4 research outputs found
Finitely Generated Groups Are Universal
Universality has been an important concept in computable structure theory. A
class of structures is universal if, informally, for any
structure, of any kind, there is a structure in with the same
computability-theoretic properties as the given structure. Many classes such as
graphs, groups, and fields are known to be universal.
This paper is about the class of finitely generated groups. Because finitely
generated structures are relatively simple, the class of finitely generated
groups has no hope of being universal. We show that finitely generated groups
are as universal as possible, given that they are finitely generated: for every
finitely generated structure, there is a finitely generated group which has the
same computability-theoretic properties. The same is not true for finitely
generated fields. We apply the results of this investigation to quasi Scott
sentences
Metal Hydrides Form Halogen Bonds: Measurement of Energetics of Binding
The
formation of halogen bonds from iodopentafluorobenzene and
1-iodoperfluorohexane to a series of bisÂ(η<sup>5</sup>-cyclopentadienyl)Âmetal
hydrides (Cp<sub>2</sub>TaH<sub>3</sub>, <b>1</b>; Cp<sub>2</sub>MH<sub>2</sub>, M = Mo, <b>2</b>, M = W, <b>3</b>; Cp<sub>2</sub>ReH, <b>4</b>; Cp<sub>2</sub>TaÂ(H)ÂCO, <b>5</b>; Cp = η<sup>5</sup>-cyclopentadienyl) is demonstrated by <sup>1</sup>H NMR spectroscopy. Interaction enthalpies and entropies for
complex <b>1</b> with C<sub>6</sub>F<sub>5</sub>I and C<sub>6</sub>F<sub>13</sub>I are reported (Δ<i>H</i>°
= −10.9 ± 0.4 and −11.8 ± 0.3 kJ/mol; Δ<i>S</i>° = −38 ± 2 and −34 ± 2 J/(mol·K),
respectively) and found to be stronger than those for <b>1</b> with the hydrogen-bond donor indole (Δ<i>H</i>°
= −7.3 ± 0.1 kJ/mol, Δ<i>S</i>° =
−24 ± 1 J/(mol·K)). For the more reactive complexes <b>2</b>–<b>5</b>, measurements are limited to determination
of their low-temperature (212 K) association constants with C<sub>6</sub>F<sub>5</sub>I as 2.9 ± 0.2, 2.5 ± 0.1, <1.5,
and 12.5 ± 0.3 M<sup>–1</sup>, respectively
Fe(III) Protoporphyrin IX Encapsulated in a Zinc Metal–Organic Framework Shows Dramatically Enhanced Peroxidatic Activity
Two MOFs, [H<sub>2</sub>NÂ(CH<sub>3</sub>)<sub>2</sub>]Â[Zn<sub>3</sub>(TATB)<sub>2</sub>Â(HCOO)]·HNÂ(CH<sub>3</sub>)<sub>2</sub>·DMF·6H<sub>2</sub>O (<b>1</b>) and Zn-HKUST-1 (<b>2</b>), were investigated
as potential hosts to encapsulate FeÂ(III) heme (FeÂ(III) protoporphyrin
IX = FeÂ(III)ÂPPIX). Methyl orange (MO) adsorption was used as an initial
model for substrate uptake. MOF <b>1</b> showed good adsorption
of MO (10.3 ± 0.8 mg g<sup>–1</sup>) which could undergo <i>in situ</i> protonation upon exposure to aqueous HCl vapor.
By contrast, MO uptake by <b>2</b> was much lower (2 ±
1 mg g<sup>–1</sup>), and PXRD indicated that structural instability
on exposure to water was the likely cause. Two methods for FeÂ(III)ÂPPIX-<b>1</b> preparation were investigated: soaking and encapsulation.
Encapsulation was verified by SEM-EDS and showed comparable concentrations
of FeÂ(III)ÂPPIX on exposed interior surfaces and on the original surface
of fractured crystals. SEM-EDS results were consistent with ICP-OES
data on bulk material (1.2 ± 0.1 mass % Fe). PXRD data showed
that the framework in <b>1</b> was unchanged after encapsulation
of FeÂ(III)ÂPPIX. MO adsorption (5.8 ± 1.2 mg g<sup>–1</sup>) by FeÂ(III)ÂPPIX-<b>1</b> confirmed there is space for substrate
diffusion into the framework, while the UV–vis spectrum of
solubilized crystals confirmed that FeÂ(III)ÂPPIX retained its integrity.
A solid-state UV–vis spectrum of FeÂ(III)ÂPPIX-<b>1</b> indicated that FeÂ(III)ÂPPIX was not in a μ-oxo dimeric form.
Although single-crystal XRD data did not allow for full refinement
of the encapsulated FeÂ(III)ÂPPIX molecule owing to disorder of the
metalloporphyrin, the Fe atom and pyrrole N atoms were located, enabling
rigid-body modeling of the porphine core. Reaction of 2,2′-azino-bisÂ(3-ethylbenzothiazoline)-6-sulfonic
acid (ABTS) with H<sub>2</sub>O<sub>2</sub>, catalyzed by FeÂ(III)ÂPPIX-<b>1</b> and -<b>2</b>, showed that FeÂ(III)ÂPPIX-<b>1</b> is significantly more efficient than FeÂ(III)ÂPPIX-<b>2</b> and
is superior to solid FeÂ(III)ÂPPIX-Cl. FeÂ(III)ÂPPIX-<b>1</b> was
used to catalyze the oxidation of hydroquinone, thymol, benzyl alcohol,
and phenyl ethanol by <i>tert</i>-butyl-hydroperoxide with <i>t</i><sub>1/2</sub> values that increase with increasing substrate
molecular volume