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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Clustering of CODEX clusters

The clustering of galaxy clusters links the spatial nonuniformity of dark matter halos to the growth of the primordial spectrum of perturbations. The amplitude of the clustering signal is widely used to estimate the halo mass of astrophysical objects. The advent of cluster mass calibrations enables using clustering in cosmological studies. Aims. We analyze the autocorrelation function of a large contiguous sample of galaxy clusters, the Constrain Dark Energy with X-ray (CODEX) sample, in which we take particular care of cluster definition. These clusters were X-ray selected using the ROentgen SATellite All-Sky Survey and then identified as galaxy clusters using the code redMaPPer run on the photometry of the Sloan Digital Sky Survey. We develop methods for precisely accounting for the sample selection effects on the clustering and demonstrate their robustness using numerical simulations. Methods. Using the clean CODEX sample, which was obtained by applying a redshift-dependent richness selection, we computed the two-point autocorrelation function of galaxy clusters in the 0.1 < z < 0.3 and 0.3 < z < 0.5 redshift bins. We compared the bias in the measured correlation function with values obtained in numerical simulations using a similar cluster mass range. Results. By fitting a power law, we measured a correlation length r 0 = 18.7 ± 1.1 and slope γ = 1.98 ± 0.14 for the correlation function in the full redshift range. By fixing the other cosmological parameters to their nine-year Wilkinson Microwave Anisotropy Probe values, we reproduced the observed shape of the correlation function under the following cosmological conditions: Ω m0 = $0.22_{-0.03}^{+0.04}$ and S 8 = σ 8 (Ω m0 /0.3)0.5 = $0.85_{-0.08}^{+0.10}$ with estimated additional systematic errors of σ Ω m0 = 0.02 and σS 8 = 0.20. We illustrate the complementarity of clustering constraints by combining them with CODEX cosmological constraints based on the X-ray luminosity function, deriving Ωm = 0.25 ± 0.01 and σ 8 = $0.81_{-0.02}^{+0.01}$ with an estimated additional systematic error of σ Ω m0 = 0.07 and σ σ8 = 0.04. The mass calibration and statistical quality of the mass tracers are the dominant source of uncertainty.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

NWPEsSe: an Adaptive-Learning Global Optimization Algorithm for Nanosized Cluster Systems

Global optimization constitutes an important and fundamental problem in theoretical studies in many chemical fields, such as catalysis, materials or separations problems. In this paper, a novel algorithm has been developed for the global optimization of large systems including neat and ligated clusters in gas phase, and supported clusters in periodic boundary conditions. The method is based on an updated artificial bee colony (ABC) algorithm method, that allows for adaptive-learning during the search process. The new algorithm is tested against four classes of systems of diverse chemical nature: gas phase Au_55, ligated Au_8^(2+), Au_8 supported on graphene oxide and defected rutile, and a large cluster assembly ?[Co?_6 Te_8 (PEt_3 )_6][C_60 ]_n, with sizes ranging between 1 to 3 nm and containing up to 1300 atoms. Reliable global minima (GMs) are obtained for all cases, either confirming published data or reporting new lower energy structures. The algorithm and interface to other codes in the form of an independent program, Northwest Potential Energy Search Engine (NWPEsSe), is freely available and it provides a powerful and efficient approach for global optimization of nanosized cluster systems. The work described in this publication was performed at Pacific Northwest National Laboratory (PNNL), which is operated by Battelle for the United States Department of Energy (DOE) under Contract DE-AC05-76RL0180. J. Z. and V.-A. G. acknowledge support from DOE, Office of Science, Office of Basic Energy Sci-ences, Chemical, Geological and Biological Sciences Division and computing resources from PNNL’s Research Computing Facility and the National Energy Research Scientific Computing Center.

Zhang, Jun↗
DOE OSTI2013

THE STAR CLUSTER SYSTEM IN THE NEARBY STARBURST GALAXY M82

We present a photometric study of star clusters in the nearby starburst galaxy M82 based on the UBVI-, YJ- and H-band Hubble Space Telescope images. We find 1105 star clusters with V < 23 mag. Of those, 1070 are located in the disk region, while 35 star clusters are in the halo region. The star clusters in the disk are composed of a dominant blue population with a color peak at (B - V){sub 0} Almost-Equal-To 0.45, and a weaker red population. The luminosity function of the disk clusters shows a power-law distribution with a power-law index {alpha} = -2.04 {+-} 0.03, and the scale height of their distribution is h{sub z} = 9.''64 {+-} 0.''40 (164 {+-} 7 pc), similar to that of the stellar thin disk of M82. We have derived the ages of {approx}630 star clusters using the spectral energy distribution fit method by comparing UBVI(YJ)H-band photometric data with the simple stellar population models. The age distribution of the disk clusters shows that the most dominant cluster population has ages ranging from 100 Myr to 1 Gyr, with a peak at about 500 Myr. This suggests that M82 has undergone a disk-wide star formation about 500 Myr ago, probably through the interaction with M81. The brightest star clusters in the nuclear region are much brighter than those in other regions, indicating that more massive star clusters are formed in the denser environments. On the other hand, the colors of the halo clusters are similar to those of globular clusters in the Milky Way, and their ages are estimated to be older than 1 Gyr. These are probably genuine old globular clusters in M82.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

A high-significance measurement of correlation between unresolved IRAS sources and optically-selected galaxy clusters

We cross-correlate the 100 μm Improved Reprocessing of the IRAS Survey (IRIS) map and galaxy clusters at 0.1 < z < 0.3 in the maxBCG catalogue taken from the Sloan Digital Sky Survey, measuring an angular cross-power spectrum over multipole moments 150 < l < 3000 at a total significance of over 40σ. The cross-spectrum, which arises from the spatial correlation between unresolved dusty galaxies that make up the cosmic infrared background (CIB) in the IRIS map and the galaxy clusters, is well-fit by a single power law with an index of −1.28±0.12, similar to the clustering of unresolved galaxies from cross-correlating far-infrared and submillimetre maps at longer wavelengths. Using a recent, phenomenological model for the spectral and clustering properties of the IRIS galaxies, we constrain the large-scale bias of the maxBCG clusters to be 2.6±1.4, consistent with existing analyses of the real-space cluster correlation function. The success of our method suggests that future CIB-optical cross-correlations using Planck and Herschel data will significantly improve our understanding of the clustering and redshift distribution of the faint CIB sources.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Randomized Algorithms for Symmetric Nonnegative Matrix Factorization

Symmetric Nonnegative Matrix Factorization (SymNMF) is a technique in data analysis and machine learning that approximates a matrix with a product of a nonnegative, low-rank matrix and it transpose. To design faster and more scalable algorithms for SymNMF we develop two randomized algorithms for its computation. The first method uses randomized matrix sketching to compute an initial low-rank approximation to the input matrix and proceeds to uses this as a low-rank input to rapidly compute a SymNMF. The second methods uses randomized leverage score sampling to approximately solve constrained least squares problems. Many successful methods for SymNMF rely on (approximately) solving sequences of constrained least squares problems. Here, we prove theoretically that leverage score sampling can approximately solve constrained least squares problems to e-accuracy. Finally we demonstrate both methods work in practice by applying them to graph clustering tasks on large real world data sets. These experiments show that our methods approximately maintain solution quality and achieve significant speed ups for both large dense and large sparse problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

The SRG/eROSITA All-Sky Survey: Optical identification and properties of galaxy clusters and groups in the western galactic hemisphere

The first SRG/eROSITA All-Sky Survey (eRASS1) provides the largest intracluster medium-selected galaxy cluster and group catalog covering the western Galactic hemisphere. Compared to samples selected purely on X-ray extent, the sample purity can be enhanced by identifying cluster candidates using optical and near-infrared data from the DESI Legacy Imaging Surveys. Using the red-sequence-based cluster findereROMaPPer, we measured individual photometric properties (redshiftz λ , richnessλ, optical center, and BCG position) for 12000 eRASS1 clusters over a sky area of 13 116 deg 2 , augmented by 247 cases identified by matching the candidates with known clusters from the literature. The median redshift of the identified eRASS1 sample isz= 0.31, with 10% of the clusters atz> 0.72. The photometric redshifts have an accuracy ofδz/(1 +z) ≲ 0.005 for 0.05 specand velocity dispersionσ) were measured a posteriori for a subsample of 3210 and 1499 eRASS1 clusters, respectively, using an extensive compilation of spectroscopic redshifts of galaxies from the literature. We infer that the primary eRASS1 sample has a purity of 86% and optical completeness >95% forz> 0.05. For these and further quality assessments of the eRASS1 identified catalog, we applied our identification method to a collection of galaxy cluster catalogs in the literature, as well as blindly on the full Legacy Surveys covering 24069 deg 2 . Using a combination of these cluster samples, we investigated the velocity dispersion-richness relation, finding that it scales with richness as log(λ norm ) = 2.401 × log(σ) − 5.074 with an intrinsic scatter ofδ in = 0.10 ± 0.01 dex. The primary product of our work is the identified eRASS1 cluster catalog with high purity and a well-defined X-ray selection process, opening the path for precise cosmological analyses presented in companion papers.

Astronomy & Astrophysics↗
NASA NTRS2003

Proposal for Testing and Validation of Vacuum Ultra-Violet Atomic Laser-Induced Fluorescence as a Method to Analyze Carbon Grid Erosion in Ion Thrusters

Previous investigation under award NAG3-25 10 sought to determine the best method of LIF to determine the carbon density in a thruster plume. Initial reports from other groups were ambiguous as to the number of carbon clusters that might be present in the plume of a thruster. Carbon clusters would certainly affect the ability to LIF; if they were the dominant species, then perhaps the LIF method should target clusters. The results of quadrupole mass spectroscopy on sputtered carbon determined that minimal numbers of clusters were sputtered from graphite under impact from keV Krypton. There were some investigations in the keV range by other groups that hinted at clusters, but at the time the proposal was presented to NASA, there was no data from low-energy sputtering available. Thus, the proposal sought to develop a method to characterize the population only of atoms sputtered from a graphite target in a test cell. Most of the ground work had been established by the previous two years of investigation. The proposal covering 2003 sought to develop an anti-Stokes Raman shifting cell to generate VUW light and test this cell on two different laser systems, ArF and YAG- pumped dye. The second goal was to measure the lowest detectable amounts of carbon atoms by 156.1 nm and 165.7 nm LIF. If equipment was functioning properly, it was expected that these goals would be met easily during the timeframe of the proposal, and that is the reason only modest funding was requested. The PI was only funded at half- time by Glenn during the summer months. All other work time was paid for by Whitworth College. The college also funded a student, Charles Shawley, who worked on the project during the spring.

Stevens, Richard↗
DOE OSTI2013

Parallel multiscale simulations of a brain aneurysm

Cardiovascular pathologies, such as a brain aneurysm, are affected by the global blood circulation as well as by the local microrheology. Hence, developing computational models for such cases requires the coupling of disparate spatial and temporal scales often governed by diverse mathematical descriptions, e.g., by partial differential equations (continuum) and ordinary differential equations for discrete particles (atomistic). However, interfacing atomistic-based with continuum-based domain discretizations is a challenging problem that requires both mathematical and computational advances. We present here a hybrid methodology that enabled us to perform the first multiscale simulations of platelet depositions on the wall of a brain aneurysm. The large scale flow features in the intracranial network are accurately resolved by using the high-order spectral element Navier–Stokes solver NεκTαr. The blood rheology inside the aneurysm is modeled using a coarse-grained stochastic molecular dynamics approach (the dissipative particle dynamics method) implemented in the parallel code LAMMPS. The continuum and atomistic domains overlap with interface conditions provided by effective forces computed adaptively to ensure continuity of states across the interface boundary. A two-way interaction is allowed with the time-evolving boundary of the (deposited) platelet clusters tracked by an immersed boundary method. The corresponding heterogeneous solvers (NεκTαr and LAMMPS) are linked together by a computational multilevel message passing interface that facilitates modularity and high parallel efficiency. Results of multiscale simulations of clot formation inside the aneurysm in a patient-specific arterial tree are presented. We also discuss the computational challenges involved and present scalability results of our coupled solver on up to 300 K computer processors. Validation of such coupled atomistic-continuum models is a main open issue that has to be addressed in future work.

60 APPLIED LIFE SCIENCES↗
NASA NTRS1991

The energy separation between the classical and nonclassical isomers of protonated acetylene - An extensive study in one- and n-particle space saturation

The energy separation between the classical and nonclassical forms of protonated acetylene has been reinvestigated in light of the recent experimentally deduced lower bound to this value of 6.0 kcal/mol. The objective of the present study is to use state-of-the-art ab initio quantum mechanical methods to establish this energy difference to within chemical accuracy (i.e., about 1 kcal/mol). The one-particle basis sets include up to g-type functions and the electron correlation methods include single and double excitation coupled-cluster (CCSD), the CCSD(T) extension, multireference configuration interaction, and the averaged coupled-pair functional methods. A correction for zero-point vibrational energies has also been included, yielding a best estimate for the energy difference between the classical and nonclassical forms of 3.7 + or - 1.3 kcal/mol.

Lindh, Roland↗
DOE OSTI2026

Quantifying Microstructure Variability in Laser Powder Bed Fusion 316 L Stainless Steel Microstructures with Spatial Statistics

Here, we have explored data-driven methods for material microstructure quantification that improve sensitivity to microstructural changes compared to traditional approaches. The methods integrate multiple microstructural properties, including grain morphology, crystallographic orientation, and material phase information. The simpler method employs maps of the Euclidean distance transformation metric to evaluate the morphology of grain boundary networks. The more intensive approach employs generalized spherical harmonic mapping for crystallographic orientations, per-pixel phase information, and a variational auto-encoder for dimensionality reduction and results in a multidimensional clustering of by microstructure similarity. Applied to an experimental dataset of additively manufactured steel, both methods detected slight variations in samples produced under nominally identical processing conditions. Both methods were able to distinguish between samples from multiple (nominally identical) builds, while the generalized spherical harmonics-based method could additionally cluster data samples rotated at two orientations on the build plate. The improved sensitivity of the methods, demonstrated through comparison with traditional microstructure characterization techniques, offers advantages for microstructure quantification and comparisons in advanced manufacturing applications.

SS316L↗
DOE OSTI2017

Computational investigation on the structures and electronic properties of the nanosized rhenium clusters

Here, the stable equilibrium geometries, relative stabilities, and electronic and magnetic characteristics of Re n (n = 2–16) clusters were investigated by density functional theory method. The calculated fragmentation energies and second-order differences of energies exhibited interestingly that the stabilities of Re n (n = 2–16) clusters show a dramatic odd-even alternative behavior of the cluster size n: with the even-numbered Ren clusters being obviously more stable than their neighboring odd-numbered Re n clusters (beside n = 11). Simultaneously, the calculated HOMO-LUMO gaps of Re n (n = 6–16) display an oscillatory feature at large-sized Ren clusters. From the calculated magnetic moments and growth behaviors of Rhenium clusters, the magnetic Re 6 unit can be seen as the building block for the novel magnetic cluster-assembled nanomaterial. Such calculated results are in good agreement with the available experimental measurements.

36 MATERIALS SCIENCE↗
DOE OSTI2015

Water droplet excess free energy determined by cluster mitosis using guided molecular dynamics

Atmospheric aerosols play a vital role in affecting climate by influencing the properties and lifetimes of clouds and precipitation. Understanding the underlying microscopic mechanisms involved in the nucleation of aerosol droplets from the vapour phase is therefore of great interest. One key thermodynamic quantity in nucleation is the excess free energy of cluster formation relative to that of the saturated vapour. In our current study, the excess free energy is extracted for clusters of pure water modelled with the TIP4P/2005 intermolecular potential using a method based on nonequilibrium molecular dynamics and the Jarzynski relation. The change in free energy associated with the “mitosis” or division of a cluster of N water molecules into two N/2 sub-clusters is evaluated. This methodology is an extension of the disassembly procedure used recently to calculate the excess free energy of argon clusters [H. Y. Tang and I. J. Ford, Phys. Rev. E 91, 023308 (2015)]. Our findings are compared to the corresponding excess free energies obtained from classical nucleation theory (CNT) as well as internally consistent classical theory (ICCT). The values of the excess free energy that we obtain with the mitosis method are consistent with CNT for large cluster sizes but for the smallest clusters, the results tend towards ICCT; for intermediate sized clusters, we obtain values between the ICCT and CNT predictions. Furthermore, the curvature-dependent surface tension which can be obtained by regarding the clusters as spherical droplets of bulk density is found to be a monotonically increasing function of cluster size for the studied range. The data are compared to other values reported in the literature, agreeing qualitatively with some but disagreeing with the values determined by Joswiak et al. [J. Phys. Chem. Lett. 4, 4267 (2013)] using a biased mitosis approach; an assessment of the differences is the main motivation for our current study.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

The range of variation of the mass of the most massive star in stellar clusters derived from 35 million Monte Carlo simulations

A growing fraction of simple stellar population models, in an aim to create more realistic simulations capable of including stochastic variation in their outputs, begin their simulations with a distribution of discrete stars following a power-law function of masses. Careful attention is needed to create a correctly sampled initial mass function (IMF), and here we provide a solid mathematical method, called MASSCLEAN IMF Sampling, for doing so. We use our method to perform 10 million MASSCLEAN Monte Carlo stellar cluster simulations to determine the most massive star in a mass distribution as a function of the total mass of the cluster. We find that a maximum mass range is predicted, not a single maximum mass. This range is (1) dependent on the total mass of the cluster and (2) independent of an upper stellar mass limit, M{sub limit} , for unsaturated clusters and emerges naturally from our IMF sampling method. We then turn our analysis around, starting with our new database of 25 million simulated clusters, to constrain the highest mass star from the observed integrated colors of a sample of 40 low-mass Large Magellanic Cloud stellar clusters of known age and mass. Finally, we present an analytical description of the maximum mass range of the most massive star as a function of the cluster's total mass and present a new M{sub max} -M{sub cluster} relation.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Probing WHIM around galaxy clusters with fast radio bursts and the Sunyaev–Zel’dovich effect

We propose a new method to probe the warm hot intergalactic medium (WHIM) beyond the virial radius (R{sub 200}) of a cluster of galaxies, where X-ray observations are not easily achievable. In this method, we use dispersion measures (DMs) of fast radio bursts (FRBs) that appear behind the cluster and the Sunyaev–Zel’dovich (SZ) effect toward the cluster. The DMs reflect the density of the intracluster medium including the WHIM. If we observe a sufficient number of FRBs in the direction of the cluster, we can derive the density profile from the DMs. Similarly, we can derive the pressure profile from the SZ effect. By combining the density and the pressure profiles, the temperature profile can be obtained. Based on mock observations of nearby clusters, we find that the density of the WHIM will be determined even at >2 R{sub 200} from the cluster center when FRB observations with the Square Kilometre Array become available. The temperature can be derived out to r∼1.5 R{sub 200}, and the radius is limited by the current sensitivity of SZ observations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Metabololipidomic profiling of functional immunoresolvent clusters and eicosanoids in mammalian tissues

Highlights: • New methods for metabololipidomics of specialized proresolving mediators (SPM) and classic eicosanoids. • Illustration from human blood coagulation. • Illustration from solid tumor. • Regulation of SPM biosynthesis by adenosine and adenosine deaminase. Metabolomics enables a systems approach to interrogate the bioactive mediators, their pathways and further metabolites involved in the physiology and pathophysiology of human and animal tissues. New metabololipidomic approaches with mass spectrometry presented in this brief review can now be utilized for the identification and profiling of lipid mediator networks that control inflammation-resolution in human blood and healthy and diseased solid tissues. Coagulation of blood is a protective response that prevents excessive bleeding on injury of blood vessels. Here, we review novel approaches to understand the relationship(s) between coagulation and resolution of inflammation and infection. To determine whether coagulation is involved in host-protective actions by lipid mediators, we used a metabololipidomic-based profiling approach with human whole blood (WB) during coagulation. We identified recently temporal clusters of endogenously produced pro-thrombotic and proinflammatory lipid mediators (eicosanoids), as well as specialized proresolving mediators (SPMs) in this vital process. In addition to the classic eicosanoids (prostaglandins, thromboxanes and leukotrienes), a specific SPM cluster was identified that consists of resolvin E1 (RvE1), RvD1, RvD5, lipoxin B{sub 4}, and maresin 1, each of which present at bioactive concentrations (0.1–1 nM). The removal of adenosine from coagulating blood samples significantly enhances SPM amounts and unleashes the biosynthesis of RvD3, RvD4, and RvD6 evident following rapid snap freezing with centrifugation before extraction and LC-MS-MS. The classic cyclooxygenase inhibitors, celecoxib and indomethacin, that block thromboxanes and prostanoids do not block production of the clot-driven SPM cluster. Unbiased mass cytometry analysis demonstrated that the SPM cluster produced in human blood targets leukocytes at the single-cell level, directly activating extracellular signaling in human neutrophils and monocytes. Human whole blood treated with the components of this SPM cluster enhanced both phagocytosis and killing of Escherichia coli by leukocytes. Thus, we identified a pro-resolving lipid mediator circuit and specific SPM cluster that promotes host defense. This new lipid mediator (LM)-SPM metabololipidomic approach now provides accessible metabolomic profiles in healthy and diseased human tissues, including cancer, for precision and personalized medicine.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2017

The Dependence of Cluster Galaxy Properties on the Central Entropy of Their Host Cluster

We present a study of the connection between brightest cluster galaxies (BCGs) and their host galaxy clusters. Using galaxy clusters at 0.1<z<0.3 from the Hectospec Cluster Survey (HeCS) with X-ray information from the Archive of Chandra Cluster Entropy Profile Tables (ACCEPT), we confirm that BCGs in low central entropy clusters are well aligned with the X-ray center. Additionally, the magnitude difference between BCG and the second brightest galaxy also correlates with the central entropy of the intracluster medium. From the red-sequence (RS) galaxies, we cannot find significant dependence of RS color scatter and stellar population on the central entropy of the intracluster medium of their host cluster. However, BCGs in low-entropy clusters are systematically less massive than those in high-entropy clusters, although this is dependent on the method used to derive the stellar mass of BCGs. In contrast, the stellar velocity dispersion of BCGs shows no dependence on BCG activity and cluster central entropy. This implies that the potential of the BCG is established earlier and the activity leading to optical emission lines is dictated by the properties of the intracluster medium in the cluster core.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRSDate not supplied

Anomaly Detection for the Roman Space Telescope Wide Field Instrument’s Science Data Processing Pipeline

The Roman Space Telescope (RST) Wide Field Instrument (WFI) will be utilizing a preliminary Science Data Processing (SDP) pipeline during its Integration and Test, and to some extent during Operations, to track basic statistics and identify known features such as cosmic rays, snowballs as well as possible anomalies in raw detector data. In our detectors, these anomalies appear as jumps in the ramp of a readout and are classified as cosmic rays if they appear as a streak or snowballs if they’re more circular. The WFI employs an array of 18 H4RG-10 detectors that collect image samples. Each set of raw frames within a non-destructive exposure is packaged by the SDP pipeline into image cubes for each detector. Each cube is a time series of 4096 × 4096 accumulating pixel frames. The preliminary analysis pipeline is used to locate anomalies in these time-series accumulation frames and identify the type of anomaly, either natural phenomena or detector characteristic. To compare different methods, we’ve implemented both heuristic-based and data-driven methods to identify anomalies. For the heuristic-based approach, we identify snowballs and cosmic rays by the size and shape of outlier pixel clusters between consecutive frames. For data driven methods, we evaluated a Convolutional Neural Network (CNN) model, and more traditional methods like Principal Component Analysis (PCA). CNN is a supervised learning/classification method. Thus, we used a labeled dataset of anomalies to perform segmentation of the image and identify anomalies. We used previously identified cosmic rays and snowballs to measure the accuracy and efficiency of the mentioned approaches. In evaluating these methods, we aim to pick the best fit for the SDP pipeline’s anomaly detection in terms of both performance and runtime.

Paul Horton↗
DOE OSTI2021

Spin-free formulation of the multireference driven similarity renormalization group: A benchmark study of first-row diatomic molecules and spin-crossover energetics

We report a spin-free formulation of the multireference (MR) driven similarity renormalization group (DSRG) based on the ensemble normal ordering of Mukherjee and Kutzelnigg (1997). This ensemble averages over all microstates of a given total spin quantum number, and therefore, it is invariant with respect to SU(2) transformations. As such, all equations may be reformulated in terms of spin-free quantities and they closely resemble those of spin-adapted closed-shell coupled cluster (CC) theory. The current implementation is used to assess the accuracy of various truncated MR-DSRG methods (perturbation theory up to third order and iterative methods with single and double excitations) in computing the constants of 33 first-row diatomic molecules. The accuracy trends for these first-row diatomics are consistent with our previous benchmark on a small subset of closed-shell diatomic molecules. We then present the first MR-DSRG application on transition-metal complexes by computing the spin splittings of the [Fe(H 2 O) 6 ] 2+ and [Fe(NH 3 ) 6 ] 2+ molecules. A focal point analysis (FPA) shows that third-order perturbative corrections are essential to achieve reasonably converged energetics. The FPA based on the linearized MR-DSRG theory with one- and two-body operators and up to a quintuple- ζ basis set predicts the spin splittings of [Fe(H 2 O) 6 ] 2+ and [Fe(NH 3 ) 6 ] 2+ to be –35.7 and –17.1 kcal mol –1 , respectively, showing good agreement with the results of local CC theory with singles, doubles, and perturbative triples.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗