Mulliken Symbols & Degrees of Freedom (9/15)

What is commuting?

Two operations where the order in which they happen does not matter.

What commutes with a rotation?

• a rotation about the same axes

• an inversion

• a reflection in a plane perpendicular to the rotation axis

What commutes with a reflection?

• another reflection on a perpendicular plane

• an inversion

• a rotation in a plane if the rotation is perpendicular to the rotation axis

What is a character table?

irreducible representation of a point group

In a character table, are the columns carried out first or the rows?

columns

What is in the upper left hand corner of a character table?

Schoenflies notation for the point group (ex. C2v)

What is in the lower left hand section of a character table?

Mulliken symbols of representations

What is in the upper middle-left section of a character table?

The operations of the point group for the point group described in upper left

What is in the lower middle-left section of a character table?

The representations of a group, entry = character

What is in the lower middle-right section of a character table?

Symbols for coordinates (xyz) and rotations (Rx Ry Rz)

What is in the lower right section of a character table?

The squares or binary products of coordinates

What does 1 and -1 mean in entries?

1 means symmetry, -1 means asymmetry

What’s always in the first row of a character table? What is this called?

All 1s - called totally symmetric

What type of atomic orbitals relate to the right column of a character tables?

d-orbitals

Describe the different d-orbitals.

The clover with leaves that don’t align with the axes are the dxy, dxz, and dyz orbitals. The clover with leaves that do align is the dx^2-y^2 orbital.

The one that looks like a p-orbital with the ring is z2.

If the Mulliken Symbol is A, what does this mean?

1 under E, 1 under Cn

If the Mulliken Symbol is B, what does this mean?

1 under E, -1 under Cn

If the Mulliken Symbol is E, what does this mean?

2 under E

If the Mulliken Symbol is T, what does this mean?

3 under E

What does the subscript of 1 mean under A or B in Mulliken Symbols?

1 under C2

What does the subscript of 2 mean under A or B in Mulliken Symbols?

-1 under C2

What does prime mean in Mulliken Symbols?

symmetric to mirror plane

What does double prime mean in Mulliken Symbols?

antisymmetric to mirror plane

How many reducible representations do molecules have?

infinite

What is the range of IR spectroscopy in mu meters?

2.5-1000

In v = (1/2pi*c) * (k/M)^1/2, what does the v stand for and what units is it in?

vibrational frequency 1/cm

In v = (1/2pi*c) * (k/M)^1/2, what does the c stand for and what units is it in?

speed of light; 299,000,000 m/s meters/second

In v = (1/2pi*c) * (k/M)^1/2, what does the k stand for and what units is it in?

Force constant

dxne/cm dxne = 1 g*cm / s^2 → dxne is the change in energy vs nuclear distance; measuring curvature of that well

In v = (1/2pi*c) * (k/M)^1/2, what does the M stand for?

reduced mass (product of masses / sum of masses).

What is the requirement for a molecule to be IR-active?

dipole moment change

What is the requirement for a molecule to be Raman-active?

polarizability change

What type of symmetry does IR have?

u

What type of symmetry does Raman have?

g

What are the two main vibrational modes?

stretching and bending

What is scattering? What are the three main types?

Scattering is going from ground to virtual energy states in photons.

• rayleigh

• stokes raman

• antistokes raman

Which type of scattering is elastic?

Rayleigh

Describe the scattering that is inelastic (loss of energy).

Stokes Raman.

Describe the scattering that is inelastic (gain of energy). What special condition does this require?

Antistokes Raman Scattering. Requires an already excited photon.

What degrees of freedom do all molecules have?

three translational: x, y, and z axes

What degrees of freedom do non-linear molecules have?

3n-6

What degrees of freedom do linear molecules have?

3n-5

What is the equation for degrees of freedom?

3n, n=number of atoms

What type of vibrational mode won’t be IR active?

symmetric stretch (no dipole moment change)