$\ell ^2$ decoupling in $\mathbb {R}^2$ for curves with vanishing curvature

Biswas, Chandan; Gilula, Maxim; Li, Linhan; Schwend, Jeremy; Xi, Yakun

doi:10.1090/proc/14954

The synthesis and crystal structures of two tris(trialkylsilyl)silyl bromide compounds, C 9 H 27 BrSi 4 ( I , HypSiBr) and C 27 H 63 BrSi 4 ( II , TipSiBr), are described. Compound I was prepared in 85% yield by free-radical bromination of 1,1,1,3,3,3-hexamethyl-2-(trimethylsilyl)trisilane using bromobutane and 2,2′-azobis(2-methylpropionitrile) as a radical initiator at 333 K. The molecule possesses threefold rotational symmetry, with the central Si atom and the Br atom being located on the threefold rotation axis. The Si—Br bond distance is 2.2990 (12) Å and the Si—Si bond lengths are 2.3477 (8) Å. The Br—Si—Si bond angles are 104.83 (3)° and the Si—Si—Si bond angles are 113.69 (2)°, reflecting the steric hindrance inherent in the three trimethylsilyl groups attached to the central Si atom. Compound II was prepared in 55% yield by free-radical bromination of 1,1,1,3,3,3-hexaisopropyl-2-(triisopropylsilyl)trisilane using N -bromosuccinimide and 2,2′-azobis(2-methylpropionitrile) as a radical initiator at 353 K. Here the Si—Br bond length is 2.3185 (7) Å and the Si—Si bond lengths range from 2.443 (1) to 2.4628 (9) Å. The Br—Si—Si bond angles range from 98.44 (3) to 103.77 (3)°, indicating steric hindrance between the three triisopropylsilyl groups.

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