Physical Chemistry , 1st ed.

rectangle is lying in. In real objects, planes that contain the principal axis are considered vertical planesof symmetry and are ...

due to the symmetry operation. For a molecule having Natoms, this will require a 3N 3 Nmatrix—but there are some major simplifi ...

with all other operations of the group. That is, ifArepresents the iden- tity operation and Brepresents any other operation, the ...

tially. For our purposes, the closure requirement is more important. Any combination of symmetry operations in a point group is ...

Example 13.2 Identify the symmetry elements in ethylene, which has the structure From the tables in Appendix 3, determine its po ...

Finally, some point groups have certain interesting symmetry elements. Any linear system possesses a Caxis along the system axi ...

elements. One can either determine all of the symmetry elements of a given molecule and compare it to the (relatively short) lis ...

a.H 2 S:C2v, just like H 2 O. b.SF 6 :Oh. This molecule has the shape of an octahedron. c.C 2 H 2 :Dh, since it is linear and s ...

Solution Because wavefunctions for molecules must have the same symmetry as the molecule, one must identify the molecule’s symme ...

x,y, and zcoordinates, so there are a total of 3N(Nnumber of atoms) to- tal coordinates for the molecule. Furthermore, one need ...

C 2 (H 2 O)   (13.2) (yz)(H 2 O)  (xz)(H 2 O)  Not only do the hydrogen atoms exchange places in (xz) and C 2 , but som ...

As such, why not simply use the number 1 to represent the effect ofEon that coordinate?* In this case, that would work fine. How ...

would be found if a larger C2vmolecule were used as an example. That set would be (1, 1,1,1). Together, these four sets of num ...

Characters of the irreducible representations of a particular point group can be multiplied by each other. The reason for doing ...

have to wait until section 13.7 to show that EEdoes satisfy the closure requirement.) b.For sums of the products of characters: ...

arbitrarily numbered Greek capital letters gamma,n, is an older system that is occasionally still seen in the literature. 13.6 ...

Wavefunctions can be labeled with appropriate irreducible representation labels. Therefore, the wavefunction of the bonding mole ...

Example 13.9 The following set of characters is for a linear combination of irreducible rep- resentations for a system having C3 ...

symmetry labels of the representation in the new point group. An example is electron subshells. The quantum number defines whic ...

The three porbitals collectively are assigned to a T 1 symmetry species. (This conclusion could have been reached by comparison ...