Can magnetic circular dichroism tackle the problem of site symmetry in solutions?

A new approach to unravel the site symmetry of lanthanides in solutions is presented. The magnetic circular dichroism spectra of Eu³⁺ in the symmetries D_3h, C_4v and D_2d are simulated. In these simulations, the main idea is to introduce the magnetic field along a 3-fold axis, being the resultant of the three equivalent X-, Y- and Z-direction of a cube. This implies that the parallel and perpendicular Zeeman effects are taken into account simultaneously.     

Infrared Spectroscopy and Structure of Trigonal Zirconium Orthophosphates with Lanthanides and Actinides

Binary zirconium orthophosphates R_1/3Zr₂(PO₄)₃ and M_1/4Zr₂(PO₄)₃, where R = Y, La, Ce, Pr, Nd, Sm, Eu, Gd, Dy, Ho, Er, Tm, Yb, Lu; M = Th, U, have been synthesized and studied by IR spectroscopy [structural family of NaZr₂(PO₄)₃ (NZP)]. Vibrational analysis for the PO₄ tetrahedron and investigation of symmetry relations among trigonal NZP phases showed that ordering of lanthanide atoms in structures of NaZr₂(PO₄)₃ type with space group R c leads to symmetry reduced to P c. The lanthanide atoms occupy the 2b sites. The phosphorus atoms occupy two independent sites: 6f with C ₂ symmetry and 12g with C ₁ symmetry. Factor group analysis admits that the IR spectrum can contain eight v₃ bands and two v₁ bands of the stretching vibrations of the PO₄ ions. The M atoms of actinides occupy statistical positions in the structure, and space group R c is retained.Original Russian Text Copyright © 2004 by V. S. Kurazhkovskaya, D. M. Bykov, and A. I. Orlova__________Translated from Zhurnal Strukturnoi Khimii, Vol. 45, No. 6, pp. 1013–1019, November–December, 2004.     

A Basis for Orbital Symmetry Rules

The influence of molecular symmetry on reaction rates is examined with an approach in which reactions are viewed as electronic transitions between states of reacants and products (described, in turn by quasiadiabatic potential surface). The moleculer Hamiltonian is used to derive selection rules for these transitions. The complete Hamilatonian has no useful symmetery. Neglect of non-Born-Oppenheimer and spin-orbit terms (and of other angular momentum coupling terms) leads to an apporixmate Hamiltonian and to selection rules which from the basis of the Woodward-Hoffmann rules. This apporch provides an alternative to the adiabatic potantial surfaces, reaction coordinates, and transition state theory used in more familiar discussions of the Woodward-Hoffmann rules. Further, it provides a particulary clear method for discussing violations of these symmetry rules, and for differentiating concerted and nonconcerted reactions.     

对称性和配合物的构型——Ⅱ.混合配体配合物

从库仑定律出发,采用最优化法,计算了MLaL_b′型配合物各种几何异构体的几何构型稳定化能。在计算中考虑了配体L、L′的相对电荷。 计算结果表明,对称性是决定构型的首要因素。具体构型与配体的相对电荷有关。 在若干配合物中,中心原子的dⁿ构型决定其构型的骨架。 配体对构型的作用也应予考虑。对共价性程度大的配合物,应考虑轨道重叠对构型的影响。     

Closed‐form rectangular atomic wave functions of an N‐dimensional atom

A closed‐form expression has been derived to obtain the N‐dimensional rectangular atomic wave functions. The wave functions can be obtained straightforwardly with the knowledge of the angular momentum quantum numbers and the dimension and there is no need to employ recursive methods as in previous works. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem 88: 263–274, 2002     

On the theory of radiative transitions in centrosymmetric complexes

The theory of radiative transitions, in centrosymmetric complexes, is examined in great detail, within the framework of the crystal field method.In connection with radiative transitions, the current method of calculations, with and without invoking closure approximation, are considered from a purely theoretical point of view, by taking advantage of the irreducible tensor method put forward by Griffith.Explicit equations are derived throughout the course of this work to account for the vibronic electric dipole moments, associated with d-d and f-f type of excitations.At high Academy of Pedagogic Sciences, Santiago, Chile.     

分子的模糊对称性

将模糊数学方法引入对分子对称点群的研究,建立描述具有不完整分子对称性的模糊点对称群(集合).建立具有模糊对称性分子轨道的模糊表示及其模糊特征标(模糊广义宇称).通过对典型的线状分子、平面分子以及非平面的立体分子等进行分析,展示了一个新的理论化学园地.初步探讨了具有模糊对称性的动态反应体系.从模糊对称性出发,探讨了分子轨道对称守恒原理的半定量特征.     

Rumer's transformation,in biology,as the negation,in classical logic

In this article, we make a connection between the Rumer transformation, used in the study of the genetic code‐doublets, and the negation of classic logic. A unified classification is given, relying on two Klein's 4‐groups describing the symmetries of the 16 doublets of nitrogenous bases and those of the 16 binary connectives of classic logic, both groups being subgroups of a larger noncommutative group with eight elements we identify as the dihedral group D₄. Also, some connections with other works are briefly considered. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

Crystal chemistry and thermodynamic properties of anisotropic Ce2Ni7H4.7 hydride

A new intermetallic deuteride Ce₂Ni₇D_4.7 with an anomalous volume expansion has been studied. Its structure was solved on the basis of in situ neutron diffraction data. Expansion proceeds along the c-axis and within the CeNi₂ slabs only. All D atoms are located inside these slabs and on the border between CeNi₂ and CeNi₅. Ordering of D atoms in the bulk of CeNi₂ is accompanied by substantial deformation of these slabs thus lowering the hexagonal symmetry to orthorhombic [space group Pmcn (No. 62); a=4.9251(3) Å, b=8.4933(4) Å, c=29.773(1) Å]. Inside the CeNi₂ layer the hydrogen sublattice is completely ordered; all D-D distances exceed 2.0 Å. Local coordination of Ni by D inside the CeNi₂ blocks is of “open”, saddle-like type. Hydrogen ordering is mainly determined by Ce-H and H-H interactions. The pressure-composition-temperature measurements yielded the following thermodynamic parameters of the formation of the hydride: ΔH=−22.4 kJ/mol_H, ΔS=−59.9 J/(K mol_H).