A4 - TQ mistakes

quantum numbers of 2 e- system

Ms = 0, S = 0 (paired up)

what to do with equations that can be expanded

always keep expanding and dont give up

ε_n for linear molecule

α + 2β cos(nπ/N+1)

c_n^r for a linear molecule

c_n^r = sqrt(2/N+1) sin(nπr/N+1)

n = site

r = MO level

How to work out E_deloc

E_actual - E_ref

what is E_actual

n(α+xβ)

(n is # of e- occupying that MO, x is the coefficiant of β for that MO)

what is E_ref

n(α+β)

The PG of the intermediate when converting from C_2v to C_2h

C₂

Steps to drawing orbital correlation diagram

1. draw the MO diagrams on each side

2. label symmetries of each level

3. Connect the opposing symmetries (a-a etc.) on each side

4. hope none of the same symmetry cross (not allowed, avoided crossing)

steps to drawing state correlation diagram

1. for one molecule, add the GS, and first few excited state electron configs.

   1. dont forget spin up/down combinations of electrons

2. label what their equivalent levels would be on the other molecule

3. draw lines between corresponding configs.

4. hope none of the same type cross or not allowed (avoided crossings etc.)

equation for finding ∆ε for perturbed systems

ε.(Uε)

Outline the Lennard Jones potential

• 4ε[(σ/r]^12 - (σ/r)^6]

• ε is the depth of the potential well / strength of interaction

• σ is finite distance when inter-particle potential is 0

  • attractive and repulsive forces balance

• r is internuclear distance

• (σ/r)^6 is for VDW forces

• (σ/r)^12 is repulsive / Pauli forces

outline the Buckingham Potential

• Aexp(-Br) - C/r^6

• C/r^6 is for VDW forces

• exp term is a more accurate description of repulsive forces

• based on exponential decay of a wavefunction

for an alternant hydrocarbon, how to find most reactive site

• star alternating carbons

• start labelling unstarred as 0

• then make starred around unstarred = 0

• highest coefficient is most reactive site

state the variational principle

E₀ ≤ <p|H|p> / <p|p>
(p= psi)

what does it mean if a hamiltonian is hermitian

• eigenfunctions are orthogonal

• <ψ_i|ψ_j> = δ_ij

2 computational methods for calculating molecular potential energy surfaces

• Hartree-Fock

• Any force field

from a Huckel matrix, where can you find the sum of the MO levels / eigenvalues

the trace (sum of diagonal)

if an orbital is out of phase, what will be the interaction in a Huckel matrix

-β

Eigenfunction equation

|H-EI| = 0