Chirality and accurate structure models by exploiting dynamical effects in continuous-rotation 3D ED data

Dynamical diffraction effects are usually considered a nuisance for structure analysis from continuous-rotation 3D electron diffraction (3D ED) data like cRED and MicroED. Here we demonstrate that by accounting for these effects during the structure refinement, significantly improved models can be obtained in terms of accuracy and reliability with up to four-fold reduction of the noise level in difference Fourier maps in comparison to the standard structure determination routines that ignore dynamical diffraction. As dynamical diffraction effects break the inversion symmetry of the diffraction, they allow a quick, easy, and reliable determination of the absolute structure of chiral crystals.

Flux synthesis, crystal structure and electronic properties of the layered rare earth metal boride silicide Er3Si5–x B. An example of a boron/silicon-ordered structure derived from the AlB2 structure type

The ternary rare earth metal boride silicide Er3Si5–x B (x = 1.17) was synthesized from the elements using the tin flux method. It crystallizes in a new structure type in the space group R32 (a = 6.5568(1) Å, c = 24.5541(1) Å, Z = 6). The structural arrangement can be derived from the AlB2 structure type with boron/silicon ordering in the layered metalloid substructure made of [Si5B] hexagons. The presence or absence of the boron atoms involved in this ordered structure is discussed on the basis of difference Fourier syntheses and structural analysis, in relation with the binary parent structures AlB2 and Yb3Si5 (Th3Pd5 type). The electronic and bonding properties of Er3Si5–x B were analyzed and discussed via density functional theory (DFT) calculations and a crystal orbital Hamiltonian population (COHP) bonding analysis.

Finite Difference/Fourier Spectral for a Time Fractional Black–Scholes Model with Option Pricing

We study the fractional Black–Scholes model (FBSM) of option pricing in the fractal transmission system. In this work, we develop a full-discrete numerical scheme to investigate the dynamic behavior of FBSM. The proposed scheme implements a known L1 formula for the α-order fractional derivative and Fourier-spectral method for the discretization of spatial direction. Energy analysis indicates that the constructed discrete method is unconditionally stable. Error estimate indicates that the 2−α-order formula in time and the spectral approximation in space is convergent with order OΔt2−α+N1−m, where m is the regularity of u and Δt and N are step size of time and degree, respectively. Several numerical results are proposed to confirm the accuracy and stability of the numerical scheme. At last, the present method is used to investigate the dynamic behavior of FBSM as well as the impact of different parameters.

Syntheses and crystal structures of a new pyrazine dicarboxamide ligand, N 2,N 3-bis(quinolin-8-yl)pyrazine-2,3-dicarboxamide, and of a copper perchlorate binuclear complex

The title pyrazine dicarboxamide ligand, N 2,N 3-bis(quinolin-8-yl)pyrazine-2,3-dicarboxamide (H2L1), C24H16N6O2, has a twisted conformation with the outer quinoline groups being inclined to the central pyrazine ring by 9.00 (6) and 78.67 (5)°, and by 79.94 (4)° to each other. In the crystal, molecules are linked by C—H...O hydrogen bonds, forming layers parallel to the (10\overline{1}) plane, which are in turn linked by offset π–π interactions [intercentroid distances 3.4779 (9) and 3.6526 (8) Å], forming a supramolecular three-dimensional structure. Reaction of the ligand H2L1 with Cu(ClO4)2 in acetonitrile leads to the formation of the binuclear complex, [μ-(3-{hydroxy[(quinolin-8-yl)imino]methyl}pyrazin-2-yl)[(quinolin-8-yl)imino]methanolato]bis[diacetonitrilecopper(II)] tris(perchlorate) acetonitrile disolvate, [Cu2(C24H15N6O2)(CH3CN)4](ClO4)3·2CH3CN or [Cu2(HL1−)(CH3CN)4](ClO4)3·2CH3CN (I). In the cation of complex I, the ligand coordinates to the copper(II) atoms in a bis-tridentate fashion. A resonance-assisted O—H...O hydrogen bond is present in the ligand; the position of this H atom was located in a difference-Fourier map. Both copper(II) atoms are fivefold coordinate, being ligated by three N atoms of the ligand and by the N atoms of two acetonitrile molecules. The first copper atom has a perfect square-pyramidal geometry while the second copper atom has a distorted shape. In the crystal, the cation and perchlorate anions are linked by a number of C—H...O hydrogen bonds, forming a supramolecular three-dimensional structure.

Structural analysis of biological targets by host:guest crystal lattice engineering

To overcome the laborious identification of crystallisation conditions for protein X-ray crystallography, we developed a method where the examined protein is immobilised as a guest molecule in a universal host lattice. We applied crystal engineering to create a generic crystalline host lattice under reproducible, predefined conditions and analysed the structures of target guest molecules of different size, namely two 15-mer peptides and green fluorescent protein (sfGFP). A fusion protein with an N-terminal endo-α-N-acetylgalactosaminidase (EngBF) domain and a C-terminal designed ankyrin repeat protein (DARPin) domain establishes the crystal lattice. The target is recruited into the host lattice, always in the same crystal form, through binding to the DARPin. The target structures can be determined rapidly from difference Fourier maps, whose quality depends on the size of the target and the orientation of the DARPin.