Big Chemical Encyclopedia

Chemical substances, components, reactions, process design ...

Articles Figures Tables About

Irreducible

This approach to synthesis is one of making a series of best local decisions. Equipment is added only if it can be justified economically on the basis of the information available, albeit an incomplete picture. This keeps the structure irreducible, and features which are technically or economically redundant are not included. [Pg.8]

The approach to heat exchanger network design discussed so far is based on the creation of an irreducible structure. No redundant features were included. Of course, when the network is optimized, some of the features might be removed by the optimization. The scope for the optimization to remove features results from the assumptions made during the creation of the initial structure. However, no attempt was made to deliberately include redundant features. [Pg.394]

In fignre A1.3.9 the Brillouin zone for a FCC and a BCC crystal are illustrated. It is a connnon practice to label high-synnnetry point and directions by letters or symbols. For example, the k = 0 point is called the F point. For cubic crystals, there exist 48 symmetry operations and this synnnetry is maintained in the energy bands e.g., E k, k, k is mvariant under sign pennutations of (x,y, z). As such, one need only have knowledge of (k) in Tof the zone to detennine the energy band tlnoughout the zone. The part of the zone which caimot be reduced by synnnetry is called the irreducible Brillouin zone. [Pg.107]

Having done this we solve the Scln-ddinger equation for the molecule by diagonalizing the Hamiltonian matrix in a complete set of known basis fiinctions. We choose the basis functions so that they transfonn according to the irreducible representations of the synnnetry group. [Pg.140]

The Hamiltonian matrix will be block diagonal in this basis set. There will be one block for each irreducible representation of the synnnetry group. [Pg.140]

As a result the eigenstates of // can be labelled by the irreducible representations of the synnnetry group and these irreducible representations can be used as good quantum numbers for understanding interactions and transitions. [Pg.140]

We have described here one particular type of molecular synnnetry, rotational symmetry. On one hand, this example is complicated because the appropriate symmetry group, K (spatial), has infinitely many elements. On the other hand, it is simple because each irreducible representation of K (spatial) corresponds to a particular value of the quantum number F which is associated with a physically observable quantity, the angular momentum. Below we describe other types of molecular synnnetry, some of which give rise to finite synnnetry groups. [Pg.140]

The characters of the irreducible representations of a synnnetry group are collected together into a character table and the character table of the group 3 is given in table A1.4.3. The construction of character tables for finite groups is treated in section 4.4 of [2] and section 3-4 of [3]. [Pg.152]

In applications of group theory we often obtain a reducible representation, and we then need to reduce it to its irreducible components. The way that a given representation of a group is reduced to its irreducible components depends only on the characters of the matrices in the representation and on the characters of the matrices in the irreducible representations of the group. Suppose that the reducible representation is F and that the group involved... [Pg.152]

The irreducible representations of a symmetry group of a molecule are used to label its energy levels. The way we label the energy levels follows from an examination of the effect of a synnnetry operation on the molecular Sclnodinger equation. [Pg.155]

The energy level of an an /-fold degenerate eigenstate can be labelled according to an /-fold degenerate irreducible representation of the synmietry group, as we now show. [Pg.157]

The rotation-vibration-electronic energy levels of the PH3 molecule (neglecting nuclear spin) can be labelled with the irreducible representation labels of the group The character table of this group is given in table Al.4.10. [Pg.177]

Whenever a fiinction can be written as a product of two or more fiinctions, each of which belongs to one of the synnnetry classes, the symmetry of the product fiinction is the direct product of the syimnetries of its constituents. This direct product is obtained in non-degenerate cases by taking the product of the characters for each symmetry operation. For example, the fiinction xy will have a symmetry given by the direct product of the syimnetries of v and ofy this direct product is obtained by taking the product of the characters for each synnnetry operation. In this example it may be seen that, for each operation, the product of the characters for Bj and B2 irreducible representations gives the character of the representation, so xy transfonns as A2. [Pg.1136]

J. S. Griffith, The Irreducible Tensor Method for Molecular Symmetry Groups, Prentice-Hall, Englewood Cliffs, NJ, 1962, p. 20. [Pg.177]


See other pages where Irreducible is mentioned: [Pg.8]    [Pg.13]    [Pg.13]    [Pg.389]    [Pg.124]    [Pg.63]    [Pg.140]    [Pg.140]    [Pg.141]    [Pg.148]    [Pg.151]    [Pg.152]    [Pg.152]    [Pg.152]    [Pg.152]    [Pg.153]    [Pg.156]    [Pg.157]    [Pg.158]    [Pg.158]    [Pg.159]    [Pg.161]    [Pg.169]    [Pg.170]    [Pg.170]    [Pg.172]    [Pg.175]    [Pg.176]    [Pg.176]    [Pg.179]    [Pg.1135]    [Pg.2843]    [Pg.210]    [Pg.379]   
See also in sourсe #XX -- [ Pg.81 ]

See also in sourсe #XX -- [ Pg.81 ]

See also in sourсe #XX -- [ Pg.167 ]




SEARCH



0 electrodynamics Einstein irreducible representations

Algebra, irreducible representation

Basis of an irreducible representation

Boson irreducible representations

Bulk volume irreducible fluid

Character of irreducible representations

Characters of irreducible

Cluster integrals irreducible

Cluster, irreducible

Complexity irreducible

Computational irreducibility

Contracted Schrodinger equation irreducible

Coordinate irreducible representation

D irreducible representations

Diagram irreducible

Diagrams irreducible diagram

Dipole irreducible three-body component

Dispersions, irreducible

Electron irreducible representation

Element irreducible

Equations irreducible sets

Fermion irreducible representations

Field tensors irreducible representations

Graph irreducible

Group irreducible

Group irreducible inequivalent

Group theory irreducible representations

Groups irreducible matrix representations

Groups irreducible representation

Groups, Abelian, irreducible representations

Groups, continuous irreducible representations

In situ ETEM studies of metal-irreducible ceramic support interactions

Integrals irreducible cluster integral

Invariant Integration and Characters of Irreducible Representations

Irreducibility

Irreducibility condition

Irreducibility criterion

Irreducibility of Finite Markov Chains

Irreducible Bloch functions

Irreducible Brillouin conditions

Irreducible Brillouin zone

Irreducible Cartesian tensors

Irreducible Components in

Irreducible Modules over Associative Rings with

Irreducible R-matrix

Irreducible Representations and Invariant Integration

Irreducible Representations of Translation Group Brillouin Zone

Irreducible Water Saturation

Irreducible character

Irreducible domain

Irreducible emergence

Irreducible equations

Irreducible fluid saturation

Irreducible fluid saturation water

Irreducible full representation

Irreducible inequivalent representations

Irreducible interaction between ions

Irreducible invariant subspace

Irreducible linear manifolds

Irreducible matrix representations

Irreducible memory functions

Irreducible module

Irreducible nets

Irreducible particle-hole

Irreducible polarization propagator

Irreducible projective

Irreducible projective representation

Irreducible representation 2- dimensional

Irreducible representation Direct products

Irreducible representation characters

Irreducible representation degenerate

Irreducible representation notation

Irreducible representation of a group

Irreducible representation properties

Irreducible representations

Irreducible representations benzene molecules

Irreducible representations definition

Irreducible representations electrodynamics

Irreducible representations electronic wave function

Irreducible representations fourfold degenerate

Irreducible representations gerade

Irreducible representations group theoretical properties

Irreducible representations invariant operators

Irreducible representations labelling

Irreducible representations nondegenerate

Irreducible representations nuclear spin function

Irreducible representations orthogonal

Irreducible representations permutational symmetry

Irreducible representations total molecular wave function

Irreducible representations triatomic molecules

Irreducible representations twofold degenerate

Irreducible representations ungerade

Irreducible representations vibrational wave function

Irreducible representations, algebraic

Irreducible representations, and

Irreducible representations, and character tables

Irreducible representations, symmetric states

Irreducible small representation

Irreducible spherical tensor

Irreducible spherical tensorial representations

Irreducible spherical tensors operators

Irreducible subspace

Irreducible supports

Irreducible symmetries

Irreducible tensor method

Irreducible tensor operators

Irreducible tensor operators definition

Irreducible tensor operators matrix elements

Irreducible tensor operators normalization

Irreducible tensor product

Irreducible tensorial sets

Irreducible tensors in the space of complex configurations

Irreducible tensors second order

Irreducible tensors third order

Irreducible uncertainty

Irreducible vertex part

Irreducible volume

Irreducible water

Irreducible wetting-phase saturations

Irreducible, ternary

Irreducible/irreducibility, generally

Irreducible/irreducibility, generally representation

Irreducible/irreducibility, generally tensor components

Loop expansion, vertex irreducible graphs and screened interaction

Markov chains irreducible

Moisture content irreducible

Normalized irreducible character

Notation for irreducible representations

Number of times an irreducible representation occurs in a reducible one

One-particle irreducibility

Operator tensor, compound irreducible

Orthogonality in Irreducible Inequivalent Representations

Products of Irreducible Representations

Projective Unitary Irreducible Representations and Spin

Reducible and Irreducible Representations

Reducible and irreducible odd alternant hydrocarbon anions

Representations, completely reduced irreducible

Rotation group irreducible representations

Saturation irreducible

Second-quantization and irreducible tensorial sets

Spectroscopy irreducible

Symmetry irreducible representations

Tables and Properties of Irreducible Representations

Tensor irreducible

Tensor irreducible parts

Tetrahedral MX4, Molecules and Degenerate Irreducible Representations

The Irreducible Element

The Labelling of Irreducible Representations

The irreducible representations

The irreducible representations of

The irreducible representations of SO

Totally symmetric irreducible representation

Unitary irreducible representations

Unitary irreducible representations finite dimensional

Wave Functions as Bases for Irreducible Representations

© 2024 chempedia.info