Test 1

Question 0

Symmetry operation

Answer 0

A movement along a symmetry element where we cant tell if something moved or not- its in the same spot.

Question 1

What are symmetry elements?

Answer 1

An imaginary geometrical identity like a line, plane, or point at which symmetry operation can be performed

Question 2

Point group

Answer 2

Collection of Symmetry operations possible for an isolated object. Symmetry elements of these operations have a center point

Question 3

Space group

Answer 3

Group of Symmetry operations valid for a continuous array. Can be point symmetry operations, translations, or combos

Question 4

Explain the identity operation E

Answer 4

Identity. Operation that moves object or all parts of an object to starting position

Question 5

Explain the symmetry operation Cn

Answer 5

Is a proper rotation. It is an operation that is themovement around an axis by 360/n where n is the order (and an integer)

Question 6

Principle axis

Answer 6

The highest order rotational axis an object possesses

Question 7

Explain the symmetry operation Sigma

Answer 7

Reflection. Occurs when a point normal to a mirror plane is found at an equivalent, opposite point

Question 8

Explain the operation i

Answer 8

Inversion. Inversion occurs if for any point there is an equivalent point through the center and on the opposite side of the object

Question 9

What is another word for an object that has inversion?

Answer 9

Centrosymmetric

Question 10

Explain the symmetry operation S

Answer 10

Improper rotation. It consists of a proper rotation followed by a reflection across a mirror plane perpendicular to the principle axis

Question 11

Define chirality

Answer 11

An object is chiral if it only has identity operation or only proper rotation. Groups that are chiral are: Cn, Dn, T, O, I

Question 12

When can a molecule have a dipole?

Answer 12

There can be a dipole if a symmetry operation must go through a certain point/vector. Dipoles can exist in C1, CS(if in mirror plane), Cn (if dipole is on axis), and Cnv ( if dipole is in axis)

No dipole if it has inversion, rotational axis |_ to mirror plane, or more than one rotational axis

Question 13

What is an irreducible representation?

Answer 13

They are the simplest, fundamental representations (of symmetry?) for a group

Question 14

What is a reducible representation?

Answer 14

Is a combination of irreducible representations

Question 15

How do we know the dimensions of an irreducible representations?

Answer 15

The character under identity operations tells us how big a matrix is

Question 16

What is the order of a point group?

Answer 16

It is the total number of symmetry operations in a group. We find if by adding all the numbers at the top of a character table

Question 17

What is a basis function?

Answer 17

The functions on the very right of a character table that calculate how an object is affected by a symmetry operation

Question 18

What is the reduction formula and what do the terms stand for?

Answer 18

N= 1/h sum( gi Xi Xr)

The number of times a irreducible representations appears in the reducible representation= 1/ order of group sum( number of operations for class x characters is reducible representation x characters in irreducible representation)

Question 19

What is a shortcut i can use when applying the reduction formula?

Answer 19

I can multiply the number of symmetry operations by the # of characters from gamma reducible

Question 20

What is a direct product?

Answer 20

It is two irreducible representations multiplied together to get a gamma reducible. From there we can use the reduction formula

Question 21

List the steps to find whether a vibration mode will show up on IR or Raman spectra.

Answer 21

Find point group
Assign vectors
Find vectors that don’t move to produce gamma reducible(remember you can have inversion if i assigned 3 vectors)
Apply reduction formula
If 3 vectors were put on each atom, take out rotational/tranlational movements
Determine which modes would show up on the specta

Question 22

Which vibrational modes show up in IR?

Answer 22

Irreducible representations with Rx, Ry, Rz or only x, y, and z

Question 23

What vibrational modes show up in Raman spectra?

Answer 23

Quadratic functions

Question 24

Can a single vibrational mode show up on both spectra?

Answer 24

No.

Question 25

What does E for gamma reducible tell us?

Answer 25

It tells us the number of vectors we have

Question 26

When do we take out translational and rotational modes?

Answer 26

When we assigned 3 vectors for each atom

Question 27

What is a unit cell?

Answer 27

It is the simplest 3D crystal from which a crystal can be made fron successive translations