1. Energy level diagram
EA - 
EA +  B A 

2. Linear combination of atomic orbitals
Rules for linear combination
1. Atomic orbitals must be roughly of the same energy.
2. The orbital must overlap one another as much as possible- atoms must be close enough for effective overlap.
3. In order to produce bonding and antibonding MOs, either the symmetry of two atomic orbital must remain unchanged when rotated about the internuclear line or both atomic orbitals must change symmetry in identical manner.

3. Rules for the use of MOs
* When two AOs mix, two MOs will be produced
* Each orbital can have a total of two electrons (Pauli principle)
* Lowest energy orbitals are filled first (Aufbau principle)
* Unpaired electrons have parallel spin (Hund’s rule)
Bond order = ½ (bonding electrons – antibonding electrons)

4. Linear Combination of Atomic Orbitals (LCAO)
The wave function for the molecular orbitals can be approximated by taking linear combinations of atomic orbitals. A B
AB = N(cA A + cBB)
c – extent to which each AO
contributes to the MO
2AB = (cA2 A2 + 2cAcB A B + cB2 B 2)
Overlap integral
Probability density

5. Amplitudes of wave functions added
Constructive interference g
bonding
cA = cB = 1
Amplitudes of wave functions added
g = N [A + B]

6. 2AB = (cA2 A2 + 2cAcB A B + cB2 B 2)
density between atoms
electron density on original atoms,

7. The accumulation of electron density between the nuclei put the electron in a position where it interacts strongly with both nuclei.
Nuclei are shielded from each other
The energy of the molecule is lower

8. Amplitudes of wave functions subtracted.
node
antibonding
u = N [A - B]
cA = +1, cB = -1 u + -
Destructive interference
Nodal plane perpendicular to the H-H bond axis (en density = 0)
Energy of the en in this orbital is higher.
Amplitudes of wave functions subtracted.
A-B

9. The electron is excluded from internuclear region  destabilizing
Antibonding

11. Molecular potential energy curve shows the variation of the molecular energy with internuclear separation.

12. Looking at the Energy Profile
Bonding orbital
called 1s orbital
s electron
The energy of 1s orbital
decreases as R decreases
However at small separation, repulsion becomes large
There is a minimum in potential energy curve

13. LCAO of n A.O  n M.O. H2 11.4 eV 109 nm Location of Bonding orbital

14. The overlap integral
The extent to which two atomic orbitals on different atom overlaps : the overlap integral

15. Bond strength depends on the
S > 0 Bonding
S < 0 anti
Bond strength depends on the
degree of overlap
S = 0 nonbonding

19. Homonuclear Diatomics
MOs may be classified according to:
(i) Their symmetry around the molecular axis.
(ii) Their bonding and antibonding character.
1s 1s* 2s 2s* 2p y(2p) = z(2p) y*(2p) z*(2p)2p*.

20. dx2-dy2 and dxy

21. B
g- identical
under inversion A
u- not identical

22. Place labels g or u in this diagram
s*u
p*g pu sg

23. First period diatomic moleculesH
Energy H2 1s g
u*
1s2
Bond order: 1
Bond order =
½ (bonding electrons – antibonding electrons)

24. 1s2, *1s2 Bond order: 0 Diatomic molecules: The bonding in He2
Energy
He2 1s g
u*
1s2, *1s2
Bond order: 0
Molecular Orbital theory is powerful because it allows us to predict whether molecules should exist or not and it gives us a clear picture of the of the electronic structure of any hypothetical molecule that we can imagine.

26. Second period diatomic moleculesLi
Li2 Li
1s2, *1s2, 2s2
Bond order: 1
2u* 2s 2s
2g
Energy
1u* 1s 1s
1g

27. Diatomic molecules: Homonuclear Molecules of the Second PeriodBe
Be2 Be
2u*
1s2, *1s2, 2s2, *2s2 2s 2s
2g
Energy
Bond order: 0
1u* 1s 1s
1g

28. Simplified

29. Simplified

30. MO diagram for B2
2g
2u*
3g
1u
1g*
3u*
Diamagnetic??

31. Li : 200 kJ/mol
F: 2500 kJ/mol

32. Same symmetry, energy mix-
the one with higher energy moves higher and the one with lower energy moves lower

33. MO diagram for B2 Paramagnetic B B2 LUMO HOMO 3u* 3u* 1g* 1g* 2p2s
2g
2u* 2p
3g
3u*
1u
1g*
(px,py)
HOMO
LUMO
Paramagnetic

34. C2
1g
1u
1g
1g
1u
1g
Diamagnetic
Paramagnetic ? X

35. General MO diagrams
1g
1u
1g
1g
1u
1g
Li2 to N2
O2 and F2

36. Orbital mixing Li2 to N2

37. Bond lengths in diatomic molecules
Filling bonding orbitals
Filling antibonding orbitals

39. Summary
From a basis set of N atomic orbitals, N molecular orbitals are constructed. In Period 2, N=8.
The eight orbitals can be classified by symmetry into two sets: 4  and 4  orbitals.
The four  orbitals from one doubly degenerate pair of bonding orbitals and one doubly degenerate pair of antibonding orbitals.
The four  orbitals span a range of energies, one being strongly bonding and another strongly antibonding, with the remaining two  orbitals lying between these extremes.
To establish the actual location of the energy levels, it is necessary to use absorption spectroscopy or photoelectron spectroscopy.

41. Distance between b-MO and AO

42. Heteronuclear Diatomics….
The energy level diagram is not symmetrical.
The bonding MOs are closer to the atomic orbitals which are lower in energy.
The antibonding MOs are closer to those higher in energy.
c – extent to which each atomic
orbitals contribute to MO
If cAcB the MO is composed principally of A

43. HF
1s 1
2s, 2p 7
 =c1 H1s + c2 F2s + c3 F2pz
Largely
nonbonding
2px and 2py
12 2214
Polar