Group theory + symmetry

Question 1

What is Raman spectra due to vs IR

Answer 1

Scattering of radiation due to vibration as opposed to absorbtion of radiation (IR)

Question 2

What are the 3 degrees of freedom

Answer 2

Translational, rotational and vibrational motion

Question 3

How to work out the number of vibrational degrees of freedom of a compound + an exception

Answer 3

3N - 6 and N is number of atoms in compound. -6 becasue 3 directions of translation (x, y, z) and 3 rotational axis. Exception: 3N - 5 for LINEAR molecules - no rotation about molecular axis

Question 4

How does IR and number of vibrational degrees of freedom corrolate

Answer 4

If 3 degrees -> 3 peaks in IR. But there are expections if molecs have high symmetry

Question 5

Difference between peaks of H2O and D2O in IR spectra

Answer 5

D2O has lower frequency because harder to vibrate heaver atoms

Question 6

What does improper rotation eg S3 do?

Answer 6

Rotate by C3 then reflect in σh

Question 7

For improper rotation, what does S3^3 (S 3 times) and S3^6 do

Answer 7

S33 = σh and S3^6 is E aka identity

Question 8

What is the character of a square matrix

Answer 8

Sum of diagonal elements (top left to bottom right), symbol: χ

Question 9

What is gamma

Answer 9

Used to describe translations

Question 10

10 steps to do gamma transfomations?

Answer 10

1) Assign point group. 2) See character table (has A1, A2, E) 3) Count unshifted atoms for every symmetry opetation. 4) Find contribution of eahc unshifted atoms = from character of sq matrix for each operation. 5) Derive reducible representation of Gamma 3N. 6) Use reduction formula. 7) gives irreducible rep of gamma 3N. 8) Derive gamma trans and gamma rotational motion. 9) Gives gamma vibrations. 10) Check answer with 3N - 6

Question 11

When will Xe form bonds/react

Answer 11

With very electronegative reactant s

Question 12

Lewisstructure if the central atom is bonded to an oxygen and has no charge

Answer 12

Double bond to O, single bond causes one -ve charge

Question 13

What does σd symmetry mean

Answer 13

Mirror planes between bonds - diagonal

Question 14

What does 3N-6 show

Answer 14

There are 3 translations, 3 rotations and 3N-6 vibrations

Question 15

Why is there 2 C4 symmetries

Answer 15

Should be 4xC4 but C4 x 4 times is E. C4 x 2 is C2 so there are only 2 C4s left so it says 2C4 in character table

Question 16

When calculating degrees of freedom from A1, A4, B1 … how much is E worth

Answer 16

2 because it is doubly degenerate

Question 17

How is translations sometimes labelled in character table

Answer 17

x, y, z instead of Tx, Ty, Tz

Question 18

Difference between working out Γ3N and Γstr, ipb and oopb

Answer 18

Γ3N uses contribution of atoms from character in matrix. Γ for the rest does not - don’t multiply with anything

Question 19

Why does Γstr + Γipb + Γoopb equal more than Γvib

Answer 19

Some are redundant. Compare each ones to see if its A1 or whatever that is redundant. Can’t increase all angles at the same time - one has to get smaller

Question 20

What does the A/B/E/T Mulliken symbols represent

Answer 20

A/B= 1x1 rep, E = 2 (double degenerate), T = 3, triply degen

Question 21

How to work out ipb and oopb for a tetrahedral

Answer 21

No plane so work out all of them together as bends

Question 22

How Raman works, very brief

Answer 22

Laser at sample cell, photons bounce off gas molecules and collected in detector. Monochromator reads it

Question 23

3 types of scattering in Raman spectroscopy

Answer 23

Stokes: Molecule absorbes energy (photon loses some), Rayleigh: no change in energy. Anti-stokes: molec absorbs energy from photon

Question 24

Which scattering is looked at in Raman

Answer 24

Stokes lines

Question 25

How is Raleigh scattering related to wavelength

Answer 25

Raleigh is inversely prop to fourth power of wavelength - eg short blue light will scatter more than longer. (sky looks blue)

Question 26

How to know if vibration appears in Raman/IR

Answer 26

Look at character table. x, y, z = IR, anything squared eg x^2, xy.. is Raman

Question 27

Whats the only vibration in Raman that gives (pol) = polarised light

Answer 27

Totally symmetric eg A1

Question 28

Do stretches or vibrations occur at higher energy in Raman + IR

Answer 28

Stretches are at higher

Question 29

What type of vibration is normally under 600 in IR

Answer 29

Bend

Question 30

How to tell if a line is B1 or B2

Answer 30

Difficult to know, just have to guess kinda

Question 31

Does ipb or oopb tend to have a lower energy in IR and Raman

Answer 31

oopb normally lower E