Extreme cases: ionic compounds (LiF)

Li transfers e- to F, forming Li+ and F-. This means it occupies a MO centered on the F

A1

A1

orbitals

Molecular orbitals for larger molecules

1. Determine point group of molecule (if linear, use D2h and C2v instead of D∞h or C∞v)

2. Assign x, y, z coordinates (z axis is higher rotation axis; if non-linear y axis in outer atoms point to central atom)

3. Find the characters of the reducible representation for the combination of 2s orbitals on the outer atoms, then for px, py, pz. (as for vibrations, orbitals that change position = 0, orbitals that do not change =1; and orbitals that remain in the same position but change sign = -1)

4. Find the irreducible representations (they correspond to the symmetry of group orbitals, also called Symmetry Adapted Linear Combinations SALC’s of the orbitals).

5. Find AO’s in central atom with the same symmetry

6. Combine AO’s from central atom with those group orbitals of same symmetry and similar E

F-H-F- D∞h, use D2h

1st consider combinations of2s and 2p orbitals on F atoms

2s 2 2 0 0 0 0 2 2Obtain the reducible rep based on equivalent F 2s orbitals.

Use Reduction Procedure to get the irreducible reps.

2s = Ag + B1u

Use the Projection Operator to obtain a SALC for each irreducible rep

Repeat for each group of equivalent atomic orbitals to obtain the full set of eight SALC.

SALC can now be treated similarly to the atomic orbitalsand combined with appropriate AO’s from H

1s(H) is Ag so it matches two SALC. The interaction can be bonding or antibonding.

Both interactions are symmetry allowed, how about energies?

Orbital potential energies (see also Table 5-1 in p. 134 of textbook)

Average energies for all electrons in the same level, e.g., 3p(use to estimate which orbitals may interact)

-13.6 eV

-40.2 eV

-18.65 eV

Good E matchStrong interaction

Poor E matchweak interaction

Bonding e

Non-bonding e

Lewis structureF-H-F-

implies 4 e around H !

MO analysisdefines 3c-2e bond

(2e delocalized over 3 atoms)

Characterize the electrons: bonding, non-bonding, antibonding.

CO2

D∞h, use D2h

(O O) group orbitals the same as for (F F)!!

But C has more AO’s to be considered than H !

CO2

D∞h, use D2h

No match

Carbon orbitals

Ag-Ag interactions of C 2s and the SALC of O 2s

The SALC of the O 2s orbitals for Ag symmetry

-32.38 eV

-19.43 eV

Ag-Ag interactions, now C 2s and the Ag SALC of the C 2pz

-19.43 eV

-10.66 eV

B1u-B1u interactions. Carbon pz with SALC of oxygen 2s

SALC

B1u-B1u interactions. Carbon pz with oxygen pz SALC

SALC of Ag and B1uSALC of Ag and B1u

Ag :2s(C); -15.9 --- SALC of 2s(O);– 32.4 : = 16.5vs

2s(C) ); -19.4 --- SALC of 2p(O); -15.9: = 3.5

Primary Ag interaction

B1u: 2pz(C); -10.7 --- SALC of 2s(O); -32.4: = 21.7 vs

2pz(C); -10.7 --- SALC 2p(O); -15.9: = 5.2

Primary B1u interaction

Symmetry allows many interactions. Energy considerations guide as to which is important.

Strengths of Interactions

Primary Ag interaction

Primary B1u interaction

Bonding

Bonding

Non-bonding

Non-bonding

4 bondsAll occupied MO’s are 3c-2e

LUMO

HOMO

The frontier orbitals of CO2

Molecular orbitals for larger molecules: H2O

1. Determine point group of molecule: C2v

2. Assign x, y, z coordinates (z axis is higher rotation axis; if non-linear y axis in outer atoms point to central atom - not necessary for H since s orbitals are non-directional)

3. Find the characters of the representation for the combination of 2s orbitals on the outer atoms, then for px, py, pz. (as for vibrations, orbitals that change position = 0, orbitals that do not change =1; and orbitals that remain in the same position but change sign = -1)

4. Find the irreducible representations (they correspond to the symmetry of group orbitals,also called Symmetry Adapted Linear Combinations SALC’s of the orbitals).

5. Find AO’s in central atom with the same symmetry

6. Combine AO’s from central atom with those group orbitals of same symmetry and similar E

For H H group orbitals

v’ two orbitals interchanged

E two orbitals unchanged

C2 two orbitals interchanged

2 20 0

v two orbitals unchanged

No match

pz

bonding

slightlybonding

antibonding

px

bonding

antibonding

py

non-bonding

a1 sym

b1 sym

b2 sym

3 10

Find reducible representation for 3H’s

Irreducible representations:

Molecular orbitals for NH3

pz

bonding

Slightlybonding

anti-bonding

bonding

anti-bonding

LUMO

HOMO

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 1 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 -donor anda -acceptor

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

The protonation of NH3

Frontier orbitals and acid-base reactions

(C3v)(Td)

(non-bonding)

(bonding)

New HOMO

New LUMO

In most acid-base reactions HOMO-LUMO combinationslead to new HOMO-LUMO of the product

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 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)

But it is also possible from HF + F-

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

Hard and soft acids and bases

Hard acids or bases are small and non-polarizableSoft acids and bases are larger and more polarizableHalide ions increase in softness: fluoride < chloride<bromide<iodide

Hard-hard or soft-soft interactions are stronger (with less soluble salts) than hard-soft interactions (which tend to be more soluble).

Most metals are classified as Hard (Class a) acids or acceptors.Exceptions shown below: acceptors metals in red box are always soft (Class b). Other metals are soft in low oxidation states and are indicated by symbol.

Class (b) or soft always Solubilities: AgF > AgCl > AgBr >AgI

But…… LiBr > LiCl > LiI > LiF

Chatt’s explanationClass (b) soft metals have d electrons available for -bonding

Higher oxidation states of elements to the right of transition metals have more class b charactersince there are electrons outside the d shell.

Ex. (Tl(III) > Tl(I), has two 6s electrons outside the 5d making them less available for π-bonding)

For transition metals: high oxidation states and position to the left of periodic table are hardlow oxidation states and position to the right of periodic table are soft

Soft donor molecules or ions that are readily polarizable and have vacant d or π* orbitalsavailable for π-bonding react best with class (b) soft metals

Model: Base donates electron density to metal acceptor. Back donation, from acid to base, may occur from the d electrons of the acid metal into vacant orbitals on the base.

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

Soft acids and bases are larger and more 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

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

Quantitative measurements

2

AI

2

AI

Absolute hardness(Pearson)

Mulliken’s absolute electronegativity(Pearson)

1

Softness

EHOMO = -I

ELUMO = -A

Energy levelsfor halogensand relations between, and HOMO-LUMO energies