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A static quantum embedding scheme based on coupled cluster theory

Here, we develop a static quantum embedding scheme that utilizes different levels of approximations to coupled cluster (CC) theory for an active fragment region and its environment. To reduce the computational cost, we solve the local fragment problem using a high-level CC method and address the environment problem with a lower-level Møller–Plesset (MP) perturbative method. This embedding approach inherits many conceptual developments from the hybrid second-order Møller–Plesset (MP2) and CC works by Nooijen [J. Chem. Phys. 111, 10815 (1999)] and Bochevarov and Sherrill [J. Chem. Phys. 122, 234110 (2005)]. We go beyond those works here by primarily targeting a specific localized fragment of a molecule and also introducing an alternative mechanism to relax the environment within this framework. We will call this approach MP-CC. We demonstrate the effectiveness of MP-CC on several potential energy curves and a set of thermochemical reaction energies, using CC with singles and doubles as the fragment solver, and MP2-like treatments of the environment. The results are substantially improved by the inclusion of orbital relaxation in the environment. Using localized bonds as the active fragment, we also report results for N=N bond breaking in azomethane and for the central C–C bond torsion in butadiene. We find that when the fragment Hilbert space size remains fixed (e.g., when determined by an intrinsic atomic orbital approach), the method achieves comparable accuracy with both a small and a large basis set. Additionally, our results indicate that increasing the fragment Hilbert space size systematically enhances the accuracy of observables, approaching the precision of the full CC solver.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Chandra measurements of gas homogeneity and turbulence at intermediate radii in the Perseus Cluster

ABSTRACT We present a Chandra study of surface brightness fluctuations in the diffuse intracluster medium of the Perseus Cluster. Our study utilizes deep, archival imaging of the cluster core as well as a new mosaic of 29 short $\, 5\,$-ks observations extending in eight different directions out to radii of $r_{500} \sim 2.2\, r_{2500}$. Under the assumption that the distribution of densities at a given radius is log-normally distributed, two important quantities can be derived from the width of the log-normal density distribution on a given spatial scale: the density bias, that is equal to the square root of the clumping factor C; and the one-component turbulent velocity, vk,1D. We forward-model all contributions to the measured surface brightness, including astrophysical and particle background components, and account for the Poisson nature of the measured signal. Measuring the distribution of surface brightness fluctuations in 1 arcmin2 regions, spanning the radial range $0.3\rm {-}2.2\, r_{2500}$ ($7.8\rm {-}57.3\,$ arcmin), we find a small to moderate average density bias of around $3{{\ \rm per\ cent}}$ at radii below $1.6\, r_{2500}$. We also infer an average turbulent velocity at these radii of V1D < 400 km s−1. Direct confirmation of our results on turbulent velocities inferred from surface brightness fluctuations should be possible using the X-ray calorimeter spectrometers to be flown aboard the XRISM and Athena observatories.

79 ASTRONOMY AND ASTROPHYSICS↗

Uptake of N 2 O 5 by aqueous aerosol unveiled using chemically accurate many-body potentials

The reactive uptake of N 2 O 5 to aqueous aerosol is a major loss channel for nitrogen oxides in the troposphere. Despite its importance, a quantitative picture of the uptake mechanism is missing. Here we use molecular dynamics simulations with a data-driven many-body model of coupled-cluster accuracy to quantify thermodynamics and kinetics of solvation and adsorption of N 2 O 5 in water. The free energy profile highlights that N 2 O 5 is selectively adsorbed to the liquid–vapor interface and weakly solvated. Accommodation into bulk water occurs slowly, competing with evaporation upon adsorption from gas phase. Leveraging the quantitative accuracy of the model, we parameterize and solve a reaction–diffusion equation to determine hydrolysis rates consistent with experimental observations. We find a short reaction–diffusion length, indicating that the uptake is dominated by interfacial features. The parameters deduced here, including solubility, accommodation coefficient, and hydrolysis rate, afford a foundation for which to consider the reactive loss of N 2 O 5 in more complex solutions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Stringent σ8 constraints from small-scale galaxy clustering using a hybrid MCMC + emulator framework

ABSTRACT We present a novel simulation-based hybrid emulator approach that maximally derives cosmological and Halo Occupation Distribution (HOD) information from non-linear galaxy clustering, with sufficient precision for DESI Year 1 (Y1) analysis. Our hybrid approach first samples the HOD space on a fixed cosmological simulation grid to constrain the high-likelihood region of cosmology + HOD parameter space, and then constructs the emulator within this constrained region. This approach significantly reduces the parameter volume emulated over, thus achieving much smaller emulator errors with fixed number of training points. We demonstrate that this combined with state-of-the-art simulations result in tight emulator errors comparable to expected DESI Y1 LRG sample variance. We leverage the new abacussummit simulations and apply our hybrid approach to CMASS non-linear galaxy clustering data. We infer constraints on σ8 = 0.762 ± 0.024 and fσ8(zeff = 0.52) = 0.444 ± 0.016, the tightest among contemporary galaxy clustering studies. We also demonstrate that our fσ8 constraint is robust against secondary biases and other HOD model choices, a critical first step towards showcasing the robust cosmology information accessible in non-linear scales. We speculate that the additional statistical power of DESI Y1 should tighten the growth rate constraints by at least another 50–60 ${{\ \rm per\ cent}}$, significantly elucidating any potential tension with Planck. We also address the ‘lensing is low’ tension, which we find to be in the same direction as a potential tension in fσ8. We show that the combined effect of a lower fσ8 and environment-based bias accounts for approximately $50{{\ \rm per\ cent}}$ of the discrepancy.

79 ASTRONOMY AND ASTROPHYSICS↗

Intelligent Experiments through Real-Time AI: Fast Data Processing and Autonomous Detector Control for High-Energy Nuclear Experiments

The aim of this project is to develop software and hardware for fast real-time data processing and autonomous detector control and calibration for the sPHENIX and the future EIC experiments. Below summarizes Georgia Tech team efforts in the past year: 1. We developed a real-time clustering algorithm and FPGA-based pipeline architecture for processing fired pixel data from ALPIDE sensors in sPHENIX experiments. Our Columnar Clustering Co-Design introduces a hardware-aware, stream-friendly approach that segments pixel data by column pairs using a Column Pair Clustering (CPC) strategy, followed by Cluster Stitching to merge adjacent subclusters. Implemented in Vitis HLS, the pipeline comprises five stages—read-in, subclustering, stitching, analysis, and write-out—connected by tagged HLS streams with custom end-of-event signaling for robust synchronization. We designed a pipelined dataflow model optimized for throughput, low latency, and minimal buffering, enabling scalable clustering across events of arbitrary size. Our system maintains spatial precision via center-of-mass and shape key extraction and efficiently handles edge cases such as fragmented or nested clusters. Compared against DBSCAN in both software and hardware, our approach demonstrates competitive performance under FPGA constraints. 2. We also conducted a comprehensive algorithm-to-hardware co-design of connected component analysis tailored for sPHENIX experiments, focusing on real-time, low-latency processing using FPGAs and High-Level Synthesis (HLS). Starting from a Python-based particle tracking pipeline, the team translated the core logic—graph traversal via DFS and Union-Find—into an HLS-compatible C++ model, replacing dynamic memory and recursion with static arrays and pipelined control flow. The final design includes a fully streamed and dataflow-compatible Union-Find kernel optimized across five iterations, incorporating loop pipelining, array partitioning, AXI/FIFO interface tuning, and function flattening. Experimental results show up to 14.8× speedup over the CPU baseline, reducing per-graph latency to 1.58 μs and demonstrating strong resource efficiency with only ~7k LUTs and zero BRAM usage. The design maintains functional correctness against the Python reference using a Python-based C-simulation framework and Mean Squared Error metrics. This work validates the potential of HLS-driven FPGA designs for edge-level HEP data acquisition, laying a scalable foundation for future integration with real-time detector pipelines and multi-graph processing systems.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Constraining the scatter in the galaxy–halo connection at Milky Way masses

In this work, we develop and implement two new methods for constraining the scatter in the relationship between galaxies and dark matter haloes. These new techniques are sensitive to the scatter at low halo masses, making them complementary to previous constraints that are dependent on clustering amplitudes or rich galaxy groups, both of which are only sensitive to more massive haloes. In both of our methods, we use a galaxy group finder to locate central galaxies in the Sloan Digital Sky Survey main galaxy sample. Our first technique uses the small-scale cross-correlation of central galaxies with all lower mass galaxies. This quantity is sensitive to the satellite fraction of low-mass galaxies, which is in turn driven by the scatter between haloes and galaxies. The second technique uses the kurtosis of the distribution of line-of-sight velocities between central galaxies and neighbouring galaxies. This quantity is sensitive to the distribution of halo masses that contain the central galaxies at fixed stellar mass. Theoretical models are constructed using peak halo circular velocity, Vpeak, as our property to connect galaxies to haloes, and all comparisons between theory and observation are made after first passing the model through the group-finding algorithm. We parametrize scatter as a lognormal distribution in M* at fixed Vpeak, σ[M*|Vpeak]. The cross-correlation technique yields a constraint of σ[M*|Vpeak] = 0.27 ± 0.05 dex at a mean Vpeak of 168 km s-1, corresponding to a scatter in log M* at fixed Mh of σ[M*|Mh] = 0.38 ± 0.06 dex at $M_\text{h}=10^{11.8}\, \text{M}_\odot$. The kurtosis technique yields σ[M*|Vpeak] = 0.30 ± 0.03 at Vpeak = 209 km s-1, corresponding to σ[M*|Mh] = 0.34 ± 0.04 at $M_\text{h}=10^{12.2}\, \text{M}_\odot$. The values of σ[M*|Mh] are significantly larger than the constraints at higher masses, in agreement with the results of hydrodynamic simulations. This increase is only partly due to the scatter between Vpeak and Mh, and it represents an increase of nearly a factor of 2 relative to the values inferred from clustering and group studies at high masses.

59 BASIC BIOLOGICAL SCIENCES↗

The many-body expansion for aqueous systems revisited: 1. Water-water interactions

We revisit the Many-Body Expansion (MBE) for water-water interactions by examining the effects of the basis set, including those resulting from the Basis Set Superposition Error (BSSE) correction, on the various terms for selected sizes of water clusters up to n = 21. The analysis is performed at the second order Møller-Plesset (MP2) perturbation theory with the family of augmented correlation consistent basis sets up to five zeta quality for the (H2O)n, n = 7, 10, 13, 16 and 21 clusters, for which we report either the complete MBE (n = 7, 10) or the one through the 6-body (n = 13) and the 5-body terms (n = 16, 21). Our results suggest that any sizeable contributions to the total cluster binding energy arising from the 5-body and larger terms are solely an artifact of the size of the basis set. Indeed, all terms above the 4-body converge monotonically to practically zero at the Complete Basis Set (CBS) limit. The magnitudes of the 5-body and above terms are accurately reproduced even with the smaller basis set of the series (aug-cc-pVDZ) once the BSSE correction is taken into account. The same level of theory (MP2/aug-cc-pVDZ, BSSEcorrected) also accurately reproduces the MP2/CBS values of the 3- and 4-body terms. The contribution of electron correlation to the 3- and 4-body terms is quite small, so that neglecting the correlation contribution in all terms above the 3-body results in an error of ??(0.1%). The BSSE correction to the largest 2-body term in the MBE was accurately estimated from the function ?? [1 + erf(-?? ??)], which is proportional to the common (overlapping) area between two Gaussian distributions whose centers are separated by R, with the constants ??, ?? fitted to the calculated BSSE corrections for the individual 2-body terms of the clusters with each basis set. Our results unquestionably demonstrate that the MBE for water-water interactions converges to the 4-body term, since any finite terms above the 4-body are artifacts of the size of the basis set and can be safely truncated at the 4-body term when either a very large basis set is used or BSSE corrections are taken into account even with the aug-cc-pVDZ basis set. We expect these findings to have important consequences in the pursuit of accurate many-body molecular dynamics simulations for aqueous systems.

Heindel, Joseph↗

An Attractive Way to Correct for Missing Singles Excitations in Unitary Coupled Cluster Doubles Theory

Coupled cluster methods based exclusively on double excitations are comparatively “cheap” and interesting model chemistries, as they are typically able to capture the bulk of the dynamic electron correlation effects. The trade-off in such approximations is that the effect of neglected excitations, particularly single excitations, can be considerable. Using standard and electron-pair-restricted T 2 operators to define two flavors of unitary coupled cluster doubles (UCCD) methods, we investigate the extent to which missing single excitations can be recovered from low-order corrections in many-body perturbation theory (MBPT) within the unitary coupled cluster (UCC) formalism. Here, our analysis includes the derivations of finite-order UCC energy functionals, which are used as a basis to define perturbative estimates of missed single excitations. This leads to the novel UCCD[4S] and UCCD[6S] methods, which consider energy corrections for missing single excitations through fourth- and sixth-order in MBPT, respectively. We also apply the same methodology to the electron-pair-restricted ansatz, but the improvements are only marginal. Our findings show that augmenting UCCD with these post hoc perturbative corrections can lead to UCCSD-quality results.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The Role of Ru in Improving the Activity of Pd toward Hydrogen Evolution and Oxidation Reactions in Alkaline Solutions

Improving the reaction kinetics of hydrogen evolution and oxidation reactions (HER/HOR) in alkaline media is critical to promote the development of alkaline fuel cells and electrolyzers. Here, we prepared Pd 3 Ru alloy nanocatalysts with Ru segregated on the surfaces, forming adatoms and clusters. This structure dramatically lowered the overpotential of Pd toward HER in 1 M KOH by 104 mV at 10 mA cm –2 . The HER activity was even higher than that of Pt (6 mV improvement at 10 mA cm –2 ). Theoretical simulation results revealed that Ru adatoms/clusters on the surface could weaken the hydrogen-binding energy and promote the OH adsorption, consequently lowering the reaction barrier of the rate-determining step in HER. Here, our findings are of significance for clarifying the role of Ru in bimetallic catalysts and rational design of more active catalysts for HER/HOR.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The brown dwarf population in the star-forming region NGC 2264

ABSTRACT The brown dwarf population in the canonical star-forming region NGC 2264 is so far poorly explored. We present a deep, multiwavelength, multiepoch survey of the star-forming cluster NGC 2264, aimed to identify young brown dwarf candidates in this region. Using criteria including optical/near-infrared (IR) colours, variability, Spitzer mid-IR colour excess, extinction, and Gaia parallax and proper motion (in order of relevance), we select 902 faint red sources with indicators of youth. Within this sample, we identify 429 brown dwarf candidates based on their IR colours. The brown dwarf candidates are estimated to span a mass range from 0.01 to 0.08 M⊙. We find rotation periods for 44 sources, 15 of which are brown dwarf candidates, ranging from 3.6 h to 6.5 d. A subset of 38 brown dwarf candidates show high-level irregular variability indicative of ongoing disc accretion, similar to the behaviour of young stars.

Pearson, Samuel↗

The Pristine survey – XVI. The metallicity of 26 stellar streams around the Milky Way detected with the STREAMFINDER in Gaia EDR3

ABSTRACT We use the photometric metallicities provided by the panoramic Pristine survey to study the veracity and derive the metallicities of the numerous stellar streams found by the application of the STREAMFINDER algorithm to the Gaia Early Data Release 3 data. All 26 streams present in Pristine show a clear metallicity distribution function, which provides an independent check of the reality of these structures, supporting the reliability of STREAMFINDER in finding streams and the power of Pristine to measure precise metallicities. We further present six candidate structures with coherent phase-space and metallicity signals that are very likely streams. The majority of studied streams are very metal-poor (14 structures with [Fe/H] < −2.0) and include three systems with [Fe/H] < −2.9 (C-11, C-19, and C-20). These streams could be the closest debris of low-luminosity dwarf galaxies or may have originated from globular clusters of significantly lower metallicity than any known current Milky Way globular cluster. Our study shows that the promise of the Gaia data for Galactic Archeology studies can be substantially strengthened by quality photometric metallicities, allowing us to peer back into the earliest epochs of the formation of our Galaxy and its stellar halo constituents.

79 ASTRONOMY AND ASTROPHYSICS↗

Resolving the Solvation Structure and Transport Properties of Aqueous Zinc Electrolytes from Salt-in-Water to Water-in-Salt Using Neural Network Potential

Zn Cl 2 solutions are promising electrolytes for aqueous zinc-ion batteries. Here, we report a joint computational and experimental study of the structural and dynamic properties of aqueous Zn Cl 2 electrolytes with concentrations ranging from salt-in-water to water-in-salt (WIS). By developing a neural network potential (NNP) model, we perform molecular dynamics (MD) simulations with accuracy but at much larger lengths and longer timescales. The NNP predicted structures are validated by the structure factors measured by X-ray total scattering experiments. The MD trajectories provide a comprehensive and quantitative picture of the Zn 2 + solvation shell structures. Additionally, we find that the O − H covalent bonds in water are strengthened with increasing salt concentration, thus expanding the electrochemical stability window of aqueous electrolytes. In terms of dynamic properties, the calculated and experimentally measured conductivities are in good agreement. Through the analysis of the calculated cation transference number, we propose a three-stage charge carrier transport mechanism with increasing concentration: independent ion transport, strongly correlated ion transport, and small positive charge carrier diffusion through negatively charged polymeric clusters. Our study provides fundamental atomic scale insights into the structure and transport properties of the Zn Cl 2 electrolyte that can aid the optimization and development of WIS electrolytes. Published by the American Physical Society 2025

25 ENERGY STORAGE↗

Non-smooth Bayesian optimization in tuning scientific applications

Tuning algorithmic parameters to optimize the performance of large, complicated computational codes is an important problem involving finding the optima and identifying regimes defined by non-smooth boundaries in black-box functions. Within the Bayesian optimization framework, the Gaussian process surrogate model produces smooth mean functions, but functions in the tuning problem are often non-smooth, which is exacerbated by the fact that we usually have limited sequential samples from the black-box function. Here, motivated by these issues encountered in tuning, we propose a novel Gaussian process model called a clustered Gaussian process (cGP), where the components are dynamically updated by clustering. In our studies, the performance of cGP can be better than stationary GPs in nearly 90% of the experiments and better than non-stationary GPs in nearly 70% of the repeated experiments while requiring less computational cost. cGP provides a novel approach for dynamic GP, computes more efficiently than recursive partitioning, and discovers non-smoothness regimes. We provide extensive experiments including high-performance computing (HPC) and industrial simulation functions to show the effectiveness of our methods.

97 MATHEMATICS AND COMPUTING↗

An analytic approximation to the covariance between pre- and post-reconstruction galaxy two-point statistics

We present a simple analytic approximation for the covariance between pre-reconstruction galaxy power spectrum measurements and post-reconstruction two-point correlation functions. This cross-covariance is essential for joint analyses that combine full-shape clustering information with baryon acoustic oscillation (BAO) measurements, as commonly performed in modern spectroscopic surveys. Our model builds on the disconnected contribution to the covariance and accounts for the damping of correlations due to the BAO reconstruction process. We validate our analytic prescription against numerical simulations from the Dark Energy Spectroscopic Instrument (DESI), testing both idealized cubic geometries and realistic survey configurations including complex footprints and fiber assignment effects. Despite neglecting survey window functions in the analytic calculation, we find excellent agreement with simulation-based covariances and demonstrate that cosmological parameter constraints are virtually unchanged when using our approximation. Our results show that the pre-post cross-covariance is sufficiently small that even approximate treatments are adequate for cosmological inference, opening a pathway toward fully analytic covariance matrices for next-generation galaxy surveys.

baryon acoustic oscillations↗

On the influence of halo mass accretion history on galaxy properties and assembly bias

Halo assembly bias is the secondary dependence of the clustering of dark matter haloes on their assembly histories at fixed halo mass. This established dependence is expected to manifest itself on galaxy clustering, a potential effect commonly known as galaxy assembly bias. Using the IllustrisTNG300 magnetohydrodynamical simulation, in this work we analyse the dependence of the properties and clustering of galaxies on the specific mass accretion history of their hosting haloes (sMAH). We first show that several halo and galaxy properties strongly correlate with the slope of the sMAH (β) at fixed halo mass. Haloes with increasingly steeper β increment their masses faster early on, and their hosted galaxies present larger stellar-to-halo mass ratios, lose their gas faster, reach the peak of their star formation histories at higher redshift, and become quenched earlier. We also demonstrate that β provides a more stable link to these key galaxy formation properties than other broadly employed halo proxies, such as formation time. Finally, we measure the secondary dependence of galaxy clustering on β at fixed halo mass. By tracing back the evolution of individual haloes, we show that the amplitude of the galaxy assembly bias signal for the progenitors of z = 0 galaxies increases with redshift, reaching a factor of 2 at z = 1 for haloes of Mhalo = 10 11.5 –10 12 h –1 M ⊙ . The measurement of the evolution of assembly bias along the merger tree provides a new theoretical perspective to the study of secondary bias. Our findings have also important implications for the generation of mock catalogues for upcoming cosmological surveys.

79 ASTRONOMY AND ASTROPHYSICS↗

Mass dependence of halo baryon fractions from the kinetic Sunyaev–Zeldovich effect

ABSTRACT We detect the kinetic Sunyaev–Zeldovich imprint of peculiar motions of galaxy groups and clusters, using the photometric Dark Energy Spectroscopic Instrument Legacy Surveys together with cosmic microwave background (CMB) maps from the Atacama Cosmology Telescope (ACT). We develop a comprehensive forward model based on the AbacusSummit cosmological simulations: Mock galaxy group catalogues and synthetic kinetic Sunyaev–Zeldovich (kSZ) maps are generated, together with a reconstructed peculiar velocity field that allows for photo-z errors, redshift-space distortions, and survey masks. We investigate possible contamination from the cosmic infrared background (CIB), finding that CIB effects are subdominant to the kSZ signal in the relevant ACT frequency channel. We then predict the kSZ signal expected when stacking CMB temperature maps around groups, taking account of their estimated radial velocities. Comparing the model with observations, we are able to constrain the total baryon fraction within haloes, as well as their internal gas profiles. We find evidence for mass dependence of the halo baryon fraction within the virial radius. The gas fraction in massive groups is consistent with the universal baryon fraction, but low-mass groups ($10^{12.5} \lesssim M\, /\, h^{-1}\, \mathrm{M}_\odot \lesssim 10^{14}$) are depleted to $0.38 \pm 0.11$ times the universal baryon fraction. We find this low virial baryon fraction to be consistent with an extended gas profile, for which the total baryon content reaches the universal value well beyond the virial radius. This conclusion is consistent with previous analyses using X-ray, kSZ, and weak lensing, and plausibly reflects energetic feedback processes from the galaxies in these haloes.

Roper, Finn A [Institute for Astronomy, University↗

Application of sulfur SAD to small crystals with a large asymmetric unit and anomalous substructure

The application of sulfur single-wavelength anomalous dispersion (S-SAD) to determine the crystal structures of macromolecules can be challenging if the asymmetric unit is large, the crystals are small, the size of the anomalously scattering sulfur structure is large and the resolution at which the anomalous signals can be accurately measured is modest. Here, as a study of such a case, approaches to the SAD phasing of orthorhombic Ric-8A crystals are described. The structure of Ric-8A was published with only a brief description of the phasing process [Zeng et al. (2019), Structure , 27 , 1137–1141]. Here, alternative approaches to determining the 40-atom sulfur substructure of the 103 kDa Ric-8A dimer that composes the asymmetric unit are explored. At the data-collection wavelength of 1.77 Å measured at the Frontier micro-focusing Macromolecular Crystallography (FMX) beamline at National Synchrotron Light Source II, the sulfur anomalous signal strength, |Δ ano |/σΔ ano ( d ′′/sig), approaches 1.4 at 3.4 Å resolution. The highly redundant, 11 000 000-reflection data set measured from 18 crystals was segmented into isomorphous clusters using BLEND in the CCP 4 program suite. Data sets within clusters or sets of clusters were scaled and merged using AIMLESS from CCP 4 or, alternatively, the phenix.scale_and_merge tool from the Phenix suite. The latter proved to be the more effective in extracting anomalous signals. The HySS tool in Phenix , SHELXC / D and PRASA as implemented in the CRANK 2 program suite were each employed to determine the sulfur substructure. All of these approaches were effective, although HySS , as a component of the phenix.autosol tool, required data from all crystals to find the positions of the sulfur atoms. Critical contributors in this case study to successful phase determination by SAD included (i) the high-flux FMX beamline, featuring helical-mode data collection and a helium-filled beam path, (ii) as recognized by many authors, a very highly redundant, multiple-crystal data set and (iii) the inclusion within that data set of data from crystals that were scanned over large ω ranges, yielding highly isomorphous and highly redundant intensity measurements.

59 BASIC BIOLOGICAL SCIENCES↗