–Fock-type propagation is presented. This enables the use of an excellent hybrid density functional theory (DFT) starting point for stochastic GW quasiparticle energy calculations. Generalized Kohn–Sham molecular orbitals and energies, rather than those of a local-DFT calculation, are used for building the Green function and effective Coulomb interaction. The use of an optimally tuned hybrid diminishes the starting point dependency in one-shot stochastic GW, effectively avoiding the need for self-consistent GW iterations.

Mixed Stochastic-Deterministic Approach for Many-Body Perturbation Theory Calculations.

We present an approach for GW calculations of quasiparticle energies with quasiquadratic scaling by approximating high-energy contributions to the Green's function in its Lehmann representation with effective stochastic vectors. The method is easy to implement without altering the GW code, converges rapidly with stochastic parameters, and treats systems of various dimensionality and screening response. Our calculations on a 5.75° twisted MoS_{2} bilayer show how large-scale GW methods include geometry relaxations and electronic correlations on an equal basis in structurally nontrivial materials.

Efficient full frequency GW for metals using a multipole approach for the dielectric screening

The properties of metallic systems with important and structured excitations at low energies, such as Cu, are challenging to describe with simple models like the plasmon pole approximation (PPA), and more accurate and sometimes prohibitive full frequency approaches are usually required. In this paper we propose a numerical approach to $GW$ calculations on metals that takes into account the frequency dependence of the screening via the multipole approximation (MPA), an accurate and efficient alternative to current full-frequency methods that was recently developed and validated for semiconductors and overcomes several limitations of PPA. We now demonstrate that MPA can be successfully extended to metallic systems by optimizing the frequency sampling for this class of materials and introducing a simple method to include the $\mathbf{q}\to 0$ limit of the intra-band contributions. The good agreement between MPA and full frequency results for the calculations of quasi-particle energies, polarizability, self-energy and spectral functions in different metallic systems confirms the accuracy and computational efficiency of the method. Finally, we discuss the physical interpretation of the MPA poles through a comparison with experimental electron energy loss spectra for Cu.

Accurate and Efficient Approximate Quasiparticle DFT‐1/2 Band Structure Calculations of Transition Metal Oxide Perovskites

The transition metal oxide perovskites are materials intensively studied due to their diversity of chemical and physical properties, as well as their potential for wide applications. From the theoretical point of view of ab initio calculations of quasiparticle (QP) energies and band structures, they remain a challenge. Herein, the performance of the low computational cost ab initio DFT‐1/2 approximate QP method is assessed for the nonmagnetic transition metal oxide perovskites, including 3d , , 4d , and 5d and . The results with experiments and a large set with other QP calculations are compared. It is demonstrated that the DFT‐1/2 method presents a remarkable accuracy for these materials, opening an avenue to study more complex systems.

Assessing the G0W0Γ0(1) Approach: Beyond G0W0 with Hedin's Full Second-Order Self-Energy Contribution.

We present and benchmark a self-energy approach for quasiparticle energy calculations that goes beyond Hedin's GW approximation by adding the full second-order self-energy (FSOS-W) contribution. The FSOS-W diagram involves two screened Coulomb interaction (W) lines, and adding the FSOS-W to the GW self-energy can be interpreted as first-order vertex correction to GW (GWΓ(1)). Our FSOS-W implementation is based on the resolution-of-identity technique and exhibits better than O(N5) scaling with system size for small- to medium-sized molecules. We then present one-shot GWΓ(1) (G0W0Γ0(1)) benchmarks for the GW100 test set and a set of 24 acceptor molecules. For semilocal or hybrid density functional theory starting points, G0W0Γ0(1) systematically outperforms G0W0 for the first vertical ionization potentials and electron affinities of both test sets. Finally, we demonstrate that a static FSOS-W self-energy significantly underestimates the quasiparticle energies.

Exact Second-Order Corrections and Accurate Quasiparticle Energy Calculations in Density Functional Theory.

We develop a second-order correction to commonly used density functional approximations (DFAs) to eliminate the systematic delocalization error. The method, based on the previously developed global scaling correction (GSC), is an exact quadratic correction to the DFA for the fractional charge behavior and uses the analytical second derivatives of the total energy with respect to fractional occupation numbers of the canonical molecular orbitals. For small and medium-size molecules, this correction leads to ground-state orbital energies that are a highly accurate approximation to the corresponding quasiparticle energies. It provides excellent predictions of ionization potentials, electron affinities, photoemission spectrum, and photoexcitation energies beyond previous approximate second-order approaches, thus showing potential for broad applications in computational spectroscopy.

Substrate screening approach for quasiparticle energies of two-dimensional interfaces with lattice mismatch

Two-dimensional (2D) materials are outstanding platforms for exotic physics and emerging applications by forming interfaces. In order to efficiently take into account the substrate screening in the quasiparticle energies of 2D materials, several theoretical methods have been proposed previously, but only applicable to interfaces of two systems' lattice constants with certain integer proportion. In this work, we analytically showed the equivalence and distinction among different approximate methods for substrate dielectric matrices. We evaluated the accuracy of these methods, by applying them to calculate quasi-particle energies of hexagonal boron nitride interface systems (heterojunctions and bilayers), and compared with explicit interface calculations. Most importantly, we developed an efficient and accurate interpolation technique for dielectric matrices that made quasiparticle energy calculations possible for arbitrarily mismatched interfaces, which is extremely important for practical 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.

Excitation Energies from the Single-Particle Green’s Function with the GW Approximation

Quasi-particle energies are important in predicting molecular ionization energies and bulk band structures. The state-of-the-art method for quasi-particle energy calculations, particularly for bulk systems, is the GW approximation. For excited state calculations, one needs to go beyond the GW approximation. The Bethe-Salpeter equation (BSE) is the commonly used approach for bulk-system excited state calculations beyond the GW approximation, which is accurate but computationally cumbersome. In this Article, we develop a new method to extract excitation energies directly from the quasi-particle energies based on the GW approximation. Starting from the ( N - 1)-electron system, we are able to calculate molecular excitation energies with orbital energies at the GW level for HOMO excitations. Our calculations demonstrate that this method can accurately capture low-lying local excitations as well as charge transfer excitations in many molecular systems. Our method is shown to outperform the time-dependent density functional theory (TDDFT) and are comparable with higher level excited state calculations, including the equation-of-motion couple cluster (EOM-CC) theory and the BSE, but with less computational effort. This new approach provides an efficient alternative to the BSE method for accurate excited state calculations.

Coupling First-Principles Calculations of Electron-Electron and Electron-Phonon Scattering, and Applications to Carbon-Based Nanostructures.

We report first-principles calculations of electronic gaps, lifetimes, and photoelectron spectra of a series of molecules, performed by efficiently combining the computation of electron-electron and electron-phonon self-energies. The dielectric matrix is represented in terms of dielectric eigenpotentials, utilized for both the calculation of G0 W0 quasi-particle energies and the diagonalization of the dynamical matrix; virtual electronic states are never explicitly computed and all self-energies are evaluated over the full frequency spectrum. Our formulation enables electronic structure calculations at the many-body perturbation theory level, inclusive of electron-phonon coupling, for systems with hundreds of electrons.

Observation of intrinsic dark exciton in Janus-MoSSe heterosturcture induced by intrinsic electric field

The nature of exciton in heterostructure exhibits distinct properties, which makes heterostructure a promising candidate for valleytronic and optoelectronic applications. Therefore, understanding of exciton behaviour in heterostructure is the key approach to design novel devices. Here, we investigate the electronic properties including quasiparticle-energy calculations (on the level of the GW approximation) and optical properties (on the level of the Bethe–Salpeter equation) of Janus-MoSSe based heterostructure. Our results show that the build-in electric field caused by spontaneous polarization of Janus-MoSSe monolayer can significantly affect the interlayer interactions within the heterostructure, giving rise to a bright-to-dark exciton transition. To shed light on this phenomenon, a theoretical model is developed, which illustrates that the dark exciton can be ascribed to a coherence cancellation at the band edge positions induced by the strong interlayer coupling. Our findings may provide a new way for modulating and developing of van der Waals heterostructure that have applications in valleytronic and optoelectronic devices.

Converged GW quasiparticle energies for transition metal oxide perovskites

The ab initio calculation of quasiparticle (QP) energies is a technically and computationally challenging problem. In condensed matter physics the most widely used approach to determine QP energies is the GW approximation. Although the GW method has been widely applied to many typical semiconductors and insulators, its application to more complex compounds such as transition metal oxide perovskites has been comparatively rare, and its proper use is not well established from a technical point of view. In this work, we have applied the single-shot G0W0 method to a representative set of transition metal oxide perovskites including 3d (SrTiO3, LaScO3, SrMnO3, LaTiO3, LaVO3, LaCrO3, LaMnO3, and LaFeO3), 4d (SrZrO3, SrTcO3, and Ca2RuO4) and 5d (SrHfO3, KTaO3 and NaOsO3) compounds with different electronic configurations, magnetic orderings, structural characteristics and bandgaps ranging from 0.1 to 6.1 eV. We discuss the proper procedure to obtain well converged QP energies and accurate bandgaps within single-shot G0W0 by comparing the conventional approach based on an incremental variation of a specific set of parameters (number of bands, energy cutoff for the plane-wave expansion and number of k-points and the basis-set extrapolation scheme [Phys. Rev. B 90, 075125 (2014)]. In addition, we have inspected the difference between the adoption of norm-conserving and ultrasoft potentials in GW calculations. A minimal statistical analysis indicates that the correlation of the GW data with the DFT gap is more robust than the correlation with the experimental gaps; moreover we identify the static dielectric constant as alternative useful parameter for the approximation of GW gap in high-throughput automatic procedures. Finally, we compute the QP band structure and spectra within the random phase approximation and compare the results with available experimental data.

Simple many-body based screening mixing ansatz for improvement of GW /Bethe-Salpeter equation excitation energies of molecular systems

We propose a simple many-body based screening mixing strategy to considerably enhance the performance of the Bethe-Salpeter equation (BSE) approach for prediction of excitation energies of molecular systems. This strategy enables us to closely reproduce results of highly correlated equation of motion coupled cluster singles and doubles (EOM-CCSD) through optimal use of cancellation effects. We start from the Hartree-Fock (HF) reference state and take advantage of local density approximation (LDA) based random phase approximation (RPA) screening, denoted as ${W}_{0}$-RPA@LDA with ${W}_{0}$ as the dynamically screened interaction built upon LDA wave functions and energies. We further use this ${W}_{0}$-RPA@LDA screening as an initial screening guess for calculation of quasiparticle energies in the framework of ${G}_{0}{W}_{0}$@HF. The ${W}_{0}$-RPA@LDA screening is further injected into the BSE. By applying such an approach on a set of 22 molecules for which the traditional $GW$/BSE approaches fail, we observe good agreement with respect to EOM-CCSD references. The reason for the observed good accuracy of this mixing ansatz (scheme A) lies in an optimal damping of HF exchange effect through the ${W}_{0}$-RPA@LDA strong screening, leading to substantial decrease of typically overestimated HF electronic gap, and hence to better excitation energies. Further, we present a second multiscreening ansatz (scheme B), which is similar to scheme A with the exception that now the ${W}_{0}$-RPA@HF screening is used in the BSE in order to further improve the overestimated excitation energies of carbonyl sulfide (COS) and disilane $({\mathrm{Si}}_{2}{\mathrm{H}}_{6})$. The reason for improvement of the excitation energies in scheme B lies in the fact that ${W}_{0}$-RPA@HF screening is less effective (and weaker than ${W}_{0}$-RPA@LDA), which gives rise to stronger electron-hole effects in the BSE.

Optimized virtual orbital subspace for faster GW calculations in localized basis.

The popularity of the GW approximation to the self-energy to access the quasiparticle energies of molecules is constantly increasing. As the other methods addressing the electronic correlation, the GW self-energy unfortunately shows a very slow convergence with respect to the basis complexity, which precludes the calculation of accurate quasiparticle energies for large molecules. Here we propose a method to mitigate this issue that relies on two steps: (i) the definition of a reduced virtual orbital subspace, thanks to a much smaller basis set; (ii) the account of the remainder through the simpler one-ring approximation to the self-energy. We assess the quality of the corrected quasiparticle energies for simple molecules, and finally we show an application to large graphene chunks to demonstrate the numerical efficiency of the scheme.

Assessment of the convergence of partially self-consistent BSE/GW calculations

ABSTRACTThe most applied ab initio method to determine the transition energies to electronically excited states, namely time-dependent density functional theory (TD-DFT), is now well mastered, but alternative approaches can be necessary to circumvent some of the specific limitations of TD-DFT. In that framework, the Bethe–Salpeter method, following a GW calculation of quasiparticle energies, is certainly an attractive approach with the same scaling with system size as TD-DFT, though its accuracy remains to be completely defined, at least for molecular systems. In the present work, we investigate the performances of a partially self-consistent BSE/GW approach in which the starting DFT eigenvalues (but not eigenvectors) are updated. We particularly focus on the convergence of the calculations, the residual impact of the starting eigenstates and the selection of an adequate atomic basis set. This study provides some guidelines allowing to apply BSE/GW in a computationally efficient way and also highlights some limitations of the non-self-consistent BSE/G0W0 approach.

Effects of self-consistency and plasmon-pole models onGWcalculations for closed-shell molecules

We present theoretical calculations of quasiparticle energies in closed-shell molecules using the GW method. We compare three different approaches: a full-frequency $G_0W_0$ (FF-$G_0W_0$) method with density functional theory (DFT-PBE) used as a starting mean field; a full-frequency $GW_0$ (FF-$GW_0$) method where the interacting Green's function is approximated by replacing the DFT energies with self-consistent quasiparticle energies or Hartree-Fock energies; and a $G_0W_0$ method with a Hybertsen-Louie generalized plasmon-pole model (HL GPP-$G_0W_0$). While the latter two methods lead to good agreement with experimental ionization potentials and electron affinities for methane, ozone, and beryllium oxide molecules, FF-$G_0W_0$ results can differ by more than one electron volt from experiment. We trace this failure of the FF-$G_0W_0$ method to the occurrence of incorrect self-energy poles describing shake-up processes in the vicinity of the quasiparticle energies.

Effect of spin-orbit interaction on the optical spectra of single-layer, double-layer, and bulk MoS2

We present converged ab-initio calculations of the optical absorption spectra of single-layer, bi-layer, and bulk MoS$_2$. Both the quasiparticle-energy calculations (on the level of the GW approximation) and the calculation of the absorption spectra (on the level of the Bethe-Salpeter equation) explicitly include spin-orbit coupling, using the full spinorial Kohn-Sham wave-functions as input. Without excitonic effects, the absorption spectra would have the form of a step-function, corresponding to the joint-density of states of a parabolic band-dispersion in 2D. This profile is deformed by a pronounced bound excitonic peak below the continuum onset. The peak is split by spin-orbit interaction in the case of single-layer and (mostly) by inter-layer interaction in the case of double-layer and bulk MoS$_2$. The resulting absorption spectra are thus very similar in the three cases but the interpretation of the spectra is different. Differences in the spectra can be seen around 3 eV where the spectra of single and double-layer are dominated by a strongly bound exciton.

Spectral representation analysis of dielectric screening in solids and molecules

We propose a new approach to identifying and rationalizing the contribution of core electron polarization to dielectric screening, based on ab initio calculations of the dielectric matrix in its eigenpotential basis. We also present calculations of phonon frequencies, dielectric constants, and quasiparticle energies of several systems, and we discuss the quantitative effect of including core polarization. Our findings illustrate efficient ways of approximating the spectral decomposition of dielectric matrices used, e.g., in many-body perturbation theory and dielectric constant calculations, with substantial computational gains for large systems composed of heavy atoms.

Strain effects and band parameters in MgO, ZnO, and CdO

We have derived consistent sets of band parameters (bandgaps, crystal-field splittings, effective masses, Luttinger, and EP parameters) and strain deformation potentials for MgO, ZnO, and CdO in the wurtzite phase. To overcome the limitations of density-functional theory in the local-density and generalized gradient approximations, we employ a hybrid functional as well as exact-exchange-based quasiparticle energy calculations in the G0W0 approach. We demonstrate that the band and strain parameters derived in this fashion are in very good agreement with the available experimental data and provide predictions for all parameters that have not been determined experimentally so far.

GW quasiparticle bandgaps of anatase TiO2 starting from DFT + U

We investigate the quasiparticle band structure of anatase TiO2, a wide gap semiconductor widely employed in photovoltaics and photocatalysis. We obtain GW quasiparticle energies starting from density-functional theory (DFT) calculations including Hubbard U corrections. Using a simple iterative procedure we determine the value of the Hubbard parameter yielding a vanishing quasiparticle correction to the fundamental bandgap of anatase TiO2. The bandgap (3.3 eV) calculated using this optimal Hubbard parameter is smaller than the value obtained by applying many-body perturbation theory to standard DFT eigenstates and eigenvalues (3.7 eV). We extend our analysis to the rutile polymorph of TiO2 and reach similar conclusions. Our work highlights the role of the starting non-interacting Hamiltonian in the calculation of GW quasiparticle energies in TiO2 and suggests an optimal Hubbard parameter for future calculations.