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DOE OSTI2025

Dark Energy Survey Year 3 Results: Cosmological Constraints from Cluster Abundances, Weak Lensing, and Galaxy Clustering

Galaxy clusters provide a unique probe of the late-time cosmic structure and serve as a powerful independent test of the $\Lambda$CDM model. This work presents the first set of cosmological constraints derived with ~16,000 optically selected redMaPPer clusters across nearly 5,000 $\rm{deg}^2$ using DES Year 3 data sets. Our analysis leverages a consistent modeling framework for galaxy cluster cosmology and DES-Y3 joint analyses of galaxy clustering and weak lensing (3x2pt), ensuring direct comparability with the DES-Y3 3x2pt analysis. We obtain constraints of $S_8 = 0.864 \pm 0.035$ and $\Omega_{\rm{m}} = 0.265^{+0.019}_{-0.031}$ from the cluster-based data vector. We find that cluster constraints and 3x2pt constraints are consistent under the $\Lambda$CDM model with a Posterior Predictive Distribution (PPD) value of $0.53$. The consistency between clusters and 3x2pt provides a stringent test of $\Lambda$CDM across different mass and spatial scales. Jointly analyzing clusters with 3x2pt further improves cosmological constraints, yielding $S_8 = 0.811^{+0.022}_{-0.020}$ and $\Omega_{\rm{m}} = 0.294^{+0.022}_{-0.033}$, a $24\%$ improvement in the $\Omega_{\rm{m}}-S_8$ figure-of-merit over 3x2pt alone. Moreover, we find no significant deviation from the Planck CMB constraints with a probability to exceed (PTE) value of $0.6$, significantly reducing previous $S_8$ tension claims. Finally, combining DES 3x2pt, DES clusters, and Planck CMB places an upper limit on the sum of neutrino masses of $\sum m_\nu < 0.26$ eV at 95% confidence under the $\Lambda$CDM model. These results establish optically selected clusters as a key cosmological probe and pave the way for cluster-based analyses in upcoming Stage-IV surveys such as LSST, Euclid, and Roman.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

DESI DR2 Reference Mocks: Clustering results from UCHUU ELGs and QSOs

High-redshift galaxy clustering provides a powerful probe of the growth of structure, testing models of dark matter, dark energy, and galaxy formation during the epoch when the Universe was rapidly evolving. Emission line galaxies (ELGs) and quasars (QSOs) are used as tracers of dark matter by the Dark Energy Spectroscopic Instrument (DESI) to probe this redshift regime. We present results from ELG and QSO mock catalogs created from the Uchuu N-body simulation and tuned to DESI Data Release 2 (DR2) clustering. Employing a modified subhalo abundance matching (SHAM) technique, we populate Uchuu halos and subhalos with QSOs between 0.8 < z < 2.1. For ELGs, we modify this method to select satellite galaxies with low velocities relative to their associated central halos, and populate a separate set of Uchuu halos and subhalos with ELGs between 0.8 < z < 1.6. In this paper, we reproduce the redshift evolution of number density and clustering statistics across the fitted range of scales. We also measure the large-scale clustering bias of both the data and mock samples. These results improve simulated lightcone construction from cosmological models and enhance our understanding of the galaxy-halo connection.

Vaisakh, R. [Southern Methodist U.] (ORCID:0009000↗
DOE OSTI2025

Selection function of clusters in Dark Energy Survey year 3 data from cross-matching with South Pole Telescope detections

Context. Galaxy clusters selected based on overdensities of galaxies in photometric surveys provide the largest cluster samples. However, modeling the selection function of such samples is complicated by noncluster members projected along the line of sight (projection effects) and the potential detection of unvirialized objects (contamination). Aims. We empirically constrained the magnitude of these effects by cross-matching galaxy clusters selected in the Dark Energy Survey data with the redMaPPer algorithm with significant detections in three South Pole Telescope surveys (SZ, pol-ECS, pol-500d). Methods. For matched clusters, we augmented the redMaPPer catalog with the SPT detection significance. For unmatched objects we used the SPT detection threshold as an upper limit on the SZe signature. Using a Bayesian population model applied to the collected multiwavelength data, we explored various physically motivated models to describe the relationship between observed richness and halo mass. Results. Our analysis reveals a clear preference for models with an additional skewed scatter component associated with projection effects over a purely log-normal scatter model. We rule out significant contamination by unvirialized objects at the high-richness end of the sample. While dedicated simulations offer a well-fitting calibration of projection effects, our findings suggest the presence of redshift-dependent trends that these simulations may not have captured. Our findings highlight that modeling the selection function of optically detected clusters remains a complicated challenge that requires a combination of simulation and data-driven approaches.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Structure–property relations of binary ferrite melts

Molten ferrite systems are used in the smelting and refining processes in steelmaking, to reduce the loss of metals in slags and to accelerate reaction rates. Here, high-energy x-ray diffraction experiments have been performed on aerodynamically levitated molten spheres of 43BaO–57FeO X and 43SrO–57FeO X at 1873 K using laser beam heating. The composition was varied within the range of x = 1–1.5 by changing the oxygen partial pressure of the levitation gas. The corresponding x-ray pair distribution functions have been interpreted using empirical potential structure refinement (EPSR) modeling. In oxygen-rich melts (x = 1.5), our EPSR models indicate very similar structures for the different alkaline-earth liquids, with both the Ba–O and Sr–O coordination numbers to be ∼8.4 and the total Fe–O coordination numbers ∼5.7. However, our models show that in reducing environments, the Fe 3+ and Fe 2+ ions exhibit very different behaviors in the Ba- and Sr-ferrite liquids. In the Ba-ferrite melt, the Fe 3+ –O coordination number decreases from 5.7 (at x = 1.5) to 5.2 (at x = 1.07), whereas Fe 2+ –O remains constant at ∼5.0 across the same compositional range. In the Sr melts, both the Fe 2+ –O and Fe 3+ –O coordination numbers rise from ∼5.7 (at x = 1.5) to 6.3 (at x = 1.07). All models show the structures to be heterogeneous with intertwined nanometer sized clusters or channels of Ba/Sr–O and Fe–O polyhedra that grow as oxygen content is reduced. Changes in the viscosity and electrical properties are interpreted in terms of the number of bridging and non-bridging oxygens associated with FeO 4 tetrahedra and concentration of charge carriers, respectively.

Benmore, Chris J. [Argonne National Laboratory (AN↗
DOE OSTI2024

Detection of the large-scale tidal field with galaxy multiplet alignment in the DESI Y1 spectroscopic survey

We explore correlations between the orientations of small galaxy groups, or ‘multiplets’, and the large-scale gravitational tidal field. Using data from the Dark Energy Spectroscopic Instrument (DESI) Y1 survey, we detect the intrinsic alignment (IA) of multiplets to the galaxy-traced matter field out to separations of $100\,h^{-1}$ Mpc. Unlike traditional IA measurements of individual galaxies, this estimator is not limited by imaging of galaxy shapes and allows for direct IA detection beyond redshift $z=1$. Multiplet alignment is a form of higher order clustering, for which the scale-dependence traces the underlying tidal field and amplitude is a result of small-scale ($\lt 1h^{-1}$ Mpc) dynamics. Within samples of bright galaxies, luminous red galaxies (LRG) and emission-line galaxies, we find similar scale-dependence regardless of intrinsic luminosity or colour. This is promising for measuring tidal alignment in galaxy samples that typically display no IA. DESI’s LRG mock galaxy catalogues created from the A BACUS S UMMIT N -body simulations produce a similar alignment signal, though with a 33 per cent lower amplitude at all scales. An analytic model using a non-linear power spectrum (NLA) only matches the signal down to 20 $h^{-1}$ Mpc. Our detection demonstrates that galaxy clustering in the non-linear regime of structure formation preserves an interpretable memory of the large-scale tidal field. Multiplet alignment complements traditional two-point measurements by retaining directional information imprinted by tidal forces, and contains additional line-of-sight information compared to weak lensing. This is a more effective estimator than the alignment of individual galaxies in dense, blue, or faint galaxy samples.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Constraints on the normal branch of DGP gravity from SPT galaxy clusters with DES and HST weak-lensing mass calibration and from P l a n c k PR4 CMB anisotropies

We present constraints on the normal branch of the Dvali-Gabadadze-Porrati (nDGP) braneworld gravity model from the abundance of massive galaxy clusters. On scales below the nDGP crossover scale r c , the nDGP model features an effective gravitylike fifth force that alters the growth of structure, leading to an enhancement of the halo mass function (HMF) on cluster scales. The enhanced cluster abundance allows for constraints on the nDGP model using cluster samples. We employ the South Pole Telescope (SPT) cluster sample, selected through the thermal Sunyaev-Zel’dovich effect with the SPT and with mass calibration using weak-lensing data from the Dark Energy Survey (DES) and the Hubble Space Telescope (HST). The cluster sample contains 1,005 clusters with redshifts 0.25 < z < 1.78 , which are confirmed with the multicomponent matched filter algorithm using optical and near-infrared data. Weak-lensing data from DES and HST enable a robust mass measurement of the cluster sample. We use DES Year 3 data for 688 clusters with redshifts z < 0.95 , and HST data for 39 clusters with redshifts 0.6 < z < 1.7 . We account for the enhancement in the HMF through a semi-analytic correction factor to the standard cosmology HMF derived from the spherical collapse model in the nDGP model. We then further calibrate this model using N -body simulations. In addition, for the first time, we analyze the primary CMB temperature and polarization anisotropy measurements from Planck PR4 within the nDGP model. We obtain a competitive constraint from the joint analysis of the SPT cluster abundance with the Planck PR4 data, and report an upper bound of 1 / H 0 r c < 1.41 at 95% when assuming a cosmology with massive neutrinos.

Vogt, S. M.L. [Munich U. Observ.; LMU Munich (main↗
DOE OSTI2024

The physical basis for solvent flow in organic solvent nanofiltration

Organic solvent nanofiltration (OSN) is an emerging membrane technology that could revolutionize chemical separations in numerous vital industries. Despite its significance, there remains a lack of fundamental understanding of solvent transport mechanisms in OSN membranes. Here, we use an extended Flory-Rehner theory, nonequilibrium molecular dynamic simulations, and organic solvent transport experiments to demonstrate that solvent flow in OSN membranes is driven by a pressure gradient. We show that solvent molecules migrate as clusters through interconnected pathways within the membrane pore structure, challenging the widely accepted diffusion-based view of solvent transport in OSN. We further reveal that solvent permeance is dependent on solvent affinity to the OSN membrane, which, in turn, controls the membrane pore structure. Our fundamental insights lay the scientific groundwork for the development of next-generation OSN membranes.

42 ENGINEERING↗
DOE OSTI2024

Discovering Dark Matter Clumps and Primordial Particles with Galaxies

Cosmological observations and galaxy dynamics seem to imply that five out of six parts in mass of all matter in the universe is composed of dark matter, which is not accounted for by the Standard Model of particles. The cold dark matter (CDM) paradigm has been extremely successful at describing observations on large-cosmological scale. However, many different dark matter candidates have the same observable effects as CDM on large-length scales. One possible avenue to distinguish between these different models is to look on much smaller-length scales, where usually dark matter models become distinguishable. This research developed the theoretical framework and statistical tools needed to map the detailed distribution of dark matter on subgalactic scales using strong gravitational lensing. A second goal of this research was to build new statistical techniques that efficiently exploit the full power of cosmic-structure data from next-generation surveys. Galaxy clustering on large scales provides significant cosmological information through the power spectrum. Additional information can be gained from higher-order statistics. This research provided new ways to understand the initial conditions of the universe from current and upcoming cosmological surveys.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Robust Dark Energy Constraints with the Dark Energy Spectroscopic Survey (Final Technical Report)

This project developed and applied advanced theoretical, computational, and data-analysis methodologies to extract robust and precise cosmological constraints from the Dark Energy Spectroscopic Instrument (DESI). The work focused on maximizing the scientific return of DESI through optimized survey strategy, novel higher-order clustering statistics, improved modeling of small-scale structure, and rigorous mitigation of observational systematics. Over the award period, the project made substantial contributions to DESI science planning, produced new methods for bispectrum and three-point correlation function analyses, advanced constraints on primordial non-Gaussianity, and delivered widely used software tools. The project also played a major role in training graduate students and a postdoctoral researcher who contributed directly to DESI key projects. The results have significantly enhanced the cosmological reach of DESI and provide a strong foundation for future surveys such as DESI-II and Stage-V experiments.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Catalytic Bias of NADH-Dependent Reduced Ferredoxin: NADP+ Oxidoreductase (Nfn) and its Relevance to Ethanol Production in Thermoanaerobacterium Saccharolyticum

NADH-dependent reduced ferredoxin: NADP+ oxidoreductase (Nfn) enzyme catalyzes an energy-conserving flavin-based electron bifurcation (FBEB) reaction. In microbial metabolism, Nfn links redox pools of three electron carriers - ferredoxin (Fd), NAD(H), and NADP(H) - through the following FBEB reaction: 2 NADPH + NAD+ + 2 Fdox 2 NADP+ + NADH + 2 Fdred + H+ The forward reaction is termed electron bifurcation, and the reverse reaction is electron confurcation. Catalytic bias describes an enzyme's tendency to favor one direction of a reversible reaction over the other and is expressed as the ratio of activities in the two directions. Thermoanaerobacterium saccharolyticum (Tsac) is a thermophilic, ethanologenic bacterium that ferments hemicellulose to ethanol at yields above 90%. Its Nfn enzyme is known to support ethanol production, presumably by operating in the confurcating direction to balance cellular cofactors, but this has not previously been demonstrated. To investigate the Tsac Nfn further, we heterologously expressed, purified, and reconstituted the proteins NfnS (NfnA), NfnL (NfnB), and the putative partner Fd with iron-sulfur cluster and/or FAD cofactors. Activity assays monitoring the oxidation or reduction of Fd showed that, across pH 5-10, Tsac Nfn is catalytically biased towards the confurcating direction, favoring NADPH generation over NADPH oxidation by at least fivefold. Using protein electrochemistry, we also determined the reduction potentials of the cofactors in NfnL and Fd. These results indicate that the energetic landscape of FBEB in Tsac Nfn is similar to that in an ortholog. However, Tsac Fd has redox properties distinct from previously assayed Fds, suggesting that the identity and redox properties of Fd may help determine the catalytic bias of Nfn. Additionally, we confirmed the standalone ferredoxin: NADP+ oxidoreductase (FNOR) activity of NfnL but found it to be low and likely insignificant for in vivo redox conversion. We also show how the catalytic bias of Nfn integrates with the hydrogen cycling mechanism proposed in Tsac to better explain cofactor balancing for ethanol production. Our work advances the understanding of electron transfer processes within metabolic networks for the generation of valuable bioproducts.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Clustering analysis of medium-band selected high-redshift galaxies

Next-generation large-scale structure spectroscopic surveys will probe cosmology at high redshifts (2.3 < z < 3.5), relying on abundant galaxy tracers such as Lyα emitters (LAEs) and Lyman break galaxies (LBGs). Medium-band photometry has emerged as a potential technique for efficiently selecting these high-redshift galaxies. In this work, we present clustering analysis of medium-band selected galaxies at high redshift, utilizing photometric data from the Intermediate Band Imaging Survey (IBIS) and spectroscopic data from the Dark Energy Spectroscopic Instrument (DESI). We interpret the clustering of such samples using both Halo Occupation Distribution (HOD) modeling and a perturbation theory description of large-scale structure. Our modeling indicates that the current target sample is composed from an overlapping mixture of LAEs and LBGs with emission lines. Despite differences in target selection, we find that the clustering properties are consistent with previous studies, with correlation lengths r 0 ≃ 3-4 h -1 Mpc and a linear bias of b ∼ 1.8-2.5. Finally, we discuss the simulation requirements implied by these measurements and demonstrate that the properties of the samples would make them excellent targets to enhance our understanding of the high-z universe.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Dark Energy Survey year 6 results: Magnification modeling and its impact on galaxy clustering and galaxy-galaxy lensing cosmology

Gravitational lensing magnification alters the observed spatial distribution of galaxies and must be accounted for to prevent biases in cosmological probes of the large-scale structure. We investigate its effects on the Dark Energy Survey Year 6 galaxy clustering and galaxy-galaxy lensing analyses using the fiducial lens (position tracer) sample M ag L im++. Magnification bias is parameterized by a coefficient that describes the response of the number of selected objects per unlensed area element to a change in the lensing convergence. We quantify this coefficient using the BALROG synthetic source injection catalog to account for the complexity of the selection function, and compare these results with simplified estimates. The resulting values of the magnification coefficients for each redshift bin are [3.16 ± 0.08, 2.76 ± 0.21, 4.09 ± 0.15, 4.42 ± 0.16, 4.90 ± 0.29, 4.83 ± 0.25]. Relative to Year 3, this analysis provides more precise and accurate magnification bias estimates through a larger BALROG area and reweighting to better match the data properties. Here, the cosmological results are robust when tested against various magnification parameter prior choices and also when adding cross-clustering between lens redshift bins. Neglecting magnification, however, introduces significant systematic shifts: relative to the fiducial analysis with Gaussian priors centered on the BALROG -derived estimates, we observe shifts of 1.37σ in S 8 and -0.84σ in Ω m (with cosmic shear included: -0.61σ in S 8 and -0.71σ in Ω m ), in agreement with findings from simulated data, demonstrating that magnification must be modeled to avoid biases. Freeing the magnification bias in lens bin 2 leads to unphysical negative values, further justifying its exclusion from the fiducial Year 6 analysis.

Cosmological parameters↗
DOE OSTI2025

Production of alternate realizations of DESI fiber assignment for unbiased clustering measurement in data and simulations

A critical requirement of spectroscopic large scale structure analyses is correcting for selection of which galaxies to observe from an isotropic target list. This selection is often limited by the hardware used to perform the survey which will impose angular constraints of simultaneously observable targets, requiring multiple passes to observe all of them. In SDSS this manifested solely as the collision of physical fibers and plugs placed in plates. In DESI, there is the additional constraint of the robotic positioner which controls each fiber being limited to a finite patrol radius. A number of approximate methods have previously been proposed to correct the galaxy clustering statistics for these effects, but these generally fail on small scales. To accurately correct the clustering we need to upweight pairs of galaxies based on the inverse probability that those pairs would be observed (Bianchi & Percival 2017). This paper details an implementation of that method to correct the Dark Energy Spectroscopic Instrument (DESI) survey for incompleteness. To calculate the required probabilities, we need a set of alternate realizations of DESI where we vary the relative priority of otherwise identical targets. These realizations take the form of alternate Merged Target Ledgers (AMTL), the files that link DESI observations and targets. We present the method used to generate these alternate realizations and how they are tracked forward in time using the real observational record and hardware status, propagating the survey as though the alternate orderings had been adopted. We detail the first applications of this method to the DESI One-Percent Survey (SV3) and the DESI year 1 data. We include evaluations of the pipeline outputs, estimation of survey completeness from this and other methods, and validation of the method using mock galaxy catalogs.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2024

High-precision Galaxy Clustering Predictions from Small-volume Hydrodynamical Simulations via Control Variates

Abstract Cosmological simulations of galaxy formation are an invaluable tool for understanding galaxy formation and its impact on cosmological parameter inference from large-scale structures. However, their high computational cost is a significant obstacle for running simulations that probe cosmological volumes comparable to those analyzed by contemporary large-scale structure experiments. In this work, we explore the possibility of obtaining high-precision galaxy clustering predictions from small-volume hydrodynamical simulations such as MillenniumTNG and FLAMINGO via control variates. In this approach, the hydrodynamical full-physics simulation is paired with a matched low-resolution gravity-only simulation. By learning the galaxy–halo connection from the hydrodynamical simulation and applying it to the gravity-only counterpart, one obtains a galaxy population that closely mimics the one in the more expensive simulation. One can then construct an estimator of galaxy clustering that combines the clustering amplitudes in the small-volume hydrodynamical and gravity-only simulations with clustering amplitudes in a large-volume gravity-only simulation. Depending on the galaxy sample, clustering statistic, and scale, this galaxy clustering estimator can have an effective volume of up to around 100 times the volume of the original hydrodynamical simulation in the nonlinear regime. With this approach, we can construct galaxy clustering predictions from existing simulations that are precise enough for mock analyses of next-generation large-scale structure surveys such as the Dark Energy Spectroscopic Instrument and the Legacy Survey of Space and Time.

Doytcheva, Alexandra (ORCID:0009000111254888)↗
DOE OSTI2026

Microscopic Dynamics Controls Coupling and Cluster Formation in Brush Particle Solids

Thermodynamics-based models predict the structure of polymer-grafted nanoparticles (PGNs) as well as their assembly behavior based on geometric parameters such as particle size, degree of polymerization, and density of grafted chains. The role of microscopic polymer dynamics, such as the mobility of repeat units in the melt state, in the evolution of the structure and properties remains unknown. Brillouin light spectroscopy (BLS), due to its capability to concurrently discern the local and global elastic properties of PGN assemblies, enables the probing of microscopic processes, such as brush interdigitation, sensitive to the annealing of the assembly. For poly(methyl methacrylate) (PMMA)-grafted silica (SiO 2 ) PGNs in the dry powder state and annealed above the glass transition temperature, BLS revealed fully reversible local elasticity, indicative of limited interdigitation between adjacent PGNs. This contrasts with polystyrene (PS)−SiO 2 analogs that displayed ready (and irreversible) fusion of brush layers during annealing. The retardation of brush interdigitation in PMMA-grafted systems is surprising, given the similar thermomechanical properties of both polymers, and is rationalized as the consequence of higher friction between PMMA repeats compared to PS. Microscopic dynamics thus has a profound impact on the kinetic path of structure (and property) evolution and thus should be considered during the processing of PGNs into functional hybrid materials.

chemical structure↗
DOE OSTI2024

Adsorption of Ag, Au, Cu, and Ni on MoS 2 : theory and experiment

Abstract Here, we present results of a computational and experimental study of adsorption of various metals on MoS2. In particular, we analyzed the binding mechanism of four metallic elements (Ag, Au, Cu, Ni) on MoS2. Among these elements, Ni exhibits the strongest binding and lowest mobility on the surface of MoS2. On the other hand, Au and Ag bond very weakly to the surface and have very high mobilities. Our calculations for Cu show that its bonding and surface mobility are between these two groups. Experimentally, Ni films exhibit a composition characterized by randomly oriented nanoscale clusters. This is consistent with the larger cohesive energy of Ni atoms as compared with their binding energy with MoS2, which is expected to result in 3D clusters. In contrast, Au and Ag tend to form atomically flat plateaued structures on MoS2, which is contrary to their larger cohesive energy as compared to their weak binding with MoS2. Cu displays a surface morphology somewhat similar to Ni, featuring larger nanoscale clusters. However, unlike Ni, in many cases Cu exhibits small plateaued surfaces on these clusters. This suggests that Cu likely has two competing mechanisms that cause it to span the behaviors seen in the Ni and Au/Ag film morphologies. These results indicate that calculations of the initial binding conditions could be useful for predicting film morphologies. In addition, out calculations show that the adsorption of adatoms with odd electron number like Ag, Au, and Cu results in 100% spin-polarization and integer magnetic moment of the system. Adsorption of Ni adatoms, with even electron number, does not induce a magnetic transition.

Harms, Haley↗
DOE OSTI2026

Definitive Assessment of the Accuracy, Variationality, and Convergence of Relativistic Coupled Cluster and Density Matrix Renormalization Group in 100-Orbital Space

Accuracy, variationality, and convergence underpin the reliability of modern electronic structure methods, yet definitive benchmarks in the relativistic regime remain elusive due to the absence of numerically exact full configuration interaction (CI) references. Recent algorithmic advances in the CI framework, enabled by the small-tensor-product (STP) decomposition approach, have dramatically extended the tractable size of the configuration space, making numerically exact CI calculations feasible in large active spaces previously beyond reach. In this paper, we employ the recently developed STP-CI framework to perform large-scale numerically exact CI calculations and directly benchmark relativistic coupled cluster and density matrix renormalization group methods. Definitive benchmarking of approximate relativistic electronic structure methods is ensured through the application of the gap theorem, which provides rigorous error bounds on the CI reference and establishes a controlled standard for assessing accuracy, variationality, and convergence.

Chemical calculations↗