Finitely Generated Groups Are Universal

Universality has been an important concept in computable structure theory. A class $\mathcal{C}$ of structures is universal if, informally, for any structure, of any kind, there is a structure in $\mathcal{C}$ 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

M−X···X‘−C Halogen-Bonded Network Formation in MX₂(4-halopyridine)₂ Complexes (M = Pd, Pt; X = Cl, I; X‘ = Cl, Br, I)

The syntheses and crystal structures of five compounds, trans-[MCl2(4-Xpy)2] (M = Pd, Pt; 4-Xpy = 4-halopyridine; X = Cl, Br) and trans-[PdI2(4-Ipy)2], are reported. All except trans-[PdCl2(4-Clpy)2] adopt crystal structures comprising 1D or 2D networks propagated via intermolecular M−X···X‘−C halogen bonds. Halogen bond geometries exhibit near linear angles (157−173°) at the organic halogen (C−X‘) and much smaller angles (85−112°) at the inorganic halogen (M−X), consistent with the behavior of these halogen environments as electrophile and nucleophile, respectively. Powder diffraction studies suggest that these compounds are polymorphic

M−X···X‘−C Halogen-Bonded Network Formation in MX₂(4-halopyridine)₂ Complexes (M = Pd, Pt; X = Cl, I; X‘ = Cl, Br, I)

The syntheses and crystal structures of five compounds, trans-[MCl2(4-Xpy)2] (M = Pd, Pt; 4-Xpy = 4-halopyridine; X = Cl, Br) and trans-[PdI2(4-Ipy)2], are reported. All except trans-[PdCl2(4-Clpy)2] adopt crystal structures comprising 1D or 2D networks propagated via intermolecular M−X···X‘−C halogen bonds. Halogen bond geometries exhibit near linear angles (157−173°) at the organic halogen (C−X‘) and much smaller angles (85−112°) at the inorganic halogen (M−X), consistent with the behavior of these halogen environments as electrophile and nucleophile, respectively. Powder diffraction studies suggest that these compounds are polymorphic

Supramolecular Chemistry of Halogens: Complementary Features of Inorganic (M−X) and Organic (C−X‘) Halogens Applied to M−X···X‘−C Halogen Bond Formation

Electronic differences between inorganic (M−X) and organic (C−X) halogens in conjunction with the anisotropic charge distribution associated with terminal halogens have been exploited in supramolecular synthesis based upon intermolecular M−X···X‘−C halogen bonds. The synthesis and crystal structures of a family of compounds trans-[MCl2(NC5H4X-3)2] (M = Pd(II), Pt(II); X = F, Cl, Br, I; NC5H4X-3 = 3-halopyridine) are reported. With the exception of the fluoropyridine compounds, network structures propagated by M−Cl···X−C halogen bonds are adopted and involve all M−Cl and all C−X groups. M−Cl···X−C interactions show Cl···X separations shorter than van der Waals values, shorter distances being observed for heavier halogens (X). Geometries with near linear Cl···X−C angles (155−172°) and markedly bent M−Cl···X angles (92−137°) are consistently observed. DFT calculations on the model dimers {trans-[MCl2(NH3)(NC5H4X-3)]}2 show association through M−Cl···X−C (X ≠ F) interactions with geometries similar to experimental values. DFT calculations of the electrostatic potential distributions for the compounds trans-[PdCl2(NC5H4X-3)2] (X = F, Cl, Br, I) demonstrate the effectiveness of the strategy to activate C−X groups toward halogen bond formation by enhancing their electrophilicity, and explain the absence of M−Cl···F−C interactions. The M−Cl···X−C halogen bonds described here can be viewed unambiguously as nucleophile−electrophile interactions that involve an attractive electrostatic contribution. This contrasts with some types of halogen−halogen interactions previously described and suggests that M−Cl···X−C halogen bonds could provide a valuable new synthon for supramolecular chemists

Self-Assembly of 1-D Chains of Different Topologies Using the Hydrogen-Bonded Inorganic Supramolecular Synthons N−H···Cl₂M or N−H···Cl₃M

Self-Assembly of 1-D Chains of Different Topologies Using the Hydrogen-Bonded Inorganic Supramolecular Synthons N−H···Cl2M or N−H···Cl3

Self-Assembly of 1-D Chains of Different Topologies Using the Hydrogen-Bonded Inorganic Supramolecular Synthons N−H···Cl₂M or N−H···Cl₃M

Self-Assembly of 1-D Chains of Different Topologies Using the Hydrogen-Bonded Inorganic Supramolecular Synthons N−H···Cl2M or N−H···Cl3

Self-Assembly of 1-D Chains of Different Topologies Using the Hydrogen-Bonded Inorganic Supramolecular Synthons N−H···Cl₂M or N−H···Cl₃M

Self-Assembly of 1-D Chains of Different Topologies Using the Hydrogen-Bonded Inorganic Supramolecular Synthons N−H···Cl2M or N−H···Cl3

Self-Assembly of 1-D Chains of Different Topologies Using the Hydrogen-Bonded Inorganic Supramolecular Synthons N−H···Cl₂M or N−H···Cl₃M

Self-Assembly of 1-D Chains of Different Topologies Using the Hydrogen-Bonded Inorganic Supramolecular Synthons N−H···Cl2M or N−H···Cl3

Supramolecular Chemistry of Halogens: Complementary Features of Inorganic (M−X) and Organic (C−X‘) Halogens Applied to M−X···X‘−C Halogen Bond Formation

Electronic differences between inorganic (M−X) and organic (C−X) halogens in conjunction with the anisotropic charge distribution associated with terminal halogens have been exploited in supramolecular synthesis based upon intermolecular M−X···X‘−C halogen bonds. The synthesis and crystal structures of a family of compounds trans-[MCl2(NC5H4X-3)2] (M = Pd(II), Pt(II); X = F, Cl, Br, I; NC5H4X-3 = 3-halopyridine) are reported. With the exception of the fluoropyridine compounds, network structures propagated by M−Cl···X−C halogen bonds are adopted and involve all M−Cl and all C−X groups. M−Cl···X−C interactions show Cl···X separations shorter than van der Waals values, shorter distances being observed for heavier halogens (X). Geometries with near linear Cl···X−C angles (155−172°) and markedly bent M−Cl···X angles (92−137°) are consistently observed. DFT calculations on the model dimers {trans-[MCl2(NH3)(NC5H4X-3)]}2 show association through M−Cl···X−C (X ≠ F) interactions with geometries similar to experimental values. DFT calculations of the electrostatic potential distributions for the compounds trans-[PdCl2(NC5H4X-3)2] (X = F, Cl, Br, I) demonstrate the effectiveness of the strategy to activate C−X groups toward halogen bond formation by enhancing their electrophilicity, and explain the absence of M−Cl···F−C interactions. The M−Cl···X−C halogen bonds described here can be viewed unambiguously as nucleophile−electrophile interactions that involve an attractive electrostatic contribution. This contrasts with some types of halogen−halogen interactions previously described and suggests that M−Cl···X−C halogen bonds could provide a valuable new synthon for supramolecular chemists

RuH₃(SiCl₂Me)(PPh₃)₃: A Trihydridosilylruthenium Complex with Three Nonclassical Ru−H···Si Interactions

The reaction of RuCl2(PPh3)3 with HSiMeCl2 in hexanes at 65 °C produced the trihydridosilylruthenium complex RuH3(SiMeCl2)(PPh3)3 (1). In the 1H{31P} NMR spectrum of 1, the ruthenium hydrides were observed at −9.76 ppm as a singlet with 29Si satellites (JSiH = 39.7 Hz), indicating the presence of nonclassical Ru···H···Si interactions. These nonclassical interactions were confirmed by a single-crystal X-ray diffraction study of 1. The silyl and phosphine groups occupy a tetrahedral arrangement around ruthenium, with the hydrides capping the faces defined by the silyl and two phosphines groups. Complex 1 exhibited a short Ru−Si bond (2.2760(4) Å) with three normal Ru−H distances (ca. 1.6 Å) and three long Si···H interactions (ca. 1.9 Å). The Ru−H and Si···H distances are consistent with interligand hypervalent interaction (IHI) theory in which Ru−H electron density is donated to Si−halogen σ* orbitals, giving rise to Ru−H···Si interactions. Differences between the three Si···H separations in the solid state reflect the asymmetry in the substituent pattern at silicon and are further reinforced by the extent to which the hydride ligands (and one chloride substituent) engage in weak hydrogen bonds with the ortho hydrogens of the phenyl groups