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Group point groups

Compound3 3b SHGC Space Group Point Group d Coefficient(s)d Cutoffe FOM... [Pg.138]

Space Group Point Group Point Group Space Group... [Pg.724]

Definition (Orthogonal group, point group, symmetry elements)... [Pg.98]

Shubnikov (Magnetic) Group Point Group Spatial Group... [Pg.249]

Pyroelectricity is a property inherent in crystals with unique polar axes that are, consequently, without a center of symmetry. However, as opposed to piezoelectricity not all symmetry groups (point groups) lacking a center of symmetry are pyroelectric, whereas all pyroelectrics are also piezoelectrics. Most pyroelectrics belong to the hnear dielectrics as the polarization is linearly dependent on the electric field. However, some-for example, KDP and Seignette salt-are nonhnear pyroelectrics-that is, they are ferroelectrics. [Pg.289]

Define the following terms symmetry operation, symmetry element, principal axis, identity operation, improper rotation, inversion, symmetry group, point group, conjugate elements, similarity transformation and class. [Pg.61]

In general, a point group synnnetry operation is defined as a rotation or reflection of a macroscopic object such that, after the operation has been carried out, the object looks the same as it did originally. The macroscopic objects we consider here are models of molecules in their equilibrium configuration we could also consider idealized objects such as cubes, pyramids, spheres, cones, tetraliedra etc. in order to define the various possible point groups. [Pg.145]

As an example, we again consider the PH molecule. In its pyramidal equilibrium configuration PH has all tlnee P-H distances equal and all tlnee bond angles Z(HPH) equal. This object has the point group synnnetry where the operations of the group are... [Pg.145]

The complete multiplication table of the point group, worked out using arguments similar to those leading to (equation A1.4.23) and (equation A1.4.24), is given in table A1.4.2. It is left as an exercise for the reader to use this table to show that the elements of satisfy the group axioms given in section Al.4.2.1. [Pg.146]

Table Al.4.2 The multiplication table of the point group using the space-fixed axis convention (see text). Table Al.4.2 The multiplication table of the point group using the space-fixed axis convention (see text).
If we were to define the operations of the point group as also rotating and reflecting the (p.q.r) axis system (in which case the axes would be tied to the positions of the nuclei), we would obtain a different multiplication table. We could call this the nuclear-fixed axis convention. To implement this the protons in the o, O2 and planes in figure Al.4.2 would be numbered H, H2 and respectively. With this convention the operation would move the a plane to the position in space originally occupied by the 02 plane. If we follow such a C3 operation by the reflection (in the plane containing Ft ) we find that, in the nuclear-fixed axis convention ... [Pg.146]

The point groups T, and /j. consist of all rotation, reflection and rotation-reflection synnnetry operations of a regular tetrahedron, cube and icosahedron, respectively. [Pg.147]

Point groups are discussed briefly in sections 4.3 and 4.4 of [1] and very extensively in chapter 3 of Cotton... [Pg.147]

As an example we consider the group introduced in (equation Al.4,19) and the point group given in (equation Al.4.22). Inspection shows that the multiplication table of in table Al.4,2 can be obtained from the multiplication table of the group (table Al.4,1) by the following mapping ... [Pg.148]

Nuclear pemuitations in the N-convention (which convention we always use for nuclear pemuitations) and rotation operations relative to a nuclear-fixed or molecule-fixed reference frame, are defined to transfomi wavefunctions according to (equation Al.4.56). These synnnetry operations involve a moving reference frame. Nuclear pemuitations in the S-convention, point group operations in the space-fixed axis convention (which is the convention that is always used for point group operations see section Al.4.2,2 and rotation operations relative to a space-fixed frame are defined to transfomi wavefiinctions according to (equation Al.4.57). These operations involve a fixed reference frame. [Pg.155]

Rigid linear molecules are a special case in which an extended MS group, rather than the MS group, is isomorphic to the point group of the equilibrium structure see chapter 17 of [1]. [Pg.182]

A detailed discussion of the relation between MS group operations and point group operations is given in section... [Pg.182]

We now turn to electronic selection rules for syimnetrical nonlinear molecules. The procedure here is to examme the structure of a molecule to detennine what synnnetry operations exist which will leave the molecular framework in an equivalent configuration. Then one looks at the various possible point groups to see what group would consist of those particular operations. The character table for that group will then pennit one to classify electronic states by symmetry and to work out the selection rules. Character tables for all relevant groups can be found in many books on spectroscopy or group theory. Ftere we will only pick one very sunple point group called 2 and look at some simple examples to illustrate the method. [Pg.1135]

Each such nonual mode can be assigned a synuuetry in the point group of the molecule. The wavefrmctions for non-degenerate modes have the following simple synuuetry properties the wavefrmctions with an odd vibrational quantum number v. have the same synuuetry as their nonual mode 2the ones with an even v. are totally symmetric. The synuuetry of the total vibrational wavefrmction (Q) is tlien the direct product of the synuuetries of its constituent nonual coordinate frmctions (p, (2,). In particular, the lowest vibrational state. [Pg.1137]


See other pages where Group point groups is mentioned: [Pg.4]    [Pg.415]    [Pg.416]    [Pg.123]    [Pg.123]    [Pg.178]    [Pg.156]    [Pg.318]    [Pg.141]    [Pg.144]    [Pg.144]    [Pg.145]    [Pg.145]    [Pg.147]    [Pg.147]    [Pg.147]    [Pg.148]    [Pg.175]    [Pg.175]    [Pg.176]    [Pg.180]    [Pg.180]    [Pg.180]    [Pg.180]    [Pg.181]    [Pg.181]    [Pg.181]    [Pg.1063]    [Pg.1135]    [Pg.1135]    [Pg.1135]    [Pg.1137]   
See also in sourсe #XX -- [ Pg.390 ]




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1.2- Dichloroethane point group

1.2- Dichloroethene point group

Abelian point group

Acetylene point group

Achiral molecules, and point groups

Achiral point groups

Achirality chiral point groups

Allene point group

Ammonia point group

Background to Point Groups

Basic Point Group Theory

Benzene point group

Boiling point group contribution models

Boiling points group 18 elements

Boric acid point group

Buckminsterfullerene point group

Bullvalene point group

C2h point group

C2v point group

C2v point group character table for

C3v point group

C4v point group

Carbon dioxide point group

Carbon monoxide point group

Character Tables for Selected Point Groups

Character point group

Character table point-group

Character tables for point groups

Character tables of point groups

Chiral molecules, and point groups

Chiral point groups

Chirality point groups

Chloroform point group

Cj point group

Classification of point groups

Cn point groups

Cnh point groups

Cnv point groups

Co-representations of magnetic point groups

Colour point groups

Continuous Point Groups

Coov point group

Crystal Symmetry The 32 Crystallographic Point Groups

Crystal point groups

Crystallographic magnetic point groups

Crystallographic point groups

Crystallography crystallographic point groups

Cubane point group

Cubic point group family

Cubic point groups

Cubic point groups described

Cubic point groups rotational symmetry

Cyclobutadiene point group

Cyclobutane point group

Cyclodec-5-en-l-one point group

Cyclohexane point group

Cyclopentadienyl-anion, point group

Cyclopropane point group

C„ point groups

C„h point groups

D h point group

D2h point group

D3 point group

D3h point group

D4h point group

D4h point group complexes

D4h point group physical properties

D6h point group

Da, point group

Determination of molecular point groups

Diborane point group

Diffraction relation between crystal point groups

Disconnection at a Functional Group or Branch Point

Dn point groups

Dnd point groups

Dnh point groups

Dodecahedrane point group

Elements of point group

Enantiomorphs chiral point groups

Establishing the Molecular Point Group

Establishing the Point Group

Ethane point group

Ethane symmetry point group

Ethylene point group

Example Point Group Assignments

Ferrocene, point group

First-Order Groups and Their Contributions for Melting Point

Fluoride symmetry point groups

Focal point group

Formaldehyde point group

General three-dimensional point groups

Group 32 crystallographic point groups

Group contribution approaches melting point

Group contribution models melting point

Group melting points

Holosymmetric point group

Hydrogen chloride point group

Hydrogen peroxide point group

Hypercoordinate Bonding to Main Group Elements The Spin-coupled Point of View

Icosahedral clusters point group

Icosahedral point group

Icosahedron, point group

Identification of molecular point groups

Identifying point groups

Ih point group

Infinite point groups

International point groups

Isomer counting using point group symmetry

Kh point group

Linear molecules point groups

Linear species point groups

Magnetic point groups

Magnetic point groups and colour symmetry

Melting points group 18 elements

Melting points group 2 metal oxides

Melting points group 2 oxides

Methane point group

Methane, symmetry point group

Methanol point group

Methylene chloride point group

Molecular point group determination

Molecular point group, from crystal

Molecular point groups establishing

Molecular point groups symmetries

Molecular symmetry, and point groups

Naphthalene point group

Near-infrared spectra point groups

Non-crystallographic point groups

Numbers crystallographic point groups

Octahedral molecules point groups

Octahedral point group

Oh point group

One- and two-dimensional lattices point groups

Orthorhombic, Point Group 222 (02) Materials

Orthorhombic, Point Group mm2 (C2v) Materials

Other point groups

Overview of the Point Groups

Permutation Groups and Point Group Symmetries

Platinum Point groups

Point Group 2 (C2) Materials

Point Group 23 (7) Materials

Point Group Theory and Electrospray Mass Spectrometry

Point Group. Electronic States

Point Group. Electronic Structure

Point Group. Isomerism

Point Group. Isomerism. Electronic Structure

Point Groups and Character Tables

Point Groups and Symmetry Operations

Point Groups and Their Character Tables

Point Groups for Various Molecules

Point factor group

Point factor group elements

Point group antisymmetry

Point group classification scheme

Point group designation

Point group determination

Point group establishing

Point group generators

Point group notation

Point group notation, Hermann-Mauguin

Point group of a molecule

Point group symmetry

Point group symmetry correction

Point group symmetry defined

Point group symmetry electronic wave function

Point group symmetry for

Point group symmetry, effects

Point groups

Point groups

Point groups Polarizability

Point groups assignment method

Point groups assignments

Point groups axial

Point groups characteristic symmetry elements

Point groups chiral molecules

Point groups class

Point groups conjugate elements

Point groups crystal systems

Point groups cyclic

Point groups definition

Point groups diagram

Point groups example molecule

Point groups examples

Point groups families

Point groups high-symmetry

Point groups identity operation

Point groups isometrics

Point groups molecular assignment

Point groups molecules

Point groups of high symmetry

Point groups of symmetry

Point groups operators

Point groups properties

Point groups quantum theory

Point groups subgroups

Point groups symmetry elements

Point groups, molecular

Point symmetry group groups

Point-group operations

Polar point groups

Poly point group

Projection operators point group

Proper point group

Properties of crystals with magnetic point groups

Rare-earth site, point group

Reflection axis point groups

Relation to point-groups

Relationships between space and point groups

Renormalization group fixed point

Representation point-group

Representations of point groups

Rotation crystallographic point groups

Rotational symmetry point groups

S4 point group

Sastri-Rao Group Contributions for Liquid Thermal onductivity at the Normal Boiling Point

Second-Order Groups and Their Contributions for Melting Point

Species of the D2h Point Group

Square-planar point group

Structural point groups, crystallography

Subject point groups

Symbols point groups

Symmetry Elements and Point Groups

Symmetry chiral point groups

Symmetry crystallographic point groups

Symmetry operations, the point group

Symmetry operators and point groups

Symmetry point group determination

Symmetry point groups Systematic absences

Symmetry point groups and

Symmetry point groups diagram

Symmetry, Point Groups and Generators

Symmetry, double point group, allowed

S„ point groups

Ta point group

Tables of the More Common Symmetry Point Groups

Td point group

Tetrahedral complexes point group

Tetrahedral point group

The Cubic Point Groups

The Hermann-Mauguin symbols for point groups

The Symmetry Point Groups

The crystallographic point groups

The ten plane crystallographic point symmetry groups

Thirty-two crystal classes (crystallographic point groups)

Time-Reversal and Point-Group Symmetry

Trigonal, Point Group 32 (03) Materials

Tris complexes point group

Uses of Point Group Symmetry

V point group

Valley symmetry point group

Vanadium group melting points

Water point group

Wavevector point-symmetry group

Z)3h point group

Z>2h point group

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