A Spatial Approach to Mereology

When do several objects compose a further object? The last twenty years have seen a great deal of discussion of this question. According to the most popular view on the market, there is a physical object composed of your brain and Jeremy Bentham’s body. According to the second-most popular view on the market, there are no such objects as human brains or human bodies, and there are also no atoms, rocks, tables, or stars. And according to the third-ranked view, there are human bodies, but still no brains, atoms, rocks, tables, or stars. Although it’s pleasant to have so many crazy-sounding views around, I think it would also be nice to have a commonsense option available. The aim of this paper is to offer such an option. The approach I offer begins by considering a mereological question other than the standard one that has been the focus of most discussions in the literature. I try to show that the road to mereological sanity begins with giving the most straightforward and commonsensical answer to this other question, and then extending that answer to further questions about the mereology of physical objects. On the approach I am recommending, it turns out that all of the mereological properties and relations of physical objects are determined by their spatial properties and relations

Reaction Pathways for Addition of H₂ to Amido-Ditetrylynes R₂N–EE–NR₂ (E = Si, Ge, Sn). A Theoretical Study

Quantum chemical calculations of the reaction profiles for addition of one and two H₂ molecules to amido-substituted ditetrylynes have been carried using density functional theory at the BP86/def2-TZVPP//BP86/def2-TZVPP level of theory for the model systems L′EEL′ and BP86/def2-TZVPP//BP86/def-SVP for the real compounds. The hydrogenation of the digermyne LGeGeL (L = N­(SiMe₃)­Ar*; Ar* = C₆H₂Me­{C­(H)­Ph₂}₂-4,2,6) follows a stepwise reaction course. The addition of the first H₂ gives the singly bridged species LGe­(μ-H)­GeHL, which rearranges with very low activation barriers to the symmetrically hydrogenated compound LHGeGeHL and to the most stable isomer LGeGe­(H)₂L, which is experimentally observed. The addition of the second H₂ proceeds with a higher activation energy under rupture of the Ge–Ge bond, yielding LGeH and LGeH₃ as reaction products. Energy calculations which consider dispersion interactions using Grimme’s D3 term suggest that the latter reaction is thermodynamically unfavorable. The second hydrogenation reaction LGeGe­(H)₂L → L­(H)₂GeGe­(H)₂L possesses an even higher activation barrier than the bond-breaking hydrogenation step. Further calculations which consider solvent effects change the theoretically predicted reaction profile very little. The calculations of the model system L′GeGeL′ (L′ = NMe₂) give a very similar reaction profile. Calculations of the model disilyne and distannyne homologues L′SiSiL′ and L′SnSnL′ suggest that the reactivity of the amido-substituted ditetrylynes always has the order Si > Ge > Sn. The most stable product of the addition of one H₂ to the distannyne L′SnSnL′ is the doubly bridged species L′Sn­(μ-H)₂SnL′, which has been experimentally observed when bulky groups are employed. Analysis of the H₂–L′EEL′ interactions in the transition state for the addition of the first H₂ with the EDA-NOCV method reveals that the HOMO–LUMO and LUMO–HOMO interactions have similar magnitudes

Low Coordinate Germanium(II) and Tin(II) Hydride Complexes: Efficient Catalysts for the Hydroboration of Carbonyl Compounds

This study details the first use of well-defined low-valent p-block metal hydrides as catalysts in organic synthesis. That is, the bulky, two-coordinate germanium­(II) and tin­(II) hydride complexes, L^†(H)­M: (M = Ge or Sn, L^† = −N­(Ar^†)­(SiPrⁱ₃), Ar^† = C₆H₂{C­(H)­Ph₂}₂Pr^<i>i</i>-2,6,4), are shown to act as efficient catalysts for the hydroboration (with HBpin, pin = pinacolato) of a variety of unactivated, and sometimes very bulky, carbonyl compounds. Catalyst loadings as low as 0.05 mol % are required to achieve quantitative conversions, with turnover frequencies in excess of 13 300 h^–1 in some cases. This activity rivals that of currently available catalysts used for such reactions

Low Coordinate Germanium(II) and Tin(II) Hydride Complexes: Efficient Catalysts for the Hydroboration of Carbonyl Compounds

This study details the first use of well-defined low-valent p-block metal hydrides as catalysts in organic synthesis. That is, the bulky, two-coordinate germanium­(II) and tin­(II) hydride complexes, L^†(H)­M: (M = Ge or Sn, L^† = −N­(Ar^†)­(SiPrⁱ₃), Ar^† = C₆H₂{C­(H)­Ph₂}₂Pr^<i>i</i>-2,6,4), are shown to act as efficient catalysts for the hydroboration (with HBpin, pin = pinacolato) of a variety of unactivated, and sometimes very bulky, carbonyl compounds. Catalyst loadings as low as 0.05 mol % are required to achieve quantitative conversions, with turnover frequencies in excess of 13 300 h^–1 in some cases. This activity rivals that of currently available catalysts used for such reactions

Reactivity of Amido-Digermynes, LGeGeL (L = Bulky Amide), toward Olefins and Related Molecules: Facile Reduction, C–H Activation, and Reversible Cycloaddition of Unsaturated Substrates

Reactions of two sterically hindered amido-digermynes, L*GeGeL* (<b>1</b>; L* = −N­(Ar*)­(SiMe₃); Ar* = C₆H₂Me­{C­(H)­Ph₂}₂-4,2,6) and L^†GeGeL^† (<b>2</b>; L^† = −N­(Ar^†)­(SiPr^<i>i</i>₃); Ar^† = C₆H₂Pr^<i>i</i>{C­(H)­Ph₂}₂-4,2,6), with a variety of olefins and related molecules are investigated. These lead to the facile reduction, C–H activation, dehydrogenation, and/or cycloaddition of the unsaturated substrate. Specifically, reaction of L^†GeGeL^† with ethylene proceeds via a formal [2 + 2 + 2] cycloaddition to give the digermabicyclo[2.2.0]­hexane L^†Ge­(μ-C₂H₄)₂GeL^† (<b>3</b>). In contrast, treating L^†GeGeL^† with norbornadiene proceeds via reductive insertion of one olefin moiety of the organic substrate into the Ge–Ge bond of <b>1</b>, yielding the norbornenediyl-bridged bis­(germylene) L^†Ge­(μ-C₇H₈)­GeL^† (<b>4</b>). Similarly, L*GeGeL* doubly reduces cyclooctatetraene (COT) to give the planar cyclooctateraenediyl inverse sandwich complex L*Ge­(μ-η²,η²-COT)­GeL* (<b>5</b>). An indication that this reaction occurs via an initial formal [2 + 2] cycloaddition intermediate comes from the reaction of L^†GeGeL^† with 1,5-cyclooctadiene (COD). This affords the [2 + 2] cycloaddition product L^†Ge­(COD)GeL^† (<b>6</b>), which exists in solution in equilibrium with <b>2</b> and free COD. A computational study indicates that <b>6</b> readily dissociates, as the reaction that gave it is close to thermoneutral. Reaction of 1,3-cyclohexadiene (1,3-CHD) with L^†GeGeL^† yields the 1,4-bis­(germylene) substituted cyclohex-2-enediyl L^†Ge­(μ-C₆H₈)­GeL^† (<b>7</b>), which is an isolated intermediate in the transfer hydrogenation, or C–H activation, reaction between L^†GeGeL^† and 1,3-CHD. Heating <b>7</b> gives benzene and the known digermene L^†(H)­GeGe­(H)­L^†. Reactions of <b>1</b> or <b>2</b> with propyne, bis­(trimethylsilyl)­butadiyne, and azobenzene all lead to reductive insertion of the unsaturated substrate into the Ge–Ge bond of the digermyne and formation of L^†Ge­{μ-HCC­(Me)}­GeL^† (<b>8</b>), L*Ge­{μ-(Me₃Si)­CC­(CCSiMe₃)}­GeL* (<b>9</b>), and L*Ge­{μ-(Ph)­NN­(Ph)}­GeL* (<b>10</b>), respectively. The reaction of 4-dimethylaminopyridine (DMAP) with L*GeGeL* gives the adduct complex L*­(DMAP)­GeGe­(DMAP)­L* (<b>11</b>). Taken as a whole, this study highlights both similarities and significant differences between the reactivities of the amido-digermynes <b>1</b> and <b>2</b> and those of their previously described terphenyl-substituted counterparts

Reactivity of Amido-Digermynes, LGeGeL (L = Bulky Amide), toward Olefins and Related Molecules: Facile Reduction, C–H Activation, and Reversible Cycloaddition of Unsaturated Substrates

Reactions of two sterically hindered amido-digermynes, L*GeGeL* (<b>1</b>; L* = −N­(Ar*)­(SiMe₃); Ar* = C₆H₂Me­{C­(H)­Ph₂}₂-4,2,6) and L^†GeGeL^† (<b>2</b>; L^† = −N­(Ar^†)­(SiPr^<i>i</i>₃); Ar^† = C₆H₂Pr^<i>i</i>{C­(H)­Ph₂}₂-4,2,6), with a variety of olefins and related molecules are investigated. These lead to the facile reduction, C–H activation, dehydrogenation, and/or cycloaddition of the unsaturated substrate. Specifically, reaction of L^†GeGeL^† with ethylene proceeds via a formal [2 + 2 + 2] cycloaddition to give the digermabicyclo[2.2.0]­hexane L^†Ge­(μ-C₂H₄)₂GeL^† (<b>3</b>). In contrast, treating L^†GeGeL^† with norbornadiene proceeds via reductive insertion of one olefin moiety of the organic substrate into the Ge–Ge bond of <b>1</b>, yielding the norbornenediyl-bridged bis­(germylene) L^†Ge­(μ-C₇H₈)­GeL^† (<b>4</b>). Similarly, L*GeGeL* doubly reduces cyclooctatetraene (COT) to give the planar cyclooctateraenediyl inverse sandwich complex L*Ge­(μ-η²,η²-COT)­GeL* (<b>5</b>). An indication that this reaction occurs via an initial formal [2 + 2] cycloaddition intermediate comes from the reaction of L^†GeGeL^† with 1,5-cyclooctadiene (COD). This affords the [2 + 2] cycloaddition product L^†Ge­(COD)GeL^† (<b>6</b>), which exists in solution in equilibrium with <b>2</b> and free COD. A computational study indicates that <b>6</b> readily dissociates, as the reaction that gave it is close to thermoneutral. Reaction of 1,3-cyclohexadiene (1,3-CHD) with L^†GeGeL^† yields the 1,4-bis­(germylene) substituted cyclohex-2-enediyl L^†Ge­(μ-C₆H₈)­GeL^† (<b>7</b>), which is an isolated intermediate in the transfer hydrogenation, or C–H activation, reaction between L^†GeGeL^† and 1,3-CHD. Heating <b>7</b> gives benzene and the known digermene L^†(H)­GeGe­(H)­L^†. Reactions of <b>1</b> or <b>2</b> with propyne, bis­(trimethylsilyl)­butadiyne, and azobenzene all lead to reductive insertion of the unsaturated substrate into the Ge–Ge bond of the digermyne and formation of L^†Ge­{μ-HCC­(Me)}­GeL^† (<b>8</b>), L*Ge­{μ-(Me₃Si)­CC­(CCSiMe₃)}­GeL* (<b>9</b>), and L*Ge­{μ-(Ph)­NN­(Ph)}­GeL* (<b>10</b>), respectively. The reaction of 4-dimethylaminopyridine (DMAP) with L*GeGeL* gives the adduct complex L*­(DMAP)­GeGe­(DMAP)­L* (<b>11</b>). Taken as a whole, this study highlights both similarities and significant differences between the reactivities of the amido-digermynes <b>1</b> and <b>2</b> and those of their previously described terphenyl-substituted counterparts

Formation of a 1,4-Diamino-2,3-disila-1,3-butadiene Derivative

A 1,4-diamino-2,3-disila-1,3-butadiene derivative of composition (Me₂-cAAC)₂(Si₂Cl₂) (Me₂-cAAC = :C­(CMe₂)₂(CH₂)­N-2,6-<i>i</i>Pr₂C₆H₃) was synthesized by reduction of the Me₂-cAAC:SiCl₄ adduct with KC₈. This compound is stable at 0 °C for 3 months in an inert atmosphere. Theoretical studies reveal that the silicon atoms exhibit pyramidal coordination, where the Cl–Si–Si–Cl dihedral angle is twisted by 43.3° (calcd 45.9°). The two silicon–carbon bonds are intermediates between single and double Si–C bonds due to twisting of the C–Si–Si–C dihedral angle (163.6°)

Formation of a 1,4-Diamino-2,3-disila-1,3-butadiene Derivative

A 1,4-diamino-2,3-disila-1,3-butadiene derivative of composition (Me₂-cAAC)₂(Si₂Cl₂) (Me₂-cAAC = :C­(CMe₂)₂(CH₂)­N-2,6-<i>i</i>Pr₂C₆H₃) was synthesized by reduction of the Me₂-cAAC:SiCl₄ adduct with KC₈. This compound is stable at 0 °C for 3 months in an inert atmosphere. Theoretical studies reveal that the silicon atoms exhibit pyramidal coordination, where the Cl–Si–Si–Cl dihedral angle is twisted by 43.3° (calcd 45.9°). The two silicon–carbon bonds are intermediates between single and double Si–C bonds due to twisting of the C–Si–Si–C dihedral angle (163.6°)

Formation of a 1,4-Diamino-2,3-disila-1,3-butadiene Derivative

A 1,4-diamino-2,3-disila-1,3-butadiene derivative of composition (Me₂-cAAC)₂(Si₂Cl₂) (Me₂-cAAC = :C­(CMe₂)₂(CH₂)­N-2,6-<i>i</i>Pr₂C₆H₃) was synthesized by reduction of the Me₂-cAAC:SiCl₄ adduct with KC₈. This compound is stable at 0 °C for 3 months in an inert atmosphere. Theoretical studies reveal that the silicon atoms exhibit pyramidal coordination, where the Cl–Si–Si–Cl dihedral angle is twisted by 43.3° (calcd 45.9°). The two silicon–carbon bonds are intermediates between single and double Si–C bonds due to twisting of the C–Si–Si–C dihedral angle (163.6°)

Additional file 1 of Alterations in trimethylamine-N-oxide in response to Empagliflozin therapy: a secondary analysis of the EMMY trial

Additional file 1: Fig. S1. Distribution of untransformed TMAO concentration (μmol/L) by treatment groups at A—baseline, B—6 weeks, and C—26 weeks. Table S1. LDL-C levels over visits by treatment groups