A New Non-centrosymmetric Microporous Fluorinated Iron Phosphate: Structural Elucidation,Spectroscopic Study and Hirshfeld Surface Analysis

The crystal structure of a new non-centrosymmetric microporous fluorinated iron phosphate, (H₃O)₂[Fe₄(H₂O)₂F₄(PO₄)₂(HPO₄)₂](H₂O), was determined by single crystal X-ray diffraction analysis and the result reveals that it belongs to the orthorhombic system with four molecules in the unit cell(space group P2₁2₁2₁). Thus, the complex was characterized by powder X-ray diffraction, spectroscopic techniques(Fourier transform infrared and Fourier transform Raman) and ¹⁹F MAS NMR. The elemental analysis of the sample was also carried out. The chiral inorganic sheets, which stacked along[100] showed the presence of FeF₂O₄ as well as FeF₂O₃H₂O octahedra, PO₄ besides HPO₄ tetrahedra, hydronium ions(H₃O⁺) and isolated water molecules. Hirshfeld surface analysis, especially d_nom surface and fingerprint plots, were used for decoding the intermolecular interactions in the crystal network and the contribution of component units for the construction of the 3D architecture. From the Hirshfeld surfaces and 2D fingerprint analysis, it was found that the subtle interactions, such as H…H associating the third intense interaction of all intercontacts, provide extra stabilization in addition to the presence of the strong hydrogen bonds mentioned above.     

On approximation of Lie groups by discrete subgroups

A locally compact group G is said to be approximated by discrete subgroups (in the sense of Tôyama) if there is a sequence of discrete subgroups of G that converges to G in the Chabauty topology (or equivalently, in the Vietoris topology). The notion of approximation of Lie groups by discrete subgroups was introduced by Tôyama in Kodai Math. Sem. Rep. 1 (1949) 36–37 and investigated in detail by Kuranishi in Nagoya Math. J. 2 (1951) 63–71. It is known as a theorem of Tôyama that any connected Lie group approximated by discrete subgroups is nilpotent. The converse, in general, does not hold. For example, a connected simply connected nilpotent Lie group is approximated by discrete subgroups if and only if G has a rational structure. On the other hand, if Γ is a discrete uniform subgroup of a connected, simply connected nilpotent Lie group G then G is approximated by discrete subgroups Γ _n containing Γ. The proof of the above result is by induction on the dimension of G, and gives an algorithm for inductively determining Γ _n . The purpose of this paper is to give another proof in which we present an explicit formula for the sequence (Γ _n ) _n?≥?0 in terms of Γ. Several applications are given.     

Effect of hydrostatic pressure on the structural, elastic and electronic properties of (B3) boron phosphide

In this paper we present the results obtained from first-principles calculations of the effect of hydrostatic pressure on the structural, elastic and electronic properties of (B3) boron phosphide, using the pseudopotential plane-wave method (PP-PW) based on density functional theory within the Teter and Pade exchange-correlation functional form of the local density approximation (LDA). The lattice parameter, molecular and crystal densities, near-neighbour distances, independent elastic constants, bulk modulus, shear modulus, anisotropy factor and energy bandgaps of (B3) BP under high pressure are presented. The results showed a phase transition pressure from the zinc blende to rock-salt phase at around 1.56?Mbar, which is in good agreement with the theoretical data reported in the literature.     

Overlapping domain decomposition methods for elliptic quasi-variational inequalities related to impulse control problem with mixed boundary conditions

In this paper we provide a maximum norm analysis of an overlapping Schwarz method on non-matching grids for quasi-variational inequalities related to impulse control problem with mixed boundary conditions. We provide that the discretization on every sub-domain converges in uniform norm. Furthermore, a result of approximation in uniform norm is given.