N

HH

H

x

y

x

y

s and pz orbitals of N atom above the center of the triangle are also A1 in C3v

x

y

3 s orbitals of 3 H atoms around C3can form 3 "group orbitals" (SALC AO's)e.g. a + b + c is of A1 symmetry in C3v

= c1N2s + c2Npz + c3(a + b +c) (1a1) + 2 others (2a1 and 3a1)

This is now one (group) orbital!

N

HH

H

= c1Npx + c2Npy + c3(a - b) + c4(2a - b - c ) (1e) + another pair 2e

x

y

3 s orbitals of 3 H atoms around C3can form a pair of "group orbitals"a - b) and a - b - c)of E symmetry in C3v

x

y

x

y

x

y

px, py orbitals of N atom above the center of the triangle are also E in C3v

N

HH

H

:

Homo is lone pair

Fundamentals of Molecular Orbital Theory

Main concepts Main SkillsMO = 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.

Acid-base and donor-acceptor chemistry

Hard and soft acids and bases

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 generaland can be interpreted in terms of MO’s

Rememberthat frontier orbitalsdefine the chemistry

of a molecule

-+

C O

C OM

C O M

CO is a a -acceptor and -donor

CO

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 ionsare called coordination compounds (or complexes)

acid baseadduct

Frontier orbitals and acid-base reactions

Remember the NH3 molecule

NH3

N-H *

N-H

Frontier orbitals and acid-base reactionsSimple example of Acid/Base Reaction.

Now more detail…

The protonation of NH3

Frontier orbitals and acid-base reactionsSimple example of Acid/Base Reaction.

(C3v)(Td)

again

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?

A base has an electron-pairin a HOMO of suitable symmetry

to interact with the LUMO of the acid

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-Dadducts form

The MO basis for hydrogen bonding

F-H-F-

Bonding e

Non-bonding e

MO diagram derived from atomic orbitals(using F…….F group orbitals + H orbitals)

As before….

But it is also possible from HF + F-, Hydrogen Bonding

Non-bonding(no E match)

Non-bonding(no symmetry match)

HOMO-LUMO of HF for interaction

First form HF

The MO basis for hydrogen bonding

F-H-F-

HOMO

LUMOHOMO

Formation of the orbitals

First take bonding and antibonding combinations.

HOMO

Similarly for unsymmetrical B-H-A

Total energy of B-H-A lower than the sum of

the energies of reactants

Poor energy match, little or no H-

bondinge.g. CH4 + H2O

Good energy match,strong H-bonding

e.g. CH3COOH + H2O

Very poor energy matchno adduct formed

H+ transfer reactione.g. HCl + H2O

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.

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+.

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:

                                                                                                    

Type A metals prefer to bind to Type A ligandsand

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.

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 complexPearson 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] basesand

Soft [Lewis] acids prefer to bind to soft [Lewis] basesAt 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.

Hard Acids

Hard Bases

Borderline Acids

Borderline Bases

Soft Acids

Soft Bases

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.

Log K for complex formation

softness

softhard

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.

Chatt’s explanation: soft metals ACIDS have d electrons available for -bonding

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:

Soft BASE molecules or ions that are readily polarizable and have vacant d or π* orbitalsavailable for π back-bonding react best with soft metals

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.

low oxidation states and position to the right of periodic table are soft

high oxidation states and position to the left of periodic table are hard

Tendency to complex with hard metal ions

N >> P > As > SbO >> S > Se > Te

F > Cl > Br > I

Tendency to complex with soft metal ions

N << P > As > SbO << S > Se ~ Te

F < Cl < Br < I

The hard-soft distinction is linked to polarizability, the degree to which a moleculeor 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 electronsshield the outer ones making the atom or ion more polarizable)

For bases, a large number of electrons or a larger size are related to soft character

Soft acids and bases are larger and more polarizable

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 energeticallymore favorable than soft-soft

An acid or a base may be hard or softand 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

Fajans’ rules

1. For a given cation, covalent character increases with increasing anion size. F<Cl<Br<I2. For a given anion, covalent character increases with decreasing cation size. K<Na<Li3. The covalent character increases

with increasing charge on either ion.4. Covalent character is greater for cations with non-noble gas electronic configurations.

A greater covalent character resulting from a soft-soft interaction is relatedto lower solubility, color and short interionic distances,

whereas hard-hard interactions result in colorless and highly soluble compounds

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

Further Development

Pearson and Parr defined the chemical hardness, , as the second derivative for how the energy with respect to the number of electrons.

Expanding with a three point approximation

1

softness

Related to Mulliken electronegativity 2

AI

Energy levelsfor halogensand relations between, and HOMO-LUMO energies

Chemical Hardness, , in electron voltAcids 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