Extreme cases: ionic compounds (LiF)

1. A1 A1 Li transfers e- to F, forming Li+ and F-. This means it occupies a MO centered on the F Extreme cases: ionic compounds (LiF) orbitals

2. 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

3. F-H-F- D∞h, use D2h 1st consider combinations of 2s and 2p orbitals on F atoms Obtain the reducible rep based on equivalent F 2s orbitals. Use Reduction Procedure to get the irreducible reps. G2s = 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.

4. SALC can now be treated similarly to the atomic orbitals and 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?

5. 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)

6. Good E match Strong interaction Poor E match weak interaction -13.6 eV -18.65 eV -40.2 eV

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

8. 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 !

9. No match CO2 D∞h, use D2h Carbon orbitals

10. Ag-Aginteractions of C 2s and the SALC of O 2s -19.43 eV -32.38 eV

11. Ag-Aginteractions, now C 2s and the Ag SALC of the C 2pz -10.66 eV -19.43 eV

12. B1u-B1uinteractions. Carbon pz with SALC of oxygen 2s SALC

13. B1u-B1uinteractions. Carbon pz with oxygen pz SALC

14. Symmetry allows many interactions. Energy considerations guide as to which is important. Primary B1u interaction Primary Ag interaction SALC of Ag and B1u SALC of Ag and B1u Strengths of Interactions Ag :2s(C); -15.9 --- SALC of 2s(O);– 32.4 : D = 16.5 vs 2s(C) ); -19.4 --- SALC of 2p(O); -15.9: D = 3.5 B1u: 2pz(C); -10.7 --- SALC of 2s(O); -32.4: D = 21.7 vs 2pz(C); -10.7 --- SALC 2p(O); -15.9: D = 5.2

15. Primary B1u interaction Primary Ag interaction

16. Non-bonding p Bonding p 4 bonds All occupied MO’s are 3c-2e Bonding s Non-bonding s

17. LUMO The frontier orbitals of CO2 HOMO

18. 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 Molecular orbitals for larger molecules: H2O

19. G 0 2 0 2 For H H group orbitals G = A1+ B1 E two orbitals unchanged C2 two orbitals interchanged sv two orbitals unchanged sv’ two orbitals interchanged

20. No match

21. antibonding antibonding px non-bonding pz py slightly bonding bonding bonding a1 sym b1 sym b2 sym

22. Molecular orbitals for NH3 Find reducible representation for 3H’s G 0 1 3 Irreducible representations: G = A1 + E

24. anti-bonding anti-bonding LUMO pz Slightly bonding HOMO bonding bonding

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

26. 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 general and can be interpreted in terms of MO’s

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

28. adduct base acid 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)

29. Frontier orbitals and acid-base reactions Remember the NH3 molecule

30. New LUMO (non-bonding) New HOMO (bonding) Frontier orbitals and acid-base reactions The protonation of NH3 (Td) (C3v)

31. 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?

32. 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 A base has an electron-pair in a HOMO of suitable symmetry to interact with the LUMO of the acid

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

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

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

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

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

38. 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

39. 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).

40. 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. Solubilities: AgF > AgCl > AgBr >AgI But…… LiBr > LiCl > LiI > LiF Class (b) or soft always

41. Chatt’s explanationClass (b) soft metals 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 d electrons of the acid metal into vacant orbitals on the base. 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 rightof 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

43. 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

44. 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

45. 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

46. 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

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

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