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Abstract We outline the “dark siren” galaxy catalog method for cosmological inference using gravitational wave (GW) standard sirens, clarifying some common misconceptions in the implementation of this method. When a confident transient electromagnetic counterpart to a GW event is unavailable, the identification of a unique host galaxy is in general challenging. Instead, as originally proposed by Schutz, one can consult a galaxy catalog and implement a dark siren statistical approach incorporating all potential host galaxies within the localization volume. Trott & Huterer recently claimed that this approach results in a biased estimate of the Hubble constant, H 0 , when implemented on mock data, even if optimistic assumptions are made. We demonstrate explicitly that, as previously shown by multiple independent groups, the dark siren statistical method leads to an unbiased posterior when the method is applied to the data correctly. We highlight common sources of error possible to make in the generation of mock data and implementation of the statistical framework, including the mismodeling of selection effects and inconsistent implementations of the Bayesian framework, which can lead to a spurious bias. 

Synthetic methods that utilise iron to facilitate C–H bond activation to yield new C–C and C–heteroatom bonds continue to attract significant interest. However, the development of these systems is still hampered by a limited molecular-level understanding of the key iron intermediates and reaction pathways that enable selective product formation. While recent studies have established the mechanism for iron-catalysed C–H arylation from aryl-nucleophiles, the underlying mechanistic pathway of iron-catalysed C–H activation/functionalisation systems which utilise electrophiles to establish C–C and C–heteroatom bonds has not been determined. The present study focuses on an iron-catalysed C–H allylation system, which utilises allyl chlorides as electrophiles to establish a C–allyl bond. Freeze-trapped inorganic spectroscopic methods ( 57 Fe Mössbauer, EPR, and MCD) are combined with correlated reaction studies and kinetic analyses to reveal a unique and rapid reaction pathway by which the allyl electrophile reacts with a C–H activated iron intermediate. Supporting computational analysis defines this novel reaction coordinate as an inner-sphere radical process which features a partial iron–bisphosphine dissociation. Highlighting the role of the bisphosphine in this reaction pathway, a complementary study performed on the reaction of allyl electrophile with an analogous C–H activated intermediate bearing a more rigid bisphosphine ligand exhibits stifled yield and selectivity towards allylated product. An additional spectroscopic analysis of an iron-catalysed C–H amination system, which incorporates N -chloromorpholine as the C–N bond-forming electrophile, reveals a rapid reaction of electrophile with an analogous C–H activated iron intermediate consistent with the inner-sphere radical process defined for the C–H allylation system, demonstrating the prevalence of this novel reaction coordinate in this sub-class of iron-catalysed C–H functionalisation systems. Overall, these results provide a critical mechanistic foundation for the rational design and development of improved systems that are efficient, selective, and useful across a broad range of C–H functionalisations. 

Abstract Since 2015 the gravitational-wave observations of LIGO and Virgo have transformed our understanding of compact-object binaries. In the years to come, ground-based gravitational-wave observatories such as LIGO, Virgo, and their successors will increase in sensitivity, discovering thousands of stellar-mass binaries. In the 2030s, the space-based LISA will provide gravitational-wave observations of massive black holes binaries. Between the $\sim 10$ ∼ 10 –10 3 Hz band of ground-based observatories and the $\sim 10^{-4}$ ∼ 1 0 − 4 –10 − 1 Hz band of LISA lies the uncharted decihertz gravitational-wave band. We propose a Decihertz Observatory to study this frequency range, and to complement observations made by other detectors. Decihertz observatories are well suited to observation of intermediate-mass ( $\sim 10^{2}$ ∼ 1 0 2 –10 4 M ⊙ ) black holes; they will be able to detect stellar-mass binaries days to years before they merge, providing early warning of nearby binary neutron star mergers and measurements of the eccentricity of binary black holes, and they will enable new tests of general relativity and the Standard Model of particle physics. Here we summarise how a Decihertz Observatory could provide unique insights into how black holes form and evolve across cosmic time, improve prospects for both multimessenger astronomy and multiband gravitational-wave astronomy, and enable new probes of gravity, particle physics and cosmology. 

Homoleptic σ‐bonded uranium–alkyl complexes have been a synthetic target since the Manhattan Project. The current study describes the synthesis and characterization of several unprecedented uranium–methyl complexes. Amongst these complexes, the first example of a homoleptic uranium–alkyl dimer, [Li(THF)₄]₂[U₂(CH₃)₁₀], as well as a seven‐coordinate uranium–methyl monomer, {Li(OEt₂)Li(OEt₂)₂UMe₇Li}_nwere both crystallographically identified. The diversity of complexes reported herein provides critical insight into the structural diversity, electronic structure and bonding in uranium–alkyl chemistry.

 

Homoleptic σ‐bonded uranium–alkyl complexes have been a synthetic target since the Manhattan Project. The current study describes the synthesis and characterization of several unprecedented uranium–methyl complexes. Amongst these complexes, the first example of a homoleptic uranium–alkyl dimer, [Li(THF)₄]₂[U₂(CH₃)₁₀], as well as a seven‐coordinate uranium–methyl monomer, {Li(OEt₂)Li(OEt₂)₂UMe₇Li}_nwere both crystallographically identified. The diversity of complexes reported herein provides critical insight into the structural diversity, electronic structure and bonding in uranium–alkyl chemistry.

 

The first direct syntheses, structural characterizations, and reactivity studies of multinuclear iron–phenyl species formed upon reaction of Fe(acac)₃and PhMgBr in THF are described.

 

The use ofN‐methylpyrrolidone (NMP) as a co‐solvent in ferric salt catalyzed cross‐coupling reactions is crucial for achieving the highly selective, preparative scale formation of cross‐coupled product in reactions utilizing alkyl Grignard reagents. Despite the critical importance of NMP, the molecular level effect of NMP on in situ formed and reactive iron species that enables effective catalysis remains undefined. Herein, we report the isolation and characterization of a novel trimethyliron(II) ferrate species, [Mg(NMP)₆][FeMe₃]₂(1), which forms as the major iron species in situ in reactions of Fe(acac)₃and MeMgBr under catalytically relevant conditions where NMP is employed as a co‐solvent. Importantly, combined GC analysis and⁵⁷Fe Mössbauer spectroscopic studies identified1as a highly reactive iron species for the selective formation generating cross‐coupled product. These studies demonstrate that NMP does not directly interact with iron as a ligand in catalysis but, alternatively, interacts with the magnesium cations to preferentially stabilize the formation of1over [Fe₈Me₁₂]⁻cluster generation, which occurs in the absence of NMP.

 

The use ofN‐methylpyrrolidone (NMP) as a co‐solvent in ferric salt catalyzed cross‐coupling reactions is crucial for achieving the highly selective, preparative scale formation of cross‐coupled product in reactions utilizing alkyl Grignard reagents. Despite the critical importance of NMP, the molecular level effect of NMP on in situ formed and reactive iron species that enables effective catalysis remains undefined. Herein, we report the isolation and characterization of a novel trimethyliron(II) ferrate species, [Mg(NMP)₆][FeMe₃]₂(1), which forms as the major iron species in situ in reactions of Fe(acac)₃and MeMgBr under catalytically relevant conditions where NMP is employed as a co‐solvent. Importantly, combined GC analysis and⁵⁷Fe Mössbauer spectroscopic studies identified1as a highly reactive iron species for the selective formation generating cross‐coupled product. These studies demonstrate that NMP does not directly interact with iron as a ligand in catalysis but, alternatively, interacts with the magnesium cations to preferentially stabilize the formation of1over [Fe₈Me₁₂]⁻cluster generation, which occurs in the absence of NMP.