Lecture 17 Molecular Orbital Theory 1) Molecular Orbitals of AH x (x = 3, 4, 6) MO diagrams can be used on a qualitative basis to understand the shape of molecules of the same stoichiometry (same x) but formed with different central atoms A (most commonly, should belong to the same period) Examples: removing electrons one by one from the highest occupied molecular orbital (HOMO) and decreasing nuclear charge of A we can get: AH: from MO’s of HF – MO’s of HO ●, HN (triplet and singlet), HC, HB (triplet and singlet), etc.; AH 2 : from MO’s of H 2 O – MO’s of H 2 N ●, H 2 C (singlet and triplet), H 2 B ●, BeH 2 etc. AH 3 : from MO’s of H 3 N – MO’s of H 3 C ●, H 3 C +, BH 3 etc. AH 4 : from MO’s of CH 4 – MO’s of NH 4 +, NH 4 + ● etc. While doing so, keep appropriate Walsh diagrams handy and take into account possible changes in s-p orbital mixing.
2) Molecular Orbitals of NH 3 (C 3v ) C 3v E2C 3 3v3v A1A1 111zx 2 +y 2, z 2 A2A2 11 E2 0(x,y) NH 3 (C 3v : E, 2C 3, 3 v ) The symmetry of 3H’s group orbitals: r = 3E+0C 3 + v = A 1 + E
3) Molecular Orbitals of CH 4 (T d ) TdTd A1A1 x 2 +y 2 +z 2 A2A2 E T1T1 T2T2 (x,y,z) The symmetry of 4H’s group orbitals: r = 4E+1C 3 +0C 2 +0S 4 +2 d = A 1 + T 2
4) Molecular Orbitals of closo-B 6 H 6 2- (O h ) OhOh E8C38C3 6C26C2 6C46C4 3C23C2 i6S46S4 8S68S6 3h3h 6d6d r()r() r ( ) = A 1g + E g + T 1u ; orbitals of these symmetries suitable for -bonding can be formed by six s or six p z atomic orbitals (two sets of six “radial” orbitals result) r()r() r ( ) = T 1g + T 2g + T 1u + T 2u ; orbitals of these symmetries suitable for B-B - bonding can be formed by six p x and six p y orbitals (twelve “tangential” orbitals)
5) Molecular Orbitals of closo-B 6 H “Radial” group orbitals Note that only one of the six 2p z boron group orbitals, namely a 1g, is bonding Six 2s and six 2p z boron group orbitals will mix to form two sets of radial orbitals. One of these two six-orbital sets will be used to combine with six 1s hydrogen group orbitals to form six bonding and 6 antibonding MO’s (B-H bonds) +
6) Molecular Orbitals of closo-B 6 H “Tangential” group orbitals Remaining twelve 2p x and 2p y boron orbitals form four sets of triply degenerate “tangential” group orbitals of t 1g, t 2g, t 1u and t 2u symmetry. Only two of these sets, t 2g and t 1u, are suitable for B-B -bonding in closo-B 6 H They form six -bonding MO’s (B-B -bonds).
7) B-B and B-H bonding MO’s of closo-B 6 H 6 2- closo-B 6 H 6 2- has 7 core bonding orbitals, 6 of them are - (t 1u & t 2g ) and one is -MO (a 1g ). In boron cages of the formula closo-(BH) x (x = 5, … 12) the optimum number of the core electron pairs is x+1 (all bonding orbitals are filled). That explains enhanced stability of dianionic species closo-(BH) x 2-.