Extreme cases: ionic compounds (LiF) Li transfers e - to F, forming Li + and F -. This means it occupies a MO centered on the F A1A1 A1A1 orbitals

Molecular orbitals for larger molecules 1. Determine point group of molecule (if linear, use D 2h and C 2v 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 p x, p y, p z. (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 D 2h 1st consider combinations of 2s and 2p orbitals on F atoms  2s Obtain the reducible rep based on equivalent F 2s orbitals. Use Reduction Procedure to get the irreducible reps.  2s = A g + B 1u 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 orbitals and combined with appropriate AO’s from H 1s(H) is A g 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 eV eV Good E match Strong interaction Poor E match weak interaction

Bonding e Non-bonding e Lewis structure F-H-F - implies 4 e around H ! MO analysis defines 3c-2e bond (2e delocalized over 3 atoms) Characterize the electrons: bonding, non-bonding, antibonding.

CO 2 D ∞h, use D 2h (O O) group orbitals the same as for (F F)!! But C has more AO’s to be considered than H !

CO 2 D ∞h, use D 2h No match Carbon orbitals

A g -A g interactions of C 2s and the SALC of O 2s eV eV

A g -A g interactions, now C 2s and the A g SALC of the C 2p z eV eV

B 1u -B 1u interactions. Carbon p z with SALC of oxygen 2s SALC

B 1u -B 1u interactions. Carbon pz with oxygen p z SALC

A g -A g interactions B 1u -B 1u interactions All four are symmetry allowed

A g -A g interactions B 1u -B 1u interactions All four are symmetry allowed

SALC of A g and B 1u A g :2s(C); SALC of 2s(O);– 32.4 :  = 16.5 vs 2s(C) ); SALC of 2p(O); -15.9:  = 3.5 Primary A g interaction B 1u : 2p z (C); SALC of 2s(O); -32.4:  = 21.7 vs 2p z (C); SALC 2p(O); -15.9:  = 5.2 Primary B 1u interaction Symmetry allows many interactions. Energy considerations guide as to which is important. Strengths of Interactions

Primary A g interaction Primary B 1u interaction

Bonding  Bonding  Non-bonding  Non-bonding  4 bonds All occupied MO’s are 3c-2e

LUMO HOMO The frontier orbitals of CO 2

Molecular orbitals for larger molecules: H 2 O 1. Determine point group of molecule: C 2v 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 p x, p y, p z. (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 C 2 two orbitals interchanged  v two orbitals unchanged    

No match

pzpz bonding slightly bonding antibonding pxpx bonding antibonding pypy non-bonding a 1 sym b 1 sym b 2 sym

 3 10 Find reducible representation for 3H’s Irreducible representations:    Molecular orbitals for NH 3

pzpz bonding Slightly bonding 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 H 3 O + ) in aqueous solution bases form hydroxide ions OH - in aqueous solution acid + base  salt + water e.g. HNO 3 + KOH  KNO 3 + H 2 O Brønsted-Lowry: acids tend to lose H + bases tend to gain H + acid 1 + base 1  base 1 + acid 2 (conjugate pairs) H 3 O + + NO 2 -  H 2 O + HNO 2 NH NH 2 -  NH 3 + NH 3 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

Remember that frontier orbitals define the chemistry of a molecule -- ++ CO COM COM CO is a  -donor and a  -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 ions are called coordination compounds (or complexes) acid baseadduct

Frontier orbitals and acid-base reactions Remember the NH 3 molecule

The protonation of NH 3 Frontier orbitals and acid-base reactions (C 3v )(Td)(Td) (non- bonding) (bonding) New HOMO New LUMO

In most acid-base reactions HOMO-LUMO combinations lead 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?

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

A base has an electron-pair in 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-D adducts 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 LUMO HOMO First take bonding and antibonding combinations.

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- bonding e.g. CH 4 + H 2 O Good energy match, strong H-bonding e.g. CH 3 COOH + H 2 O Very poor energy match no adduct formed H+ transfer reaction e.g. HCl + H 2 O

Hard and soft acids and bases Hard acids or bases are small and non-polarizable Soft acids and bases are larger and more polarizable Halide 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 character since 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 hard low 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* orbitals available 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 > Sb O >> S > Se > Te F > Cl > Br > I Tendency to complex with soft metal ions N As > Sb O Se ~ Te F < Cl < Br < I

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 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 electrons Shield 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 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

Fajans’ rules 1.For a given cation, covalent character increases with increasing anion size. F<Cl<Br<I 2.For a given anion, covalent character increases with decreasing cation size. K<Na<Li 3.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 related to lower solubility, color and short interionic distances, whereas hard-hard interactions result in colorless and highly soluble compounds

Quantitative measurements Absolute hardness (Pearson) Mulliken’s absolute electronegativity (Pearson) Softness E HOMO = -I E LUMO = -A

Energy levels for halogens and relations between ,  and HOMO- LUMO energies