ΔSCF Method Research Articles

Fluorescent Rhodopsins: A Challenging Test for Cost-Effective QM/MM Approaches.

In this study, we evaluate the performance of two cost-effective models, namely, TD-DFT and ΔSCF methods, combined with different molecular mechanics models, to predict the photophysical and photochemical properties of a set of fluorescent mutants of the microbial rhodopsin Archaerhodopsin-3. We investigate absorption energies and excited-state isomerization barriers of the embedded retinal protonated Schiff-base chromophore by comparing different DFT functionals as well as different approximations of the embedding model. For absorption energies, CAM-B3LYP demonstrates the most consistent alignment with experiments among the functionals tested, whereas the embedding potentials exhibit similar accuracy. However, incorporating linear response corrections within the polarizable TD-DFT/MM framework enhances accuracy. The photoisomerization barriers, instead, exhibit a pronounced sensitivity to the choice of embedding model, underscoring the complex role that environmental factors play in modulating predictions of excited-state processes. For the two properties here investigated, ΔSCF/MM presents qualitatively similar behavior with respect to TD-DFT for all the tested embedding models.

Benchmark computations of nearly degenerate singlet and triplet states of N-heterocyclic chromophores. II. Density-based methods.

In this paper, we demonstrate the performance of several density-based methods in predicting the inversion of S1 and T1 states of a few N-heterocyclic triangulene based fused ring molecules (popularly known as INVEST molecules) with an eye to identify a well performing but cost-effective preliminary screening method. Both conventional linear-response time-dependent density functional theory (LR-TDDFT) and ΔSCF methods (namely maximum overlap method, square-gradient minimization method, and restricted open-shell Kohn-Sham) are considered for excited state computations using exchange-correlation (XC) functionals from different rungs of Jacob's ladder. A well-justified systematism is observed in the performance of the functionals when compared against fully internally contracted multireference configuration interaction singles and doubles and/or equation of motion coupled-cluster singles and doubles (EOM-CCSD), with the most important feature being the capture of spin-polarization in the presence of correlation. A set of functionals with the least mean absolute error is proposed for both the approaches, LR-TDDFT and ΔSCF, which can be more cost-effective alternatives for computations on synthesizable larger derivatives of the templates studied here. We have based our findings on extensive studies of three cyclazine-based molecular templates, with additional studies on a set of six related templates. Previous benchmark studies for subsets of the functionals were conducted against the domain-based local pair natural orbital-similarity transformed EOM-CCSD (STEOM-CCSD), which resulted in an inadequate evaluation due to deficiencies in the benchmark theory. The role of exact-exchange, spin-contamination, and spin-polarization in the context of DFT comes to the forefront in our studies and supports the numerical evaluation of XC functionals for these applications. Suitable connections are drawn to two and three state exciton models, which identify the minimal physics governing the interactions in these molecules.

High-Throughput Search for Photostrictive Materials Based on a Thermodynamic Descriptor.

Photostriction is a phenomenon that can potentially improve the precision of light-driven actuation, the sensitivity of photodetection, and the efficiency of optical energy harvesting. However, known materials with significant photostriction are limited, and effective guidelines to discover new photostrictive materials are lacking. In this study, we perform a high-throughput computational search for new photostrictive materials based on simple thermodynamic descriptors, namely, the band gap pressure and stress coefficients. Using the Δ-SCF method based on density functional theory, we establish that these descriptors can accurately predict intrinsic photostriction in a wide range of materials. Subsequently, we screened over 4770 stable semiconductors with a band gap below 2 eV from the Materials Project database to search for strongly photostrictive materials. This search identifies Te2I as the most promising candidate, with photostriction along out-of-plane direction exceeding 8 × 10-5 with a moderate photocarrier concentration of 1018 cm-3. Furthermore, we provide a detailed analysis of factors contributing to strong photostriction, including bulk moduli and band-edge orbital interactions. Our results provide physical insights into the photostriction of materials and demonstrate the effectiveness of using simple descriptors in high-throughput searches for new functional materials.

Thermal Quenching Mechanism of Mn4+ in Na2SiF6, NaKSiF6, and K2SiF6 Phosphors: Insights from the First-Principles Analysis.

This study aims to identify the key factors governing the thermal quenching of Mn4+ ion luminescence in fluoride-based phosphor materials used as red emitters in modern-day phosphor-converted LED devices. Here, we employ first-principles calculations for Mn4+-doped Na2SiF6, NaKSiF6, and K2SiF6 hosts to explore how host properties and local coordination environments influence thermal quenching behavior. The ΔSCF method was used to model the geometric structures of the Mn4+4A2 (ground) and 2E, 4T2 (excited) states and the energies of the optical transitions between these states. Our results reveal that thermal quenching in Na2SiF6 and K2SiF6 phosphors occurs through thermally activated 2E → 4T2 → 4A2 crossover. In contrast, thermal quenching in NaKSiF6 is due to other nonradiative decay pathways. Investigations of the mechanical stability of these fluorides show that NaKSiF6 is mechanically unstable. We suggest that this property of the host limits the luminescence efficiency of the embedded Mn4+ ions. We also determined the reason for the difference in the intensity of the 2E → 4A2 emission transition (ZPL) in the systems. These findings advance our fundamental understanding of the thermal quenching mechanism of Mn4+ ion luminescence in fluorides, and the results can aid future discoveries of technologically useful phosphors through high-throughput design methodologies.

Accelerated Computer-Aided Screening of Optical Materials: Investigating the Potential of Δ-SCF Methods to Predict Emission Maxima of Large Dye Molecules.

Accurate simulation of electronic excited states of large chromophores is often difficult due to the computationally expensive nature of existing methods. Common approximations such as fragmentation methods that are routinely applied to ground-state calculations of large molecules are not easily applicable to excited states due to the delocalized nature of electronic excitations in most practical chromophores. Thus, special techniques specific to excited states are needed. Δ-SCF methods are one such approximation that treats excited states in a manner analogous to that for ground-state calculations, accelerating the simulation of excited states. In this work, we employed the popular initial maximum overlap method (IMOM) to avoid the variational collapse of the electronic excited state orbitals to the ground state. We demonstrate that it is possible to obtain emission energies from the first singlet (S1) excited state of many thousands of dye molecules without any external intervention. Spin correction was found to be necessary to obtain accurate excitation and emission energies. Using thousands of dye-like chromophores and various solvents (12,318 combinations), we show that the spin-corrected initial maximum overlap method accurately predicts emission maxima with a mean absolute error of only 0.27 eV. We further improved the predictive accuracy using linear fit-based corrections from individual dye classes to achieve an impressive performance of 0.17 eV. Additionally, we demonstrate that IMOM spin density can be used to identify the dye class of chromophores, enabling improved prediction accuracy for complex dye molecules, such as dyads (chromophores containing moieties from two different dye classes). Finally, the convergence behavior of IMOM excited state SCF calculations is analyzed briefly to identify the chemical space, where IMOM is more likely to fail.

Exploiting the Correlation between the 1s, 2s, and 2p Energies for the Prediction of Core-Level Binding Energies of Si, P, S, and Cl species.

The binding energies (BEs) of the 1s, 2s, and 2p core electrons of third-period elements (Si, P, S, Cl) were calculated using Hartree-Fock (HF) and B3LYP, BH&HLYP, and LC-BOP ΔSCF, and the shifted KS ΔSCF methods. Linear relationships between two BEs were derived and compared with the Auger parameter. The derived lines are essentially parallel, with only the intercepts differing. The difference in intercepts is due to the lack of electron correlation effects in HF and the self-interaction errors (SIEs) of the functional. The slope is the slope of the linear relationship between the chemical shifts. The straight lines between the 2s and 2p BEs also coincided with the Auger parameter lines, which have a slope of 1 by definition and an intercept being the difference between the 2s and 2p BEs. The shifted KS ΔSCF scheme compensates for SIEs, yielding equations that are approximately invariant. The calculated average gaps for the 2s and 2p BEs are 51.21 eV for Si, 57.48 eV for P, 63.85 eV for S, and 70.48 eV for Cl. The straight lines representing the relationships between the BEs of the 1s and 2s and 1s and 2p electrons are also parallel to each other in ΔSCF and converge into a single line in the shifted ΔSCF scheme. However, these lines are steeper than the Auger parameter line. The derived relationships can be used to predict unknown BEs, which we have applied to many molecules. The results are highly accurate, with mean absolute errors (MAEs) of less than 0.2 eV compared to experimental values.

Unraveling Broadband Near-Infrared Luminescence in Cr3+-Doped Ca3Y2Ge3O12 Garnets: Insights from First-Principles Analysis.

In this study, we conducted an extensive investigation into broadband near-infrared luminescence of Cr3+-doped Ca3Y2Ge3O12 garnet, employing first-principles calculations within the density functional theory framework. Our initial focus involved determining the site occupancy of Cr3+ activator ions, which revealed a pronounced preference for the Y3+ sites over the Ca2+ and Ge4+ sites, as evidenced by the formation energy calculations. Subsequently, the geometric structures of the excited states 2E and 4T2, along with their optical transition energies relative to the ground state 4A2 in Ca3Y2Ge3O12:Cr3+, were successfully modeled using the ΔSCF method. Calculation convergence challenges were effectively addressed through the proposed fractional particle occupancy schemes. The constructed host-referred binding energy diagram provided a clear description of the luminescence kinetics process in the garnet, which explained the high quantum efficiency of emission. Furthermore, the accurate prediction of thermal excitation energy yielded insights into the thermal stability of the compound, as illustrated in the calculated configuration coordinate diagram. More importantly, all calculated data were consistently aligned with the experimental results. This research not only advances our understanding of the intricate interplay between geometric and electronic structures, optical properties, and thermal behavior in Cr3+-doped garnets but also lays the groundwork for future breakthroughs in the high-throughput design and optimization of luminescent performance and thermal stability in Cr3+-doped phosphors.

First-principles study of luminescence and electronic properties of Ce-doped Y2SiO5.

The transition of energy from the 4f to the 5d state is a fundamental element driving various applications, such as phosphors and optoelectronic devices. The positioning of the 4f ground states and the 5d excited states significantly influences this energy shift. In our research, we delve into the placement of these states utilizing a hybrid density functional theory (DFT) combined with spin-orbit coupling (SOC) via the supercell method. Additionally, we scrutinize the transition energy, applying the constrained density functional theory (cDFT) approach in conjunction with the ΔSCF method. Our study illustrates that the synergy of cDFT and SOC generates a discrepancy of about 2% for Ce1 and 4% for Ce2 when comparing the calculated results to experimental data. Moreover, We have determined the positions of the 4f ground states to be 2.73eV above the Valence Band Maximum (VBM) for Ce1 and 2.70eV for Ce2. We also note a tight correlation between the 5d levels identified in the experimental data and the theoretical outcomes derived from wave function calculations at the CASPT2 accuracy level.

Core-Level 2s and 2p Binding Energies of Third-Period Elements (P, S, and Cl) Calculated by Hartree-Fock and Kohn-Sham ΔSCF Theory.

In the present study, we investigate the use of the ΔSCF method and Slater's transition state (STS) theory to calculate the binding energies of the 2s and 2p electrons of third-period elements (P, S, and Cl). Both the Hartree-Fock (HF) and Kohn-Sham (KS) approximations are examined. The STS approximation performs well in reproducing the ΔSCF values. However, for the ΔSCF method itself, while the binding energy of the 2p electrons is accurately predicted, the results for 2s are fairly sensitive to the functional, exhibiting significant variations due to self-interaction errors (SIE). Nonetheless, the variations in chemical shifts between different species remain relatively small, and the values agree with experiments due to the cancellation of SIE. A notable observation is that the chemical shifts of the 2s and 2p electrons are similar, indicating a perturbation caused by the valence electrons. The error in the absolute binding energy of KS ΔSCF against the experiment is nearly constant for the same element in different molecules, and it depends largely on the functional owing to SIE. A shifting scheme previously developed can be employed to reproduce the experimental 2s and 2p binding energies, with dependence on the functional and atom but not on the molecule even for 2s KS ΔSCF binding energies. Upon obtaining the corrected binding energies, we find that the gap between 2s and 2p binding energy is nearly independent of chemical environment for a given element: 57.5, 63.9, and 70.9 eV for the elements P, S, and Cl, respectively.

Target State Optimized Density Functional Theory for Electronic Excited and Diabatic States.

A flexible self-consistent field method, called target state optimization (TSO), is presented for exploring electronic excited configurations and localized diabatic states. The key idea is to partition molecular orbitals into different subspaces according to the excitation or localization pattern for a target state. Because of the orbital-subspace constraint, orbitals belonging to different subspaces do not mix. Furthermore, the determinant wave function for such excited or diabatic configurations can be variationally optimized as a ground state procedure, unlike conventional ΔSCF methods, without the possibility of collapsing back to the ground state or other lower-energy configurations. The TSO method can be applied both in Hartree-Fock theory and in Kohn-Sham density functional theory (DFT). The density projection procedure and the working equations for implementing the TSO method are described along with several illustrative applications. For valence excited states of organic compounds, it was found that the computed excitation energies from TSO-DFT and time-dependent density functional theory (TD-DFT) are of similar quality with average errors of 0.5 and 0.4 eV, respectively. For core excitation, doubly excited states and charge-transfer states, the performance of TSO-DFT is clearly superior to that from conventional TD-DFT calculations. It is shown that variationally optimized charge-localized diabatic states can be defined using TSO-DFT in energy decomposition analysis to gain both qualitative and quantitative insights on intermolecular interactions. Alternatively, the variational diabatic states may be used in molecular dynamics simulation of charge transfer processes. The TSO method can also be used to define basis states in multistate density functional theory for excited states through nonorthogonal state interaction calculations. The software implementing TSO-DFT can be accessed from the authors.

Excitonic Effects in X-ray Absorption Spectra of Fluoride Salts and Their Surfaces

Given their natural abundance and thermodynamic stability, fluoride salts may appear as evolving components of electrochemical interfaces in Li-ion batteries and emergent multivalent ion cells. This is due to the practice of employing electrolytes with fluorine-containing species (salt, solvent, or additives) that electrochemically decompose and deposit on the electrodes. Operando X-ray absorption spectroscopy (XAS) can probe the electrode–electrolyte interface with a single-digit nanometer depth resolution and offers a wealth of insights into the evolution and Coulombic efficiency or degradation of prototype cells, provided that the spectra can be reliably interpreted in terms of local oxidation state, atomic coordination, and electronic structure about the excited atoms. To this end, we explore fluorine K-edge XAS of mono- (Li, Na, and K) and di-valent (Mg, Ca, and Zn) fluoride salts from a theoretical standpoint and discover a surprising level of detailed electronic structure information about these materials despite the relatively predictable oxidation state and ionicity of the fluoride anion and the metal cation. Utilizing a recently developed many-body approach based on the ΔSCF method, we calculate the XAS using density functional theory and experimental spectral profiles are well reproduced despite some experimental discrepancies in energy alignment within the literature, which we can correct for in our simulations. We outline a general methodology to explain shifts in the main XAS peak energies in terms of a simple exciton model and explain line-shape differences resulting from the mixing of core-excited states with metal d character (for K and Ca specifically). Given ultimate applications to evolving interfaces, some understanding of the role of surfaces and their terminations in defining new spectral features is provided to indicate the sensitivity of such measurements to changes in interfacial chemistry.

Assessing the performance of ΔSCF and the diagonal second-order self-energy approximation for calculating vertical core excitation energies.

Vertical core excitation energies are obtained using a combination of the ΔSCF method and the diagonal second-order self-energy approximation. These methods are applied to a set of neutral molecules and their anionic forms. An assessment of the results with the inclusion of relativistic effects is presented. For core excitations involving delocalized symmetry orbitals, the applied composite method improves upon the overestimation of ΔSCF by providing approximate values close to experimental K-shell transition energies. The importance of both correlation and relaxation contributions to the vertical core-excited state energies, the concept of local and nonlocal core orbitals, and the consequences of breaking symmetry are discussed.

Spin–Orbit Couplings for Nonadiabatic Molecular Dynamics at the ΔSCF Level

A procedure for the calculation of spin-orbit coupling (SOC) at the delta self-consistent field (ΔSCF) level of theory is presented. Singlet and triplet excited electronic states obtained with the ΔSCF method are expanded into a linear combination of singly excited Slater determinants composed of ground electronic state Kohn-Sham orbitals. This alleviates the nonorthogonality between excited and ground electronic states and introduces a framework, similar to the auxiliary wave function at the time-dependent density functional theory (TD-DFT) level, for the calculation of observables. The ΔSCF observables of the formaldehyde system were compared to reference TD-DFT values. Our procedure gives all components (energies, gradients, nonadiabatic couplings, and SOC terms) at the ΔSCF level of theory for conducting efficient, full-atomistic nonadiabatic molecular dynamics with intersystem crossing, particularly in condensed phase systems.

Robust ΔSCF calculations with direct energy functional minimization methods and STEP for molecules and materials.

The direct energy functional minimization method using the orbital transformation (OT) scheme in the program package CP2K has been employed for Δ self-consistent field (ΔSCF) calculations. The OT method for non-uniform molecular orbitals occupations allows us to apply the ΔSCF method for various kinds of molecules and periodic systems. Vertical excitation energies of heteroaromatic molecules and condensed phase systems, such as solvated ethylene and solvated uracil obeying periodic boundary conditions, are reported using the ΔSCF method. In addition, a Re-phosphate molecule attached to the surface of anatase (TiO2) has been investigated. Additionally, we have implemented a recently proposed state-targeted energy projection ΔSCF algorithm [K. Carter-Fenk and J. M. Herbert, J. Chem. Theory Comput. 16(8), 5067-5082 (2020)] for diagonalization based SCF in CP2K. It is found that the OT scheme provides a smooth and robust SCF convergence for all investigated excitation energies and (non-)periodic systems.

The ΔSCF method for non-adiabatic dynamics of systems in the liquid phase.

Computational studies of ultrafast photoinduced processes give valuable insights into the photochemical mechanisms of a broad range of compounds. In order to accurately reproduce, interpret, and predict experimental results, which are typically obtained in a condensed phase, it is indispensable to include the condensed phase environment in the computational model. However, most studies are still performed in vacuum due to the high computational cost of state-of-the-art non-adiabatic molecular dynamics (NAMD) simulations. The quantum mechanical/molecular mechanical (QM/MM) solvation method has been a popular model to perform photodynamics in the liquid phase. Nevertheless, the currently used QM/MM embedding techniques cannot sufficiently capture all solute-solvent interactions. In this Perspective, we will discuss the efficient ΔSCF electronic structure method and its applications with respect to the NAMD of solvated compounds, with a particular focus on explicit quantum mechanical solvation. As more research is required for this method to reach its full potential, some challenges and possible directions for future research are presented as well.

Predicting core electron binding energies in elements of the first transition series using the Δ-self-consistent-field method.

The Δ-Self-Consistent-Field (ΔSCF) method has been established as an accurate and computationally efficient approach for calculating absolute core electron binding energies for light elements up to chlorine, but relatively little is known about the performance of this method for heavier elements. In this work, we present ΔSCF calculations of transition metal (TM) 2p core electron binding energies for a series of 60 molecular compounds containing the first row transition metals Ti, V, Cr, Mn, Fe and Co. We find that the calculated TM 2p3/2 binding energies are less accurate than the results for the lighter elements with a mean absolute error (MAE) of 0.73 eV compared to experimental gas phase photoelectron spectroscopy results. However, our results suggest that the error depends mostly on the element and is rather insensitive to the chemical environment. By applying an element-specific correction to the binding energies the MAE is reduced to 0.20 eV, similar to the accuracy obtained for the lighter elements.

Simulation of Low-Lying Singlet and Triplet Excited States of Multiple-Resonance-Type Thermally Activated Delayed Fluorescence Emitters by Delta Self-Consistent Field (ΔSCF) Method.

The delta self-consistent field (ΔSCF) method was applied to the simulation of low-lying singlet and triplet excited states of multiple-resonance (MR)-type thermally activated delayed fluorescence (TADF) molecules, which form a promising group for organic light-emitting diode (OLED) emitters. A comparison with the experimental values of 13 emitters from the literature showed that ΔSCF gave fairly accurate S1 and T1 excitation energies (mean absolute errors (MAEs) of 0.092 and 0.055 eV, respectively) as well as quite accurate ΔEST (S1-T1 gap, MAE of 0.041 eV), which could not be calculated with sufficient accuracy by the conventional time-dependent density functional theory (TDDFT). ΔSCF also demonstrated its utility for the analysis of photophysical properties through a simulation of the reverse intersystem crossing (RISC) process of an MR-type emitter.

Importance of Long‐Range Channel Sr Displacements for the Narrow Emission in Sr[Li2Al2O2N2]:Eu2+Phosphor

AbstractThe recently discovered Sr[Li2Al2O2N2]:Eu2+red phosphor, candidate for the next generation of eco‐efficient white light‐emitting diodes, exhibits excellent emission spectral position and exceptionally small linewidth. It belongs to the UCr4C4‐structure family of phosphors containing many potential candidates for commercial phosphors, whose small linewidth, tentatively ascribed to the high‐symmetry cuboid environment of the doping site, has drawn the attention of researchers in the last five years. Density functional theory, ΔSCF method, and configuration coordinate models (CCM) are used to provide a complete characterization of this material. Using a multi‐dimensional CCM, an accurate description of the coupling of the vibronic structure with the electronic 5d→4f transition is obtained, including the partial Huang–Rhys factors and frequency of the dominant modes. It is shown that, in addition to the first‐coordination shell cuboid deformation mode, low‐frequency phonon modes involving chains of strontium atoms along the tetragonal axis shape the emission linewidth in Sr[Li2Al2O2N2]:Eu2+. This finding sheds new light on the emission properties of UCr4C4‐structure phosphors, possessing similar Ca/Sr/Ba channel. The approach provides a robust theoretical framework to systematically study the emission spectra of such Eu‐doped phosphors, and predict candidates with expected similar or even sharper linewidth.

Examination of How Well Long-Range-Corrected Density Functionals Satisfy the Ionization Energy Theorem.

We calculated the vertical ionization energies (VIE) of 99 species in two ways to examine the accuracy of several long-range-corrected (LC) hybrid meta functionals in comparison with a gradient approximation (GA), global hybrids, and doubly hybrids. In the category of LC functionals, we examined both those with meta ingredients (i.e., that depend on the kinetic energy density) and those without them. The LC-hybrid meta functionals examined are M11, revM11, M11plus, and ωB97M-V. The reference data used to assess accuracy consist of 95 molecules and 4 atoms in the GW100 set. The two methods studied are the ΔSCF method (involving the difference of neutral and cation self-consistent field (SCF) energies) and the ionization energy theorem (involving the orbital energy of the highest occupied molecular orbital, HOMO). We calculated linear correlation coefficients (r2) and mean absolute deviations (MADs) between each approach and the reference VIE value from the CCSD(T)/def2-TZVPP level of theory. We compared the new LC-hybrid meta calculations to calculations with the 10 functionals in a previous VIE study by Brémond et al. and to the calculations with LC-BLYP (LC-Becke, Lee-Yang-Parr), CAM-B3LYP (Coulomb-attenuating-method Becke-3-parameter Lee-Yang-Parr), LC-ωHPBE, and ωB97X-D. The results show that Minnesota LC-hybrid meta functionals have the smallest mean absolute deviation of ionization energy theorem VIEs with the reference data; the LC-ωHPBE functional also does quite well in this test. This is very encouraging and indicates that LC-hybrid meta functionals would be the best starting points for the tuning strategy that has been shown to be a very good procedure for improving time-dependent density functional calculations, and it also helps explain the good success of LC-hybrid meta functionals for molecular excitation energies.

Methods to accelerate high-throughput screening of atomic qubit candidates in van der Waals materials

The discovery of atom-like spin emitters associated with defects in two-dimensional (2D) wide-bandgap (WBG) semiconductors presents new opportunities for highly tunable and versatile qubits. So far, the study of such spin emitters has focused on defects in hexagonal boron nitride (hBN). However, hBN necessarily contains a high density of nuclear spins, which are expected to create a strong incoherent spin-bath that leads to poor coherence properties of spins hosted in the material. Therefore, identification of new qubit candidates in other 2DWBG materials is necessary. Given the time demands of ab initio methods, new approaches for rapid screening and calculations of identifying properties of suitable atom-like qubits are required. In this work, we present two new methods for rapid estimation of the zero-phonon line (ZPL), a key property of atomic qubits in WBG materials. First, the ZPL is calculated by exploiting Janak’s theorem. For finite changes in occupation, we provide the leading-order estimate of the correction to the ZPL obtained using Janak’s theorem, which is more rapid than the standard method (ΔSCF). Next, we demonstrate an approach to converging excited states that is faster for systems with small strain than the standard approach used in the ΔSCF method. We illustrate these methods using the case of the singly negatively charged calcium vacancy in SiS2, which we are the first to propose as a qubit candidate. This work has the potential to assist in accelerating the high-throughput search for quantum defects in materials, with applications in quantum sensing and quantum computing.