Some Remarks on the Definition of Boltzmann, Shannon and Kolmogorov Entropy

We give an alternative definition of Shannon and Kolmogorov-Sinai entropies based on the Boltzmann formula S = k log W. We prove the equivalence of those new definitions with the traditional ones using some tools from Information Theory such as information function and empirical entropy. Lecture held in the Seminario Matematico e Fisico on November 29, 2004 Received: April 2005     

Insights into the Crystallization and Structural Evolution of Glycine Dihydrate by In Situ Solid‐State NMR Spectroscopy

In situ solid‐state NMR spectroscopy is exploited to monitor the structural evolution of a glycine/water glass phase formed on flash cooling an aqueous solution of glycine, with a range of modern solid‐state NMR methods applied to elucidate structural properties of the solid phases present. The glycine/water glass is shown to crystallize into an intermediate phase, which then transforms to the β polymorph of glycine. Our in situ NMR results fully corroborate the identity of the intermediate crystalline phase as glycine dihydrate, which was first proposed only very recently.     

2‐(4′‐Pyridyl‐N‐oxide)‐Substituted Hemithioindigos as Photoresponsive Guests for a Super Aryl‐Extended Calix[4]pyrrole Receptor

We report the synthesis of two 2‐(4′‐pyridyl‐N‐oxide)‐substituted hemithioindigos (HTIs). We probed their photoisomerization by using UV/Vis and ¹H NMR spectroscopy techniques. Light irradiation at λ=450 nm provoked the isomerization of the HTI Z isomer to the E counterpart to a large extent (≈80 % at the photostationary state). ¹H NMR titration experiments revealed the formation of thermodynamically and kinetically stable 1:1 inclusion complexes of the (Z)‐HTI isomers with a super aryl‐extended host (association constant>10⁴ m ^?1). Photoirradiation at λ=450 nm of the inclusion complexes induced the isomerization of the bound HTI N‐oxide to afford the (E)‐HTI?calix[4]pyrrole complex. We determined accurate association constant values for the 1:1 inclusion complexes of the (Z)‐ and (E)‐HTI isomers by using isothermal titration calorimetry experiments. The results showed that the stability constants of the (E)‐HTI complexes were 2.2–2.8‐fold lower than those of the (Z)‐HTI counterparts, which explains the lack of light‐induced release of the former to the bulk solution.     

Separation of intact proteins on γ‐ray‐induced polymethacrylate monolithic columns: A highly permeable stationary phase with high peak capacity for capillary high‐performance liquid chromatography with high‐resolution mass spectrometry

Polymethacrylate‐based monolithic capillary columns, prepared by γ‐radiation‐induced polymerization, were used to optimize the experimental conditions (nature of the organic modifiers, the content of trifluoroacetic acid and the column temperature) in the separation of nine standard proteins with different hydrophobicities and a wide range of molecular weights. Because of the excellent permeability of the monolithic columns, an ion‐pair reversed‐phase capillary liquid chromatography with high‐resolution mass spectrometry method has been developed by coupling the column directly to the mass spectrometer without a flow‐split and using a standard electrospray interface. Additionally, the high working flow and concomitant high efficiency of these columns allowed us to employ a longer column (up to 50 cm) and achieve a peak capacity value superior to 1000. This work is motivated by the need to develop new materials for high‐resolution chromatographic separation that combine chemical stability at elevated temperatures (up to 75°C) and a broad pH range, with a high peak capacity value. The advantage of the γ‐ray‐induced monolithic column lies in the batch‐to‐batch reproducibility and long‐term high‐temperature stability. Their proven high loading capacity, recovery, good selectivity and high permeability, moreover, compared well with that of a commercially available poly(styrene‐divinylbenzene) monolithic column, which confirms that such monolithic supports might facilitate analysis in proteomics.     

Magnetic “Molecular Oligomers” Based on Decametallic Supertetrahedra: A Giant Mn49 Cuboctahedron and its Mn25Na4 Fragment

Two nanosized Mn₄₉ and Mn₂₅Na₄ clusters based on analogues of the high‐spin (S=22) [Mn^III₆Mn^II₄(μ₄‐O)₄]¹⁸⁺ supertetrahedral core are reported. Mn₄₉ and Mn₂₅Na₄ complexes consist of eight and four decametallic supertetrahedral subunits, respectively, display high virtual symmetry (O_h), and are unique examples of clusters based on a large number of tightly linked high nuclearity magnetic units. The complexes also have large spin ground‐state values (Mn₄₉: S=61/2; Mn₂₅Na₄: S=51/2) with the Mn₄₉ cluster displaying single‐molecule magnet (SMM) behavior and being the second largest reported homometallic SMM.     

Synthesis of Bioctacene-Incorporated Nanographene with Near-Infrared Chiroptical Properties

We report the synthesis of a hexabenzoperihexacene (HBPH) with two incorporated octacene substructures, which was unambiguously characterized by single-crystal X-ray analysis. The theoretical isomerization barrier of the (P,P)-/(P,M)-forms was estimated to be 38.4 kcal mol⁻¹, and resolution was achieved by chiral HPLC. Notably, the enantiomers exhibited opposite circular dichroism responses up to the near-infrared (NIR) region (830 nm) with a high g_abs value of 0.017 at 616 nm. Moreover, HBPH demonstrated NIR emission with a maximum at 798 nm and an absolute PLQY of 41 %. The excited-state photophysical properties of HBPH were investigated by ultrafast transient absorption spectroscopy, revealing an intriguing feature that was attributed to the rotational and/or conformational dynamics of HBPH after excitation. These results provide new insight into the design of chiral nanographene with NIR optical properties for potential chiroptical applications.     

Combining Solid-State NMR with Structural and Biophysical Techniques to Design Challenging Protein-Drug Conjugates

Several protein-drug conjugates are currently being used in cancer therapy. These conjugates rely on cytotoxic organic compounds that are covalently attached to the carrier proteins or that interact with them via non-covalent interactions. Human transthyretin (TTR), a physiological protein, has already been identified as a possible carrier protein for the delivery of cytotoxic drugs. Here we show the structure-guided development of a new stable cytotoxic molecule based on a known strong binder of TTR and a well-established anticancer drug. This example is used to demonstrate the importance of the integration of multiple biophysical and structural techniques, encompassing microscale thermophoresis, X-ray crystallography and NMR. In particular, we show that solid-state NMR has the ability to reveal effects caused by ligand binding which are more easily relatable to structural and dynamical alterations that impact the stability of macromolecular complexes.     

Stereoselective dimerization of racemic C3-symmetric Ti(IV) amine triphenolate complexes

A novel, mononuclear Ti(IV) amine triphenolate complex obtained by reaction of Ti(OiPr)(4) with tris(2-hydroxy-3-phenylbenzyl)amine bearing phenyl ortho-substituents affords quantitatively and spontaneously the corresponding heterochiral micro-oxo dinuclear compound whereas an analogous chiral, enantiopure complex maintains its mononuclear structure even in the presence of an excess of water.     

Manganese(II) pyrimidine-4,6-dicarboxylates: synthetic, structural, magnetic, and adsorption insights

A series of manganese(II) coordination polymers containing the bridging ligand pyrimidine-4,6-dicarboxylate (pmdc) have been prepared. The stoichiometries and structural features of these materials, which range from the one-dimensional (1D) chains in ([Mn(mu-pmdc)(H2O)3].2H2O)n (1) and ([Mn2(mu-pmdc)2(H2O)5].2H2O)n (2) to the two-dimensional layers in ([Mn(mu3-pmdc)(H2O)].H2O)n (3) or the three-dimensional porous network in ([Mn(pmdc)].2H2O)n (4), are extremely dependent on the synthetic conditions (i.e., temperature and solvent). In spite of the structural diversity of these systems, crystallographic studies revealed that the pmdc ligand typically displays a tetradentate mu-(kappaO,kappaN:kappaO',kappaN') coordination mode with the carboxylate groups almost coplanar with the pyrimidine ring [as in compounds 1 and 2 and compound 5 described below)]. In compound 3, the pmdc moiety adopts a pentadentate mu3-(kappaO,kappaN:kappaO',kappaN':kappaO) coordination mode. The thermal, magnetic, and adsorption properties of these systems were also studied. The results showed that these compounds behave as antiferromagnets as a consequence of efficient magnetic exchange through the pmdc bridges. Compound 4 possesses permanent porosity, as proved by gas sorption data (N2 at 77 K and CO2 at 293 K). Finally, the heteronuclear iron(II)/manganese(II) compound ([FeMn(mu-pmdc)2(H2O)5].2H2O)n (5), which is isomorphous to 2, was also prepared and fully characterized.