Inherited causes of clonal haematopoiesis in 97,691 whole genomes.

Age is the dominant risk factor for most chronic human diseases, but the mechanisms through which ageing confers this risk are largely unknown1. The age-related acquisition of somatic mutations that lead to clonal expansion in regenerating haematopoietic stem cell populations has recently been associated with both haematological cancer2-4 and coronary heart disease5-this phenomenon is termed clonal haematopoiesis of indeterminate potential (CHIP)6. Simultaneous analyses of germline and somatic whole-genome sequences provide the opportunity to identify root causes of CHIP. Here we analyse high-coverage whole-genome sequences from 97,691 participants of diverse ancestries in the National Heart, Lung, and Blood Institute Trans-omics for Precision Medicine (TOPMed) programme, and identify 4,229 individuals with CHIP. We identify associations with blood cell, lipid and inflammatory traits that are specific to different CHIP driver genes. Association of a genome-wide set of germline genetic variants enabled the identification of three genetic loci associated with CHIP status, including one locus at TET2 that was specific to individuals of African ancestry. In silico-informed in vitro evaluation of the TET2 germline locus enabled the identification of a causal variant that disrupts a TET2 distal enhancer, resulting in increased self-renewal of haematopoietic stem cells. Overall, we observe that germline genetic variation shapes haematopoietic stem cell function, leading to CHIP through mechanisms that are specific to clonal haematopoiesis as well as shared mechanisms that lead to somatic mutations across tissues.

Genome-wide significant risk loci for mood disorders in the Old Order Amish founder population.

Genome-wide association studies (GWAS) of mood disorders in large case-control cohorts have identified numerous risk loci, yet pathophysiological mechanisms remain elusive, primarily due to the very small effects of common variants. We sought to discover risk variants with larger effects by conducting a genome-wide association study of mood disorders in a founder population, the Old Order Amish (OOA, n = 1,672). Our analysis revealed four genome-wide significant risk loci, all of which were associated with >2-fold relative risk. Quantitative behavioral and neurocognitive assessments (n = 314) revealed effects of risk variants on sub-clinical depressive symptoms and information processing speed. Network analysis suggested that OOA-specific risk loci harbor novel risk-associated genes that interact with known neuropsychiatry-associated genes via gene interaction networks. Annotation of the variants at these risk loci revealed population-enriched, non-synonymous variants in two genes encoding neurodevelopmental transcription factors, CUX1 and CNOT1. Our findings provide insight into the genetic architecture of mood disorders and a substrate for mechanistic and clinical studies.

DOCSIC: A Mean-Field Method for Orbital-by-Orbital Self-Interaction Correction.

We introduce a new method to remove the one-electron self-interaction error in approximate density functional calculations on an orbital-by-orbital basis, as originally proposed by Perdew and Zunger [Phys. Rev. B 1981, 23, 5048]. This method is motivated by a recent proposal by Pederson et al. [J. Chem. Phys. 2014, 140, 121103] to remove self-interaction that employs orbitals derived from the real-space density matrix, known as FLOSIC (Fermi Löwdin orbitals self-interaction correction). However, instead of Fermi Löwdin orbitals, our scheme utilizes columns of the density matrix to determine localized orbitals, like the localization procedure proposed by Fuemmeler et al. [J. Chem. Theory Comput. 2023, 19, 8572]. The new method, dubbed DOCSIC for density matrix as orbital coefficients self-interaction correction, contrasts with traditional Perdew-Zunger or FLOSIC in that it does not incorporate additional optimization parameters, and, unlike the average density self-interaction correction of Ciofini et al. [Chem. Phys. Lett. 2003, 380, 12], it makes use of localized orbitals. Another advantage of DOCSIC is that it can be implemented as a mean-field formalism. We show details of the self-consistent generalized Kohn-Sham implementation, some illustrative results, and we finally highlight its advantages and limitations.

Bond length alternation of π-conjugated polymers predicted by the Fermi-Löwdin orbital self-interaction correction method.

π-conjugated polymers have been used in a wide range of practical applications, partly due to their unique properties that originate in the delocalization of electrons through the polymer backbone. The level of delocalization can be characterized by the induced bond length alternation (BLA), with shorter BLA connected with strong delocalization and vice versa. The accurate description of this structural parameter can be considered a benchmark for testing the capability of different electronic structure methods for self-interaction error (SIE) removal and electron correlation inclusion. Density functional theory (DFT), in its local or semi-local flavors, suffers from SIE and, thus, underestimates the BLA compared to self-interaction-free methods. In this work, we utilize the Fermi-Löwdin orbital self-interaction correction (FLOSIC) method for one-electron self-interaction removal to characterize the BLA of five oligomers with increasing length extrapolated to the polymeric limit. We compare the self-interaction-free BLA to several DFT approximations, Møller-Plesset second-order perturbation theory (MP2), and the BLA obtained with the domain based local pair natural orbital CCSD(T) [DLPNO-CCSD(T)] approximation. Our findings show that FLOSIC corrects for the small BLA given by (semi-)local DFT approximations, but it tends to overcorrect with respect to CAM-B3LYP, MP2, and DLPNO-CCSD(T).

The rise and fall of stretched bond errors: Extending the analysis of Perdew-Zunger self-interaction corrections of reaction barrier heights beyond the LSDA.

Incorporating self-interaction corrections (SIC) significantly improves chemical reaction barrier height predictions made using density functional theory methods. We present a detailed orbital-by-orbital analysis of these corrections for three semi-local density functional approximations (DFAs) situated on the three lowest rungs of Jacob's ladder of approximations. The analysis is based on Fermi-Löwdin Orbital Self-Interaction Correction (FLOSIC) calculations performed at several steps along the reaction pathway from the reactants (R) to the transition state (TS) to the products (P) for four representative reactions selected from the BH76 benchmark set. For all three functionals, the major contribution to self-interaction corrections of the barrier heights can be traced to stretched bond orbitals that develop near the TS configuration. The magnitude of the ratio of the self-exchange-correlation energy to the self-Hartree energy (XC/H) for a given orbital is introduced as an indicator of one-electron self-interaction error. XC/H = 1.0 implies that an orbital's self-exchange-correlation energy exactly cancels its self-Hartree energy and that the orbital, therefore, makes no contribution to the SIC in the FLOSIC scheme. For the practical DFAs studied here, XC/H spans a range of values. The largest values are obtained for stretched or strongly lobed orbitals. We show that significant differences in XC/H for corresponding orbitals in the R, TS, and P configurations can be used to identify the major contributors to the SIC of barrier heights and reaction energies. Based on such comparisons, we suggest that barrier height predictions made using the strongly constrained and appropriately normed meta-generalized gradient approximation may have attained the best accuracy possible for a semi-local functional using the Perdew-Zunger SIC approach.

Assessment of calcium alginate gels as wall materials for encapsulation systems.

BACKGROUND: Calcium alginate gels are widely used to encapsulate active compounds. Some characteristic parameters of these gels are necessary to describe the release of active compounds through mechanistic mathematical models. In this work, transport and kinetics properties of calcium alginate gels were determined through simple experimental techniques. RESULTS: The weight-average molecular weight ( M ¯ w = 192 × 103 Da) and the fraction of residues of α-l-guluronic acid ( F G = 0.356) of sodium alginate were determined by capillary viscometry and 1 H-nuclear magnetic resonance at 25 °C, respectively. Considering the half egg-box model, both values were used to estimate the molecular weight of calcium alginate as M g = 2.02 × 105 Da. An effective diffusion coefficient of water ( D eff , w = 2.256 × 10-9 m2 s-1 ) in calcium alginate was determined using a diffusion cell at 37 °C. Finally, a kinetics constant of depolymerization ( k m = 9.72 × 10-9 m3 mol-1 s-1 ) of calcium alginate was obtained considering dissolution of calcium to a medium under intestinal conditions. CONCLUSION: The experimental techniques used are simple and easily reproducible. The obtained values may be useful in the design, production, and optimization of the alginate-based delivery systems that require specific release kinetics of the encapsulated active compounds. © 2023 Society of Chemical Industry.

Cell surface receptor kinase FERONIA linked to nutrient sensor TORC signaling controls root hair growth at low temperature linked to low nitrate in Arabidopsis thaliana.

Root hairs (RH) are excellent model systems for studying cell size and polarity since they elongate several hundred-fold their original size. Their tip growth is determined both by intrinsic and environmental signals. Although nutrient availability and temperature are key factors for a sustained plant growth, the molecular mechanisms underlying their sensing and downstream signaling pathways remain unclear. We use genetics to address the roles of the cell surface receptor kinase FERONIA (FER) and the nutrient sensing TOR Complex 1 (TORC) in RH growth. We identified that low temperature (10°C) triggers a strong RH elongation response in Arabidopsis thaliana involving FER and TORC. We found that FER is required to perceive limited nutrient availability caused by low temperature. FERONIA interacts with and activates TORC-downstream components to trigger RH growth. In addition, the small GTPase Rho of plants 2 (ROP2) is also involved in this RH growth response linking FER and TOR. We also found that limited nitrogen nutrient availability can mimic the RH growth response at 10°C in a NRT1.1-dependent manner. These results uncover a molecular mechanism by which a central hub composed by FER-ROP2-TORC is involved in the control of RH elongation under low temperature and nitrogen deficiency.

Density Matrix Implementation of the Fermi-Löwdin Orbital Self-Interaction Correction Method.

The Fermi-Löwdin orbital self-interaction correction (FLOSIC) method effectively provides a transformation from canonical orbitals to localized Fermi-Löwdin orbitals which are used to remove the self-interaction error in the Perdew-Zunger (PZ) framework. This transformation is solely determined by a set of points in space, called Fermi-Löwdin descriptors (FODs), and the occupied canonical orbitals or the density matrix. In this work, we provide a detailed workflow for the implementation of the FLOSIC method for removal of self-interaction error in DFT calculations in an orbital-by-orbital basis that takes advantage of the unitary invariant nature of the FLOSIC method. In this way, it is possible to cast the self-consistent energy minimization at fixed FODs in the same manner than standard Kohn-Sham with one additional term in the Kohn-Sham Hamiltonian that introduces the PZ self-interaction correction. Each energy minimization iteration is divided in two substeps, one for the density matrix and one for the FODs. Expressions for the effective Kohn-Sham matrix and FOD gradients are provided such that its implementation is suitable for most electronic structure codes. We analyze the convergence characteristics of the algorithm and present applications for the evaluation of NMR shielding constants and real-time time-dependent DFT simulations based on the Liouville-von Neumann equation to calculate excitation energies.

Convolutional Neural Networks to Assist the Assessment of Lattice Parameters from X-ray Powder Diffraction.

This article presents the development of convolutional neural networks (CNNs) for the estimation of lattice parameters in organic compounds across various crystal systems. A comprehensive collection of 92,085 organic compounds was utilized to train the CNNs, encompassing crystals with unit cells containing up to 512 atoms and a maximum unit cell volume of 8000 Å3. Simulated diffraction patterns were generated for each compound, comprising four diffraction patterns with different crystal sizes. These diffraction patterns were generated within a 2θ window of 3-60°, employing a step size of 0.02051°. Two distinct CNN architectures were developed with differing input data. The first CNN, referred to as XRD-CNN, was trained solely on diffraction patterns. In the test set, XRD-CNN demonstrated a mean absolute percentage error (MAPE) of 11.04% for unit cell vectors, 7.40% for angles, and 26.83% for unit cell volume. The second CNN, XRDElem-CNN, incorporated a binary representation of atoms within the unit cell as an additional input. XRDElem-CNN achieved improved performance, yielding MAPE values of 4.73% for unit vectors, 6.49% for angles, and 6.05% for the unit cell volume. To validate the performance of XRDElem-CNN, real diffraction patterns obtained from a conventional laboratory diffractometer (Cu Kα wavelength) were employed. Various representations of atoms within the unit cell were proposed, which were computationally efficient for evaluation with the CNNs. The assessed lattice parameters by XRDElem-CNN were validated using the Lp-search method, showing agreement with the reported values.

Generalized spin σ-SCF method.

We introduce a generalization of the σ-SCF method to approximate noncollinear spin ground and excited single-reference electronic states by minimizing the Hamiltonian variance. The new method is based on the σ-SCF method, originally proposed by Ye et al. [J. Chem. Phys. 147, 214104 (2017)], and provides a prescription to determine ground and excited noncollinear spin states on an equal footing. Our implementation was carried out utilizing an initial simulated annealing stage followed by a mean-field iterative self-consistent approach to simplify the cumbersome search introduced by generalizing the spin degrees of freedom. The simulated annealing stage ensures a broad exploration of the Hilbert space spanned by the generalized spin single-reference states with random complex element-wise rotations of the generalized density matrix elements in the simulated annealing stage. The mean-field iterative self-consistent stage employs an effective Fockian derived from the variance, which is utilized to converge tightly to the solutions. This process helps us to easily find complex spin structures, avoiding manipulating the initial guess. As proof-of-concept tests, we present results for Hn (n = 3-7) planar rings and polyhedral clusters with geometrical spin frustration. We show that most of these systems have noncollinear spin excited states that can be interpreted in terms of geometric spin frustration. These states are not directly targeted by energy minimization methods, which are meant to converge to the ground state. This stresses the capability of the σ-SCF methodology to find approximate noncollinear spin structures as mean-field excited states.

Use of FLOSIC for understanding anion-solvent interactions.

An Achille's heel of lower-rung density-functional approximations is that the highest-occupied-molecular-orbital energy levels of anions, known to be stable or metastable in nature, are often found to be positive in the worst case or above the lowest-unoccupied-molecular-orbital levels on neighboring complexes that are not expected to accept charge. A trianionic example, [Cr(C2O4)3]3-, is of interest for constraining models linking Cr isotope ratios in rock samples to oxygen levels in Earth's atmosphere over geological timescales. Here we describe how crowd sourcing can be used to carry out self-consistent Fermi-Löwdin-Orbital-Self-Interaction corrected calculations (FLOSIC) on this trianion in solution. The calculations give a physically correct description of the electronic structure of the trianion and water. In contrast, uncorrected local density approximation (LDA) calculations result in approximately half of the anion charge being transferred to the water bath due to the effects of self-interaction error. Use of group-theory and the intrinsic sparsity of the theory enables calculations roughly 125 times faster than our initial implementation in the large N limit reached here. By integrating charge density densities and Coulomb potentials over regions of space and analyzing core-level shifts of the Cr and O atoms as a function of position and functional, we unambiguously show that FLOSIC, relative to LDA, reverses incorrect solute-solvent charge transfer in the trianion-water complex. In comparison to other functionals investigated herein, including Hartree-Fock and the local density approximation, the FLOSIC Cr 1s eigenvalues provide the best agreement with experimental core ionization energies.

Comparison of five commercial kits for isolation of total RNA in samples of WSSV-infected shrimp.

Viral diseases are the most serious threat to the expansion and development of shrimp aquaculture. Rapid diagnosis of the white spot syndrome virus (WSSV), a lethal shrimp pathogen, is essential to restrict its spread and reduce the mortality of infected shrimp. This virus has globally affected the shrimp farming industry, with a devastating economic impact. Several studies have focused on the expression of WSSV transcripts to understand the molecular mechanisms governing the pathological development of the disease. Since gene expression studies and molecular diagnostics at the early stages of infection depend on the efficient isolation of high-quality RNA, the extraction methods should be carefully selected. However, previous comparisons of the performance of RNA isolation kits have yet to be systematically investigated. In this study, 5 commercial RNA extraction methods were compared in WSSV-infected shrimp. The highest total RNA yield (ng mg-1 tissue) was obtained using TRIzol. Even though the 260/280 nm absorption ratios showed significant differences, the methods showed good purity values (>2.0). RNA integrity was evaluated in a denaturing agarose gel electrophoresis, and degradation was observed after the total RNA samples were treated with DNase I. Finally, the method that allowed the earlier detection of WSSV transcripts by qRT-PCR was the Zymo Direct-zol RNA MiniPrep kit. This study shows that the amount of observed (or estimated) WSSV transcripts might be affected because of the RNA isolation method. In addition, these results may contribute to improve the accuracy of the results obtained in gene expression studies, for more sensitive and robust detection of WSSV.

Self-interaction error overbinds water clusters but cancels in structural energy differences.

We gauge the importance of self-interaction errors in density functional approximations (DFAs) for the case of water clusters. To this end, we used the Fermi-Löwdin orbital self-interaction correction method (FLOSIC) to calculate the binding energy of clusters of up to eight water molecules. Three representative DFAs of the local, generalized gradient, and metageneralized gradient families [i.e., local density approximation (LDA), Perdew-Burke-Ernzerhof (PBE), and strongly constrained and appropriately normed (SCAN)] were used. We find that the overbinding of the water clusters in these approximations is not a density-driven error. We show that, while removing self-interaction error does not alter the energetic ordering of the different water isomers with respect to the uncorrected DFAs, the resulting binding energies are corrected toward accurate reference values from higher-level calculations. In particular, self-interaction-corrected SCAN not only retains the correct energetic ordering for water hexamers but also reduces the mean error in the hexamer binding energies to less than 14 meV/[Formula: see text] from about 42 meV/[Formula: see text] for SCAN. By decomposing the total binding energy into many-body components, we find that large errors in the two-body interaction in SCAN are significantly reduced by self-interaction corrections. Higher-order many-body errors are small in both SCAN and self-interaction-corrected SCAN. These results indicate that orbital-by-orbital removal of self-interaction combined with a proper DFA can lead to improved descriptions of water complexes.

Surgical mortality in patients in extremis: futility in emergency abdominal surgery.

BACKGROUND: The number of older patients with multiple comorbidities in the emergency service is increasingly frequent, which implies the risk of incurring in futile surgical interventions. Some interventions generate false expectations of survival or quality of life in patients and families and represent a negligible therapeutic benefit in patients whose chances of survival are minimal. In order to address this dilemma, we describe mortality in a cohort of patients undergoing emergency laparotomy with a risk ≥ 75% per the ACS NSQIP Surgical Risk Calculator. METHODS: A retrospective observational study was designed to analyze postoperative mortality and factors associated with postoperative mortality in a cohort of patients undergoing emergency laparotomy between January 2018 and December 2021 in a high-complexity hospital who had a mortality risk ≥ 75% per the ACS NSQIP Surgical Risk Calculator. RESULTS: A total of 890 emergency laparotomies were performed during the study period, and 50 patients were included for the analysis. Patient median age was 82.5 (IQR: 18.25) years old and 33 (66.00%) were male. The most frequent diagnoses were mesenteric ischemia 21 (42%) and secondary peritonitis 18 (36%). Mortality in the series was 92%. Twenty-four (54.34%) died within the first 24 h of the postoperative period; 11 (23.91%) within 72 h and 10 (21.73%) within 30 days. APACHE II and SOFA scores were statistically significantly higher in patients who died. CONCLUSIONS: All available tools should be used to make decisions, with the most reliable and objective information possible, and be particularly vigilant in patients at extreme risk (mortality risk greater than 75% according to ACS NSQIP Surgical Risk Calculator) to avoid futility and its consequences. The available information should be shared with the patient, the family, or their guardians through an assertive and empathetic communication strategy. It is necessary to insist on a culture of surgical ethics based on reflection and continuous improvement in patient care and to know how to accompany them in order to have a proper death.

Impact of Rare and Common Genetic Variants on Diabetes Diagnosis by Hemoglobin A1c in Multi-Ancestry Cohorts: The Trans-Omics for Precision Medicine Program.

Hemoglobin A1c (HbA1c) is widely used to diagnose diabetes and assess glycemic control in individuals with diabetes. However, nonglycemic determinants, including genetic variation, may influence how accurately HbA1c reflects underlying glycemia. Analyzing the NHLBI Trans-Omics for Precision Medicine (TOPMed) sequence data in 10,338 individuals from five studies and four ancestries (6,158 Europeans, 3,123 African-Americans, 650 Hispanics, and 407 East Asians), we confirmed five regions associated with HbA1c (GCK in Europeans and African-Americans, HK1 in Europeans and Hispanics, FN3K and/or FN3KRP in Europeans, and G6PD in African-Americans and Hispanics) and we identified an African-ancestry-specific low-frequency variant (rs1039215 in HBG2 and HBE1, minor allele frequency (MAF) = 0.03). The most associated G6PD variant (rs1050828-T, p.Val98Met, MAF = 12% in African-Americans, MAF = 2% in Hispanics) lowered HbA1c (-0.88% in hemizygous males, -0.34% in heterozygous females) and explained 23% of HbA1c variance in African-Americans and 4% in Hispanics. Additionally, we identified a rare distinct G6PD coding variant (rs76723693, p.Leu353Pro, MAF = 0.5%; -0.98% in hemizygous males, -0.46% in heterozygous females) and detected significant association with HbA1c when aggregating rare missense variants in G6PD. We observed similar magnitude and direction of effects for rs1039215 (HBG2) and rs76723693 (G6PD) in the two largest TOPMed African American cohorts, and we replicated the rs76723693 association in the UK Biobank African-ancestry participants. These variants in G6PD and HBG2 were monomorphic in the European and Asian samples. African or Hispanic ancestry individuals carrying G6PD variants may be underdiagnosed for diabetes when screened with HbA1c. Thus, assessment of these variants should be considered for incorporation into precision medicine approaches for diabetes diagnosis.

Genetic influence on cognitive development between childhood and adulthood.

Successful cognitive development between childhood and adulthood has important consequences for future mental and physical wellbeing, as well as occupational and financial success. Therefore, delineating the genetic influences underlying changes in cognitive abilities during this developmental period will provide important insights into the biological mechanisms that govern both typical and atypical maturation. Using data from the Philadelphia Neurodevelopmental Cohort (PNC), a large population-based sample of individuals aged 8 to 21 years old (n = 6634), we used an empirical relatedness matrix to establish the heritability of general and specific cognitive functions and determine if genetic factors influence cognitive maturation (i.e., Gene × Age interactions) between childhood and early adulthood. We found that neurocognitive measures across childhood and early adulthood were significantly heritable. Moreover, genetic variance on general cognitive ability, or g, increased significantly between childhood and early adulthood. Finally, we did not find evidence for decay in genetic correlation on neurocognition throughout childhood and adulthood, suggesting that the same genetic factors underlie cognition at different ages throughout this developmental period. Establishing significant Gene × Age interactions in neurocognitive functions across childhood and early adulthood is a necessary first step in identifying genes that influence cognitive development, rather than genes that influence cognition per se. Moreover, since aberrant cognitive development confers risk for several psychiatric disorders, further examination of these Gene × Age interactions may provide important insights into their etiology.

Genetic determinants of metabolic biomarkers and their associations with cardiometabolic traits in Hispanic/Latino adolescents.

BACKGROUND: Metabolic regulation plays a significant role in energy homeostasis, and adolescence is a crucial life stage for the development of cardiometabolic disease (CMD). This study aims to investigate the genetic determinants of metabolic biomarkers-adiponectin, leptin, ghrelin, and orexin-and their associations with CMD risk factors. METHODS: We characterized the genetic determinants of the biomarkers among Hispanic/Latino adolescents of the Santiago Longitudinal Study (SLS) and identified the cumulative effects of genetic variants on adiponectin and leptin using biomarker polygenic risk scores (PRS). We further investigated the direct and indirect effect of the biomarker PRS on downstream body fat percent (BF%) and glycemic traits using structural equation modeling. RESULTS: We identified putatively novel genetic variants associated with the metabolic biomarkers. A substantial amount of biomarker variance was explained by SLS-specific PRS, and the prediction was improved by including the putatively novel loci. Fasting blood insulin and insulin resistance were associated with PRS for adiponectin, leptin, and ghrelin, and BF% was associated with PRS for adiponectin and leptin. We found evidence of substantial mediation of these associations by the biomarker levels. CONCLUSIONS: The genetic underpinnings of metabolic biomarkers can affect the early development of CMD, partly mediated by the biomarkers. IMPACT: This study characterized the genetic underpinnings of four metabolic hormones and investigated their potential influence on adiposity and insulin biology among Hispanic/Latino adolescents. Fasting blood insulin and insulin resistance were associated with polygenic risk score (PRS) for adiponectin, leptin, and ghrelin, with evidence of some degree of mediation by the biomarker levels. Body fat percent (BF%) was also associated with PRS for adiponectin and leptin. This provides important insight on biological mechanisms underlying early metabolic dysfunction and reveals candidates for prevention efforts. Our findings also highlight the importance of ancestrally diverse populations to facilitate valid studies of the genetic architecture of metabolic biomarker levels.

Synthesis, Structure, and Magnetic Properties of an Fe36 Dimethylarsinate Cluster: The Largest "Ferric Wheel".

The synthesis and characterization of a high-nuclearity FeIII/O/arsinate cluster is reported within the salt [Fe36O12(OH)6(O2AsMe2)63(O2CH)3(H2O)6](NO3)12 (1). The compound was prepared from the reaction of Fe(NO3)3·9H2O, dimethylarsinic acid (Me2AsO2H), and triethylamine in a 1:2:4 molar ratio in acetonitrile. The Fe36 cation of 1 is an unprecedented structural type consisting of nine Fe4 butterfly units of two types, three {FeIII4(µ3-O)2} units A, and six {FeIII4(µ3-O)(µ3-OH)} units B, linked by multiple bridging Me2AsO2- groups into an Fe36 triangular wheel/loop with C3 crystallographic and D3 virtual symmetry that looks like a guitar plectrum. The unusual structure has been rationalized on the basis of the different curvatures of units A and B, the presence of intra-Fe36 hydrogen bonding, and the tendency of Me2AsO2- groups to favor µ3-bridging modes. The cations stack into supramolecular nanotubes parallel to the crystallographic c axis and contain badly disordered solvent and NO3- anions. The cation of 1 is the highest-nuclearity "ferric wheel" to date and also the highest-nuclearity Fe/O cluster of any structural type with a single contiguous Fe/O core. Variable-temperature direct-current magnetic susceptibility data and alternating-current in-phase magnetic susceptibility data indicate that the cation of 1 possesses an S = 0 ground state and dominant antiferromagnetic interactions. The Fe2 pairwise Ji,j couplings were estimated by the combined use of a magnetostructural correlation for high-nuclearity FeIII/oxo clusters and density functional theory calculations using broken-symmetry methods and the Green's function approach. The three methods gave satisfyingly similar Ji,j values and allowed the identification of spin-frustration effects and the resulting relative spin-vector alignments and thus rationalization of the S = 0 ground state of the cation.

Magnetic Properties of High-Nuclearity Fex-oxo (x = 7, 22, 24) Clusters Analyzed by a Multipronged Experimental, Computational, and Magnetostructural Correlation Approach.

The synthesis, structure, and magnetic properties of three related iron(III)-oxo clusters are reported, [Fe7O3(O2CPh)9(mda)3(H2O)] (1), [Fe22O14(OH)3(O2CMe)21(mda)6](ClO4)2 (2), and [Fe24O15(OH)4(OEt)(O2CMe)21(mda)7](ClO4)2 (3), where mdaH2 is N-methyldiethanolamine. 1 was prepared from the reaction of [Fe3O(O2CPh)6(H2O)3](NO3) with mdaH2 in a 1:2 ratio in MeCN, whereas 2 and 3 were prepared from the reaction of FeCl3/NaO2CMe/mdaH2 in a 2:∼13:2 ratio and FeCl3/NaO2CMe/mdaH2/pyridine in a 2:∼13:2:25 ratio, respectively, both in EtOH. The core of 1 consists of a central octahedral FeIII ion held within a nonplanar Fe6 loop by three µ3-O2- and three µ2-RO- arms from the three mda2- chelates. The cores of the cations of 2 and 3 consist of an A:B:A three-layer topology, in which a central Fe6 (2) or Fe8 (3) layer B is sandwiched between two Fe8 layers A. The A layers structurally resemble 1 with the additional Fe added at the center to retain virtual C3 symmetry. The central Fe6 layer B of 2 consists of a {Fe4(µ4-O)2(µ3-OH)2}6+ cubane with an Fe on either side attached to cubane O2- ions, whereas that of 3 has the same cubane but with an {Fe3(µ3-O)(µ-OH)} unit attached on one side and a single Fe on the other. Variable-temperature dc and ac magnetic susceptibility studies revealed dominant antiferromagnetic coupling in all complexes leading to ground-state spins of S = 5/2 for 1 and S = 0 for 2 and 3. All Fe2 pairwise exchange parameters (Jij) for 1-3 were estimated by two independent methods: density functional theory (DFT) calculations using broken symmetry methods and a magnetostructural correlation previously developed for high-nuclearity FeIII/O complexes. The two approaches gave satisfyingly similar Jij values, and the latter allowed rationalization of the experimental ground states by identification of the spin frustration effects operative and the resultant relative spin vector alignments at each FeIII ion.

Validation of the Green's Function Approximation for the Calculation of Magnetic Exchange Couplings.

In this work, we assess the potential of the Green's function approximation to predict isotropic magnetic exchange couplings and to reproduce the standard broken-symmetry energy difference approach for transition metal complexes. To this end, we have selected a variety of heterodinuclear, homodinuclear, and polynuclear systems containing 3d transition metal centers and computed the couplings using both the Green's function and energy difference methods. The Green's function approach is shown to have mixed results for the cases tested. For dinuclear complexes with large strength couplings (≳50 cm-1), the Green's function method is unable to reliably reproduce the energy difference values. However, for weaker dinuclear couplings, the Green's function approach acceptably reproduces broken-symmetry energy difference couplings. In polynuclear cases, the Green's function approximation worked remarkably well, especially for FeIII complexes. On the other hand, for a NiII polynuclear complex, qualitatively wrong couplings are predicted. Overall, the evaluation of exchange couplings from local rigid magnetization rotations offers a powerful alternative to time-consuming energy differences methods for large polynuclear transition metal complexes, but to achieve a quantitative agreement, some improvements to the method are needed.