Extreme cases ionic compounds Li F orbitals A
Extreme cases: ionic compounds (Li. F) orbitals A 1 Li transfers e- to F, forming Li+ and F-. This means it occupies a MO centered on the F
Molecular orbitals for larger molecules 1. Determine point group of molecule (if linear, use D 2 h and C 2 v 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 2 s 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 D 2 h 1 st consider combinations of 2 s and 2 p orbitals on F atoms Obtain the reducible rep based on equivalent F 2 s orbitals. G 2 s Use Reduction Procedure to get the irreducible reps. G 2 s = Ag + B 1 u 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. 2 2 0 0 2 2
SALC can now be treated similarly to the atomic orbitals and combined with appropriate AO’s from H 1 s(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. , 3 p (use to estimate which orbitals may interact)
-13. 6 e. V Good E match Strong interaction -18. 65 e. V Poor E match weak interaction -40. 2 e. V
Characterize the electrons: bonding, non-bonding, antibonding. Lewis structure F-H-Fimplies 4 e around H ! MO analysis defines 3 c-2 e bond (2 e delocalized over 3 atoms) Bonding e Non-bonding e
CO 2 D∞h, use D 2 h (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 2 h No match Carbon orbitals
Ag-Ag interactions of C 2 s and the SALC of O 2 s -19. 43 e. V -32. 38 e. V
Ag-Ag interactions, now C 2 s and the Ag SALC of the C 2 pz -10. 66 e. V -19. 43 e. V
B 1 u-B 1 u interactions. Carbon pz with SALC of oxygen 2 s SALC
B 1 u-B 1 u interactions. Carbon pz with oxygen pz SALC
Symmetry allows many interactions. Energy considerations guide as to which is important. Primary B 1 u interaction Primary Ag interaction SALC of Ag and B 1 u Strengths of Interactions Ag : 2 s(C); -15. 9 --- SALC of 2 s(O); – 32. 4 : D = 16. 5 vs 2 s(C) ); -19. 4 --- SALC of 2 p(O); -15. 9: D = 3. 5 B 1 u: 2 pz(C); -10. 7 --- SALC of 2 s(O); -32. 4: D = 21. 7 vs 2 pz(C); -10. 7 --- SALC 2 p(O); -15. 9: D = 5. 2
Primary B 1 u interaction Primary Ag interaction
Non-bonding p Bonding s Non-bonding s 4 bonds All occupied MO’s are 3 c-2 e
LUMO The frontier orbitals of CO 2 HOMO
Molecular orbitals for larger molecules: H 2 O 1. Determine point group of molecule: C 2 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 - not necessary for H since s orbitals are non-directional) 3. Find the characters of the representation for the combination of 2 s 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
G For H 2 0 H group orbitals E two orbitals unchanged C 2 two orbitals interchanged sv two orbitals unchanged sv’ two orbitals interchanged G = A 1 + B 1
No match
antibonding a 1 sym antibonding px b 1 sym b 2 sym non-bonding pz py slightly bonding
Molecular orbitals for NH 3 Find reducible representation for 3 H’s G 3 0 1 Irreducible representations: G = A 1 + E
anti-bonding LUMO pz Slightly bonding HOMO bonding
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 solut • 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 + acid 2 (conjugate pairs) H 3 O+ + NO 2 - H 2 O + HNO 2 NH 4+ + NH 2 - NH 3 + NH 3 In any solvent, the reaction always favors the formation of the weaker acids or bas 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 is a s-donor and a p-acceptor d+ d- C O M
Acids and bases (the Lewis concept) A base is an electron-pair donor An acid is an electron-pair acceptor acid adduct base Lewis acid-base adducts involving metal ions are called coordination compounds (or complexes)
Frontier orbitals and acid-base reactions Remember the NH 3 molecule
Frontier orbitals and acid-base reactions The protonation of NH 3 New LUMO (nonbonding) New HOMO (bonding) (Td) (C 3 v)
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?
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
The MO basis for hydrogen bonding F-H-F-
MO diagram derived from atomic orbitals (using F……. F group orbitals + H orbitals) Bonding e Non-bonding e
But it is also possible from HF + F- First form HF HOMO-LUMO of HF for s interaction Non-bonding (no symmetry match) Non-bonding (no E match)
The MO basis for hydrogen bonding F-H-F- HOMO LUMO HOMO First take bonding and antibonding combinations.
Similarly for unsymmetrical B-HA Total energy of B-H-A lower than the sum of the energies of reactants
Poor energy match, little or no Hbonding 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 Other metals are soft in low oxidation states and are indicated by symbol. Class (b) or soft always Solubilities: Ag. F > Ag. Cl > Ag. Br >Ag. I But…… Li. Br > Li. Cl > Li. I > Li. F
Chatt’s explanation. Class (b) soft metals have d electrons available for p-bondin 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 chara since there are electrons outside the d shell. Ex. (Tl(III) > Tl(I), has two 6 s electrons outside the 5 d making them less available for π-bond 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* orb available for π-bonding react best with class (b) soft metals
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
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 elec 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 cha
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) EHOMO = -I ELUMO = -A Softness
Energy levels for halogens and relations between c, h and HOMOLUMO energies
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