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At least 109 records · Page 6

Computing molecular excited states on a D-Wave quantum annealer

Abstract The possibility of using quantum computers for electronic structure calculations has opened up a promising avenue for computational chemistry. Towards this direction, numerous algorithmic advances have been made in the last five years. The potential of quantum annealers, which are the prototypes of adiabatic quantum computers, is yet to be fully explored. In this work, we demonstrate the use of a D-Wave quantum annealer for the calculation of excited electronic states of molecular systems. These simulations play an important role in a number of areas, such as photovoltaics, semiconductor technology and nanoscience. The excited states are treated using two methods, time-dependent Hartree–Fock (TDHF) and time-dependent density-functional theory (TDDFT), both within a commonly used Tamm–Dancoff approximation (TDA). The resulting TDA eigenvalue equations are solved on a D-Wave quantum annealer using the Quantum Annealer Eigensolver (QAE), developed previously. The method is shown to reproduce a typical basis set convergence on the example $$\hbox {H}_2$$ H 2 molecule and is also applied to several other molecular species. Characteristic properties such as transition dipole moments and oscillator strengths are computed as well. Three potential energy profiles for excited states are computed for $$\hbox {NH}_3$$ NH 3 as a function of the molecular geometry. Similar to previous studies, the accuracy of the method is dependent on the accuracy of the intermediate meta-heuristic software called qbsolv.

74 ATOMIC AND MOLECULAR PHYSICS↗

The Pixel Anomaly Detection Tool : a user-friendly GUI for classifying detector frames using machine-learning approaches

Data collection at X-ray free electron lasers has particular experimental challenges, such as continuous sample delivery or the use of novel ultrafast high-dynamic-range gain-switching X-ray detectors. This can result in a multitude of data artefacts, which can be detrimental to accurately determining structure-factor amplitudes for serial crystallography or single-particle imaging experiments. Here, a new data-classification tool is reported that offers a variety of machine-learning algorithms to sort data trained either on manual data sorting by the user or by profile fitting the intensity distribution on the detector based on the experiment. This is integrated into an easy-to-use graphical user interface, specifically designed to support the detectors, file formats and software available at most X-ray free electron laser facilities. The highly modular design makes the tool easily expandable to comply with other X-ray sources and detectors, and the supervised learning approach enables even the novice user to sort data containing unwanted artefacts or perform routine data-analysis tasks such as hit finding during an experiment, without needing to write code.

47 OTHER INSTRUMENTATION↗

Improving Cost and Efficiency of the Scalable Solid Oxide Fuel Cells Power System

The objective of this project was to design and develop a 20kW range small-scale solid oxide fuel cells (SOFC) power system for applications such as data centers and commercial buildings. The original plan included a 5,000 hours demonstration and a Techno-Economic Analysis (TEA) which were dropped as part of project termination. The original project plan was to use a stack with a cross-flow cell design which had previously been tested for 500 hours at a community college in Malta, NY. However, it was decided to move to the advanced R-SOFC co-flow cell developed under Department of Energy Award DE-FE0031971. The advanced cell design has the advantage of a larger active area for the same manufacturing footprint which results in fewer required cells for the same stack power, hence a higher volumetric power density (kW/L) and lower cost per kW than the original cross-flow cell design. A full SOFC system Simulink model was developed and calibrated with testing data from a fuel cell stack and BOP (balance of plant) components. The simulation results from the calibrated model showed an acceptable match with the experimental data. A structural analysis conducted for various load scenarios indicated no high stress areas for all spatial directions. Major electrical system components were acquired, built and successfully tested. System sensors were verified and validated against controls. Safety checks, a diagnostic check, PID tuning, and control software commissioning tasks were also conducted. The power electronics prototype was delivered and trial testing completed. Balance of Plant component testing and simulation work was conducted to characterize Reformer-Heat Exchanger heat transfer and backpressure and reformer catalyst methane conversion and product selectivity. Simulations were conducted to design the Anode and Cathode fluid passages and size the air-air and fuel-fuel heat exchangers. A Burner operation map was created from test data and the Anode Gas Recirculation blower was tested to evaluate its durability. The SOFC system used a horizontal style design where components sit directly on a casting with a direct connection to the skid. This design has efficient packaging and a small footprint with approximate dimensions of 750 mm x 700 mm x 1700 mm. An SOFC system was built and successfully tested at the Malta, NY facility The system for over 500 hours under load of which over 300 hours was at full load of 20 kW.

30 DIRECT ENERGY CONVERSION↗

Real-time 3D analysis during electron tomography using tomviz

The demand for high-throughput electron tomography is rapidly increasing in biological and material sciences. However, this 3D imaging technique is computationally bottlenecked by alignment and reconstruction which runs from hours to days. We demonstrate real-time tomography with dynamic 3D tomographic visualization to enable rapid interpretation of specimen structure immediately as data is collected on an electron microscope. Using geometrically complex chiral nanoparticles, we show volumetric interpretation can begin in less than 10 minutes and a high-quality tomogram is available within 30 minutes. Real-time tomography is integrated into tomviz, an open-source and cross-platform 3D data analysis tool that contains intuitive graphical user interfaces (GUI), to enable any scientist to characterize biological and material structure in 3D.

36 MATERIALS SCIENCE↗

Non-Adiabatic Excited State Molecular Dynamics Methodologies: comparison and convergence

Direct atomistic simulation of nonadiabatic molecular dynamics is a challenging goal that allows important insights into fundamental physical phenomena. A variety of frameworks, ranging from fully quantum treatment of nuclei to semiclassical and mixed quantum–classical approaches, were developed. These algorithms are then coupled to specific electronic structure techniques. Such diversity and lack of standardized implementation make it difficult to compare the performance of different methodologies when treating realistic systems. Here, we compare three popular methods for large chromophores: Ehrenfest, surface hopping, and multiconfigurational Ehrenfest with ab initio multiple cloning (MCE-AIMC). These approaches are implemented in the NEXMD software, which features a common computational chemistry model. The resulting comparisons reveal the method performance for population relaxation and coherent vibronic dynamics. Finally, we study the numerical convergence of MCE-AIMC algorithms by considering the number of trajectories, cloning thresholds, and Gaussian wavepacket width. Our results provide helpful reference data for selecting an optimal methodology for simulating excited-state molecular dynamics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Atomate2: modular workflows for materials science

High-throughput density functional theory (DFT) calculations have become a vital element of computational materials science, enabling materials screening, property database generation, and training of “universal” machine learning models. While several software frameworks have emerged to support these computational efforts, new developments such as machine learned force fields have increased demands for more flexible and programmable workflow solutions. This manuscript introduces atomate2, a comprehensive evolution of our original atomate framework, designed to address existing limitations in computational materials research infrastructure. Key features include the support for multiple electronic structure packages and interoperability between them, along with generalizable workflows that can be written in an abstract form irrespective of the DFT package or machine learning force field used within them. Our hope is that atomate2's improved usability and extensibility can reduce technical barriers for high-throughput research workflows and facilitate the rapid adoption of emerging methods in computational material science.

97 MATHEMATICS AND COMPUTING↗

MBX V1.2: Accelerating Data-Driven Many-Body Molecular Dynamics Simulations

The MBX software provides an advanced platform for molecular dynamics simulations, leveraging state-of-the-art MB-pol and MB-nrg data-driven many-body potential energy functions. Developed over the past decade, these potential energy functions integrate physics-based and machine-learned many-body terms trained on electronic structure data calculated at the "gold standard" coupled-cluster level of theory. Recent advancements in MBX have focused on optimizing its performance, resulting in the release of MBX v1.2. While the inherently many-body nature of MB-pol and MB-nrg ensures high accuracy, it poses computational challenges. MBX v1.2 addresses these challenges with significant performance improvements, including enhanced parallelism that fully harnesses the power of modern multicore CPUs. In conclusion, these advancements enable simulations on nanosecond time scales for condensed-phase systems, significantly expanding the scope of high-accuracy, predictive simulations of complex molecular systems powered by data-driven many-body potential energy functions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

CERES : a cryo-EM re-refinement system for continuous improvement of deposited models

The field of electron cryomicroscopy (cryo-EM) has advanced quickly in recent years as the result of numerous technological and methodological developments. This has led to an increase in the number of atomic structures determined using this method. Recently, several tools for the analysis of cryo-EM data and models have been developed within the Phenix software package, such as phenix.real_space_refine for the refinement of atomic models against real-space maps. Also, new validation metrics have been developed for low-resolution cryo-EM models. To understand the quality of deposited cryo-EM structures and how they might be improved, models deposited in the Protein Data Bank that have map resolutions of better than 5 Å were automatically re-refined using current versions of Phenix tools. The results are available on a publicly accessible web page (https://cci.lbl.gov/ceres). The implementation of a Cryo-EM Re-refinement System ( CERES ) for the improvement of models deposited in the wwPDB, and the results of the re-refinements, are described. Based on these results, contents are proposed for a `cryo-EM Table 1', which summarizes experimental details and validation metrics in a similar way to `Table 1' in crystallography. The consistent use of robust metrics for the evaluation of cryo-EM models and data should accompany every structure deposition and be reported in scientific publications.

59 BASIC BIOLOGICAL SCIENCES↗

Evaluating Cryo–TEM Reconstruction Accuracy of Self–Assembled Polymer Nanostructures

Cryogenic transmission electron microscopy (cryo–TEM) combined with single particle analysis (SPA) is an emerging imaging approach for soft materials. However, the accuracy of SPA–reconstructed nanostructures, particularly those formed by synthetic polymers, remains uncertain due to potential packing heterogeneity of the nanostructures. In this study, the combination of molecular dynamics (MD) simulations and image simulations is utilized to validate the accuracy of cryo–TEM 3D reconstructions of self–assembled polypeptoid fibril nanostructures. Using CryoSPARC software, image simulations, 2D classifications, ab initio reconstructions, and homogenous refinements are performed. By comparing the results with atomic models, the recovery of molecular details is assessed, heterogeneous structures are identified, and the influence of extraction location on the reconstructions is evaluated. In conclusion, these findings confirm the fidelity of single particle analysis in accurately resolving complex structural characteristics and heterogeneous structures, exhibiting its potential as a valuable tool for detailed structural analysis of synthetic polymers and soft materials.

36 MATERIALS SCIENCE↗

Electron Cloud Measurements in Fermilab Booster

Fermilab Booster synchrotron requires an intensity upgrade from 4.5x1012 to 6.5x1012 protons per pulse as a part of Fermilab's Proton Improvement Plan-II (PIP-II). One of the factors which may limit the high-intensity performance is the fast transverse instabilities caused by electron cloud effects. According to the experience in the Recycler, the electron cloud gradually builds up over multiple turns inside the combined function magnets and can reach final intensities orders of magnitude greater than in a pure dipole. Since the Booster synchrotron also incorporates combined function magnets, it is important to measure the presence of electron cloud. The presence or apparent absence of the electron cloud was investigated using two different methods: measuring bunch-by-bunch tune shift by changing the bunch train structure at different intensities and propagating a microwave carrier signal through the beampipe and analyzing the phase modulation of the signal. This paper presents the results of the two methods and corresponding simulation results conducted using PyECLOUD software.

43 PARTICLE ACCELERATORS↗

BinaryCIF and CIFTools—Lightweight, efficient and extensible macromolecular data management

3D macromolecular structural data is growing ever more complex and plentiful in the wake of substantive advances in experimental and computational structure determination methods including macromolecular crystallography, cryo-electron microscopy, and integrative methods. Efficient means of working with 3D macromolecular structural data for archiving, analyses, and visualization are central to facilitating interoperability and reusability in compliance with the FAIR Principles. We address two challenges posed by growth in data size and complexity. First, data size is reduced by bespoke compression techniques. Second, complexity is managed through improved software tooling and fully leveraging available data dictionary schemas. To this end, we introduce BinaryCIF, a serialization of Crystallographic Information File (CIF) format files that maintains full compatibility to related data schemas, such as PDBx/mmCIF, while reducing file sizes by more than a factor of two versus gzip compressed CIF files. Moreover, for the largest structures, BinaryCIF provides even better compression—factor ten and four versus CIF files and gzipped CIF files, respectively. Herein, we describe CIFTools, a set of libraries in Java and TypeScript for generic and typed handling of CIF and BinaryCIF files. Together, BinaryCIF and CIFTools enable lightweight, efficient, and extensible handling of 3D macromolecular structural data.

59 BASIC BIOLOGICAL SCIENCES↗

Improved AlphaFold modeling with implicit experimental information

Machine-learning prediction algorithms such as AlphaFold and RoseTTAFold can create remarkably accurate protein models, but these models usually have some regions that are predicted with low confidence or poor accuracy. We hypothesized that by implicitly including new experimental information such as a density map, a greater portion of a model could be predicted accurately, and that this might synergistically improve parts of the model that were not fully addressed by either machine learning or experiment alone. An iterative procedure was developed in which AlphaFold models are automatically rebuilt on the basis of experimental density maps and the rebuilt models are used as templates in new AlphaFold predictions. We show that including experimental information improves prediction beyond the improvement obtained with simple rebuilding guided by the experimental data. This procedure for AlphaFold modeling with density has been incorporated into an automated procedure for interpretation of crystallographic and electron cryo-microscopy maps.

59 BASIC BIOLOGICAL SCIENCES↗

Materials Challenges and Opportunities for Energy Generation, Conversion, Delivery, and Storage (Applied Energy Tri-Laboratory Consortium Workshop Report)

This report documents the outcomes of the Tri-Laboratory Materials Workshop that was held July 31 and August 1, 2019 to begin addressing the needs, opportunities, and challenges associated with the development, fabrication, and testing of the needed materials and components for integrated hybrid energy systems (i.e., incorporating nuclear, fossil, and renewables for electric and thermal applications). This was accomplished by assembling the research program leads and principal investigators at Idaho National Laboratory (INL), National Energy Technology Laboratory (NETL), and National Renewable Energy Laboratory (NREL), who support the research and development of new technology and system integration. The team then identified and prioritized key materials development needs. This effort was intended to enhance communications and synergy among the Tri-Lab partners. Advanced functional and structural materials are central to transformative energy technologies for energy generation, conversion, delivery, and storage. With that in mind, the workshop focused on identifying and assessing the foundational materials research needs at both the basic and applied levels. Materials challenges include the ability to withstand harsh environments, such as high temperatures and pressures, corrosion, oxidation, or irradiation while maintaining flexible mission profiles and long service lifespans. Advanced energy system material challenges and needs range from materials for the capture, upgrading/concentration, storage, and delivery of low-grade heat to materials for high temperature environments that involve liquid metals, molten salt, and very high temperature gas heat delivery and storage systems. Material improvements are needed for hybrid energy systems due to accelerated corrosion and stress-fatigue failure of materials and equipment, which results from increased frequency and amplitude of thermal, mechanical, and electrical cycling of systems components. Multifunctional materials are needed for high temperature solid-oxide fuel cells, advanced electrochemical reactors, and in-process separation. Relative to materials manufacturing, application of advanced additive and subtractive methods need to be understood to develop both thin-layer homogenous materials and materials of graded composition. Materials modeling and machine learning will be critical to accelerate the design and production of power electronics, and nuclear reactor materials and fuel, as well as to gain an understanding of beneficial materials phenomena or deleterious microstructure evolution. There is also a need for standardized models, computational structures, data reporting protocols and modeling tools across the three laboratories. This would allow consistent results, analysis, and data sharing. Combining computational capabilities between the three laboratories (e.g., hardware, software) would greatly increase computational capabilities and throughput. The workshop identified the need for laboratories to anticipate and address problems that will occur during scale-up. Laboratory work must connect with industry to ensure that research focuses on processes that are scalable and marketable. Industry input and perspective are essential to guide laboratory research to meet these requirements and deploy new technology in industrial demonstrations. Another aspect of scale-up is the integration of multiple systems since new challenges often arise at the subsystem interfaces. Establishing a scale-up manufacturing demonstration/pilot plant, potentially as an industrial user facility, would be beneficial to the laboratories and industry. That modular scale-up manufacturing demonstration/pilot plant would allow researchers to find and resolve interface problems that cannot be identified by focusing only on individual parts. Communication exchanges among the organizers, attendees, and workshop survey responses indicate that the workshop was successful in achieving its goal to identify key technology gaps and research needs. Strong positive feedback was received on the sharing of ideas, capabilities, talent, and passion to move forward on the materials-related action items.

36 MATERIALS SCIENCE↗

Automated Energy-Dispersive X-ray Spectroscopy Analysis for Multi-Modal Few-Shot Learning

Scanning transmission electron microscopy (STEM) is a powerful tool that allows for the atomic-scale analysis of a materials’ structure, chemistry, and defect domains (Akers et al. 2021). The current generation of microscopes generate vast amounts of data, surpassing the limits of effective manual analysis traditionally performed by domain experts (Spurgeon et al. 2021). While recent strides in machine learning have significantly enhanced the processing of large and intricate datasets acquired through electron microscopy, the prevalent use of proprietary software packages for initial data collection poses a challenge. In many cases, these software packages act as a ‘black box’, constraining user functionality and hindering the output of data in a format that is conducive to seamless integration into machine learning models. This work addresses these challenges by adapting HyperSpy, an open-source Python library, for the analysis and quantification of raw energy dispersive spectroscopy (EDS) data acquired through STEM. The modified HyperSpy code successfully facilitates user-defined segmentation of the data, enabling the integration of atomic %, weight %, and raw EDS spectra for each segmented region into an existing few-shot machine learning model. While initial results reveal discrepancies in quantified atomic and weight percentages when compared to proprietary software, ongoing efforts aim to rectify this issue by refining the fit of the HyperSpy model to the EDS spectra. Overall, this research underscores the potential of open-source tools like HyperSpy to enhance the accessibility of analytical tools, fostering a transparent and user-friendly environment for seamlessly incorporating electron microscopy data into machine learning models.

36 MATERIALS SCIENCE↗

Improving ICARUS Track Reconstruction Algorithms

The ICARUS experiment is part of the Short-Baseline Neutrino (SBN) program at Fermilab. The main goal of the experiment is to investigate the possibility of sterile neutrinos in the O(1 eV) mass region and provide clarification of the anomaly detected from the Liquid Scintillator Neutrino Detector (LSND) and MiniBooNE experiments. The ICARUS-T600 detector is a Liquid Argon Time Projection Chamber (LAr-TPC), that can provide excellent 3D imaging and calorimetric reconstruction of any ionizing particles. This detection technique allows a detailed study of neutrino interactions, spanning a wide energy spectrum (from a few keV to several hundreds of GeV). The detector consists of two identical adjacent modules, filled with a total of 760 tons of ultra-pure liquid argon. Each module houses two LAr-TPCs separated by a common cathode with a maximum drift distance of 1.5 m, equivalent to about 1 ms drift time for the nominal $500$ V/m electric drift field. The anode is made of three parallel wire planes positioned 3 mm apart, where the stainless-steel wires are oriented on each plane at a different angle with respect to the horizontal direction ($+60^\degree$,$-60^\degree$,$0^\degree$). The first two planes (Induction 1 and Induction 2) provide a non-destructive charge measurement, whereas the ionization charge is fully collected by the last collection plane. In total, 53248 wires with a 3 mm pitch and length up to 9 m are installed in the detector. In the first stage of the reconstruction, segments of waveforms corresponding to physical signals (hits) are searched for in the deconvolved wire waveform with a threshold-based hit-finding algorithm. Each hit is then fitted with a Gaussian, whose area is proportional to the number of drift electrons generating the signal. In the second stage of the reconstruction, hits are passed as input to Pandora, a framework software composed of different pattern recognition algorithms, that performs a 3D reconstruction of the full image recorded in the collected event, including the identification of interaction vertices and tracks and showers inside the TPC. These are organized into a hierarchical structure (called slice) of particles generated starting from a primary interaction vertex. In some cases, related to the inefficiencies in the hit detection or excessive deflection of the particle trajectory, Pandora breaks the particle's track into two or more smaller pieces and considers each piece as an independent track. We studied this phenomenon focusing on primary muons from ν_μ CC interactions contained in a single module with a track at least 20 cm long, to exclude delta rays. The study determined that about $7-8\%$ of the muon tracks are broken. Approximately $80\%$ of the times, Pandora assigns all segments of the track to the same slice (intra-slice track split), while in the remaining $20\%$ of the cases, one of the segments is associated with another slice (extra-slice track split). To mitigate this phenomenon, we designed an algorithm that detects and stitches the tracks broken by Pandora for the intra-slice split. In Monte Carlo simulations, the algorithm showed an efficiency exceeding $80\%$ and a purity exceeding $93\%$.

Ricci, Alessandro Maria [Pisa U.; INFN, Pisa] (ORC↗

Bridging the time scale in exascale computing of chemical systems (Final Technical Report)

This report summarizes the work carried out with support of the United States Department of Energy under Award DE-SC0019441. The theme of this project was to develop and apply methods that allowed for the acceleration of atomistic calculations, particularly in challenging areas such as multiphase systems, electrified interfaces, uncertainty estimation, and applications requiring chemical accuracy, which tend to be applications where simulation time is severely bottlenecked by the computational time requirements. Much of the focus was on the application of emerging machine-learning methodologies, although a wide range of methodologies were employed. This report has two major sections. The first focuses on the methodological advances themselves. Within this part, we report a number of major advances, a few examples of which are described here. We report the first machine-learning scheme for the acceleration of electronically grand-canonical calculations (that is, those applicable to electrochemistry). We report new methods of performing transfer learning, in which physics-based priors can be used to provide predictions, often with uncertainty estimates, of images well outside of training sets; we also offer ways to fine-tune these transfer-learning models. We provide a new systematic means to generate and apply minimal training data sets to very large (10,000’s of atoms) systems, with only small training sets appropriate for electronic structure. We developed new methodologies to integrate surface vibrations into surface adsorption calculations. We made advances to the applicability of diffusion Monte Carlo methods to allow (learned) force prediction, finite-size error correction, and force-free means of searching for transition states. We integrated machine-learned atomistic predictions into mechanism generation codes. Additionally, we released new software including AmpTorch, a modernized version of our original atomistic machine-learning code Amp. The second part of this report focuses on the scientific applications that accompanied, and were often enabled by, the methodological advances described earlier. A few examples follow, but full details are in the individual chapters of the report. For example, we developed a general theory of phonon-induced friction on molecular adsorbates. We showed fundamentally how solvent influences the adsorption and desorption process and how it differs from the processes typically involved at the solid–gas interface, making aqueous-phase and electrocatalysis different from traditional thermocatalysis. We examined how metal–insulator and magnetic transitions can be probed, and accelerated exciton dynamics via Frenkel Hamiltonian parameters. We showed that the nearsighted force-training approach, developed within this project, can predict both the stability and reactivity of large nanoparticles, and can also lead to insights on catalyst coverage on binding energies and entropies. These applied studies, which generally integrated with our method development, allowed us to push forward the theoretical understanding of several reaction classes.

08 HYDROGEN↗

Analysis of X-ray images and spectra (aXis2000): A toolkit for the analysis of X-ray spectromicroscopy data

Spectromicroscopy refers to analytical methods that combine imaging and spectroscopy to provide detailed, spatially resolved analytical information about a sample, such as the type and quantitative spatial distributions of chemical components, geometric or magnetic alignment information, crystal structure, etc. The analysis of X-ray images and spectra (aXis2000) software described in this work provides a set of routines within a single, integrated, graphical-oriented package to read, display, manipulate and analyze spectromicroscopy data, with particular focus on soft X-ray spectromicroscopy methods such as scanning transmission X-ray microscopy (STXM), X-ray photoemission electron microscopy (XPEEM), scanning photoelectron X-ray microscopy (SPEM) and transmission X-ray microscopy (TXM). Here, this free software is described and compared to other software that can provide similar or complementary capabilities. Examples of spectromicroscopic analyses using advanced features of aXis2000 are provided.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Kohn-Sham Solver (KSSOLV) v2.0

KSSOLV is a MATLAB toolbox for solving Kohn-Sham density functional theory based electronic structure eigenvalue problems. It uses an object oriented features of MATLAB to represent atom, molecules, wavefunctions and Hamiltonians and their operations. It is designed to make it easier for users to prototype and test new algorithms for solving the Kohn-Sham problem. KSSOLV2.0 contains significant improvement over the original KSSOLV described in a paper published in ACM Transaction on Mathematical Software (attached). In addition to performing ground state calculation for small molecules, it can also perform geometry optimization for both molecules and solids. It uses standard pseudopotentials and implements local density approximation, generalized gradient approximation and hybrid functionals. Future releases will also include time-dependent DFT and post DFT calculations such as the GW quasi-particle energy calculation and Bethe-Salpeter equation solver for optical absorption.

Yang, Chao↗