Self-interacting scalar field cosmologies: unified exact solutions and symmetries

We investigate a mechanism that generates exact solutions of scalar field cosmologies in a unified way. The procedure investigated here permits to recover almost all known solutions, and allows one to derive new solutions as well. In particular, we derive and discuss one novel solution defined in terms of the Lambert function. The solutions are organised in a classification which depends on the choice of a generating function which we have denoted by x(phi) that reflects the underlying thermodynamics of the model. We also analyse and discuss the existence of form-invariance dualities between solutions. A general way of defining the latter in an appropriate fashion for scalar fields is put forward.

Synthesis and Coordination Chemistry of a New N-4-Polydentate Class of Pyridyl-Functionalized Scorpionate Ligands: Complexes of Fe-II, Zn-II, V-IV, Pd-II and Use for Heterobimetallic Systems

The new potentially N-4-multidentate pyridyl-functionalized scorpionates 4-((tris-2,2,2-(pyrazol-1-ypethoxy)methyl)pyridine (TpmPy, (1)) and 4-((tris-2,2,2-(3-phenylpyrazol-1-yl)ethoxy)methyl)pyridine (TpmPy(Ph), (2)) have been synthesized and their coordination behavior toward Fe-II, Ni-II, Zn-II, Cu-II, Pd-II, and V-III centers has been studied. Reaction of (1) with Fe(BF4)(2)center dot 6H(2)O yields [Fe(TpmPy)(2)](BF4)(2) (3), that, in the solid state, shows the sandwich structure with trihapto ligand coordination via the pyrazolyl arms, and is completely low spin (LS) until 400 K. Reactions of 2 equiv of (1) or (2) with Zn-II or Ni-II chlorides give the corresponding metal complexes with general formula [MCl2(TpmPy*)(2)] (M = Zn, Ni; TpmPy* = TpmPy, TpmPy(Ph)) (4-7) where the ligand is able to coordinate through either the pyrazolyl rings (in case of [Ni(TpmPy)(2)Cl-2 (5)) or the pyridyl-side (for [ZnCl2(TpmPy)(2)] (4), [ZnCl2(TpmPy(Ph))(2)] (6) and [NiCl2(TpmPy(Ph))(2)] (7)). The reaction of (1) with VCl3 gives [VOCl2(TpmPy)] (8) that shows the N-3-pyrazolyl coordination-mode. Moreover, (1) and react with cis-[PdCl2(CH3CN)(2)] to give the disubstituted complexes [PdCl2(TprnPy)(2)] (9) and [PdCl2(TpmPy(Ph))(2)] (10), respectively, bearing the scorpionate coordinated via the pyridyl group. Compounds (9) and (10) react with Fe(BF4)(2) to give the heterobimetallic Pd/Fe systems [PdCl2(mu-TpmPy)(2)-Fe](BF4)(2) (11) and [PdCl2(mu-TpmPy(Ph))(2)Fe-2(H2O)(6)]BF4)(4) (13), respectively. Compound (11) can also be formed from reaction of (3) with cis-[PdCl2(CH3CN)(2)], while reaction of (3) with Cu(NO3)(2).2.5H(2)O generates [Fe(mu-TpmPy)(2)-Cu(NO3)(2)](BF4)(2) (12), confirming the multidentate ability of the new chelating ligands. The X-ray diffraction analyses of compounds (1), (3), (4), (5), and (9) are also reported.