Character Table

“Mulliken Symbol​” Meaning: Designates symmetry with respect to inversion center​

“Mulliken Symbol​” In D Point Groups: Meaning: Designate symmetry with respect to ⊥C2​

“Mulliken Symbol​” In C Point Groups: Meaning: Designate symmetry with respect to σ<span>v</span>

Properties of Multiplication Tables A symmetric multiplication table of a finite group implies the group is _____.

Properties of Multiplication Tables Every row and column contains each element exactly once. True or False

A group whose elements are all members of another higher order group, both being subject to the same operations.

Properties of the Character Table The square of any irreducible representation will include the_____.

Around the Character Table Identify the highlighted property of the character table below.

Around the Character Table Identify the highlighted property of the character table below.

Around the Character Table Identify the highlighted property of the character table below.

Around the Character Table What is the symmetry of a rotation along the x-axis in a D3h symmetric molecule?

The D4h molecule [PtCl4]2- has a b1g bending mode: Applying the the project operator for b1g yields with θ1 as the basis: Pb1g(θ1)=N(θ1 + θ3- θ2 - θ4) What does the bending motion look like?

The facial isomer of MCl3(CO)3 has Cl streching modes with the irreducible representations of: Γ​=A1+E How many Cl streching modes are there in MCl3(CO)3

What is the subgroup(s) of C3V based on the multiplication table below?

To have a subgroup g in a higher order group G, the divisor of the orders must be an integral value (e.g h/g ) True or False

Use the multiplication table below: C4*σx= ?

A group whose group operation between two elements does not depend on the order in which they are written.

If a multiplication table’s values are symmetric along its diagonal axis, then that is an _______.

Around the Character Table What is the symmetry of the dipole moment along the z-axis in a D3h symmetric molecule?

Around the Character Table The highlighted operations are ordered in what way?

Properties of Irreducible Representations Each irreduible representation is _______ to all other irreducible representation of that group.

Properties of Irreducible Representations The number of irreducible representations of the group equals____.

The characters of all operations in the same class.

Representations that are the combinations of irreducible representations.