Iteratively reweighted least squares and slime mold dynamics: connection and convergence

Mathematical Programming - We present a connection between two dynamical systems arising in entirely different contexts: the Iteratively Reweighted Least Squares (IRLS) algorithm used in compressed...     

Key aspects of crystalline Mo-V-O-based catalysts active in the selective oxidation of propane

Mo-V-O-based complex metal oxide catalysts were synthesized hydrothermally for the first time, characterized structurally and tested in the selective oxidation of propane to acrylic acid, and the results obtained were compared on the basis of catalyst crystal structures in order to clarify key aspects of alkane selective oxidation over multifunctional metal oxide catalysts. The catalysts tested were black solids of rod-shaped crystals, which had a layer structure in the direction of fiber axis and various high dimensional arrangements of metal octahedra in the cross-section plane. A strong dependency on the octahedra arrangements and a facet dependency were observed, and the roles of metal elements in the course of selective oxidation of propane were clarified by comparing the catalytic performance of various Mo-V-O-based catalysts. We discuss the multi-functional character derived from high dimensional structures of the catalysts and mechanism of the selective oxidation of propane.     

Nonequilibrium melting and crystallization of a model Lennard-Jones system

Nonequilibrium melting and crystallization of a model Lennard-Jones system were investigated with molecular dynamics simulations to quantify the maximum superheating/supercooling at fixed pressure, and over-pressurization/over-depressurization at fixed temperature. The temperature and pressure hystereses were found to be equivalent with regard to the Gibbs free energy barrier for nucleation of liquid or solid. These results place upper bounds on hysteretic effects of solidification and melting in high heating- and strain-rate experiments such as shock wave loading and release. The authors also demonstrate that the equilibrium melting temperature at a given pressure can be obtained directly from temperatures at the maximum superheating and supercooling on the temperature hysteresis; this approach, called the hysteresis method, is a conceptually simple and computationally inexpensive alternative to solid-liquid coexistence simulation and thermodynamic integration methods, and should be regarded as a general method. We also found that the extent of maximum superheating/supercooling is weakly pressure dependent, and the solid-liquid interfacial energy increases with pressure. The Lindemann fractional root-mean-squared displacement of solid and liquid at equilibrium and extreme metastable states is quantified, and is predicted to remain constant (0.14) at high pressures for solid at the equilibrium melting temperature.     

Ferrocenecarbothioamide and N-ethoxycarbonylferrocenecarbothioamide: Synthesis, structure and application in synthesis of 2,4-diferrocenylthiazole

Ferrocenecarbothioamide (1) and its N-ethoxycarbonyl derivative (2) were synthesised by a Friedel-Crafts type reaction of ferrocene with potassium thiocyanate and ethoxycarbonyl isothiocyanate, respectively, in a strongly acidic medium. The X-ray structure of 1 was determined and shows conjugation between the ferrocene moiety and the thioamido group. Compound 1 reacts with chloroacetylferrocene affording 2,4-diferrocenylthiazole, whose structure was determined by X-ray diffraction and electronic properties studied by cyclic voltammetry.     

Host-guest chemistry of the chromium-wheel complex [Cr8F8(tBuCO2)16]: prediction of inclusion capabilities by using an electrostatic potential distribution determined by modeling synchrotron X-ray structure factors at 16 K

The structure and detailed electron density distribution (EDD) of the large octanuclear chromium-wheel host complex [Cr8F8(tBuCO2)16] (1) has been determined from synchrotron X-ray structure factors collected at 16(5) K. The complex has a central cavity with a minimum entry distance between carbon atoms of the pivalate methyl groups (pivalic acid = tBuCO2H) of 4.027(4) A on one side of the molecule and 7.273(4) A on the other. The screened side of the molecule can be "opened" by rotation of methyl groups to create a strained host structure, which is compensated for by improved host-guest and host-solvent interaction. The EDD of the 272-atom complex (1144 e-) was determined by multipole modeling based on the experimental structure factors. 3d orbital populations on the Cr atoms and topological analysis of the EDD show that the covalent part of the metal-ligand interactions consists mainly of sigma donation from the ligands, but that overall the interactions are predominantly electrostatic. The electrostatic potential (EP) has been calculated from the experimental EDD. Knowledge of the geometry of the naked complex 1 as well as the EP in the central cavity of this molecule allows us to deduce which characteristic properties guest molecules must have to be accepted into the void. To probe these predictions, a series of complexes of 1 with different guest inclusions were synthesized (2 = 1 + N,N'-dimethylformamide (DMF), 3 = 1 + N,N'-dimethylacetamide (DMA), 4 = 1 + DMA + DMF, 5 = 1 + 2CH3CN), and their structures were examined by using X-ray diffraction data measured at 120(1) K. Results of these studies indicate that in the crystalline state, the optimal guest molecule should be linear and possess a permanent dipole. Attempts to crystallize the host complex with cations incorporated into the cavity were fruitless, although electrospray ionization mass spectrometry showed that a [1 + potassium]+ entity pre-exists in solution and can be transferred intact into the gas phase.     

Diastereoselective addition of dimethyl phosphite to 3,3′,4,4′-tetramethyl-1,1′-diphosphaferrocene-2-carboxaldehyde

Addition of dimethyl phosphite to racemic 3,3′,4,4′-tetramethyl-1,1′-diphosphaferrocene-2-carboxaldehyde gives almost exclusively one diastereomer of the corresponding α-hydroxyphosphonate (d.r. ?96:4). Its absolute configuration (S, R_p)-(R, S_p) was established by X-ray diffraction.     

On the viability of small endohedral hydrocarbon cage complexes: X@C4H4, X@C8H8, X@C8H14, X@C10H16, X@C12H12, AND X@C16H16

Small hydrocarbon complexes (X@cage) incorporating cage-centered endohedral atoms and ions (X = H(+), H, He, Ne, Ar, Li(0,+), Be(0,+,2+), Na(0,+), Mg(0,+,2+)) have been studied at the B3LYP/6-31G(d) hybrid HF/DFT level of theory. No tetrahedrane (C(4)H(4), T(d)()) endohedral complexes are minima, not even with the very small hydrogen atom or beryllium dication. Cubane (C(8)H(8), O(h)()) and bicyclo[2.2.2]octane (C(8)H(14), D(3)(h)()) minima are limited to encapsulating species smaller than Ne and Na(+). Despite its intermediate size, adamantane (C(10)H(16), T(d)()) can enclose a wide variety of endohedral atoms and ions including H, He, Ne, Li(0,+), Be(0,+,2+), Na(0,+), and Mg(2+). In contrast, the truncated tetrahedrane (C(12)H(12), T(d)()) encapsulates fewer species, while the D(4)(d)() symmetric C(16)H(16) hydrocarbon cage (see Table of Contents graphic) encapsulates all but the larger Be, Mg, and Mg(+) species. The host cages have more compact geometries when metal atoms, rather than cations, are inside. This is due to electron donation from the endohedral metals into C-C bonding and C-H antibonding cage molecular orbitals. The relative stabilities of endohedral minima are evaluated by comparing their energies (E(endo)) to the sum of their isolated components (E(inc) = E(endo) - E(cage) - E(x)) and to their exohedral isomer energies (E(isom) = E(endo) - E(exo)). Although exohedral binding is preferred to endohedral encapsulation without exception (i.e., E(isom) is always exothermic), Be(2+)@C(10)H(16) (T(d)(); -235.5 kcal/mol), Li(+)@C(12)H(12) (T(d)(); 50.2 kcal/mol), Be(2+)@C(12)H(12) (T(d)(); -181.2 kcal/mol), Mg(2+)@C(12)H(12) (T(d)(); -45.0 kcal/mol), Li(+)@C(16)H(16) (D(4)(d)(); 13.3 kcal/mol), Be(+)@C(16)H(16) (C(4)(v)(); 31.8 kcal/mol), Be(2+)@C(16)H(16) (D(4)(d)(); -239.2 kcal/mol), and Mg(2+)@C(16)H(16) (D(4)(d)(); -37.7 kcal/mol) are relatively stable as compared to experimentally known He@C(20)H(20) (I(h)()), which has an E(inc) = 37.9 kcal/mol and E(isom) = -35.4 kcal/mol. Overall, endohedral cage complexes with low parent cage strain energies, large cage internal cavity volumes, and a small, highly charged guest species are the most viable synthetic targets.     

The kinetics of the E-Z-E isomerisation and liquid-crystalline properties of selected azobenzene derivatives investigated by the prism of the ester group inversion

Two new groups of azobenzene ester derivatives were synthesised: alkyl 4-[4-(nonyloxy)phenyl]diazenyl]benzoates and 4-[4-(nonyloxy)phenyl]diazenyl]phenyl alkanoates. All 35 presented homologues are mesogenic. Moreover, some of the above-mentioned compounds exhibit rich liquid-crystalline polymorphism likewise tetramorphism. During this investigation by the use of polarising optical microscopy, differential scanning calorimetry and X-Ray studies, six types of mesophases were detected: nematic, smectics (A, C, I, F) and G. Furthermore, due to the presence of the photosensitive azo moiety, the E–Z isomerisation reaction is possible. This process, which is initiated by the UV irradiation, causes significant changes in the UV-Vis absorption spectra of investigated compounds. However, the photoisomerisation is a reversible process and in the dark the thermal relaxation of Z isomer takes place. Based on the achieved data, the kinetic constants of the isomerisation and relaxation processes were calculated. It shows that conversion of the ester bond makes some changes in the optical properties. The shift of about 7 nm of the absorbance maximum was observed. Surprisingly, the inversion of the ester group has significant influence on the liquid-crystalline polymorphism replacing one mesophase (for benzoates) into four (for alkanoates).