Truncation of small matrix elements based on the Euclidean norm for blocked data structures

Methods for the removal of small symmetric matrix elements based on the Euclidean norm of the error matrix are presented in this article. In large scale Hartree-Fock and Kohn-Sham calculations it is important to be able to enforce matrix sparsity while keeping errors under control. Truncation based on some unitary-invariant norm allows for control of errors in the occupied subspace as described in (Rubensson et al. J Math Phys 49, 032103). The Euclidean norm is unitary-invariant and does not grow intrinsically with system size and is thus suitable for error control in large scale calculations. The presented truncation schemes repetitively use the Lanczos method to compute the Euclidean norms of the error matrix candidates. Ritz value convergence patterns are utilized to reduce the total number of Lanczos iterations.     

Supercritical fluid extraction of amino acids from birch (Betula pendula Roth) leaves and their liquid chromatographic determination with fluorimetric detection

A method for supercritical fluid extraction (SFE) of amino acids was adapted and optimal experimental conditions were selected for a matrix consisting of dry leaves. The matrix-dependent SFE method uses a mixture of MeOH-H(2)O-acetonitrile (10:10:1 v/v/v) as a modifier (0.5 mL in situ, 300 muL on-line) at 70 degrees C and 40 MPa and no HCl is needed as an entrainer. The amino acids were quantified using high-performance liquid chromatography with fluorimetric detection (HPLC/FLD) after gradient elution on Zorbax Eclipse AAA columns (4.6x150 mm, 3.5 mum) with aqueous Na(2)HPO(4 )buffer of pH 7.8 and ACN-MeOH-water as a mobile phase. In comparison with Soxhlet extraction, SFE gave higher recovery and selectivity, but it required longer extraction time (90 min) and it was more labor-intensive (clean-up step after the pre-concentration). Both methods should be used separately or in combination according to the matrix, number of samples, and levels of ballast compounds.     

Recursive inverse factorization

A recursive algorithm for the inverse factorization S(-1)=ZZ(*) of Hermitian positive definite matrices S is proposed. The inverse factorization is based on iterative refinement [A.M.N. Niklasson, Phys. Rev. B 70, 193102 (2004)] combined with a recursive decomposition of S. As the computational kernel is matrix-matrix multiplication, the algorithm can be parallelized and the computational effort increases linearly with system size for systems with sufficiently sparse matrices. Recent advances in network theory are used to find appropriate recursive decompositions. We show that optimization of the so-called network modularity results in an improved partitioning compared to other approaches. In particular, when the recursive inverse factorization is applied to overlap matrices of irregularly structured three-dimensional molecules.     

Sequential reactions from catalytic hydroformylation toward the synthesis of amino compounds

Different families of new amino compounds were efficiently synthesized, through optimized sequential processes, involving rhodium catalyzed hydroformylation as the key step. The selection of appropriate hydroformylation catalytic systems and reaction conditions allowed obtaining aldehydes derived from several n-alkyl olefins, cholest-4-ene and 3-vinyl-1H-indole, which were subsequently transformed, in one-pot, in to α-amino acids via hydroformylation/Strecker reaction, and in to tertiary amines via hydroaminomethylation, with excellent yields.     

Synergistic effects of encapsulated phthalocyanine complexes in MIL-101 for the selective aerobic oxidation of tetralin

Metal phthalocyanine complexes encapsulated in MIL-101, and used as "ship-in-a-bottle" catalysts, show outstanding TONs in the aerobic oxidation of tetralin.