1. = c1N2s + c2Npz + c3(a + b +c) (1a1)
+ 2 others (2a1 and 3a1)
This is now one (group) orbital!

2. = c1Npx + c2Npy + c3(a - b) + c4(2a - b - c ) (1e)
+ another pair 2e

3. Homo is lone pair

4. Fundamentals of Molecular Orbital Theory
Main concepts
Main Skills
MO = LCAO
Mathematical for of the AO
Many electron problem  One electron proble
Eigenequation
Perturbation Theory
Point Groups
Symmetry control of orbital formation
Simple Huckel Theory
SALC
PhotoElectron Spectroscopy
Orbital mixing
IR and Raman
Particle in a box
Using Simple Huckel Theory
Small Molecules
Interpreting PES
Assigning a point group to a molecule
Obtaining reducible representations
Reducing to irreducible representations.
Projection Operator to obtain SALC
Interaction Diagrams
Obtaining allowed vibrational excitations.

5. Acid-base and donor-acceptor chemistry
Hard and soft acids and bases

6. Classical concepts Arrhenius:
acids form hydrogen ions H+ (hydronium, oxonium H3O+) in aqueous solution
bases form hydroxide ions OH- in aqueous solution
acid + base  salt + water
e.g. HNO3 + KOH  KNO3 + H2O
Brønsted-Lowry:
acids tend to lose H+
bases tend to gain H+
acid 1 + base 2  base 1 + acid 2 (conjugate pairs)
H3O+ + NO2-  H2O + HNO2
NH4+ + NH2-  NH3 + NH3
In any solvent, the reaction always favors the formation
of the weaker acids or bases
The Lewis concept is more general
and can be interpreted in terms of MO’s

7. that frontier orbitalsCO
Remember
that frontier orbitals
define the chemistry
of a molecule
CO is a a p-acceptor
and s-donor d- d+ C O M

8. A base is an electron-pair donor An acid is an electron-pair acceptor
Acids and bases (the Lewis concept)
A base is an electron-pair donor
An acid is an electron-pair acceptor
acid
base
adduct
Lewis acid-base adducts involving metal ions
are called coordination compounds (or complexes)

9. NH3 Frontier orbitals and acid-base reactions N-H s*
Remember the NH3 molecule
N-H s

10. Frontier orbitals and acid-base reactions
Simple example of Acid/Base Reaction.
Now more detail…

11. The protonation of NH3 Frontier orbitals and acid-base reactions
Simple example of Acid/Base Reaction.
The protonation of NH3
again
(Td)
(C3v) 11

12. But remember that there must be useful overlap (same symmetry)
and similar energies to form new bonding and antibonding orbitals
What reactions take place if energies are very different?

13. Frontier orbitals and acid-base reactions
Even when symmetries match several reactions are possible,
depending on the relative energies
LUMO
HOMO

14. Frontier orbitals and acid-base reactions
Very different energies like A-B or A-E
get reaction but no adducts form
Similar energies like A-C or A-D
adducts form
A base has an electron-pair
in a HOMO of suitable symmetry
to interact with the LUMO of the acid

15. The MO basis for hydrogen bonding
F-H-F-

16. MO diagram derived from atomic orbitals
As before….
MO diagram derived from atomic orbitals
(using F…….F group orbitals + H orbitals)
Non-bonding e
Bonding e

17. But it is also possible from HF + F-, Hydrogen Bonding
First form HF
HOMO-LUMO of HF for s interaction
Non-bonding
(no symmetry match)
Non-bonding
(no E match)

18. F-H-F- The MO basis for hydrogen bonding LUMO HOMO HOMO
First take bonding and antibonding combinations.

19. The MO basis for hydrogen bonding
F-H-F-
LUMO
HOMO
HOMO
Bonding

20. Total energy of B-H-A lower than the sum of the energies of reactants
Similarly for unsymmetrical B-H-A
Total energy of B-H-A lower than the sum of the energies of reactants

21. Poor energy match, little or no H-bonding
Good energy match,
strong H-bonding
e.g. CH3COOH + H2O
Poor energy match, little or no H-bonding
e.g. CH4 + H2O
Very poor energy match
no adduct formed
H+ transfer reaction
e.g. HCl + H2O

22. Ralph Pearson introduced the Hard Soft [Lewis] Acid Base (HSAB) principle in the early nineteen sixties, and in doing so attempted to unify inorganic and organic reaction chemistry.
The impact of the new idea was immediate, however over time the HSAB principle has rather fallen by the wayside while other approaches developed at the same time, such as frontier molecular orbital (FMO) theory and molecular mechanics, have flourished.

23. The Irving-Williams stability series (1953) pointed out that for a given ligand the stability of dipositive metal ion complexes increases:
It was also known that certain ligands formed their most stable complexes with metal ions like Al3+, Ti4+ and Co3+ while others formed stable complexes with Ag+, Hg2+ and Pt2+.

24. In 1958 Ahrland classified metal cations as Type A and Type B, where:
Type A metal cations included:
• Alkali metal cations: Li+ to Cs+ • Alkaline earth metal cations: Be2+ to Ba2+ • Lighter transition metal cations in higher oxidation states: Ti4+, Cr3+, Fe3+, Co3+ • The proton, H+
Type B metal cations include:
• Heavier transition metal cations in lower oxidation states:
Cu+, Ag+, Cd2+, Hg+, Ni2+, Pd2+, Pt2+.
Ligands were classified as Type A or Type B depending upon
whether they formed more stable complexes with Type A or Type B metals:
                                                                                                    

25. Type A metals prefer to bind to Type A ligands and
Type B metals prefer to bind to Type B ligands
These empirical (experimentally derived)
rules tell us that Type A metals are more likely
to form oxides, carbonates, nitrides and fluorides,
Type B metals are more likely to form
phosphides, sulfides and selinides.
This type of analysis is of great economic importance
because some metals are found in
nature as sulfide ores: PbS, CdS, NiS, etc.,
while other are found as carbonates:
MgCO3 and CaCO3 and others as oxides: Fe2O3 and TiO2.

26. In the nineteen sixties, Ralph Pearson developed the
Type A and and Type B logic by explaining the
differential complexation behaviour of cations and ligands in terms of
electron pair donating Lewis bases and electron pair accepting Lewis acids:
Lewis acid   +   Lewis base            Lewis acid/base complex
Pearson classified Lewis acids and Lewis bases as
hard, borderline or soft.
According to Pearson's hard soft [Lewis] acid base (HSAB) principle:
Hard [Lewis] acids prefer to bind to hard [Lewis] bases
and
Soft [Lewis] acids prefer to bind to soft [Lewis] bases
At first sight, HSAB analysis seems
rather similar to the Type A and Type B system.
However, Pearson classified a very wide range of
atoms,
ions,
molecules and
molecular ions
as hard, borderline or soft Lewis acids or Lewis bases,
moving the analysis from traditional metal/ligand inorganic chemistry
into the realm of organic chemistry.

27. Hard Acids
Hard Bases

28. Borderline Acids
Borderline Bases

29. Soft Acids
Soft Bases

30. Most metals are classified as Hard acids or acceptors.
Exceptions: acceptors metals in red box are always soft .
Solubilities: (S-H)AgF > AgCl > AgBr >AgI (S-S)
But…… LiBr > LiCl > LiI > LiF
Green boxes are soft
in low oxidation states.
Orange boxes are soft in high oxidation states.

31. Log K for complex formation
hard
soft
softness

32. Most metals are classified as Hard acids or acceptors.
Exceptions: acceptors metals in red box are always soft .
Solubilities: (S-H)AgF > AgCl > AgBr >AgI (S-S)
But…… LiBr > LiCl > LiI > LiF
Green boxes are soft
in low oxidation states.
Orange boxes are soft in high oxidation states. 32

33. Chatt’s explanation: soft metals ACIDS have d electrons available for p-bonding
Model: Base donates electron density to metal acceptor. Back donation, from acid to base, may occur from the metal d electrons into vacant orbitals on the base.
Higher oxidation states of elements to the right of transition metals
have more soft character.
There are electrons outside the d shell which interfere with pi bonding.
In higher oxidation states they are removed.
For transition metals:
high oxidation states and position to the left of periodic table are hard
low oxidation states and position to the right of periodic table are soft
Soft BASE molecules or ions that are readily polarizable and have vacant d or π* orbitals
available for π back-bonding react best with soft metals

34. Tendency to complex with hard metal ions N >> P > As > Sb
O >> S > Se > Te
F > Cl > Br > I
Tendency to complex with soft metal ions
N << P > As > Sb
O << S > Se ~ Te
F < Cl < Br < I

35. Hard acids or bases are small and non-polarizable
The hard-soft distinction is linked to polarizability, the degree to which a molecule
or ion may be easily distorted by interaction with other molecules or ions.
Hard acids or bases are small and non-polarizable
Hard acids are cations with high positive charge (3+ or greater),
or cations with d electrons not available for π-bonding
Soft acids are cations with a moderate positive charge (2+ or lower),
Or cations with d electrons readily availbale for π-bonding
The larger and more massive an ion, the softer (large number of internal electrons
shield the outer ones making the atom or ion more polarizable)
Soft acids and bases are larger and more polarizable
For bases, a large number of electrons
or a larger size are related to soft character

36. In general, hard-hard combinations are energetically
Hard acids tend to react better with hard bases and soft acids with soft bases, in order to produce hard-hard or soft-soft combinations
In general, hard-hard combinations are energetically
more favorable than soft-soft
An acid or a base may be hard or soft
and at the same time it may be strong or weak
Both characteristics must always be taken into account
e.g. If two bases equally soft compete for the same acid,
the one with greater basicity will be preferred
but if they are not equally soft, the preference may be inverted

37. to lower solubility, color and short interionic distances,
Fajans’ rules
For a given cation, covalent character increases
with increasing anion size. F<Cl<Br<I
For a given anion, covalent character increases
with decreasing cation size. K<Na<Li
The covalent character increases
with increasing charge on either ion.
Covalent character is greater for cations with non-noble gas
electronic configurations.
A greater covalent character resulting from a soft-soft interaction is related
to lower solubility, color and short interionic distances,
whereas hard-hard interactions result in colorless and highly soluble compounds

38. Examples
Harder nucleophiles like alkoxide ion, R-O–, attack the acyl (carbonyl) carbon.
Softer nucleophiles like the cyanide ion, NC–, and the thioanion, R-S–, attack the "beta" alkyl carbon

40. Further Development
Pearson and Parr defined the chemical hardness, h, as the second derivative for how the energy with respect to the number of electrons.
Expanding with a three point approximation
Related to Mulliken electronegativity
softness

41. Mulliken’s absolute electronegativity
Quantitative measurements
EHOMO = -I
ELUMO = -A
Absolute hardness
(Pearson)
Mulliken’s absolute electronegativity
(Pearson)
Softness

42. Energy levels
for halogens
and relations between
, h and HOMO-LUMO energies

43. Chemical Hardness, , in electron volt
Acids
Bases
Hydrogen H+
infinite
Fluoride F- 7
Aluminum
Al3+
45.8
Ammonia
NH3
6.8
Lithium
Li+
35.1
hydride H-
Scandium
Sc3+
24.6
carbon monoxide CO
6.0
Sodium
Na+
21.1
hydroxyl
OH-
5.6
Lanthanum
La3+
15.4
cyanide
CN-
5.3
Zinc
Zn2+
10.8
phosphane
PH3
5.0
Carbon dioxide
CO2
nitrite
NO2-
4.5
Sulfur dioxide
SO2
Hydrosulfide
SH-
4.1
Iodine I2
3.4
Methane
CH3-
4.0