Connection between the regular approximation and the normalized elimination of the small component in relativistic quantum theory

The regular approximation to the normalized elimination of the small component (NESC) in the modified Dirac equation has been developed and presented in matrix form. The matrix form of the infinite-order regular approximation (IORA) expressions, obtained in [Filatov and Cremer, J. Chem. Phys. 118, 6741 (2003)] using the resolution of the identity, is the exact matrix representation and corresponds to the zeroth-order regular approximation to NESC (NESC-ZORA). Because IORA (=NESC-ZORA) is a variationally stable method, it was used as a suitable starting point for the development of the second-order regular approximation to NESC (NESC-SORA). As shown for hydrogenlike ions, NESC-SORA energies are closer to the exact Dirac energies than the energies from the fifth-order Douglas-Kroll approximation, which is much more computationally demanding than NESC-SORA. For the application of IORA (=NESC-ZORA) and NESC-SORA to many-electron systems, the number of the two-electron integrals that need to be evaluated (identical to the number of the two-electron integrals of a full Dirac-Hartree-Fock calculation) was drastically reduced by using the resolution of the identity technique. An approximation was derived, which requires only the two-electron integrals of a nonrelativistic calculation. The accuracy of this approach was demonstrated for heliumlike ions. The total energy based on the approximate integrals deviates from the energy calculated with the exact integrals by less than 5 x 10(-9) hartree units. NESC-ZORA and NESC-SORA can easily be implemented in any nonrelativistic quantum chemical program. Their application is comparable in cost with that of nonrelativistic methods. The methods can be run with density functional theory and any wave function method. NESC-SORA has the advantage that it does not imply a picture change.     

Synthesis of 3-aminomethyl-2-aryl- 8-bromo-6-chlorochromones

[reaction: see text] An efficient synthetic route to Cbz-protected 3-aminomethyl-2-aryl-8-bromo-6-chlorochromones has been developed. 3-Aryl-1-(3-bromo-5-chloro-2-hydroxyphenyl)-2-propen-1-one or 2-aryl-8-bromo-6-chlorochroman-4-one could be reacted under Mannich conditions yielding 2-aryl-8-bromo-6-chloro-3-methylenechroman-4-one, which was further converted to the target compound via an aza-Michael reaction followed by an SeO(2) oxidation. This procedure represents a new method to introduce a primary aminomethyl group at the 3-position of a 2-arylchromone scaffold. The Cbz-protected 3-aminomethyl-2-aryl-8-bromo-6-chlorochromones can, e.g., be used in the synthesis of chromone-based beta-turn peptidomimetics.     

Two Ce(SO4)2·4H2O polymorphs: Crystal structure and thermal behavior

Syntheses, crystal structures and thermal behavior of two polymorphic forms of Ce(SO₄)₂·4H₂O are reported. The first modification, α-Ce(SO₄)₂·4H₂O (I), crystallizes in the orthorhombic space group Fddd, with a=5.6587(1), b=12.0469(2), c=26.7201(3) Å and Z=8. The second modification, β-Ce(SO₄)₂·4H₂O (II), crystallizes in the orthorhombic space group Pnma, with a=14.6019(2), b=11.0546(2), c=5.6340(1) Å and Z=4. In both structures, the cerium atoms have eight ligands: four water molecules and four sulfate groups. The mutual position of the ligands differs in (I) and (II), resulting in geometrical isomerism. Both these structures are built up by layers of Ce(H₂O)₄(SO₄)₂ held together by a hydrogen bonding network. The dehydration of Ce(SO₄)₂·4H₂O is a two step (I) and one step (II) process, respectively, forming Ce(SO₄)₂ in both cases. During the decomposition of the anhydrous form, Ce(SO₄)₂, into the final product CeO₂, intermediate xCeO₂·yCe(SO₄)₂ species are formed.     

Calculation of indirect nuclear spin-spin coupling constants within the regular approximation for relativistic effects

A new method for calculating the indirect nuclear spin-spin coupling constant within the regular approximation to the exact relativistic Hamiltonian is presented. The method is completely analytic in the sense that it does not employ numeric integration for the evaluation of relativistic corrections to the molecular Hamiltonian. It can be applied at the level of conventional wave function theory or density functional theory. In the latter case, both pure and hybrid density functionals can be used for the calculation of the quasirelativistic spin-spin coupling constants. The new method is used in connection with the infinite-order regular approximation with modified metric (IORAmm) to calculate the spin-spin coupling constants for molecules containing heavy elements. The importance of including exact exchange into the density functional calculations is demonstrated.     

Synthesis of adenosine-based fluorosides containing a novel heterocyclic ring system

A novel class of fluorescent adenosine derivatives (fluorosides) containing the previously unreported 8-(3H-[1,2,3]triazol-4-yl)-9H-purine heterocyclic ring system is reported, with Sonogashira cross-coupling and [3+2]-cycloaddition reactions being the key steps in the synthesis.     

Preparation of cis-5-methoxy-and-7-methoxy-1-acetoxy-1,2,3,4,4a,10a- hexahydro-9(10H)-phenanthrenone. An epoxide-arene reaction involving a selective 1,2-alkyl shift rearrangement.

The preparation of cis-1-acetoxy-7-methoxy-1,2,3,4,4a,10a-hexahydro-9(10H)- phenanthrenone 5 was accomplished starting from 6-methoxy-1-tetralone. Reduction of 7-methoxy-1,2,3, 4,9,10-hexahydro-1-oxo-phenanthrene 8, acetylation and subsequent oxidation delivered 5. Application of an analogus procedure to the preparation of cis-1β-acetoxy-5-methoxy-1,2,3,4,,4a,10a-hexahydro-9(10H)- phenanthrenone 6 was not feasible. A more elaborate route was developed for the synthesis of compound 6, where an epoxide-arene reaction involving a 1,2-alkyl shift rearrangement, constituted a highly selective key transformation.     

The solution chemistry of ethylmethylglyoxime : Part I. The proton complex

The solubility of ethylmethylglyoxime (EMG) was studied as a function of pH. The solubility K_sl in 0.1 M aqueous solution is 0.0132 ±0.0006 M. The distribution constants K_Dl of EMG between various organic solvents and 0.1 M aqueous solution were found to be —0.47 for chloroform, —0.51 for benzene, —1.10 for carbon tetrachloride and —1.83 for hexane. The acid dissociation constants were determined from potentiometric titrations; the values pK_a1=10.51 and pK_a2=12.02 were obtaining by fitting the experimental data to normalized curves. The UV spectra of 5·10^-5M EMG solutions of varying pH were measured between 210 and 290 nm. It is shown that H₂A has an absorption maximum at 226 nm and HA^-and A^2- have absorption maxima at nearly the same wavelengths, i.e. 258 and 266 nm, respectively. The spectra of HA^- and A^2- have approximately the same form. The data are compared with those of dimethylglyoxime (DMG). The distribution constants (org/aq) are 4–5 times higher for EMG. The acid dissociation constants are about the same for EMG and DMG, but EMG is more soluble in water than DMG (13.2 and 5.0 mmoles/l, respectively). The UV spectra of EMG and DMG are very similar.     

Future independent times and Markov chains

Summary A random timeT is a future independent time for a Markov chain (X _n ) ₀ ifT is independent of (X _T+n ) _n ^/ =0 and if (X _T+n ) _n ^/ =0 is a Markov chain with initial distribution and the same transition probabilities as (X _n ) ₀ . This concept is used (with the conditional stationary measure) to give a new and short proof of the basic limit theorem of Markov chains, improving somewhat the result in the null-recurrent case.This work was supported by the Swedish Natural Science Research Council and done while the author was visiting the Department of Statistics, Stanford University     

Self-reproduction of chirality on α-aminophosphonates: asymmetric synthesis of α-alkylated diethyl pyrrolidin-2-yl-phosphonate

A simple method for the asymmetric synthesis of α-substituted diethyl pyrrolidin-2-yl-phosphonate is described. The chiral oxazolopyrrolidine phosphonate was alkylated diastereospecifically with an alkyl halide. The key intermediate is an α-phosphonate-stabilized carbanion that can be alkylated without loss of optical activity and a single enantiomer of product was formed exclusively in 10-80% yield. The configurational assignment of the products relied on ¹H-¹H NOESY analysis of the alkylated oxazolopyrrolidine phosphonates. This represents an unprecedented case of self-regeneration of stereocenters (SRS) of cyclic aminophosphonates. The enantiomerically pure α-aminophosphonate diethyl-(2S)-(2-methylpyrrolidin-2-yl)-phosphonate, a surrogate of 2-methyl proline, was obtained upon hydrogenolysis of the chiral auxiliary in 83% yield.     

Use of different types of mesoporous materials as tools for organic synthesis

Mesoporous materials have been investigated as auxiliary agents for organic synthesis comprising reactants with widely different solubility characteristics. The finely divided oxide material was immersed in an aqueous solution of a water-soluble reactant, potassium iodide, and the loaded particles were kept under stirring in the hydrophobic reactant, 4-tert-butylbenzyl bromide, or in a hydrocarbon solution of this reactant. The reaction proceeded well in alumina and silica of either bicontinuous cubic or hexagonal geometry. It was shown for silica that the particle size was an important parameter; the smaller the size the faster the reaction. Titania gave a much lower reaction rate than alumina and silica. It was found that the hexagonal mesoporous alumina could be reused either as a slurry or in a column procedure. Attempts were also made to use hydrophobic mesoporous materials, either mesoporous graphite or mesoporous oxide treated with chlorotrimethylsilane, in the reversed mode. The hydrophobic solid was then immersed in a solution of the hydrophobic reactant and subsequently dispersed in an aqueous solution of the water-soluble reactant. Two nucleophilic substitution reactions and one oxidation reaction were investigated but the yields were low in all cases.