Synthesis and reactions of the transition metal substituted tin hydride HSn[Mo(CO)3C5H5]3

Reaction of HMo(CO)₃C₅H₅ and Sn(C₅H₅)₂ produces the tin hydride HSn[Mo(CO)₃C₅H₅]₃ (I). Reaction of I with CCl₄, CHCl₃, or CH₂Cl₂ gives ClSn[Mo(CO)₃C₅H₅]₃ (II). With hydrogen chloride the hydride I reacts to produce the dichloride Cl₂Sn[Mo(CO)₃C₅H₅]₂. The first step in this reaction is cleavage of the SnH bond to produce the chloride II. The hydride I reacts with acetic acid to produce the diacetate (CH₃COO)₂Sn[Mo(CO)₃C₅H₅]₂.     

Synthesis and Structure of a 1,3-alternate-Thiacalix[4]arene diamide Derivative

A novel receptor possessing two complexation sites and bearing 1,3-alternate conformation based on thiacalix[4]arene, confirmed by single crystal X-ray analysis, was prepared. The tetrathiacalix[4]arene diamide shows strong intramolecular hydrogen bonding. The binding behavior towards K⁺ and halides has been examined by ¹H NMR titration experiments.     

Polynomial rings over Goldie-Kerr commutative rings II

An overlooked corollary to the main result of the stated paper (Proc. Amer. Math. Soc. 120 (1994), 989--993) is that any Goldie ring of Goldie dimension 1 has Artinian classical quotient ring , hence is a Kerr ring in the sense that the polynomial ring satisfies the on annihilators . More generally, we show that a Goldie ring has Artinian when every zero divisor of has essential annihilator (in this case is a local ring; see Theorem ). A corollary to the proof is Theorem 2: A commutative ring has Artinian iff is a Goldie ring in which each element of the Jacobson radical of has essential annihilator. Applying a theorem of Beck we show that any ring that has Noetherian local ring for each associated prime is a Kerr ring and has Kerr polynomial ring (Theorem 5).

     

Exotic differentiable structures and general relativity

We review recent developments in differential topology with special concern for their possible significance to physical theories, especially general relativity. In particular we are concerned here with the discovery of the existence of non-standard (fake or exotic) differentiable structures on topologically simple manifolds such asS ⁷, ⁴ andS ³ X ¹. Because of the technical difficulties involved in the smooth case, we begin with an easily understood toy example looking at the role which the choice of complex structures plays in the formulation of two-dimensional vacuum electrostatics. We then briefly review the mathematical formalisms involved with differentiable structures on topological manifolds, diffeomorphisms and their significance for physics. We summarize the important work of Milnor, Freedman, Donaldson, and others in developing exotic differentiable structures on well known topological manifolds. Finally, we discuss some of the geometric implications of these results and propose some conjectures on possible physical implications of these new manifolds which have never before been considered as physical models.     

Photoelectron spectroscopy of phosphorus hydride anions

Negative-ion photoelectron spectroscopy is applied to the PH-, PH2-, P2H-, P2H2-, and P2H3-molecular anions. Franck-Condon simulations of the photoelectron spectra are used to analyze the spectra and to identify various P2H(n)- species. The simulations employ density-functional theory calculations of molecular geometries and vibrational frequencies and normal modes, and coupled-cluster theory calculations of electron affinities. The following electron affinities are obtained: EA0(PH) = 1.027 +/- 0.006 eV, EA0(PH2) = 1.263 +/- 0.006 eV, and EA0(P2H) = 1.514 +/- 0.010 eV. A band is identified as a mixture of trans-HPPH- and cis-HPPH-. Although the trans and cis bands cannot be definitively assigned from experimental information, using theory as a guide we obtain EA0(trans-HPPH)= 1.00 +/- 0.01 eV and EA0(cis-HPPH) = 1.03 +/- 0.01 eV. A weak feature tentatively assigned to P2H3- has a vertical detachment energy of 1.74 eV. The derived gas-phase acidity of phosphine is delta(acid)G298(PH3) < or = 1509.7 +/- 2.1 kJ mo1(-1).