Path-Dependency of Energy Decomposition Analysis & the Elusive Nature of Bonding

Here, we provide evidence of the path-dependency of the energy components of the energy decomposition analysis scheme, EDA, by studying a set of thirty-one closed-shell model systems with D2h symmetry point group. For each system, we computed EDA components from nine different pathways and numerically showed that the relative magnitudes of the components differ substantially from one path to the other. Not surprisingly, yet unfortunately, the most significant variations in the relative magnitudes of the EDA components appear in the case of species with bonds within the grey zone of covalency and ionicity. We further discussed that the role of anions and their effect on arbitrary Pauli repulsion energy components affects the nature of bonding defined by EDA. The outcome variation by the selected partitioning scheme of EDA might bring arbitrariness when a careful comparison is overlooked.

X-Ray Diffraction

X-rays diffraction is fundamental to understanding the structure and crystallography of biological, geological, or technological materials. X-rays scatter predominantly by the electrons in solids, and have an elastic (coherent, Thompson) and an inelastic (incoherent, Compton) component. The atomic scattering factor is largest (= Z) for forward scattering, and decreases with increasing scattering angle and decreasing wavelength. The amplitude of the diffracted wave is the structure factor, F hkl, and its square gives the intensity. In practice, intensities are modified by temperature (Debye-Waller), absorption, Lorentz-polarization, and the multiplicity of the lattice planes involved in diffraction. Diffraction patterns reflect the symmetry (point group) of the crystal; however, they are centrosymmetric (Friedel law) even if the crystal is not. Systematic absences of reflections in diffraction result from glide planes and screw axes. In polycrystalline materials, the diffracted beam is affected by the lattice strain or grain size (Scherrer equation). Diffraction conditions (Bragg Law) for a given lattice spacing can be satisfied by varying θ or λ — for study of single crystals θ is fixed and λ is varied (Laue), or λ is fixed and θ varied to study powders (Debye-Scherrer), polycrystalline materials (diffractometry), and thin films (reflectivity). X-ray diffraction is widely applied.

Chaotic mixing in crystalline granular media

We study the Lagrangian kinematics of steady three-dimensional Stokes flow over simple cubic (SC) and body-centred cubic (BCC) lattices of close-packed spheres, and uncover the mechanisms governing chaotic mixing in these crystalline structures. Due to the cusp-shaped sphere contacts, the topology of the skin friction field is fundamentally different to that of continuous (non-granular) media, such as open pore networks, with significant implications for fluid mixing. Weak symmetry breaking of the flow orientation with respect to the lattice symmetries imparts a transition from regular to strong chaotic mixing in the BCC lattice, whereas the SC lattice only exhibits weak mixing. Whilst the SC and BCC lattices posses the same symmetry point group, these differences are explained in terms of their space groups. This insight is used to develop accurate predictions of the Lyapunov exponent distribution over the parameter space of mean flow orientation. These results point to a general theory of mixing and dispersion based upon the inherent symmetries of arbitrary crystalline structures.

Comparison study of CC and CH vibration frequencies and eelectronic properties for mono, Di, Tri, and tetra-rings layer of arm chair (SWCNTs)

Semi-empirical methods were applied for calculating the vibration frequencies and IR absorption intensities for normal coordinates of the {mono (C56H28), di (C84H28), tri (C112H28) and tetra (C140H28)} -rings layer for (7,7) armchair single wall carbon nanotube at their equilibrium geometries which were all found to have D7d symmetry point group. Assignment of the modes of vibration (3N-6) was done depending on the pictures of their modes by applying (Gaussian 03) program. Comparison of the vibration frequencies of (mono, di, tri and tetra) rings layer which are active in IR, and inactive in Ramman spectra. For C-H stretching vibrations, the results showed that vibration frequencies value increased with increased of length nano tube (rings layer SWCNT). The results include the relation for axial bonds, which are the vertical C-C bonds (annular bonds) in the rings and for circumferential bonds which are the outer ring bonds. Also include the assignment of puckering, breathing and clock-anticlockwise bending vibrations. They allow a comparative view of the charge density at the carbon atom too.

Quantum mechanical study of electronic properties of zigzag nanotubes (9,0) (SWCNTs)

Quantum calculations on the most stable structure were carriedout for calculating the electronic properties, energies and the chargedensity at the Carbon and Hydrogen atoms by Semi-empiricalmethod (PM3) of zigzag carbon nano tube CNT (9,0) (SWCNTs), atthe equilibrium geometry depending on the pictures of ZigzagCNT(9,0) which was found to has D3d symmetry point group byapplying for (Gaussian 2003) program. In this work the resultsinclude calculation the relation for axial bonds length, which are thevertical C-C bonds (annular bonds) in the rings and bonds lengthwhich are in the outer ring that called the circumferential bonds. Alsoinclude a different kind of vibration modes like breathing, puckering,and deformation bending. They allow a comparative view of thecharge density at the carbon atom too. The aromaticity is gradedaccording to the space distribution of the atoms in zigzag nano tube(9,0), the nature of their molecular orbitals depend on, theirsymmetry, and chirality. Many studies were done measurements tocharacterize nanotube mechanical properties for successfulapplications in nanotechnology.

Structure, vibrational spectroscopy, and photochemistry of 5-phenoxy-1-phenyltetrazole in argon and nitrogen cryomatrices

The molecular structure, infrared spectra, and photochemistry of 5-phenoxy-1-phenyltetrazole (5PPT) isolated in argon and N2 cryogenic matrices were investigated by infrared spectroscopy and theoretical calculations (DFT(B3LYP)/6-311++G(d,p)). Calculations yield two dissimilar minima on the potential energy surface of the molecule, both being eightfold degenerate by symmetry and belonging to the C1 symmetry point group. Extensive analysis of the potential energy landscape of the molecule was performed. Upon consideration of the zero-point vibrational correction to the energy, the calculations predict that the higher energy minimum shall relax barrierlessly to the lower energy form, leading to conclude that the compound exists in a single conformer in the gas phase. Accordingly, a single conformer was observed and fully characterized spectroscopically upon isolation of the monomer of the compound in argon and nitrogen cryomatrices. UV-laser irradiation (λ = 250 nm) of matrix-isolated 5PPT leads to photocleavage of the tetrazole ring, with release of N2 and formation of the corresponding carbodiimide.

Di-μ-hydroxido-κ4O:O-di-μ-perchlorato-κ4O:O′-bis[(2,2′-bipyridine-κ2N,N′)copper(II)]

In the title binuclear copper(II) complex, [Cu2(ClO4)2(OH)2(C10H8N2)2], the CuIIion is coordinated in the form of a Jahn–Teller distorted octahedron by two bipyridine N atoms, two perchlorate O atoms and two hydroxide O atoms, and displays a distorted octahedral geometry. The molecule belongs to the symmetry point groupC2h. The CuIIion is located on a twofold rotation axis and the hydroxide and perchlorate ligands are located on a mirror plane. Within the dinuclear molecule, the Cu...Cu separation is 2.8614 (7) Å. The crystal structure exhibits O—H...O, C—H...O and π–π [centroid–centroid distance = 3.5374 (13) Å] interactions.

X-ray diffraction study of a pseudo single crystal prepared from a crystal belonging to point group 2

A pseudo single crystal (a composite of matrix resin and powder crystallites, wherein the individual crystallites are aligned three-dimensionally) was prepared from a powder of sucrose, and its X-ray diffraction pattern was studied. A powder of sucrose crystals suspended in a UV-curable resin precursor was subjected to magnetic alignment in order to align the individual crystallites three-dimensionally, and then the resin precursor was photopolymerized to maintain this orientation. The pseudo single crystal thus obtained produced a well resolved X-ray diffraction profile that is similar to that produced by a twin crystal. The origin of the twin orientation was explained in terms of the interplay between the symmetry of magnetic susceptibility axes and the crystal symmetry (point group 2) of sucrose. The crystal structure of sucrose solved using the pseudo single crystal was in excellent agreement with that solved using a single crystal.