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1. Bis(catecholato-κ ² O , O ′)bis(dimethyl sulfoxide-κ O )titanium(IV)

   https://doi.org/10.1107/S2056989022002638  

   Hewage, Nisansala; Mastriano, Carolyn; Brückner, Christian; Zeller, Matthias (April 2022, Acta Crystallographica Section E Crystallographic Communications)

   Bis(benzene-1,2-diolato-κ 2 O , O ′)bis(dimethyl sulfoxide-κ O )titanium(IV), [Ti(C 6 H 4 O 2 ) 2 (C 2 H 6 OS) 2 ], crystallizes with two crystallographically independent molecules in the space group P 2 1 / c emulating orthorhombic Pbca symmetry (β = 90.0445 (9)°]. The two molecules are related by pseudo-glide symmetry, broken by modulation of each one catecholate and dimethyl sulfoxide (DMSO) ligand. Twinning by pseudomerohedry was observed [twin ratio 0.5499 (7):0.4401 (7)]. Complex 3 was obtained by heating of diprotonated titanium tris-catecholate precursor 2 H in DMSO, by formal displacement of a catechol molecule by two DMSO molecules. Complex 3 is just the second heteroleptic, mono-nuclear, neutral bis-catecholate complex with TiO 6 metal coordination, the only other one being its bis-DMF analogue 6 . The two molecules of 3 exhibit a distorted octahedral geometry. The geometry and distortions from ideal symmetry of 3 are discussed and compared to 6 and to cationic tris-catecholate titanium complexes. 

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2. Crystal structures of trans -acetyldicarbonyl(η ⁵ -cyclopentadienyl)(1,3,5-triaza-7-phosphaadamantane)molybdenum(II) and trans -acetyldicarbonyl(η ⁵ -cyclopentadienyl)(3,7-diacetyl-1,3,7-triaza-5-phosphabicyclo[3.3.1]nonane)molybdenum(II)

   https://doi.org/10.1107/S2056989020003679  

   Anstey, Mitchell R.; Bost, John L.; Grumman, Anna S.; Kennedy, Nicholas D.; Whited, Matthew T. (April 2020, Acta Crystallographica Section E Crystallographic Communications)

   null (Ed.)

   The title compounds, [Mo(C 5 H 5 )(COCH 3 )(C 6 H 12 N 3 P)(CO) 2 ], (1), and [Mo(C 5 H 5 )(COCH 3 )(C 9 H 16 N 3 O 2 P)(C 6 H 5 ) 2 ))(CO) 2 ], (2), have been prepared by phosphine-induced migratory insertion from [Mo(C 5 H 5 )(CO) 3 (CH 3 )]. The molecular structures of these complexes are quite similar, exhibiting a four-legged piano-stool geometry with trans -disposed carbonyl ligands. The extended structures of complexes (1) and (2) differ substantially. For complex (1), the molybdenum acetyl unit plays a dominant role in the organization of the extended structure, joining the molecules into centrosymmetrical dimers through C—H...O interactions with a cyclopentadienyl ligand of a neighboring molecule, and these dimers are linked into layers parallel to (100) by C—H...O interactions between the molybdenum acetyl and the cyclopentadienyl ligand of another neighbor. The extended structure of (2) is dominated by C—H...O interactions involving the carbonyl groups of the acetamide groups of the DAPTA ligand, which join the molecules into centrosymmetrical dimers and link them into chains along [010]. Additional C—H...O interactions between the molybdenum acetyl oxygen atom and an acetamide methyl group join the chains into layers parallel to (101). 

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3. Vibrational Spectroscopy and Structural Analysis of V⁺(C₂H₆)_n Clusters (n = 1–4)

   https://doi.org/10.1021/acs.jpca.3c00301  

   Marcum, Jesse C; Metz, Ricardo B (June 2023, The Journal of Physical Chemistry A)

   The vibrational structure and binding motifs of vanadium cation-ethane clusters, V(+)(C2H6)n, for n = 1 – 4 are probed using infrared photodissociation spectroscopy in the C-H stretching region (2550 – 3100 cm-1). Comparison of spectra to scaled harmonic frequency spectra obtained using density functional theory suggest that ethane exhibits two primary binding motifs when interacting with the vanadium cation, an end-on 𝜂2 configuration and a side-on configuration. The lower-energy side-on configuration predominates in smaller clusters, but the end-on configuration becomes important for larger clusters as it helps to maintain a roughly square planar geometry about the central vanadium. Proximate C-H bonds exhibit elongation and large red-shifts when compared to bare ethane, particularly in the case of the side-on isomer, which are underestimated by scaled harmonic frequency calculations, demonstrating initial effects of C-H bond activation. 

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4. trans -Acetyldicarbonyl(η ⁵ -cyclopentadienyl)[tris(3,5-dimethylphenyl)phosphane-κ P ]molybdenum(II)

   https://doi.org/10.1107/S2414314617000426  

   Whited, Matthew T.; Ruffer, Eli J.; Zhang, Jia; Rabaey, Dominique J.; Janzen, Daron E. (January 2017, IUCrData)

   The title compound, [Mo(C 5 H 5 )(C 2 H 3 O)(C 24 H 27 P)(CO) 2 ], was prepared by reaction of [Mo(C 5 H 5 )(CO) 3 (CH 3 )] with tris(3,5-dimethylphenyl)phosphane. The complex exhibits a four-legged piano-stool geometry with trans -disposed acetyl and phosphane ligands. The molecular geometry is nearly identical to that of the triphenylphosphane derivative, but introduction of methyl groups on the aromatic phosphane substituents significantly impacts supramolecular organization. In the crystal, non-classical C—H...O interactions involving the acetyl carbonyl group lead to a chain motif along [010], and another set of C—H...O close contacts join inversion-related molecules. 

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5. Twistors, Self-Duality, and Spin^c Structures

   https://doi.org/10.3842/SIGMA.2021.102  

   LeBrun, Claude (November 2021, Symmetry, Integrability and Geometry: Methods and Applications)

   The fact that every compact oriented 4-manifold admits spin^c structures was proved long ago by Hirzebruch and Hopf. However, the usual proof is neither direct nor transparent. This article gives a new proof using twistor spaces that is simpler and more geometric. After using these ideas to clarify various aspects of four-dimensional geometry, we then explain how related ideas can be used to understand both spin and spin^c structures in any dimension. 

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