Probing the limit of weak host-guest interactions: insertion compounds of mercury(II) halides with microporous SiO(2) hosts

Mercury(II) halides HgX(2) (X=Cl, Br, I) were inserted into the voids of the crystalline microporous SiO(2) modifications deca-dodecasil 3R (short term: DDR), silica-theta-1 (TON), silica-ferrierite (FER) and silicalite-1 (MFI) by vapour phase loading. The properties of the occluded guest species were studied by X-ray absorption spectroscopy (X-ray absorption near-edge structure (XANES) and extended X-ray absorption fine structure (EXAFS) analysis), UV/Vis spectroscopy, and IR and Raman spectroscopy. The methods reveal the presence of HgX(2) molecules in the insertion compounds. The interactions between these electroneutral guest molecules and the electroneutral surrounding SiO(2) framework are weak. In addition, no indication of any significant guest-guest interaction between the embedded molecules was found, in contrast to the analogous iodine insertion compounds, where these become more important with increasing pore dimensionality (G. Wirnsberger et al., Angew. Chem. 1996, 108, 2951-2953; Angew. Chem. Int. Ed. Engl. 1996, 35, 2777). Analysis of the HgL(3) EXAFS confirms a coordination number of two for Hg and gives HgX bond lengths of 2.26 +/- 0.02, 2.38 +/- 0.02 and 2.57 +/- 0.02 A for the trapped HgCl(2), HgBr(2) and HgI(2) molecules, respectively. These values are very close to those of the corresponding molecules in the vapour phase and are the shortest determined for HgX(2) molecules in solid-state compounds to date (a comparably short distance only appears in the recently reported [Cu(2-pyrazinecarboxylato)(2)HgI(2)] x HgI(2) with d(Hg[bond]I)=2.577(2) A; Dong et al., Angew. Chem. 2000, 112, 4441-4443; Angew. Chem. Int. Ed. 2000, 39, 4271). Thus, there emerges a picture of almost unperturbed HgX(2) molecules, similar to those in the vapour phase or in non-coordinating solvents, in a solid crystalline matrix of high temperature stability, a very unusual state of matter. Despite the weakness of the host-guest interactions, investigations on small crystallites of the HgX(2)-TON composites using a Raman microscope show a strong polarization dependence, providing evidence for an orientational alignment of the HgX(2) molecules inside the one-dimensional pore system of this host. For these reasons, the host matrices used in this study can be viewed as orienting solid solvents, coordinating only very weakly to the inserted HgX(2) guest molecules, but exhibiting a strong geometrical template function for their alignment. The concept of using electroneutral SiO(2) modifications as host components for a modular construction of new host-guest compounds thus allows the designed construction of ordered guest assemblies, with the pore systems of the rigid host matrices acting as space-confining and ordering templates for the guest components.     

The discretized flow on domains of attraction: a structural stability result

It is well known that, for stepsize sufficiently small, compactattractors of ordinary differential equations persist underdiscretization. The present paper describes the structure ofthe discrete-time dynamical system obtained via discretizationon A(M_h)\M_h where M_h is the approximate attractor and A(M_h)is its domain of attraction. The existence of a smooth embeddinginto a continuous-time parallelizable flow is proved. The constructioncan be used to define sections for discretizations and can beinterpreted as a justification of the method of modified equations.