Theory of helicenic hydrocarbons. Part 1: Invariants and symmetry

Helicenes form a subclass of polyhexes and correspond to hydrocarbons of considerable chemical interest. This paper is the first part of a general graph-theoretical treatment of helicenes. The invariants are studied: the relations between them, their possible values, and their upper and lower bounds in helicenes. Extremal helicenes and circular helicenes are useful definitions of subclasses of the systems under consideration. Finally an account of symmetry of helicenes is given.On leave from: Department of Mathematics, Xinjiang University, Wulumuqi Xinjiang 830046, People's Republic of China.     

The Wave Function with Symplectic Symmetry and Its Application

The antisymmetrized geminal power (AGP) and sequential product of geminals(SPG) functions, the basis functions with symplectic symmetry, are linearly combined to calculate the ground state of the LiH molecule. The calculation results show that the AGP or SPG function gives the same ground state results as the linear combination.     

利用分子对称性简化天然有机产物合成设计的策略

本文综述了利用分子对称性简化天然有机产物合成设计的策略,讨论了具有下述四种对称性的分子的合成:一、对称中心和旋转对称轴;二、对称平面;三、潜在的对称性;四、局部的对称性。     

Correlated intermolecular interaction components from asymptotically corrected Kohn-Sham orbitals

In these years there was considerable interest inunderstanding of intermolecular forces in energetic(explosive) systems[1—3]. The supermolecular approach(SM) is widely adopted for calculating ab initio in-termolecular interactions. Nevertheless, it is unable toprovide physically meaningful interaction contribu-tions such as electrostatic, induction, repulsion anddispersion energies. In contrast, the symmetry-adaptedperturbation theory (SAPT)[4—8] has the ability to de-rive these correlated…     

分子轨道图形理论中对称轴定理

本文试图以浅显明确的形式描述对称轴定理，使之能与对称面定理相媲美，并对对称轴定理作一定的扩展，给出分子轨道构造定理。     

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