Eine Bemerkung zum Axiomensystem des Morgenstern/Thompson-Außenhandelsmodells

Zusammenfassung Es kann gezeigt werden, daß sich im Außenhandelsmodell vonMorgenstern/ Thompson gewisse Aussagen nicht unbedingt als Resultate aus dem vorgeschlagenen Axiomensystem ergeben. Werden diese Aussagen in das Axiomensystem aufgenommen, so bleibt das System unabhängig.

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Summary In the Open Expanding Economy Model ofMorgenstern/Thompson it can be shown that some of the statements do not follow from the axioms. Adding these statements to the given system of axioms the new system is still independent.

     

Understanding Refractive Index Changes in Homologous Series of Unbranched Organic Compounds Based on Beer's Law

Changes of the refractive index for homologous series of hydrocarbons are usually plotted versus the density. While there is a clear linear dependence for alkanes and alkenes, the linearity deteriorates for homologous series with functional groups involving heteroatoms. The slope can even become negative, e. g., for carboxylic acids. For gaining a deeper understanding and to establish a more general correlation, we reinvestigate the corresponding theories starting with the Newton-Laplace, Gladstone-Dale and the Lorentz-Lorenz rules. We revisit the concept of molar refractivity pioneered by Landolt and Brühl and show that it is closely connected with a twin of Beer's law. We conclude that the refractive index of homologues series should better be plotted versus the molar concentration of the main UV-chromophore, the C−H bond, which actually causes the refractive index changes. This new approach is not limited to alkanes and alkenes but holds for homologous series with functional groups including heteroatoms.     

Dimerization of alkynes promoted by a pincer-ligated iridium complex. C-C reductive elimination inhibited by steric crowding

The pincer-ligated species (PCP)Ir (PCP = kappa3-C6H3-2,6-(CH2PtBu2)2) is found to promote dimerization of phenylacetylene to give the enyne complex (PCP)Ir(trans-1,4-phenyl-but-3-ene-1-yne). The mechanism of this reaction is found to proceed through three steps: (i) addition of the alkynyl C-H bond to iridium, (ii) insertion of a second phenylacetylene molecule into the resulting Ir-H bond, and (iii) vinyl-acetylide reductive elimination. Each of these steps has been investigated, by both experimental and computational (DFT) methods, to yield unexpected conclusions of general interest. (i) The product of alkynyl C-H addition, (PCP)Ir(CCPh)(H) (3), has been isolated and, in accord with experimental observations, is calculated to be 29 kcal/mol more stable than the analogous product of benzene C-H addition. (ii) Insertion of a second PhCCH molecule into the Ir-H bond of 3 proceeds rapidly, but with a 1,2-orientation. This orientation gives (PCP)Ir(CCPh)(CPh=CH2) (4) which would yield the 1,3-diphenyl-enyne if it were to undergo C-C elimination; however, the insertion is reversible, which represents the first example, to our knowledge, of simple beta-H elimination from a vinyl group to give a terminal hydride. The 2,1-insertion product (PCP)Ir(CCPh)(CH=CHPh) (6) forms more slowly, but unlike the 1,2 insertion product it undergoes C-C elimination to give the observed enyne. (iii) The failure of 4 to undergo C-C elimination is found to be general for (PCP)Ir(CCPh)(vinyl) complexes in which the vinyl group has an alpha-substituent. Thus, although C-C elimination relieves crowding, the reaction is inhibited by increased crowding. Density-functional theory (DFT) calculations support this surprising conclusion and offer a clear explanation. Alkynyl-vinyl bond formation in the C-C elimination transition state involves the vinyl group pi-system; this requires that the vinyl group must rotate (around the Ir-C bond) by ca. 90 degrees to achieve an appropriate orientation. This rotation is severely inhibited by steric crowding, particularly when the vinyl group bears an alpha-substituent.     

Preparation,Crystal Structures,and Thermal Studies of Alkaline Earth Nitrocarboxylates

The preparation, crystal structures, and thermal properties of [Ca(pyr)₂(4‐nba)₂]_n ( 1 ) (pyr = pyrazole; 4‐nba = 4‐nitrobenzoate) {[Ca(H₂O)₂(3‐npth)] · H₂O}_n ( 2 ) (3‐npth = 3‐nitrophthalate), [Mg(H₂O)₅(3‐npth)] · 2H₂O ( 3 ), and [Mg(H₂O)₄(2‐nba)₂] ( 4 ) (2‐nba = 2‐nitrobenzoate) are reported. The anhydrous Ca^II compound 1 and the diaqua Ca^II‐3‐nitrophthalate monohydrate 2 are one‐dimensional coordination polymers containing a hexacoordinate Ca^II ion located on a center of inversion in 1 and a heptacoordinated Ca^II ion in 2 . In 1 , the 4‐nitrobenzoate moiety acts as a μ₂‐bridging bidentate ligand, whereas the 3‐nitrophthalate anion exhibits a μ₃‐bridging pentadentate coordination mode in 2 . The hexacoordinate Mg^II‐containing compounds 3 and 4 do not contain a [Mg(H₂O)₆]²⁺ unit and the central Mg^II ion is coordinated to at least one monodentate carboxylate unit namely the monodentate 3‐npth molecule in 3 and two trans monodentate 2‐nba molecules in 4 . Hydrogen bonding between the lattice water molecules results in the formation of a water dimer in 3 . A comparative study of 17 alkaline earth nitrocarboxylates is described.     

Synthesis and Crystal Structure of Tellurium(II) bis(2‐methoxycarbonylethanethiolate): A Novel Coordination Mode of Tellurium

The tellurium(II) dithiolates Te[SCH₂CH₂C(O)OCH₃]₂, ( 1 ), Te[SCH₂CH₂CH₂SC(O)CH₃]₂, ( 2 ), and Te[SCH₂CH₂CH₂CH₂SC(O)CH₃]₂, ( 3 ) were synthesized from Te(S^tBu)₂ and the corresponding thiol. All compounds are sensitive toward higher temperatures and light and decompose to elemental tellurium and the disulfide. In the solid state, the Te atom of 1 exhibits the novel Te(S₂Te₂) coordination mode. Additionally to the two Te—S bonds, each Te atom forms two long Te···Te contacts to neighboring molecules, leading to a coordination number of four and a distorted sawhorse configuration. No intramolecular Te···O interactions are present in the solid state, in accordance with ab initio calculations (MP2/ecp‐basis) for the isolated molecule. ¹²⁵Te NMR shifts of all compounds lay within a narrow range and close to the respective shift of other Te(SCH₂R)₂ compounds. VT ¹²⁵Te NMR spectra gave no hint to donor acceptor interactions in solution for any of the compounds and thus corroborate results from IR‐spectroscopy, ab initio geometry optimizations, and thermochemical calculations.     

On the mechanism of (PCP)Ir-catalyzed acceptorless dehydrogenation of alkanes: a combined computational and experimental study

Pincer complexes of the type ((R)PCP)IrH(2), where ((R)PCP)Ir is [eta(3)-2,6-(R(2)PCH(2))(2)C(6)H(3)]Ir, are the most effective catalysts reported to date for the "acceptorless" dehydrogenation of alkanes to yield alkenes and free H(2). We calculate (DFT/B3LYP) that associative (A) reactions of ((Me)PCP)IrH(2) with model linear (propane, n-PrH) and cyclic (cyclohexane, CyH) alkanes may proceed via classical Ir(V) and nonclassical Ir(III)(eta(2)-H(2)) intermediates. A dissociative (D) pathway proceeds via initial loss of H(2), followed by C-H addition to ((Me)PCP)Ir. Although a slightly higher energy barrier (DeltaE(+ +)) is computed for the D pathway, the calculated free-energy barrier (DeltaG(+ +)) for the D pathway is significantly lower than that of the A pathway. Under standard thermodynamic conditions (STP), C-H addition via the D pathway has DeltaG(o)(+ +) = 36.3 kcal/mol for CyH (35.1 kcal/mol for n-PrH). However, acceptorless dehydrogenation of alkanes is thermodynamically impossible at STP. At conditions under which acceptorless dehydrogenation is thermodynamically possible (for example, T = 150 degrees C and P(H)2 = 1.0 x 10(-7) atm), DeltaG(+ +) for C-H addition to ((Me)PCP)Ir (plus a molecule of free H(2)) is very low (17.5 kcal/mol for CyH, 16.7 kcal/mol for n-PrH). Under these conditions, the rate-determining step for the D pathway is the loss of H(2) from ((Me)PCP)IrH(2) with DeltaG(D)(+ +) approximately DeltaH(D)(+ +) = 27.2 kcal/mol. For CyH, the calculated DeltaG(o)(+ +) for C-H addition to ((Me)PCP)IrH(2) on the A pathway is 35.2 kcal/mol (32.7 kcal/mol for n-PrH). At catalytic conditions, the calculated free energies of C-H addition are 31.3 and 33.7 kcal/mol for CyH and n-PrH addition, respectively. Elimination of H(2) from the resulting "seven-coordinate" Ir-species must proceed with an activation enthalpy at least as large as the enthalpy change of the elimination step itself (DeltaH approximately 11-13 kcal/mol), and with a small entropy of activation. The free energy of activation for H(2) elimination (DeltaG(A)(+ +)) is hence found to be greater than ca. 36 kcal/mol for both CyH and n-PrH under catalytic conditions. The overall free-energy barrier of the A pathway is calculated to be higher than that of the D pathway by ca. 9 kcal/mol. Reversible C-H(D) addition to ((R)PCP)IrH(2) is predicted to lead to H/D exchange, because the barriers for hydride scrambling are extremely low in the "seven-coordinate" polyhydrides. In agreement with calculation, H/D exchange is observed experimentally for several deuteriohydrocarbons with the following order of rates: C(6)D(6) > mesitylene-d(12) > n-decane-d(22) > cyclohexane-d(12). Because H/D exchange in cyclohexane-d(12) solution is not observed even after 1 week at 180 degrees C, we estimate that the experimental barrier to cyclohexane C-D addition is greater than 36.4 kcal/mol. This value is considerably greater than the experimental barrier for the full catalytic dehydrogenation cycle for cycloalkanes (ca. 31 kcal/mol). Thus, the experimental evidence, in agreement with calculation, strongly indicates that the A pathway is not kinetically viable as a segment of the "acceptorless" dehydrogenation cycle.