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.     

Catalytic transesterification of dialkyl phosphates by a bioinspired dicopper(II) macrocyclic complex

For a number of phosphoryltransfer enzymes, including the exonuclease subunit of DNA polymerase I, a mechanism involving two-metal ions and double Lewis-acid activation of the substrate, combined with leaving group stabilization, has been proposed. Inspired by the active site structure of this enzyme, we have designed as a synthetic phosphoryl transfer catalyst the dicopper(II) macrocyclic complex LCu(2). Crystal structures of complexes [(L)Cu(2)(mu-NO(3))(NO(3))](NO(3))(2) (1), [(L)Cu(2)(mu-CO(3))(CH(3)OH)](BF(4))(2) (2), and [(L)Cu(2)(mu-O(2)P(OCH(3))(2))(NO(3))](NO(3))(2) (3) illustrate various possibilities for the interaction of oxoanions with the dicopper(II) site. 1 efficiently promotes the transesterification of dimethyl phosphate (DMP) in CD(3)OD, k(cat) = 2 x 10(-)(4) s(-)(1) at 55 degrees C. 1 is the only available catalyst for the smooth transesterification of highly inert simple dialkyl phosphates. From photometric titrations and the pH dependence of reactivity, we conclude that a complex [(L)Cu(2)(DMP)(OCH(3))](2+) is the reactive species. Steric bulk at the -OR substituents of phosphodiester substrates O(2)P(OR)(2)(-) drastically reduces the reactivity of 1. This is explained with -OR leaving group stabilization by Cu coordination, an interaction which is sensitive to steric crowding at the alpha-C-atom of substituent R. A proposed reaction mechanism related to that of the exonuclease unit of DNA polymerase I is supported by DFT calculations on reaction intermediates. The complex [(L)Cu(3)(mu(3)-OH)(mu-CH(3)O)(2)(CH(3)CN)(2)](ClO(4))(3) (4) incorporates a [Cu(OH)(OCH(3))(2)(CH(3)CN)(2)](-) complex anion, which might be considered as an analogue of the [PO(2)(OCH(3))(2)(OCD(3))](2)(-) transition state (or intermediate) of DMP transesterification catalyzed by LCu(2).     

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).     

Light induced refractive index changes in PMMA films doped with styrene

Solutions of poly(methyl methacrylate) in styrene are used to produce thin polymer films (1m–20m) saturated with styrene monomer. In the illuminated areas refractive index changes up to 10^–2 are achieved by photoinduced polymerisation. The index patterns may be fixed by annealing treatments removing the residual monomer.We thank P. Hertel, M. Kopietz, M. D. Lechner and D. Steinmeier for valuable discussions. Financial support of the Stiftung Volkswagenwerk is gratefully acknowledged.