Two Notions Of Safety

Timothy Williamson (1992, 224–5) and Ernest Sosa (1996) have ar- gued that knowledge requires one to be safe from error. Something is said to be safe from happening iff it does not happen at “close” worlds. I expand here on a puzzle noted by John Hawthorne (2004, 56n) that suggests the need for two notions of closeness. Counterfac- tual closeness is a matter of what could in fact have happened, given the specific circumstances at hand. The notion is involved in the semantics for counterfactuals and is the one epistemologists have typically assumed. Normalized closeness is rather a matter of what could typically have happened, that is, what would go on in a class of normal alternatives to actuality, irrespectively of whether or not they could have happened in the circumstances at hand

Mechanism for Polymorphic Transformation of Artemisinin during High Temperature Extrusion

A novel, green, and continuous method for solid-state polymorphic transformation of artemisinin by high temperature extrusion has recently been demonstrated. This communication describes attempts to understand the mechanisms causing phase transformation during the extrusion process. Polymorphic transformation was investigated using hot stage microscopy and a model shear cell. At high temperature, phase transformation from orthorhombic to the triclinic crystals was observed through a vapor phase. Under mechanical stress, the crystalline structure was disrupted continuously, exposing new surfaces and accelerating the transformation process

“<i>In-Silico</i> Seeding”: Isostructurality and Pseudoisostructurality in a Family of Aspirin Derivatives

Novel crystal packings of the aspirin molecule and 17 molecules that are related to aspirin by substitution are studied using a computational approach. The packings are created by taking a crystal structure for which the crystal packing and molecular geometry have been determined experimentally and replacing the native molecule with a different one. The resulting crystal structures are optimized using molecular mechanics, followed by a quantum mechanical method based on density functional theory and including a correction for dispersive interactions. There are 21 known, experimental, crystal structures for the molecules considered, some of which are polymorphic. For any given molecule, the lowest, calculated lattice energy is always found to be that of a crystal structure which corresponds to experiment. For the three polymorphic molecules, the second lowest lattice energy is also found to correspond to an experimental structure. The agreement between the observation of a particular packing and its low rank in the list of possible packings is evidence of the accuracy of the method for calculating the lattice energy. Further analysis of the results shows patterns reflecting the underlying supramolecular constructs that are common to the different packings of these molecules. This leads to some speculation as to the possibilities of finding new polymorphs for some of these molecules

Crystal Structure Prediction of a Flexible Molecule of Pharmaceutical Interest with Unusual Polymorphic Behavior

Crystal structure prediction methods have been used to explore the potential energy landscape for crystals of a melatonin agonist (MA). All known experimental polymorphs were found in the search for crystal packing alternatives with a single molecule in the asymmetric unit, and the predicted order of stability agrees with experiment. The crystal structure corresponding to the global minimum has not been observed experimentally, but analysis of the crystal structures of similar molecules in the Cambridge Structural Database (CSD) indicates that the packing motif present in the predicted structure is also found in nature. To date it has not been experimentally possible to crystallize the most stable polymorph of the biologically active <i>R</i>-enantiomer, whereas the <i>S</i>-enantiomer readily crystallizes in the stable form. Analysis of the results shows that this polymorph has an uncommon packing motif which is found just once among the 12 lowest energy predicted structures but is seen in two crystal structures of MA-like molecules whose structures are stored in the CSD. On the basis of the calculations and comparisons with experimental crystal structures, suggestions are made as to possible routes for crystallizing the, as yet unknown, polymorph of MA, which corresponds to the predicted structure with the lowest lattice energy

Chrysomela goettingensis

Crystal structure prediction methods have been used to explore the potential energy landscape for crystals of a melatonin agonist (MA). All known experimental polymorphs were found in the search for crystal packing alternatives with a single molecule in the asymmetric unit, and the predicted order of stability agrees with experiment. The crystal structure corresponding to the global minimum has not been observed experimentally, but analysis of the crystal structures of similar molecules in the Cambridge Structural Database (CSD) indicates that the packing motif present in the predicted structure is also found in nature. To date it has not been experimentally possible to crystallize the most stable polymorph of the biologically active <i>R</i>-enantiomer, whereas the <i>S</i>-enantiomer readily crystallizes in the stable form. Analysis of the results shows that this polymorph has an uncommon packing motif which is found just once among the 12 lowest energy predicted structures but is seen in two crystal structures of MA-like molecules whose structures are stored in the CSD. On the basis of the calculations and comparisons with experimental crystal structures, suggestions are made as to possible routes for crystallizing the, as yet unknown, polymorph of MA, which corresponds to the predicted structure with the lowest lattice energy

Synthesis, Prediction, and Determination of Crystal Structures of (<i>R</i>/<i>S</i>)- and (<i>S</i>)‑1,6-Dinitro-3,8-dioxa-1,6‑diazaspiro[4.4]nonane-2,7-dione

Spiro-cyclic compounds frequently have screw-type symmetry (<i>C</i>₂) and are therefore optically active even though they do not contain an asymmetric carbon atom. (<i>R</i>/<i>S</i>)-1,6-Dinitro-3,8-dioxa-1,6-diazaspiro­[4.4]­nonane-2,7-dione is such a molecule. A blind crystal structure prediction study of structures containing one molecule in the asymmetric unit and considering all 230 space groups was undertaken using a dispersion-corrected density functional approach, which found a packing that matched the experimental structure of the (<i>R</i>/<i>S</i>) form as the lowest energy packing alternative. The densities of (<i>R</i>/<i>S</i>)<i>-</i> and (<i>S</i>)- or (<i>R</i>)-1,6-dinitro-3,8-dioxa-1,6-diazaspiro­[4.4]­nonane-2,7-dione calculated for the optimized experimental crystal structures confirmed that there is a small difference in the densities of the racemate and the optically active compound, with the optically active material being slightly more dense (1.875 versus 1.842 g/cm³). (<i>R</i>/<i>S</i>)-1,6-Dinitro-3,8-dioxa-1,6-diazaspiro­[4.4]­nonane-2,7-dione was synthesized as previously described. Synthesis of the pure (<i>S</i>)-stereoisomer was accomplished by resolution of the racemic dithiourethane using a previously described method, followed by reaction of the pure enantiomer with acetyl nitrate. The absolute configuration of the <i>l</i>-3,8-dioxa-1,6-diazaspiro­[4.4]­nonane-2,7-dithione was established as (<i>S</i>)- by redetermining the crystal structure at 150 K. The racemate crystallizes in space group <i>P</i>2₁/<i>n</i> with a density of 1.835 g/cm³ (296 K). The (<i>S</i>)-compound crystallizes in space group <i>P</i>2₁2₁2₁ with a density of 1.854 g/cm³ (296 K). This is the first demonstration of a difference in the density between the racemic mixture and the optically pure stereoisomer of an energetic material. It is also an apparent violation of Wallach’s rule, which states that racemic crystals tend to be denser than their optically active counterparts

Synthesis, Prediction, and Determination of Crystal Structures of (<i>R</i>/<i>S</i>)- and (<i>S</i>)‑1,6-Dinitro-3,8-dioxa-1,6‑diazaspiro[4.4]nonane-2,7-dione

Spiro-cyclic compounds frequently have screw-type symmetry (<i>C</i>₂) and are therefore optically active even though they do not contain an asymmetric carbon atom. (<i>R</i>/<i>S</i>)-1,6-Dinitro-3,8-dioxa-1,6-diazaspiro­[4.4]­nonane-2,7-dione is such a molecule. A blind crystal structure prediction study of structures containing one molecule in the asymmetric unit and considering all 230 space groups was undertaken using a dispersion-corrected density functional approach, which found a packing that matched the experimental structure of the (<i>R</i>/<i>S</i>) form as the lowest energy packing alternative. The densities of (<i>R</i>/<i>S</i>)<i>-</i> and (<i>S</i>)- or (<i>R</i>)-1,6-dinitro-3,8-dioxa-1,6-diazaspiro­[4.4]­nonane-2,7-dione calculated for the optimized experimental crystal structures confirmed that there is a small difference in the densities of the racemate and the optically active compound, with the optically active material being slightly more dense (1.875 versus 1.842 g/cm³). (<i>R</i>/<i>S</i>)-1,6-Dinitro-3,8-dioxa-1,6-diazaspiro­[4.4]­nonane-2,7-dione was synthesized as previously described. Synthesis of the pure (<i>S</i>)-stereoisomer was accomplished by resolution of the racemic dithiourethane using a previously described method, followed by reaction of the pure enantiomer with acetyl nitrate. The absolute configuration of the <i>l</i>-3,8-dioxa-1,6-diazaspiro­[4.4]­nonane-2,7-dithione was established as (<i>S</i>)- by redetermining the crystal structure at 150 K. The racemate crystallizes in space group <i>P</i>2₁/<i>n</i> with a density of 1.835 g/cm³ (296 K). The (<i>S</i>)-compound crystallizes in space group <i>P</i>2₁2₁2₁ with a density of 1.854 g/cm³ (296 K). This is the first demonstration of a difference in the density between the racemic mixture and the optically pure stereoisomer of an energetic material. It is also an apparent violation of Wallach’s rule, which states that racemic crystals tend to be denser than their optically active counterparts