Local Density Functional Approximation Research Articles

First-Principles Anharmonic Infrared and Raman Vibrational Spectra of Materials: Fermi Resonance in Dry Ice.

We introduce a computational tool for the quantum-mechanical simulation of anharmonic infrared and Raman vibrational spectra of materials. The approach, implemented in the CRYSTAL software, stems from Taylor's expansion of the potential energy surface (PES) on the basis of normal modes up to cubic and quartic terms. The PES can be sampled with four different numerical schemes at the level of density functional theory (DFT), with local, generalized-gradient, and hybrid density functional approximations. Anharmonic states are obtained by solving Shrödinger's nuclear equation with either the vibrational self-consistent field (VSCF) or vibrational configuration interaction (VCI) methods. Nuclear quantum effects (NQEs) are thus fully accounted for. Infrared intensities are computed numerically through a Berry phase approach or analytically through a coupled-perturbed (CP) approach. Raman intensities are computed analytically via the CP approach. A variety of anharmonic features of vibrational spectra of materials can be simulated, including band shifts, combination bands, overtones, resonances (first-order Fermi, second-order Darling-Dennison), and hot bands. We showcase the effectiveness of the approach on the description of a first-order Fermi resonance (FR) in CO2 dry ice: a challenging test-case given that the FR occurs in the Raman spectrum, requires NQEs, and involves two- and three-mode couplings. Fundamental mechanistic differences with respect to the well-known FR in molecular CO2 are addressed. This application represents the first quantum-mechanical, periodic description of FR in dry ice.

Photoionization and core resonances from range-separated time-dependent density-functional theory for open-shell states: Example of the lithium atom.

We consider the calculations of photoionization spectra and core resonances of open-shell systems using range-separated time-dependent density-functional theory. Specifically, we use the time-dependent range-separated hybrid (TDRSH) scheme, combining a long-range Hartree-Fock exchange potential and kernel with a short-range potential and kernel from a local density-functional approximation, and the time-dependent locally range-separated hybrid (TDLRSH) scheme, which uses a local range-separation parameter. To efficiently perform the calculations, we formulate a spin-unrestricted linear-response Sternheimer approach in a non-orthogonal B-spline basis set using appropriate frequency-dependent boundary conditions. We illustrate this approach on the Li atom, which suggests that TDRSH and TDLRSH are adequate simple methods for estimating the single-electron photoionization spectra of open-shell systems.

How good are recent density functionals for ground and excited states of one-electron systems?

Sun et al. [J. Chem. Phys. 144, 191101 (2016)] suggested that common density-functional approximations (DFAs) should exhibit large energy errors for excited states as a necessary consequence of orbital nodality. Motivated by self-interaction corrected density-functional calculations on many-electron systems, we continue their study with the exactly solvable 1s, 2p, and 3d states of 36 hydrogenic one-electron ions (H-Kr35+) and demonstrate with self-consistent calculations that state-of-the-art DFAs indeed exhibit large errors for the 2p and 3d excited states. We consider 56 functionals at the local density approximation (LDA), generalized gradient approximation (GGA) as well as meta-GGA levels, and several hybrid functionals such as the recently proposed machine-learned DM21 local hybrid functional. The best non-hybrid functional for the 1s ground state is revTPSS. As predicted by Sun et al., the 2p and 3d excited states are more difficult for DFAs, and LDA functionals turn out to yield the most systematic accuracy for these states among non-hybrid functionals. The best performance for the three states overall is observed with the BHandH global hybrid GGA functional, which contains 50% Hartree-Fock exchange and 50% LDA exchange. The performance of DM21 is found to be inconsistent, yielding good accuracy for some states and systems and poor accuracy for others. Based on these results, we recommend including a variety of one-electron cations in future training of machine-learned density functionals.

First-principles calculations to investigate structural, electronic and phonon properties of sodium bromide (NaBr) and sodium iodide (NaI) crystals

In this paper, the first-principles study is performed to calculate the structural, electronic and phonon properties of alkali halides NaBr and NaI. The calculations for structural and electronic properties have been carried out using the full-potential linearized augmented plane-wave (FP-LAPW) method that is employed in the WIEN2k code, whereas the phonon properties are studied using the Quantum Espresso program based on density-functional theory within plane-wave fundamental sets and pseudo-potentials approaches. The calculation of structural, electronic band properties were carried out using generalized gradient approximation (GGA), local-density approximation (LDA) and a combination of modified Becke-Johnson exchange potential with LDA and GGA (TB-mBJ-GGA/LDA) for exchange-correlation potential. The calculated structural parameters are in good agreement with experimental results. In our electronic calculations, the obtained bandgaps are underestimated by LDA and GGA functionals compared to empirically derived results, which is an expected result. However, the calculated bandgaps by the modified Becke-Johnson exchange potential are in perfect agreement with the experiment. Finally, the dynamic properties of NaBr and NaI compounds were investigated. Both phonon dispersion and phonon density of states curves were calculated for compounds along with the high symmetry directions in the Brillouin region. The dynamical properties of NaBr and NaI crystals are analyzed and discussed.

Effects of pseudopotentials and exchange-correlation functionals on phase transition of LaH10

To assess the effects of pseudopotentials and exchange-correlation functionals on trigonal to face-centered cubic phase transition of LaH10, we performed density functional theory based first-principles calculations by employing three-types of pseudopotentials with LDA (local density approximation) and GGA (generalized gradient approximation) exchange-correlation functionals. We found that the lattice parameters such as cell angle or cell volume and phase transition pressure exhibit a significant variation with LDA and GGA functionals whereas they exhibit a weak dependence on the pseudopotentials. In general, LDA calculations result in a lower phase transition pressure than GGA calculations. We also investigated the effects of pseudopotentials and exchange-correlation functionals on the electronic properties by calculating the total and partial density of state functions for face-centered cubic phase of LaH10 at 150 GPa. Computed electronic densities of states at the Fermi level are found to exhibit a weak dependence on the exchange-correlation functionals.

First-principles calculations for studying effect of Tellurium (Te) doping on electronic properties, half-metallic ferromagnetism and “Curie temperature of V-doped AlSb DMS compound

The electronic structure and magnetic features of intrinsic Al1-xVxSb, AlSb1-yTey and Al1-xVxSb1-yTey Tey diluted magnetic semiconductors (DMSs) compounds at various doping concentrations of x and y have been calculated in this study using Korringa-Kohn-Rostoker coherent-potential approximation (KKR-CPA), using a coupling local-density-functional approx-imation (LDA). Our structural parameters results showed generally agreement with the previous experimental and theoretical findings. The results of DOS demonstrate that incorporation of V-3d develops a half-metallic (HM) property in our compounds with an engendered bandgap at the Fermi energy in the down-spin state. In these materials, the stability of ferromagnetism (FM) is explained by contribution of both p-d interaction and Zener's double-exchange interaction mechanisms. Accordingly, it has been shown in our studied systems that ferromagnetic (FM) ground states are easily attainable, and that the measured Curie temperature (TC) of the (V, Te)-codoped AlSb system reaches a maximum of 1142.48K (Tcmax) and is far above room temperature (RT) and to that measured of V-doped AlSb compound (Tcmax = 364.18K) This fact and the very large Curie temperature of (V, Te)-codoped AlSb compound make inevitably this material a serious candidate for future electronic applications, especially for spintronics devices.

Assessing the Accuracy of Local Hybrid Density Functional Approximations for Molecular Response Properties.

A comprehensive overview of the performance of local hybrid functionals for molecular properties like excited states, ionization potentials within the GW framework, polarizabilities, magnetizabilities, NMR chemical shifts, and NMR spin-spin coupling constants is presented. We apply the generalization of the kinetic energy, τ, with the paramagnetic current density to all magnetic properties and the excitation energies from time-dependent density functional theory. This restores gauge invariance for these properties. Different ansätze for local mixing functions such as the iso-orbital indicator, the correlation length, the Görling-Levy second-order limit, and the spin polarization are compared. For the latter, we propose a modified version of the corresponding hyper-generalized gradient approximation functional of Perdew, Staroverov, Tao, and Scuseria (PSTS) [Phys. Rev. A 2008, 78, 052513] to allow for a numerically stable evaluation of the exchange-correlation kernel and hyperkernel. The PSTS functional leads to a very consistent improvement compared to the related TPSSh functional. It is further shown that the "best" choice of the local mixing function depends on the studied property and molecular class. While functionals based on the iso-orbital indicator lead to rather accurate excitation energies and ionization energies, the results are less impressive for NMR properties, for which a considerable dependence on the considered molecular test set and nuclei is observed. Johnson's local hybrid functional based on the correlation length yields remarkable results for NMR shifts of compounds featuring heavy elements and also for the excitation energies of organic compounds.

Critical assessment of Co-Cu phase diagram from first-principles calculations

Using first-principles alloy theory, we perform a systematic study of the Co-Cu phase diagram. Calculations are carried out for ferromagnetic and paramagnetic ${\mathrm{Co}}_{1\ensuremath{-}x}{\mathrm{Cu}}_{x}$ solid solutions with face-centered-cubic (fcc) crystal structure. We find that the equilibrium volumes and magnetic states are crucial for a quantitative description of the thermodynamics of the Co-Cu system at temperatures up to 1400 K. In particular, the paramagnetic state of Cu-rich alloys with persisting local magnetic moments is shown to be responsible for the solubility of a small amount of Co in fcc Cu whereas the excess entropy in the ferromagnetic Co-rich region critically depends on the adopted lattice parameters. None of the common local or semilocal density functional theory approximations have the necessary accuracy for the lattice parameters when compared to the experimental data. The predicted ab initio Co-Cu phase diagram is in good agreement with the measurements and CALPHAD data, making it possible to gain a deep insight into the various contributions to the Gibbs free energy. The present study provides an atomic-level description of the thermodynamic quantities controlling the limited mutual solubility of Co and Cu and highlights the importance of high-temperature magnetism.

An improved seminumerical Coulomb and exchange algorithm for properties and excited states in modern density functional theory.

A seminumerical algorithm capable of performing large-scale (time-dependent) density functional theory (TD-DFT) calculations to extract excitation energies and other ground-state and excited-state properties is outlined. The algorithm uses seminumerical integral techniques for evaluating Coulomb and exchange parts for a set of density matrices as occurring in standard TD-DFT or similar methods for the evaluation of vibrational frequencies. A suitable optimized de-aliasing procedure is introduced. The latter does not depend on further auxiliary quantities and retains the symmetry of a given density matrix. The algorithm is self-contained and applicable to any orbital basis set available without the need for further auxiliary basis sets or optimized de-aliasing grids. Relativistic two-component excited-state TD-DFT calculations are reported for the first time using the developed seminumerical algorithm for standard and local hybrid density functional approximations. Errors are compared with the widely used "resolution of the identity" (RI) approximations for Coulomb (RI-J) and exchange integrals (RI-K). The fully seminumerical algorithm does not exhibit an enlarged error for standard DFT functionals compared to the RI approximation. For the more involved local hybrid functionals and within strong external fields, accuracy is even considerably improved.

The Fermi-Löwdin self-interaction correction for ionization energies of organic molecules.

(Semi)-local density functional approximations (DFAs) suffer from self-interaction error (SIE). When the first ionization energy (IE) is computed as the negative of the highest-occupied orbital (HO) eigenvalue, DFAs notoriously underestimate them compared to quasi-particle calculations. The inaccuracy for the HO is attributed to SIE inherent in DFAs. We assessed the IE based on Perdew-Zunger self-interaction correction on 14 small to moderate-sized organic molecules relevant in organic electronics and polymer donor materials. Although self-interaction corrected DFAs were found to significantly improve the IE relative to the uncorrected DFAs, they overestimate. However, when the self-interaction correction is interiorly scaled using a function of the iso-orbital indicator zσ, only the regions where SIE is significant get a correction. We discuss these approaches and show how these methods significantly improve the description of the HO eigenvalue for the organic molecules.

Effect of N-type doping and vacancy formation on the thermodynamic, electrical, structural, and bonding properties of Si: X. (X = P, As, and Sb): a theoretical study

We investigated the effect of n-type doping and vacancy formation on the thermodynamic, electrical, structural, and bonding properties of Si:X (X = P, As, and Sb) using first-principles calculations. Density functional theory calculations show that the lattice parameter of Si1 − y P y decreases with higher P concentrations due to the incorporation of smaller P atoms, while that of Si1 − y As y and Si1 − y Sb y increases with higher As and Sb concentrations. Moreover, both local density functional approximation and GGAgeneralized gradient approximation –Perdew, Burke, and Ernzerhof functionals demonstrate that donor-vacancy complex (X4V) is the most energetically favorable structure for Si:X for all n-type dopants. With most energetically favorable structure (P4V), the effect of the vacancy formation on the lattice parameter is greatly reduced, and thus the lattice parameters of P4 and P4V are similar. However, in case of As- and Sb-doped Si, we found that the relaxed lattice parameter in the form of As n and Sb n is not strongly influenced by the environment around V. For all n-type dopants, the relaxed lattice parameter is same, regardless of the dopant distribution such as random alloys or X n . Both bond length and angle in X4V decrease compared to those of X4 due to the greater electron repulsions caused by one lone pair of two electrons in the nonbonding region. Direct observation of the lone electron pair in P4V, As4V, and Sb4V using ELF shows that the vacancy plays a critical role in determining the structural and electrical properties of Si materials doped with n-type dopants. Theoretical findings in this study help to understand and predict the materials properties of Si doped with n-type atoms in fundamental researches as well as in industrial applications.

Structural, vibrational, mechanical, and optoelectronic properties of LiBH4 for hydrogen storage and optoelectronic devices: First‐principles study

AbstractIn order to cope with the energy crisis and global warming issues, researchers are rendering their efforts and paying attention to analyzing and fabricating hydrogen storage devices. That is why comprehensive investigations are made to unfold the structural, vibrational, mechanical, and optoelectronic properties of lithium borohydride (LiBH4), a hydrogen storage material. For this purpose, calculations of the structural properties were performed using local, nonlocal, and hybrid functionals within the framework of density functional theory. For the determination of lattice constants in the orthorhombic phase, local density approximation (LDA), Perdew‐Burke‐Ernzerhof (PBE), and Heyd‐Scuseria‐Ernzerhof (HSE06) density functionals were chosen, and their results were compared with available experimental and theoretical studies. In order to determine infrared (IR) and Raman active modes of vibrations, vibrational spectroscopy was utilized through density functional perturbation theory. Li, B, and H atoms are noted to contribute in different modes of vibrations among various ranges of frequencies, that is, 0 to 400 cm−1, 1100 to 1300 cm−1, and 2250 to 2400 cm−1. Values of the energy band gap are found to be 6.35, 6.81, and 7.58 eV for LDA, PBE, and HSE06 functionals, respectively, indicating the insulating nature of LiBH4. Such fascinating properties make these compounds promising candidates for future applications in optoelectronic devices. Mechanical analysis revealed that LiBH4 is a brittle and stiffer material. Other optical properties, such as dielectric constant, refractive index, reflectivity, absorptivity, conductivity, and loss function, were also calculated with the assistance of the well‐recognized Kramer‐Kronig relation. The energy loss function depicted a plasma frequency of 13.7 eV, noted from the highest loss peak. It can be concluded that this material is not only suitable for hydrogen storage but also for optoelectronic devices.

The Electron Affinity as the Highest Occupied Anion Orbital Energy with a Sufficiently Accurate Approximation of the Exact Kohn-Sham Potential.

Negative ions are not accurately represented in density functional approximations (DFAs) such as (semi)local density functionals (LDA or GGA or meta-GGA). This is caused by the much too high orbital energies (not negative enough) with these DFAs compared to the exact Kohn–Sham values. Negative ions very often have positive DFA HOMO energies, hence they are unstable. These problems do not occur with the exact Kohn–Sham potential, the anion HOMO energy then being equal to minus the electron affinity. It is therefore desirable to develop sufficiently accurate approximations to the exact Kohn–Sham potential. There are further beneficial effects on the orbital shapes and the density of using a good approximation to the exact KS potential. Notably the unoccupied orbitals are not unduly diffuse, as they are in the Hartree–Fock model, with hybrid functionals, and even with (semi)local density functional approximations (LDFAs). We show that the recently developed B-GLLB-VWN approximation [Gritsenko et al. J. Chem. Phys.2016, 144, 204114] to the exact KS potential affords stable negative ions with HOMO orbital energy close to minus the electron affinity.

Site-occupation Green's function embedding theory: A density functional approach to dynamical impurity solvers

A reformulation of site-occupation embedding theory (SOET) in terms of Green's functions is presented. Referred to as site-occupation--Green's function embedding theory (SOGET), this novel extension of density-functional theory for model Hamiltonians shares many features with dynamical mean-field theory (DMFT) but is formally exact (in any dimension). In SOGET, the impurity-interacting correlation potential becomes a density-functional self-energy which is frequency-dependent and in principle non-local. A simple local density-functional approximation (LDA) combining the Bethe Ansatz (BA) LDA with the self-energy of the two-level Anderson model is constructed and successfully applied to the one-dimensional Hubbard model. Unlike in previous implementations of SOET, no many-body wavefunction is needed, thus reducing drastically the computational cost of the method.

Multicomponent density functional theory: Including the density gradient in the electron-proton correlation functional for hydrogen and deuterium.

Multicomponent density functional theory (DFT) has many practical advantages for incorporating nuclear quantum effects into quantum chemistry calculations. Within the nuclear-electronic orbital (NEO) framework, specified nuclei, typically protons, are treated quantum mechanically on the same level as the electrons. Previously, electron-proton correlation functionals based on the local density approximation (LDA), denoted epc17 and epc18, were developed and shown to provide more accurate proton densities and energies compared to the neglect of electron-proton correlation, but a quantitatively accurate description of both densities and energies simultaneously has remained elusive. Herein, an electron-proton correlation functional that depends on the electron and proton density gradients, as well as the densities, is derived and implemented. Compared to the LDA functionals, the resulting generalized gradient approximation functional, denoted epc19, is able to simultaneously provide accurate proton densities and energies, as well as reproduce the impact of nuclear quantum effects on optimized geometries. In addition, without further parameterization, the NEO-DFT/epc19 method provides accurate densities and energies for deuterium as well as hydrogen. These results demonstrate that the form of the epc19 functional is able to capture the essential aspects of electron-proton correlation and highlights the importance of including gradient terms. This approach will enable the exploration of nuclear quantum effects and isotope effects in a wide range of systems.

Towards density functional approximations from coupled cluster correlation energy densities.

(Semi)local density functional approximations (DFAs) are the workhorse electronic structure methods in condensed matter theory and surface science. The correlation energy density ϵc(r) (a spatial function that yields the correlation energy Ec upon integration) is central to defining such DFAs. Unlike Ec, ϵc(r) is not uniquely defined, however. Indeed, there are infinitely many functions that integrate to the correct Ec for a given electron density ρ. The challenge for constructing useful DFAs is thus to find a suitable connection between ϵc(r) and ρ. Herein, we present a new such approach by deriving ϵc(r) directly from the coupled-cluster (CC) energy expression. The corresponding energy densities are analyzed for prototypical two-electron systems. As a proof-of-principle, we construct a semilocal functional to approximate the numerical CC correlation energy densities. Importantly, the energy densities are not simply used as reference data but guide the choice of the functional form, leading to a remarkably simple and accurate correlation functional for the helium isoelectronic series. While the resulting functional is not transferable to many-electron systems (due to a lack of same-spin correlation), these results underscore the potential of the presented approach.

Theory and practice of modeling van der Waals interactions in electronic-structure calculations.

The accurate description of long-range electron correlation, most prominently including van der Waals (vdW) dispersion interactions, represents a particularly challenging task in the modeling of molecules and materials. vdW forces arise from the interaction of quantum-mechanical fluctuations in the electronic charge density. Within (semi-)local density functional approximations or Hartree-Fock theory such interactions are neglected altogether. Non-covalent vdW interactions, however, are ubiquitous in nature and play a key role for the understanding and accurate description of the stability, dynamics, structure, and response properties in a plethora of systems. During the last decade, many promising methods have been developed for modeling vdW interactions in electronic-structure calculations. These methods include vdW-inclusive Density Functional Theory and correlated post-Hartree-Fock approaches. Here, we focus on the methods within the framework of Density Functional Theory, including non-local van der Waals density functionals, interatomic dispersion models within many-body and pairwise formulation, and random phase approximation-based approaches. This review aims to guide the reader through the theoretical foundations of these methods in a tutorial-style manner and, in particular, highlight practical aspects such as the applicability and the advantages and shortcomings of current vdW-inclusive approaches. In addition, we give an overview of complementary experimental approaches, and discuss tools for the qualitative understanding of non-covalent interactions as well as energy decomposition techniques. Besides representing a reference for the current state-of-the-art, this work is thus also designed as a concise and detailed introduction to vdW-inclusive electronic structure calculations for a general and broad audience.

Comparing the performance of LDA and GGA functionals in predicting the lattice thermal conductivity of III-V semiconductor materials in the zincblende structure: The cases of AlAs and BAs

In this contribution we assess the performance of two different exchange-correlation functionals in the first-principles prediction of the lattice thermal conductivity of bulk semiconductors, namely the local density approximation (LDA) and the Perdew-Burke-Ernzerhof implementation of the generalized gradient approximation (GGA). Both functionals are shown to give results in good agreement with experimental measurements. Such a consistency between the two functionals may seem a bit surprising, as the LDA is known to overbind and the GGA to soften the interatomic bonds. Such features ought to greatly affect the value of the system interatomic force constants (IFCs) which are necessary for the first-principles prediction of the lattice thermal conductivity. We choose AlAs and BAs to represent III-V semiconductors in the zincblende structure.We show that, in the case of AlAs, the errors introduced by the approximate exchange-correlation functionals tend to cancel themselves. In the case of LDA, the overbinding generates larger absolute third-order IFCs, which tend to increase the three-phonon scattering rates. On the other hand, larger absolute second-order IFCs lead to a larger acoustic-optical phonon band gap which in turns decrease the available phase space for three-phonon scattering, compensating the increase in the scattering rates due to stiffer IFCs. As AlAs is a typical III-V semiconductor in the zincblende structure, we expect these findings to hold for general compounds of the same family. On the other hand, BAs can be considered a special instance thereof: due to the large gap between acoustic and optical phonons, the available scattering volume for three-phonon processes is already very limited in both LDA and PBE. In this case we find that the LDA increase in scattering rates due to stiffer bonds is partially compensated by an increase in phonon group velocities.

Density functional approximations for orbital energies and total energies of molecules and solids.

The relation of Kohn-Sham (KS) orbital energies to ionization energies and electron affinities is different in molecules and solids. In molecules, the local density approximation (LDA) and generalized gradient approximations (GGA) approximate the exact ionization energy (I) and affinity (A) rather well with self-consistently calculated (total energy based) ILDFA and ALDFA, respectively. The highest occupied molecular orbital (HOMO) energy and lowest unoccupied molecular orbital (LUMO) energy, however, differ significantly (by typically 4-6 eV) from these quantities, ϵHLDFA(mol)>-I(mol)≈-ILDFA(mol), ϵLLDFA(mol)<-A(mol)≈-ALDFA(mol). In solids, these relations are very different, due to two effects. The (almost) infinite extent of a solid makes the difference of orbital energies and (L)DFA calculated ionization energy and affinity disappear: in the solid state limit, ϵH(L)DFA(solid)=-I(L)DFA(solid) and ϵL(L)DFA(solid)=-A(L)DFA(solid). Slater's relation ∂E/∂ni = ϵi for local density functional approximations (LDFAs) [and Hartree-Fock (HF) and hybrids] is useful to prove these relations. The equality of LDFA orbital energies and LDFA calculated -ILDFA and -ALDFA in solids does not mean that they are good approximations to the exact quantities. The LDFA total energies of the ions with a delocalized charge are too low, hence ILDFA(solid) < I and ALDFA(solid) > A, due to the local-approximation error, also denoted delocalization error, of LDFAs in extended systems. These errors combine to make the LDFA orbital energy band gap considerably smaller than the exact fundamental gap, ϵLLDFA(solid)-ϵHLDFA(solid)=ILDFA(solid)-ALDFA(solid)<I-A (the LDFA band gap problem). These results for density functional approximations are compared to exact KS and to HF and hybrids. For the exact KS HOMO energy, one has ϵHKS=-I. The exact KS LUMO energy does not approximate the experimental -A (neither in molecules nor in solids), but is considerably below, which is the main reason for the exact KS HOMO-LUMO energy gap being considerably below the fundamental gap I - A (the exact KS band gap problem).

Revisiting the GW approach to d - and f -electron oxides

Accurate description of electronic band structure of strongly correlated $d$- or $f$-electron materials has been regarded as a great challenge for first-principles electronic structure theory. Previous theoretical studies based on the $GW$ approach has met mixed success, and in particular, the one-short (${G}_{0}{W}_{0}$) or partially self-consistent (${GW}_{0}$) approaches with the local or semilocal density functional approximations plus the Hubbard $U$ correction ($GW$@LDA+$U$) as the reference systematically underestimate the binding energies of occupied $d$ or $f$ states. In this work we have investigated quasiparticle electronic band structures of a series of $d$- or $f$-electron oxides including late transition metal mono-oxides (TMO, TM = Mn, Fe, Co, and Ni), ${\mathrm{La}}_{2}{\mathrm{O}}_{3}$, ${\mathrm{CeO}}_{2}$, ${\mathrm{Ce}}_{2}{\mathrm{O}}_{3}$, and ${\mathrm{UO}}_{2}$. It is shown that a large part of the errors observed in previous $GW$ studies can be attributed to numerical errors related to the inaccuracy of unoccupied states and the incompleteness of the summation of states, which can be effectively overcome by including high-energy local orbitals (HLOs) in the linearized augmented plane waves (LAPW) framework.