Micheal Bearpark

Question 1

What insight does molecular symmetry give us?

Answer 1

Ø Can a molecule have degenerate electronic states?
Ø Will a molecule have a static dipole moment?
Ø Is a molecule chiral?

Spectroscopic selection rules are based on symmetries: we can predict
whether a transition between electronic states is allowed (intensity non-zero)
or forbidden (intensity zero).
Symmetry can also tell us whether orbitals interact, hence bonding

Question 2

What is molecular symmetry?

Answer 2

A molecule has symmetry if we can do something to it, and the result is
indistinguishable – looks unchanged – from what we started with

Question 3

What is the difference between a symmetry element and a symmetry operation?

Answer 3

Symmetry element is what the symmetry is relative to, like an axis
Symmetry operation is what action we have done to the molecule about a symmetry element, for example rotate 180 degrees

Question 4

What is a C2 operation?

Answer 4

Where we rotate a molecule 180 degrees aroundan axis and it looks unchanged. Rotating it by 360 is the same as doing nothing so we call that E

Question 5

What is a C3 axis?

Answer 5

When an molecule rotates through 120 degrees around an axis C3(2) is 240 degrees, all in all rotates 3 times

Question 6

Can molecules have more than one axis of symmetry?

Answer 6

Yes, BF3 and other trigonal planar molecules have 3C2 axis going through each of the F molecules and 1 C3 axis going through the boron centre. Principle axis is one with the highest order

Question 7

What is reflection symmetry?

Answer 7

When you cut a molecule in half down an axis, it looks the same on either half, labelled sigma.

Question 8

How much symmetry does water have altogether?

Answer 8

4 operations in total- E, C2, sigma V and sigma deriv V. 2 roatational 2 reflection

Question 9

Can a molecule have more than one mirror plane? use BF3 as example.

Answer 9

Yes, BF3 has 3 relfections that all contain the C3 axis , reflections across each bond. It then also has a mirror plan orthogonal to the C3 axis which is delta H.

Question 10

What is inversion symmetry?

Answer 10

For any point in a molecule, inversion i swaps (x,y,z) with (-x,-y,-z)
through a centre of inversion

Question 11

What is improper rotation Sn?

Answer 11

rotate 180° (C2)
§ then reflect in a plane perpendicular to the rotation axis (sh)

Question 12

What are point groups of symmetry operations?

Answer 12

‘point’ - a molecule’s symmetry elements all intersect at a point in
the centre, which isn’t moved by any symmetry operation.
(There doesn’t have to be an atom at the centre, e.g. benzene).
‘group’ - a mathematical property of the set of symmetry
operations of a molecule. (Not the symmetry elements!)

Question 13

How to describe the molecular orbitals in H2+

Answer 13

We take a minimal basis set which is the smallest amount of AO’s required to desribe the MO for a molecule. For H2+ we just need the 1S orbital of both Hydrogens

H2+ is also centrosymmetric so there is equal chance of finding the electron in either AO. c2A = +-c2B. There will be constructive and destructive interference.

Question 14

How do we describe the constructive and destructive interference in the AO’s of H2+

Answer 14

Constructive interference = 1sA(RA) + 1sB(RB)
Destructive interference = 1sA(RA) - 1sB(RB)

Question 15

Can you understand basic Dirac notation?

Answer 15

n > = ψn
| m > = ψ m
Aˆ | m > ⇔ Aˆψ m
< m | n > = ψ mψn ∫ dV
< m | Aˆ | n > = ψ m Aˆψn ∫ dV

Question 16

Calculating energy of a wave function in dirac notation and standard notation?

Answer 16

premultiply each side by the wavefunction, combine and divide through by <i | i>. If wavefunction is normalised, we can get rid of that expression anyways because it equals 1

Question 17

what is cA and cB in molecular orbital theory?

Answer 17

cA and cB are molecular orbital coeffiencts of atom A and B, how much their orbitals contribte to the molecular orbital

Question 18

How to determine H2+ molecular orbital coefficient cA?

Answer 18

Can be calculated through normalisation. The combination of hydrogen A and hydrogen B wavefunctions is 1 due to normalisation. Combining two A and two B will equal 1 for normalised AOs and combining A and B will give the integral SAB and SBA which are equal to each other. These can be positive or negative depending on the constructive or destructive interference. This leads to cA, after rearranging, to equal 1 / sqr(2(1+-SAB)

Question 19

What is the overlap integral?

Answer 19

When combining AO’s, the overlap integral is the extent to which two AOs overlap. If they are far apart the integral tends to 0 if they are close together it tends to 1

Question 20

What do you get when you combine two AO’s and what do these things look like how do they differ to each other?

Answer 20

if you combine N AO’s you get N MO’s so combine two you get two out etc. These will be a bonding, ground state low energy orbital and an antibonding, excited state high energy orbital. Bonding orbitals will have even parity g and antibonding willbe odd parity u. Bonding are stable and high e- density between nuclei and antibonding are unstable with low e- between nuclei

Question 20

How to find energy of H2+ MO

Answer 20

use E = <wf|H|wf>
sub in orbital coefficient and 1sA and 1sB orbitals. HAA and HBB are the same and HAB and HBA are the same. once combined everything
E+- = HAA +- HAB/ 1 +- SAB

Question 21

How can we simplify energy calculation for H2+ MO?

Answer 21

can say that HAA is relatively equal to E1s(H)
SAB«1
so we can rewrite equation to E = E1s +- HAB
in this case the bonding & anti-bonding MOs are energetically symmetrical
about E1s(H)

Question 22

what is the relationshipbetween HAB and SAB in regards to R

Answer 22

As R, separation between the two nuclei, increases to large values, SAB and HAB are proportional

Question 23

What is the effect of nuclear separation?

Answer 23

HAA= E1s in this scenario, shows that E+ is more stable and E- is less stable than E1s
for R > R0 : HAB proportional SAB
* if SAB is small then HAB is small

Question 24

Variational theorem, what is it?

Answer 24

For such a simple molecule like H2+, we can determine MOs from symmetry arguments and the fact both atoms joining were the same. For my complex molecules, we use the variational theorem, following the same equation just with guesses for wavefunctions.

Question 25

What are the key considerations in variational theorem?

Answer 25

– provides a means of optimising free parameters
– the true ground-state energy is always lower than the guess
– the best approx WF has the lowest energy

Question 26

How do we estimate MOs using variational theorem?

Answer 26

cannot group HAA and HBB together now, or cA and cB so used separately, all H combinations / all S combinations

Question 27

What is Z in the variation theorem?

Answer 27

Z is a tuning parameter to improve the approximation, the value of Z that minimises energy will give the best approximation.

Question 28

How do atomic wavefunctions change in a molecule?

Answer 28

When brougt together in a molecule, AOs change shaped, extending along the bonding axis and compressing perpendicular to the axis