= c1?N2s c2?Npz c3(?a ?b ?c) (1a1)

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• c1?N2s c2?Npz c3(?a ?b ?c) (1a1)
• 2 others (2a1 and 3a1)

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• c1?Npx c2?Npy c3(?a - ?b) c4(2?a - ?b -
  ?c ) (1e)
• another pair 2e

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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.
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Acid-base and donor-acceptor chemistry Hard and
soft acids and bases
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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 MOs
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CO
Remember that frontier orbitals define the
chemistry of a molecule
CO is a a p-acceptor and s-donor
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Acids and bases (the Lewis concept)
A base is an electron-pair donor An acid is an
electron-pair acceptor
Lewis acid-base adducts involving metal ions are
called coordination compounds (or complexes)
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NH3
Frontier orbitals and acid-base reactions
N-H s
Remember the NH3 molecule
N-H s
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Frontier orbitals and acid-base reactions Simple
example of Acid/Base Reaction.
Now more detail
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Frontier orbitals and acid-base reactions Simple
example of Acid/Base Reaction.
The protonation of NH3
again
(C3v)
(Td)
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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?
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Frontier orbitals and acid-base reactions
Even when symmetries match several reactions are
possible, depending on the relative energies
LUMO
HOMO
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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
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The MO basis for hydrogen bonding
F-H-F-
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As before.
MO diagram derived from atomic orbitals (using
F.F group orbitals H orbitals)
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But it is also possible from HF F-, Hydrogen
Bonding
First form HF
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The MO basis for hydrogen bonding
F-H-F-
LUMO
HOMO
HOMO
First take bonding and antibonding combinations.
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The MO basis for hydrogen bonding
F-H-F-
LUMO
HOMO
HOMO
Bonding
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Similarly for unsymmetrical B-H-A
Total energy of B-H-A lower than the sum of the
energies of reactants
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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.
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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.
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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                                         
                                                  
          
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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.
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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.
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Hard Acids
Hard Bases
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Borderline Acids
Borderline Bases
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Soft Acids
Soft Bases
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Most metals are classified as Hard acids or
acceptors. Exceptions acceptors metals in red
box are always soft .
Solubilities (S-H)AgF gt AgCl gt AgBr gtAgI
(S-S) But LiBr gt LiCl gt LiI gt LiF
Green boxes are soft in low oxidation states.
Orange boxes are soft in high oxidation states.
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Log K for complex formation
hard
soft
softness
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Most metals are classified as Hard acids or
acceptors. Exceptions acceptors metals in red
box are always soft .
Solubilities (S-H)AgF gt AgCl gt AgBr gtAgI
(S-S) But LiBr gt LiCl gt LiI gt LiF
Green boxes are soft in low oxidation states.
Orange boxes are soft in high oxidation states.
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Chatts 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 p
orbitals available for p back-bonding react best
with soft metals
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Tendency to complex with hard metal ions N gtgt P
gt As gt Sb O gtgt S gt Se gt Te F gt Cl gt Br gt I
Tendency to complex with soft metal ions N ltlt P
gt As gt Sb O ltlt S gt Se Te F lt Cl lt Br lt I
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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 p-bonding
Soft acids are cations with a moderate positive
charge (2 or lower), Or cations with d electrons
readily availbale for p-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
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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
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Fajans rules

• For a given cation, covalent character increases
• with increasing anion size. FltClltBrltI
• For a given anion, covalent character increases
• with decreasing cation size. KltNaltLi
• 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
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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

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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
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Quantitative measurements
EHOMO -I ELUMO -A
Absolute hardness (Pearson)
Mullikens absolute electronegativity (Pearson)
Softness
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• Energy levels
• for halogens
• and relations between
• , h and HOMO-LUMO energies

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Chemical Hardness, , in electron volt Chemical Hardness, , in electron volt Chemical Hardness, , in electron volt Chemical Hardness, , in electron volt Chemical Hardness, , in electron volt Chemical Hardness, , in electron volt
Acids Acids Acids Bases Bases Bases
Hydrogen H infinite Fluoride F- 7
Aluminum Al3 45.8 Ammonia NH3 6.8
Lithium Li 35.1 hydride H- 6.8
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 10.8 nitrite NO2- 4.5
Sulfur dioxide SO2 5.6 Hydrosulfide SH- 4.1
Iodine I2 3.4 Methane CH3- 4.0

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