			Home About us Contact

Irreducible Representations (irreducible + representation)

Distribution by Scientific Domains

Chemistry	75%

Selected Abstracts

Symmetry point group description of second harmonic generation in carbon nanotubes

LASER PHYSICS LETTERS, Issue 4 2004
L. De Dominicis
Abstract The role played by symmetry properties of a carbon nanotube in the generation of second harmonic radiation is studied by using the formalism of irreducible representation of the symmetry point group. Experimental results of second harmonic generation in a carbon nanotube sample are discusses in view of the theoretical prediction obtained. (© 2004 by ASTRO, Ltd. Published exclusively by WILEY-VCH Verlag GmbH & Co. KGaA) [source]

Symmetry rules and strain/order-parameter relationships for coupling between octahedral tilting and cooperative Jahn,Teller transitions in ABX3 perovskites.

ACTA CRYSTALLOGRAPHICA SECTION B, Issue 2 2009

The structural evolution of selected perovskites containing Jahn,Teller cations has been investigated in the light of a formal analysis of symmetry hierarchies for phase transitions driven by octahedral tilting and Jahn,Teller cooperative distortions. General expressions derived from the strain/order-parameter coupling relationships allowed by symmetry are combined with observed changes in lattice parameters to reveal details of order-parameter evolution and coupling. LuVO3, YbVO3, YVO3 and CeVO3 are representative of systems which develop Jahn,Teller ordering schemes associated with irreducible representations and of the space group . Tilting of their octahedra is associated with and . The Pnma ( tilting) ,P21/a ( tilting, Jahn,Teller order) transition below room temperature is close to second order in character. Shear strains which depend primarily on tilt angles show little variation, implying that there is only weak coupling between the tilting and Jahn,Teller order parameters. The subsequent P21/a,Pnma ( tilting, Jahn,Teller order) is first order in character, and involves either a reduction in the tilt angle or a change in the strength of tilt/Jahn,Teller order-parameter coupling. In LaMnO3, the isosymmetric Pnma ( tilting) ,Pnma ( tilting, Jahn,Teller order) transition can be described in terms of a classical first-order transition conforming to a 246 Landau expansion with negative fourth-order coefficients. Strain evolution in Ba-doped samples suggests that the transition becomes second order in character and reveals a new strain relaxation mechanism in LaMnO3 which might be understood in terms of local strain heterogeneities due to the disordering of distorted MnO6 octahedra. Transitions in PrAlO3 and La0.5Ba0.5CoO3 illustrate the transformation behaviour of systems in which the Jahn,Teller ordering scheme is associated with the irreducible representation . Overall, coupled tilting + Jahn,Teller phase transitions in perovskites conform to mean-field behaviour, consistent with the underlying role of strain in promoting long interaction lengths. [source]

Bond Orders between Molecular Fragments

CHEMISTRY - A EUROPEAN JOURNAL, Issue 8 2006
Adam J. Bridgeman Dr.
Abstract An extension of the Mayer bond order for the interaction between molecular fragments is presented. This approach allows the classical chemical concepts of bond order and valence to be utilised for fragments and the interactions between the fragments and symmetry-adapted linear combinations to be analysed. For high-symmetry systems, the approach allows the contribution from each irreducible representation to be assessed and provides a semiquantitative measure of the role of each bonding mode to interfragment interactions. The utility of this tool has been examined by a study of the bonding in symmetrical sandwich complexes. The validity of the frontier-orbital approach and the contributions from each frontier-orbital interaction can also be assessed within this model. As demonstrated by a study of a number of mixed-sandwich complexes, the model proves to be especially useful for low-symmetry systems in which separation of the ,, , and , roles in bonding of the ligand is difficult to assess. The fragment bond order describes the interaction between preoptimized fragment orbitals and is independent of the charges that are placed on these fragments. Although the method allows the chemist to define fragments in any way they choose, most insight is gained by using the same frontier orbitals employed so successfully in perturbational molecular-orbital approaches. The results are free from the influence of the electron-counting method used to describe fragments, such as the rings and metals in sandwich complexes. [source]

Understanding chemical shielding tensors using group theory, MO analysis, and modern density-functional theory

CONCEPTS IN MAGNETIC RESONANCE, Issue 2 2009
Cory M. Widdifield
Abstract In this article, the relationships between molecular symmetry, molecular electronic structure, and chemical shielding (CS) tensors are discussed. First, a brief background on the CS interaction and CS tensors is given. Then, the visualization of the three-dimensional nature of CS is described. A simple method for examining the relationship between molecular orbitals (MOs) and CS tensors, using point groups and direct products of irreducible representations of MOs and rotational operators, is outlined. A number of specific examples are discussed, involving CS tensors of different nuclei in molecules of different symmetries, including ethene (D2h), hydrogen fluoride (C,v), trifluorophosphine (C3v), and water (C2v). Finally, we review the application of this method to CS tensors in several interesting cases previously discussed in the literature, including acetylene (D,h), the PtX42, series of compounds (D4h) and the decamethylaluminocenium cation (D5d). © 2009 Wiley Periodicals, Inc. Concepts Magn Reson Part A 34A: 91,123, 2009. [source]

MODY: a program for calculation of symmetry-adapted functions for ordered structures in crystals

JOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 6 2004
awa Sikora
This paper describes a computer program, based on the theory of groups and representations, which calculates symmetry-adapted functions used for the description of various ordered structures in crystals. It is assumed that the ordered structure, which is formed by a configuration of occupational probabilities, ion displacements, magnetic moments, quadrupolar moments or other local physical quantities, is obtained from a high-symmetry crystal structure with a given space group G, as a result of a symmetry-lowering phase transition. The detailed characteristics of the phase transition are given by the specification of the irreducible representations of group G, active in the transition. The symmetry-adapted functions obtained from the calculation are perfect tools for the construction of model structures, which can be used for comparison with experimental (e.g. neutron diffraction) data, and can be a great help in numerical data elaboration by reducing the number of adjustable parameters describing the structure of a given symmetry. [source]

Study of electronic spectra of free-base porphin and Mg-porphin: Comprehensive comparison of variety of ab initio, DFT, and semiempirical methods

JOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 3 2005
Josef
Abstract SAC (symmetry adapted cluster)/SAC-CI and CASPT2 (multiconfigurational second-order perturbation theory) electron excitation spectra of free-base porphin and magnesium-porphin were determined using basis set functions augmented by both the polarization and diffuse functions,6-31+G(d). Such basis is recommended for correct description of the spectra because diffuse functions play fundamental roles in the formation of Rydberg MOs. The obtained results indicated that already the lowest roots in Au, B1u, B2g, and B3g irreducible representations display Rydberg character. The calculated spectra are in a good agreement with both experimental and recently calculated electronic transitions. It is concluded that the SAC/SAC-CI level spectral lines are significantly affected by configuration selection when energy thresholds 5.0 × 10,6 and 5.0 × 10,7 a.u. are used for the determination of ground and excited state properties. © 2004 Wiley Periodicals, Inc. J Comput Chem 26: 294,303, 2005 [source]

A symmetry based approach to evaluation of carbon nanotube electronic hyperpolarizability

LASER PHYSICS LETTERS, Issue 12 2004
L. De Dominicis
Abstract The properties of the carbon nanotubes (CNTs) hyperpolarizability , due to , electrons is studied by using the formalism of the irreducible representations of CNT space symmetry group (G). The main contribution to the second order nonlinearity is demonstrated to come from electrons at the origin of the Brillouin zone (k = 0). Within this scheme, a description based on the isogonal point group associated to G accounts for the relevant properties of ,. (© 2004 by ASTRO, Ltd. Published exclusively by WILEY-VCH Verlag GmbH & Co. KGaA) [source]

The full symmetry and irreducible representations of nanotori

ACTA CRYSTALLOGRAPHICA SECTION A, Issue 3 2009
Majid Arezoomand
The full symmetry groups of carbon nanotori are investigated. It is shown that that the symmetry group of a chiral (n1, n2) nanotorus is isomorphic to D2mq/n, where m and q are the number of lattice points on the torus circumference vector and the number of graphene hexagons in the nanotorus unit cell, respectively, and n = gcd(n1, n2). It is also shown that the symmetry group of zigzag and armchair (achiral) nanotori is , where D2k and are the dihedral group of order 2k and the cyclic group of order k, respectively. The irreducible representations and characters of these groups are discussed. [source]

Application of modern tensor calculus to engineered domain structures.

ACTA CRYSTALLOGRAPHICA SECTION A, Issue 2 2006

This article is a roadmap to a systematic calculation and tabulation of tensorial covariants for the point groups of material physics. The following are the essential steps in the described approach to tensor calculus. (i) An exact specification of the considered point groups by their embellished Hermann,Mauguin and Schoenflies symbols. (ii) Introduction of oriented Laue classes of magnetic point groups. (iii) An exact specification of matrix ireps (irreducible representations). (iv) Introduction of so-called typical (standard) bases and variables , typical invariants, relative invariants or components of the typical covariants. (v) Introduction of Clebsch,Gordan products of the typical variables. (vi) Calculation of tensorial covariants of ascending ranks with consecutive use of tables of Clebsch,Gordan products. (vii) Opechowski's magic relations between tensorial decompositions. These steps are illustrated for groups of the tetragonal oriented Laue class D4z, 4z2x2xy of magnetic point groups and for tensors up to fourth rank. [source]

Octahedral tilting in cation-ordered Jahn,Teller distorted perovskites , a group-theoretical analysis

ACTA CRYSTALLOGRAPHICA SECTION B, Issue 1 2010
Christopher J. Howard
Computer-based group-theoretical methods are used to enumerate structures arising in A2BB,X6 perovskites, with either rock-salt or checkerboard ordering of the B and B, cations, under the additional assumption that one of these two cations is Jahn,Teller active and thereby induces a distortion of the BX6 (or B,X6) octahedron. The requirement to match the pattern of Jahn,Teller distortions to the cation ordering implies that the corresponding irreducible representations should be associated with the same point in the Brillouin zone. Effects of BX6 (and B,X6) octahedral tilting are included in the usual way. Finally, an analysis is presented of more complex models of ordering and distortion as might lead to the doubling of the long axis of the common Pnma perovskite, observed in systems such as Pr1,,,xCaxMnO3 (x, 0.5). The structural hierarchies derived in this work should prove useful in interpreting experimental results. [source]

Symmetry rules and strain/order-parameter relationships for coupling between octahedral tilting and cooperative Jahn,Teller transitions in ABX3 perovskites.

ACTA CRYSTALLOGRAPHICA SECTION B, Issue 2 2009

Space groups, order-parameter and strain/order-parameter coupling relationships in ABX3 perovskite structures which combine cooperative Jahn,Teller distortions and octahedral tilting have been investigated from the perspective of group theory using the computer program ISOTROPY. Two common Jahn,Teller ordering schemes are associated with the irreducible representations and of the space group . A third, less-common ordering scheme is associated with . These combine with tilting instabilities associated with and to generate a predicted suite of Jahn,Teller structure types that includes many of the known structures of manganites, vanadates, Cu and Cr halides. Order-parameter coupling and possible phase transitions are described using Landau free-energy expansions, and general expressions for the relationships between symmetry-adapted spontaneous strains and particular order-parameter components are presented. These provide a general formal framework for determining structural evolution across multi-component order-parameter space and for characterizing the influence of tilting instabilities on Jahn,Teller instabilities or of Jahn,Teller ordering on octahedral tilting. [source]

Symmetry rules and strain/order-parameter relationships for coupling between octahedral tilting and cooperative Jahn,Teller transitions in ABX3 perovskites.