Linear scaling computation of the Fock matrix. VII. Periodic density functional theory at the Gamma point

Linear scaling quantum chemical methods for density functional theory are extended to the condensed phase at the Gamma point. For the two-electron Coulomb matrix, this is achieved with a tree-code algorithm for fast Coulomb summation [M. Challacombe and E. Schwegler, J. Chem. Phys. 106, 5526 (1997)], together with multipole representation of the crystal field [M. Challacombe, C. White, and M. Head-Gordon, J. Chem. Phys. 107, 10131 (1997)]. A periodic version of the hierarchical cubature algorithm [M. Challacombe, J. Chem. Phys. 113, 10037 (2000)], which builds a telescoping adaptive grid for numerical integration of the exchange-correlation matrix, is shown to be efficient when the problem is posed as integration over the unit cell. Commonalities between the Coulomb and exchange-correlation algorithms are discussed, with an emphasis on achieving linear scaling through the use of modern data structures. With these developments, convergence of the Gamma-point supercell approximation to the k-space integration limit is demonstrated for MgO and NaCl. Linear scaling construction of the Fockian and control of error is demonstrated for RBLYP6-21G* diamond up to 512 atoms.     

High-pressure investigations under CO/H2 of rhodium complexes containing hemispherical diphosphites

The two rhodium complexes [Rh(acac)(L(R))] (L(R)=(S,S)-5,11,17,23-tetra-tert-butyl-25,27-di(OR)-26,28-bis(1,1'-binaphthyl-2,2'-dioxyphosphanyloxy)calix[4]arene; 6: R=benzyl, 7: R=fluorenyl), each based on a hemispherical chelator forming a pocket about the metal centre upon chelation, are active in the hydroformylation of 1-octene and styrene. As expected for this family of diphosphanes, both complexes resulted in remarkably high selectivity towards the linear aldehyde in the hydroformylation of 1-octene (l/b≈15 for both complexes). Linear aldehyde selectivity was also observed when using styrene, but surprisingly only 6 displayed a marked preference for the linear product (l/b=12.4 (6) vs. 1.9 (7)). A detailed study of the structure of the complexes under CO or CO/H(2) in toluene was performed by high-pressure NMR (HP NMR) and FT-IR (HP-IR) spectroscopies. The spectroscopic data revealed that treatment of 6 with CO gave [Rh(acac)(CO)(η(1)-L(benzyl))] (8), in which the diphosphite behaves as a unidentate ligand. Subsequent addition of H(2) to the solution resulted in a well-defined chelate complex with the formula [RhH(CO)(2)(L(benzyl))] (9). Unlike 6, treatment of complex 7 with CO only led to ligand dissociation and concomitant formation of [Rh(acac)(CO)(2)], but upon addition of H(2) a chelate complex analogous to 9 was formed quantitatively. In both [RhH(CO)(2)(L(R))] complexes the diphosphite adopts the bis-equatorial coordination mode, a structural feature known to favour the formation of linear aldehydes. As revealed by variable-temperature NMR spectroscopy, these complexes show the typical fluxionality of trigonal bipyramidal [RhH(CO)(2)(diphosphane)] complexes. The lower linear selectivity of 7 versus 6 in the hydroformylation of styrene was assigned to steric effects, due to the pocket in which the catalysis takes place being less adapted to accommodate CO or larger olefins and, therefore, possibly leading to facile ligand decoordination. This interpretation was corroborated by an X-ray structure determination carried out for 7.     

Chiral selectors for enantioresolution and quantitation of the antidepressant drug fluoxetine in pharmaceutical formulations by (19)F NMR spectroscopic method

¹⁹F NMR spectroscopy was applied to the quantitative determination of fluoxetine enantiomers using different chiral recognition agents in pharmaceutical formulations. Several parameters affecting the enantioresolution including the type and concentration of chiral selector, concentration of fluoxetine and temperature were studied. The chiral selectors investigated are the cyclic oligosaccharides α-, β- and γ-cyclodextrin and a diamino derivative of methylated α-cyclodextrin (DAM-α-CD), linear polysaccharides (maltodextrin with dextrose equivalents of 4.0-7.0, 13.0-17.0 and 16.5-19.5) and the macrocyclic antibiotic vancomycin. Among the chiral selectors used, DAM-α-CD turned out to give the best resolution of the ¹⁹F NMR signals of (R)- and (S)-fluoxetine. The calibration curve was linear for (R)- and (S)-fluoxetine over the range 0.10-1.35 mg mL⁻¹, the detection limits (S/N = 3) being 5.9 and 7.5 μg mL⁻¹ for the pure solutions of (R)- and (S)-fluoxetine, respectively. The recovery studies performed on pharmaceutical samples ranged from about 90 to 110% with relative standard deviations of <8%. The results showed that the proposed method is rapid, precise and accurate. Applying statistical Student's t-test revealed insignificant difference between the real and measured contents at the 95% confidence level.     

Synthesis of Optically Active Polystyrene Catalyzed by Monophosphine Pd Complexes

Cationic Pd^II monophosphine complexes derived from α‐ and β‐cyclodextrins (CDs) promote the homopolymerization of styrene under carbon monoxide pressure. Although reversible CO coordination takes place under catalytic conditions according to ¹³C NMR studies with ¹³C‐enriched CO, both complexes catalyze the formation of CO‐free styrene polymers. These macromolecules display optical activity as a result of the presence of stereoregular sequences within the overall atactic polymer.     

Raman spectroscopic study of the molecular structure of the uranyl mineral zippeite from Jáchymov (Joachimsthal), Czech Republic

Raman spectra at 298 and 77K and infrared spectra of the uranyl sulfate mineral zippeite from Jáchymov (Joachimsthal), Czech Republic, K(0.6)(H(3)O)0.4[(UO(2))6(SO(4))3(OH)7].8H2O, were studied. Observed bands were tentatively attributed to the (UO(2))2+ and (SO(4))2- stretching and bending vibrations, the OH stretching vibrations of water molecules, hydroxyls and oxonium ions, and H(2)O, oxonium, and delta U-OH bending vibrations. Empirical relations were used for the calculation of U-O bond lengths in uranyl R (A)=f(nu(3) or nu(1)(UO(2))2+). Calculated U-O bond lengths are in agreement with U-O bond lengths from the single crystal structure analysis and those inferred for uranyl anion sheet topology of uranyl pentagonal dipyramidal coordination polyhedra. The number of observed bands supports the conclusion from single crystal structure analysis that at least two symmetrically distinct U6+ (in uranyls) and S6+ (in sulfates), water molecules and hydroxyls may be present in the crystal structure of the zippeite studied. Strong to very weak hydrogen bonds present in the crystal structure of zippeite studied were inferred from the IR spectra.     

A Lead‐Selective Membrane Electrode Based Upon a Phosphorylated Hexahomotrioxacalix[3]Arene

Solvent extraction of a mixture of Pb^II, Mn^II, Fe^III, Co^II, Ni^II and Cd^II in aqueous perchlorate medium by a phosphorylated hexahomotrioxacalix[3]arene (calix‐3) in dichloromethane shows a significant selectivity towards lead ions. The ligand can also be incorporated into a membrane to provide a new lead ion‐selective electrode (Pb^II‐ISE). A plasticized PVC membrane containing 30% PVC, 53.5% ortho‐nitrophenyloctylether (NPOE), 4.5% sodium tetraphenylborate (NaTPB) and 12% ionophore was directly coated on a graphite rod. This sensor gave a good Nernstian response of 29.7 ± 0.7 mV decade^?1 over a concentration range of 1 × 10^?8 – 1 × 10^?4 M of lead ions, independent of pH in the range 3‐7, with a detection limit of 0.4 × 10^?8 M. The dynamic response time of the electrode to achieve a steady potential was very fast and found to be less than 7 s. The selectivity relative to Ag⁺, NH₄⁺, Li⁺, Na⁺, K⁺, Ca²⁺, Sr²⁺, Ba²⁺, Mn²⁺, Fe²⁺, Co²⁺, Ni²⁺, Cu²⁺, Zn²⁺, Cd²⁺, Fe³⁺, La³⁺, Sm³⁺, Dy³⁺, Er³⁺, Y³⁺ and Th⁴⁺ was examined. The electrode exhibits adequate stability with good reproducibility (with a slope of 29.6 ± 1.5 mV for 8 weeks). The characteristics of the sensor are compared with those of a tetraphosphorylated calix[4]arene (calix‐4) based Pb^II‐ISE, reported recently. The electrode was successfully used as an indicator electrode for a potentiometric titration of a lead solution using a standard solution of EDTA. The applicability of the sensor for lead ion measurements in various synthetic samples was also investigated.     

Playing with podands based on cone-shaped cavities. How can a cavity influence the properties of an appended metal centre?

The potential of molecules that combine the properties of a conical cavity with those of a covalently-linked transition-metal centre is highlighted through the assessment of cyclodextrin- and calixarene-derived podands ("cavitand" ligands) in coordination chemistry and catalysis. Metallocavitands with coordination sites directed towards the interior of the generic cavity provide interesting systems for studying host-guest complexation processes, their enhanced strength of metal-ion binding allowing for regioselective catalysis in a confined environment, and stabilisation of coordination complexes of unusual forms. Where cavitands have exo-oriented podand arms, the intrinsic dynamics of the cavity can dramatically modify metal chelation behaviour and the catalytic properties of the complexes. Such functionalised cavities are also useful as metal-ion transporters.     

A novel strategy for the asymmetric synthesis of chiral cyclopropane carboxaldehydes

A new way of combining chiral auxiliaries and substrate-directable reactions for asymmetric synthesis is described that employs a three-step sequence of aldol-cyclopropanation-retro-aldol reactions for the stereoselective synthesis of enantiopure cyclopropane carboxaldehydes.     

Near-infrared spectroscopy of torbernites and metatorbernites

A suite of torbernites and metatorbernites have been analysed by near-infrared spectroscopy. The spectra of torbernites and metatorbernites in the first HOH fundamental overtone are different and the spectra of torbernites of different origins in the 6000-7500 cm(-1) region vary. NIR spectroscopy provides a method of studying the hydration of cations in the interlayer of torbernite. NIR spectroscopy shows that the spectra of torbernites from different origins in the water HOH first fundamental overtone and combination regions are different. This difference implies the hydration of cations is different for torbernite minerals. The structural arrangement of the water molecules in the interlayer is sample dependent. The NIR spectra of metatorbernites are different from that of torbernites and a similarity of the spectra of metatorbernites suggests that the water structure in metatorbernites is similar.     

Synthesis and Properties of TRANSDIP,a Rigid Chelator Built upon a Cyclodextrin Cavity: Is TRANSDIP an Authentic trans‐Spanning Ligand?

The C2-symmetrical diphosphane TRANSDIP was obtained in high yield by treating 6A,6B,6D,6E-tetramesylated, permethylated alpha-cyclodextrin with PPhLi2 in excess. The double cascade cyclisation thus produced is regioselective as phosphinidene capping involves only adjacent glucose units. It is also stereospecific, as both lone pairs on the phosphorus atoms are orientated towards the cyclodextrin axis. The restricted flexibility of the phosphorus atoms, which are part of nine-membered heterocyclic rings, is responsible for JP,C spin-spin couplings with the eight-bond distant CH2OMe carbon atoms of glucose units C and F. The treatment of TRANSDIP with Group 10 metal dihalides quantitatively gave square-planar chelate complexes, in which a M--X bond points towards the centre of the cavitand. The favourable P...P separation and the directional control of the lone pairs on the phosphorus atoms rule out the possibility of forming binuclear complexes or higher oligomers. Further, in all the complexes, the phosphorus atoms are in a trans arrangement. TRANSDIP may therefore be regarded as an authentic trans-spanning diphosphane. In the complex [NiBr2TRANSDIP], the cavity provides effective protection of the encapsulated M--X bond towards nucleophilic attack by MeLi. The same complex, upon activation with methylaluminoxane, efficiently dimerises ethene and propene.