# Browsing by Author "Blum, Volker"

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Item Open Access Algorithms and Software Infrastructure for High-Performance Electronic Structure Based Simulations(2020) Yu, WenzheComputer simulations based on electronic structure theory, particularly Kohn-Sham density-functional theory (KS-DFT), are facilitating scientific discoveries across a broad range of disciplines such as chemistry, physics, and materials science. The tractable size of KS-DFT is often limited by an algebraic eigenproblem, the computational cost of which scales cubically with respect to the problem size. There have been continuous efforts to improve the performance of eigensolvers, and develop alternative algorithms that bypass the explicit solution of the eigenproblem. As the number of algorithms grows, it becomes increasingly difficult to comparatively assess their relative computational cost and implement them efficiently in electronic structure codes.

The research in this dissertation explores the feasibility of integrating different electronic structure algorithms into a single framework, combining their strengths, assessing their accuracy and computational cost relative to each other, and understanding their scope of applicability and optimal use regime. The research has led to an open-source software infrastructure, ELSI, providing the electronic structure community with access to a variety of high-performance solver libraries through a unified software interface. ELSI supports and enhances conventional cubic scaling eigensolvers, linear scaling density-matrix-based algorithms, and other reduced scaling methods in between, with reasonable default parameters for each of them. Flexible matrix formats and parallelization strategies adopted in ELSI fit the need of most, if not all, electronic structure codes. ELSI has been connected to four electronic structure code projects, allowing us to rigorously benchmark the performance of the solvers on an equal footing. Based on the results of a comprehensive set of benchmarks, we identify factors that strongly affect the efficiency of the solvers and regimes where conventional cubic scaling eigensolvers are outperformed by lower scaling algorithms. We propose an automatic decision layer that assists with the algorithm selection process.

The ELSI infrastructure is stimulating the optimization of existing algorithms and the development of new ones. Following the worldwide trend of employing graphical processing units (GPUs) in high-performance computing, we have developed and optimized GPU acceleration in the two-stage tridiagonalization eigensolver ELPA2, targeting distributed-memory, hybrid CPU-GPU architectures. A significant performance boost over the CPU-only version of ELPA2 is achieved, as demonstrated in routine KS-DFT simulations comprising thousands of atoms, for which a couple of GPU-equipped supercomputer nodes reach the throughput of some tens of conventional CPU supercomputer nodes. The GPU-accelerated ELPA2 solver can be used through the ELSI interface, smoothly and transparently bringing GPU support to all the electronic structure codes connected with ELSI. To reduce the computational cost of systems containing heavy elements, we propose a frozen core approximation with proper orthonormalization of the wavefunctions. This method is tolerant of errors due to the finite precision of numerical integrations in electronic structure codes. A considerable saving in the computational cost can be achieved, with the electron density, energies, and forces all matching the accuracy of all electron calculations.

This research shows that by integrating a broad range of electronic structure algorithms into one infrastructure, new algorithmic developments and optimizations can take place at a faster pace. The outcome is open and beneficial to the entire electronic structure community, instead of being restricted to one particular code project. The ELSI infrastructure has already been utilized to accelerate large-scale electronic structure simulations, some of which were not feasible before.

Item Open Access Chiral Cation Doping for Modulating Structural Symmetry of 2D Perovskites.(Journal of the American Chemical Society, 2023-08) Xie, Yi; Morgenstein, Jack; Bobay, Benjamin G; Song, Ruyi; Caturello, Naidel AMS; Sercel, Peter C; Blum, Volker; Mitzi, David BCation mixing in two-dimensional (2D) hybrid organic-inorganic perovskite (HOIP) structures represents an important degree of freedom for modifying organic templating effects and tailoring inorganic structures. However, the limited number of known cation-mixed 2D HOIP systems generally employ a 1:1 cation ratio for stabilizing the 2D perovskite structure. Here, we demonstrate a chiral-chiral mixed-cation system wherein a controlled small amount (<10%) of chiral cation S-2-MeBA (S-2-MeBA = (*S*)-(-)-2-methylbutylammonium) can be doped into (S-BrMBA)_{2}PbI_{4}(S-BrMBA = (*S*)-(-)-4-bromo-α-methylbenzylammonium), modulating the structural symmetry from a higher symmetry (*C*2) to the lowest symmetry state (*P*1). This structural change occurs when the concentration of S-2-MeBA, measured by solution nuclear magnetic resonance, exceeds a critical level─specifically, for 1.4 ± 0.6%, the structure remains as*C*2, whereas 3.9 ± 1.4% substitution induces the structure change to*P*1 (this structure is stable to ∼7% substitution). Atomic occupancy analysis suggests that one specific S-BrMBA cation site is preferentially substituted by S-2-MeBA in the unit cell. Density functional theory calculations indicate that the spin splitting along different k-paths can be modulated by cation doping. A true circular dichroism band at the exciton energy of the 3.9% doping phase shows polarity inversion and a ∼45 meV blue shift of the Cotton-effect-type line-shape relative to (S-BrMBA)_{2}PbI_{4}. A trend toward suppressed melting temperature with higher doping concentration is also noted. The chiral cation doping system and the associated doping-concentration-induced structural transition provide a material design strategy for modulating and enhancing those emergent properties that are sensitive to different types of symmetry breaking.Item Open Access Electronic Structure Based Investigations of Hybrid Perovskites and Their Nanostructures(2023) Song, RuyiPerovskites are a category of semiconductors with outstanding optoelectronic properties. Especially in the last decades, three-dimensionally connected (“3D”) hybrid perovskites gained an important position as an innovative solar-cell material by including organic cations. Related molecularly engineered materials, for example, atomic-scale two-dimensionally connected (“2D”) layered crystals and nano-scale structures offer a wide range of compositional, structural, and electronic tunability. Based on quantum chemistry simulations (specifically, density functional theory), this dissertation aims to contribute to the understanding of the relationship between the components and structure of hybrid perovskites and their electronic properties, related to alloying, energy level alignment in quantum wells, impact of chiral organic constituents on the atomic structure of 2D perovskites and resulting spin character of the electronic levels, and on the structure of related perovskite nanostructures.First, to investigate the tunability of 2D hybrid perovskites, 1) the author simulated the Sn/Pb alloying at the central metal site and explained the corresponding “bowing effect” on the bandgap values with different contribution preferences towards the conduction bands versus valence bands from different elements; 2) taking the conjugation length in different oligothiophene cations and the inorganic layer thickness as two independent factors, the author confirmed a gradual change of quantum well types. Second, to gain an in-depth understanding of the spin properties of the energy bands (specifically, the spin-selectivity) in hybrid perovskites, 1) the author analyzed the frontier bands of the 2D hybrid perovskite S-1-(1-naphthyl)ethylammonium lead bromide and revealed a giant spin-splitting originated from the inorganic moiety; 2) the author (together with experimental collaborators) identified a difference in the inter-octahedron Pb-X-Pb (X stands for the halides) distortion angles as the crucial geometric descriptor for spin-splitting in 2D hybrid perovskites by a correlation analysis of 22 experimental and relaxed structures with various chiral or achiral organic cations; 3) for perovskite nano-crystals with chiral surface ligands, simulations by the author helped to attribute the chirality transfer between organic cations and inorganic substrate to the geometric distortions driven by hydrogen bonds. Third, the author investigated 2D hybrid perovskites containing oligoacene organic cations, validated the theoretical method for geometry evaluation and predicted the expected quantum well type, crystal symmetry, and detailed expected spin-splitting properties that determine the potential for spin-selective transport and optoelectronics Finally, driven by the computational needs of large-scale hybrid perovskites DFT simulations, the application of an innovative hardware, tensor processing units (designed by Google), to quantum chemistry calculations (specifically, to solve for the density matrix) was explored. The author removed the code bottleneck to facilitate the largest “end-to-end” O(N^3) DFT simulations ever reported and benchmarked the accuracy and performance of this new hardware with test cases from biomolecular systems to solid-state and nano-scale materials.

Item Open Access First-Principles Studies of Electronic, Optical and Defect Properties of Photovoltaic Materials(2019) Zhu, TongThe development of the technology depends heavily on the development of materials. However, how to select the best materials for a specific purpose — i.e. materials selection, is a tricky problem in academia, industry, and our daily lives. Recently, because of the rapid development of computers, ab initio theoretical calculations can be used to aid in materials selection. However, since many approximations in the theoretical calculations exist, choosing appropriate approximations to obtain accurate and predictable materials properties is still difficult. This is the main focus of this thesis. More specifically, we will focus on the materials selection for photovoltaics, which plays a significant role in the energy field today. While modern commercial thin-film PV cells, e.g., based on metal chalcogenide zinc-blende-type materials (Cu(In,Ga)(S,Se)2 (CIGSSe), CdTe) suffer from problems like relying on elements that are either toxic or rare in the earth’s crust, a recent alternative candidate based on kesterite Cu2ZnSn(S,Se)4 (CZTS) peaked at relatively low efficiencies (12.6%) due to the limited open circuit voltage (Voc) caused by the prevalent anti-site structure disorder (e.g. Cu on Zn, Zn on Cu). A possible path forward to reduce this antisite disorder is to pursue materials in which the Cu/Zn combination is replaced by elements that are chemically less similar but that retain the same valence. Recently, Cu2 BaSnS4 ́x Sex (CBTSSe) materials with a trigonal structure (space group P31 ) and composed of only earth abundant metals have been proposed and demonstrated as emerging PV absorbers to address the above issues of CZTSSe. Results obtained as part of this thesis elucidated the band structure and electronic properties of the CBTSSe alloys. A recent device prepared from the Cu2BaSnS4 ́xSex (x « 3) has now been demonstrated with power conversion efficiency (PCE) exceeding 5%. Starting from this early prototype, many avenues remain to optimize the materials, including the underlying chemical positions, the electronic, optical and defect properties of specific compounds. In this thesis, we expand on the CBTSSe paradigm by exploring 16 related compounds, denoted I2-II-IV-VI4 (I=Cu,Ag; II=Sr,Ba; IV=Ge,Sn; VI=S,Se), and some of their alloys for their possible utility as thin-film PV absorbers.

A main methodological result of this thesis concerns the appropriate approximations we can use to obtain accurate and predictable structure, electronic, optical and defect properties for photovoltaic materials. Specifically, structure optimization using computationally expensive hybrid density functional theory is more appropriate than the normally used (semi)local functional (PBE, LDA) and can lead to reasonable and predictable structure and electronic properties. Furthermore, a detailed approach to obtain accurate carrier effective masses is pursued. For the optical properties, the effect of different broadening functions on the onset of absorption coefficients is discussed, and the correct onset behavior can be obtained using Gaussian broadening. At last, a validation of the infinite-size limit of charged defect formation energies calculated by supercell approach is given based on a benchmark study for the gallium vacancy (within charge state q = 0, -1, -2, -3) in GaAs. In general, the bare supercell approach, a supercell approach developed earlier by Freysoldt and coworkers, and a cluster approach can lead to the same infinite-size limit for the charged defect formation energies. Then, based on the appropriate approximations mentioned above, a study of materials properties is described in the I2-II-IV-VI4 (I=Cu,Ag; II=Sr,Ba; IV=Ge,Sn; VI=S,Se) 16 compound systems based on the theoretical structure, electronic and optical properties. Four compounds (Cu2BaSnS4, Cu2BaSnSe4, Cu2BaGeSe4, Cu2SrSnSe4) are identified as potential PV candidates based on their appropriate electronic, and optical properties. Then, two further re- finements are pursued for the Cu2BaSnS4 and Cu2BaGeSe4 compounds. The specific alloys Cu2BaGe1 ́xSnxSe4 (x « 3/4) and Cu2BaSnS4 ́xSex (x « 3) prove to be the best candidates for photovoltaics absorbers among the alloys of these two compounds.

Item Embargo Impact of Dynamics and Disorder on Structure and Electronic Levels of Hybrid Organic-Inorganic Perovskites(2023) Qin, XixiHybrid Organic-Inorganic Perovskites (HOIPs) have been attracting significant attention in photovoltaic and various light-emission fields due to their excellent semiconductor characteristics and high structural versatility. Structure determines electronic properties, which in turn dictate the optoelectronic properties. While the electronic structure of static HOIPs has been extensively studied, there has been less focus on understanding the dynamics and atomic disorder in HOIPs through first-principles calculations. Gaining a deeper understanding of the impact of these effects on electronic and optoelectronic properties is crucial for improving the optoelectronic, spintronic, and other properties of HOIPs for future practical applications.The electronic properties of HOIPs can be effectively tuned by atomic disorder, whether induced extrinsically through alloying or inherently via thermal vibration. For instance, the tunable band gap of the mixed halide perovskite (PEA)2Pb(I1−xBrx)4 as a function of x was predicted by first calculating its phase diagram using semi-local density functional calculations with van der Waals dispersion correction. By utilizing the lowest energy structures, the trend of tunable band gaps is predicted with hybrid DFT incorporating spin-orbit coupling effects, aligning with the photoluminescence spectra observations. Beyond inorganic halide alloying, the introduction of mixed organic cations offers another route to modulate the electronic and optoelectronic behaviors in 2D HOIPs. This is evident when comparing [S-MePEA][C4A]PbBr4 and [S-MePEA][C4A]PbI4 to their purely chiral cation analogs, [S-MePEA]2PbBr4 and [S-MePEA]2PbI4. Such variations are supported by atomic structures determined experimentally via XRD and by theoretical electronic and spin texture calculation results. Next, the thesis investigates atomic disorder induced by inherent thermodynamic effects, as well as their impacts on the electronic and optoelectronic properties of HOIPs. For example, a detailed examination of local and dynamic disorders in MAPbBr3 is conducted, with parameterization through Pb-Br pair distribution function (PDF), PbBr62- octahedron distortion, and MA+ dynamics derived from AIMD simulation trajectories at various temperatures. These findings reveal that the structural disorder in MAPbBr3 primarily stems from thermally activated anharmonic dynamics, not static disorder, aligning with experimental observations. The dynamic spin splitting in (PEA)2PbI4 is studied using AIMD and DFT-PBE+SOC band structure calculations. The results show that the average spin-splitting energy in the dynamic structures is not zero but is localized and short-lived. This dynamic spin-splitting characteristic diminishes over extensive time and spatial scales. Electron-phonon interactions and phonon-polaronic coupling effects play pivotal roles in understanding the fundamental electronic and charge-carrier properties of HOIPs, providing active mechanisms to manipulate charge carrier transportation or polaron oscillation properties. For instance, it is demonstrated that the electron-phonon coupling (AE2T)2AgBiI8 can induce coherent charge transfer kinetics (AE2T)2AgBiI8. This occurs through the oscillation of energy levels between the organic and inorganic components, which then causes the hole population to shift controllably between these components. When simulating polaron populations with static exciton calculations combined with phonon calculations for CsPbBr3, it's indicated that the stretching phonon mode at 140 cm-1, which is responsible for the dephasing of polaron oscillation, remains stable even at high excitation densities. This stability suggests a weak coupling between the stretching modes and the low-energy rocking modes. Experimental evidence shows that the rocking modes are strongly coupled to the polaronic system, protecting its coherent oscillation from dephasing and leading to the phenomenon of superfluorescence. Furthermore, chiral phonon calculations in [S-MePEA]2PbI4 predict the presence of both transverse and longitudinal chiral phonons, in alignment with experimental observations. These chiral phonons are predominantly found in the acoustic phonon branches near the Γ point, signifying that they are long-range, low-frequency phonon modes, which is consistent with experimental findings. This thesis has unraveled the profound influence of both extrinsic and inherent thermodynamic atomic disorders on the electronic properties of HOIPs. Moreover, this thesis illuminated the potential of leveraging electron-phonon coupling to intentionally modulate atomic disorder and thereby to manipulate the electronic properties of HOIPs with precision and control. The findings underscore the great potential of HOIPs in optoelectronic applications.

Item Open Access Investigation of the Chemical Evolution of InAs Native Oxide and Its Impact on the Surface Electronic Properties(2022) Hitchcock, KatherineThe evolution of compound semiconductor native oxides, formed under ambient conditions, remains poorly understood. Herein, we use XPS to study the evolution of the InAs native oxide using six samples with different surface preparation techniques. For times of exposure in ambient conditions between 2.5 min and 24 hours, the As-species composition varies significantly between samples during the exposures of less than 20 minutes. However, we find that after 2 hours, the oxide composition, thickness, and correlated semiconductor band-bending converges to values with much less variation.

Item Embargo Structure and Electronic Properties of Quaternary Chalcogenide Semiconductors from First Principles(2023) Wang, TianlinThe development of computer technology and the understanding of ab initio theoretical formalisms gave birth to computational materials science. Scientists thus have a powerful tool to keep exploring for new materials. At the same time, the necessity and desire to seek for new energy resource are undiminished. As solar energy plays an increasingly important role in environmentally friendly energy, researchers hope to find novel materials to replace silicon, which has been used in the field for decades. Utilizing computational materials science with the help of powerful supercomputers and well-developed approximate approaches to pursue material exploration is the focus of this thesis. There have been some commercially successful photovoltaic absorbers other than silicon, including CdTe and Cu (In,Ga)(S,Se)2. However, the low abundances of element Te and In, or the toxicity of Cd hinder terawatt deployment. To find substances taking the place of these toxic or rare elements, the kesterite Cu2ZnSn(S,Se)4 (CZTSSe), which substitutes In and Ga with Zn and Sn, is one alternative pathway, though the record achievable photovoltaic efficiency only reached 12.6% due to the antisite disorder enabled by the chemical and ionic size similarity of Zn and Cu. One solution to reduce antisite disorder is to replace Zn by Ba in Cu2BaSn(S,Se)4 (CBTSSe). Not only are the toxicity and rarity of the constituent elements avoided, but the coordination of Ba is also changed from 4-fold to 8-fold. The structure is therefore thought to become more resistant to the formation of structural defects. Since then, further substitutions of element in all four sites were pursued by exploring I2-II-IV-X4 (I = Li, Cu, Ag; II = Zn, Cd, Mn, Fe, Ba, Sr, Pb; IV = Si, Ge, Sn; X = S, Se), quaternary chalcogenides semiconductor material. At the outset of this thesis, the electronic, optical and structural properties were computed and analyzed using density functional theory for several compounds from the I2-II-IV-X4 family, which were successfully synthesized by colleagues from the experimental group of Dr. David Mitzi, including: Ag2BaSiS4 (indirect gap: 2.2 eV), Ag2PbSiS4 (indirect gap: 1.9 eV), Cu2PbGeS4 (indirect gap: 1.55 eV), Cu2SrSiS4 (direct gap: 3.4 eV), Ag2SrSiS4 (indirect gap: 2.08 eV) and Ag2SrGeS4 (indirect gap: 1.73 eV). Among them, Ag2PbSiS4, with direct band gap at about 2 eV (larger than optimal for single junction PV) and strong optical response within the visible spectrum, could be useful for tandem junction solar cells; though Cu2PbGeS4 shows strongest optical response, the indirect nature of bandgap is not ideal for application in PV devices; the high degree of band curvature (prospects of low effective masses and high mobilities) renders Ag2SrSiS4 and Ag2SrGeS4 suitable as PV buffer layer materials, and the inversion symmetry breaking enables them candidates for non-linear optical (NLO) applications. Broadening the I2-II-IV-X4 quaternary chalcogenide stoichiometry, this thesis next studies the quaternary chalcogenides in cubic phases of different stoichiometries. The study of I-II-IV-X (II = Sr, Pb; IV = Si, Ge, Sn; X = S, Se) involves solving partial site occupancies from the experimental geometry and electronic properties analysis to study the effect from geometric structure to band structure. Through an examination of the Ag-Pb-Si-S and Ag-Sr-Sn-S prototype element systems, they form in a cubic structure with vacancy-disordered Ag sites in stoichiometry of 2:3:2:8 instead of an orthorhombic structure with stoichiometry of 2:1:1:4. Ag2Pb3Si2S8 (direct gap: 1.95 eV), Ag2Sr3Si2S8 (direct gap: 2.66 eV), Ag2Sr3Si2S8 (direct gap: 2.87 eV), Ag2Sr3Ge2S8 (direct gap: 1.95 eV) and Ag2Sr3Ge2Se8 (direct gap: 1.90 eV) all have noncentrosymmetric crystal structure, indicating potential for frequency doubling devices. Ag2Pb3Si2S8 and Ag2Sr3Ge2Se8 have band gaps within a reasonable regime for light-assisted water-splitting applications. The third thrust of the thesis focuses on the I2-I’-V-X4. Ag2(NH4)AsS4, which has been synthesized previously and has an experimental band gap of 2.05 eV, is researched by molecular dynamics to understand the local configuration of ammonium and to quantify the effect of ammonium movement on the electronic properties. Ammonium is found to rotate freely within the cage of eight S atoms, connected with band gap fluctuations up to approximately 0.3 eV. The final chapter of the thesis focuses on divalent Eu, a rare-earth element with suitable ionic radius to form quaternary chalcogenides as I2-Eu-IV-X4 (I = Li, Cu, Ag; IV = Si, Ge, Sn; X = S, Se). This project uses the hybrid density functional HSE06 to determine an appropriate choice of the exchange parameter ? to accurately describe the highly correlated f orbitals of Eu, a key prerequisite to understand the accuracy and limit of this class of theory for predicting energy band structures in these f electron containing systems. While higher α values are needed to capture the f band position in literature ARPES benchmark data for EuS, a lower range of ? values, about 0.3, appears to empirically cover diffuse reflectance spectroscopy (DRS) determined band gaps in I2-II-IV-X4 compounds, consistent with the case of Cu2EuSnSe4. Comprehensive prediction of properties across I2-Eu-IV-X4 chalcogenides reveals a significant dependence on I-site composition. It is found that Ag-based compounds have indirect band gaps and are most stable in the I222 and 〖Ama2〗^†(APGS) space groups. In contrast, Li-based compounds favor the I4 ̅2m space group and have a direct gap. Though the bandgap transition in Li-based compounds is direct, the predicted band gap values are too large for most photovoltaic applications. Cu-based compounds energetically prefer the Ama2 and P31 space groups and contain the most promising direct bandgap materials for photovoltaics. From the band structure, and subsequent experimental results, Cu2EuSnSe4 (direct band gap: 1.53 eV (Ama2)) emerges as a promising candidate for photovoltaic application due to its direct band gap and strong optical response within the visible light range.

Item Open Access Tunable Electronic Excitations in Hybrid Organic-Inorganic Materials: Ground-State and Many-Body Perturbation Approaches(2019) LIU, CHIThree-dimensional (3D) Hybrid Organic-Inorganic Perovskites (HOIPs) have been investigated intensively for application in photovoltaics in the last decade due to their extraordinary properties, including ease of fabrication, suitable band gap, large absorption, high charge carrier mobility, etc. However, the structure and properties of their two-dimensional (2D) counterparts, especially those with complex organic components, are not understood as deeply as the 3D HOIPs. Due to the easing of spatial constraints for the organic cations, 2D HOIPs potentially have more structural flexibility and thus higher tunability of their electronic properties compared to the 3D HOIPs. Motivated by a desire to demonstrate such flexibility and tunability, a series of 2D HOIPs with oligothiophene derivative as the organic cations and lead halide is investigated in the first part of this work. Initial computational models with variable organic and inorganic components are constructed from the experimental structure of 5,5''-bis(aminoethyl)-2,2':5',2''':5'',2'''-quaterthiophene lead bromide (AE4T\ch{PbBr4}). \textit{Ab initio} first-principles calculations are performed for these materials employing density functional theory with corrections for van der Waals interactions and spin-orbit coupling. The set of 2D HOIPs investigated is found to be understandable within a quantum-well-like model with distinctive localization and nature of the electron and hole carriers. The band alignment types of the inorganic and organic component can be varied by rational variation of the inorganic or organic component. With the computational protocol shown to work for the above series of oligothiophene-based lead halides, a more extensive family of the oligothiophene-based 2D HOIPs is then investigated to demonstrate their structural and electronic tunability. For AE2T\ch{PbI4}, the disorder of the organic cations are investigated systematically in synergy between theoretical techniques and experimental reference data provided by a collaborating group. A staggered arrangement of AE2T cations is revealed to be the most stable packing pattern with the correct band alignment types, in agreement with experiment results from optical spectroscopy. Another representative class of 2D HOIPs based on oligoacene derivatives is investigated to show structural and electronic tunability similar with their oligothiophene based counterparts. In the final part of the thesis, an all-electron implementation of Bethe-Salpeter equation (BSE) approach based on the $GW$ approximation is developed using numeric atom centered orbital basis sets, with the aim of developing first steps to a formal many-body theory treatment of neutral excitations, which goes beyond the independent-particle picture of density functional theory. Benchmarks of this implementation are performed for the low-lying excitation energies of a popular molecular benchmark set (``Thiel's" set) using results obtained using the Gaussian-orbital based MolGW code as reference values. The agreement between the BSE results computed by these two codes when using the same $GW$ quasiparticle energies validate our implementation. The impact of different underlying technical approximations to the $GW$ method is evaluated for the so-called ``two-pole" and ``Pad{\' e}" approximate evaluation techniques of the $GW$ self-energy and resulting quasiparticle energies. To reduce the computational cost in both time and memory, the convergence of the BSE results with respect to basis sets and unoccupied states is examined. An augmented numeric atom centered orbital basis set is proposed to obtain numerical converged results.