Lecture 17

Molecular Orbital Theory 1) Molecular Orbitals of AHx (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.;

AH2: from MO’s of H2O – MO’s of H2N●, H2C (singlet and triplet), H2B●, BeH2 etc.

AH3: from MO’s of H3N – MO’s of H3C●, H3C+, BH3 etc.

AH4: from MO’s of CH4 – MO’s of NH4+, NH4

+● etc.

While doing so, keep appropriate Walsh diagrams handy and take into account possible changes in s-p orbital mixing.

2) Molecular Orbitals of NH3 (C3v)

C3v E 2C3 3v

A1 1 1 1 z x2+y2, z2

A2 1 1 -1

E 2 -1 0 (x,y)

• NH3 (C3v: E, 2C3, 3v)

The symmetry of 3H’s group orbitals:

r = 3E+0C3+v = A1 + E

z

x

NH3

H(1)H(2)

H(3)

y

3 HN

a1 (2pz)

a1 (2s)

e (2px, 2py)

e

a1 2s1 - s2 - s3

- s2 + s3

-25.6 eV

-15.5 eV

-13.5 eV

s1 + s2 + s3

symmetry adapted linear combinations (SALC) of three 1s orbitals can be found with help of the "projection operator" technique (F.A. Cotton, p. 114)

3a1

1e

2e

-17.0 eV

2a1-31.0 eV

4a1

3) Molecular Orbitals of CH4 (Td)

Cx

y

z

H(2)H(1)

H(3)

H(4)

4 H

s1+s2+s3+s4

s1+s2-s3-s4

s1-s2+s3-s4

s1-s2-s3+s4

a1

t2

t2

t2

C

a1 (2s)

t2 (2px, 2py, 2pz)

t2

a1

-22.3 eV

-11.7 eV

-13.5 eV

Td

A1 x2+y2+z2

A2

E

T1

T2 (x,y,z)

The symmetry of 4H’s group orbitals:

r = 4E+1C3+0C2+0S4+2d = A1 + T2

2a1

3a1

-25.7 eV(-23, PhES)

1t2

2t2

-14.8 eV(-14, PhES)

4) Molecular Orbitals of closo-B6H62- (Oh)

Oh E 8C3 6C2 6C4 3C2 i 6S4 8S6 3h 6d

r() 6 0 0 2 2 0 0 0 4 2

r() = A1g + Eg + T1u; orbitals of these symmetries suitable for -bonding can be formed by six s or six pz atomic orbitals (two sets of six “radial” orbitals result)

S4, C4, C2

C2S6, C3

h

d

d

xy

z

basis set for -bonding

x1

y1

basis set for -bonding;vectors x and y are in h planes

BH

B

B B

B

B

H

H

H

H

H

2-

r() 12 0 0 0 -4 0 0 0 0 0

r() = T1g + T2g + T1u + T2u ; orbitals of these symmetries suitable for B-B -bonding can be formed by six px and six py orbitals (twelve “tangential” orbitals)

5) Molecular Orbitals of closo-B6H62-. “Radial” group orbitals

a1g

eg

t1u

6H and 6B 2s symmetry adapted atomic orbitals

a1g

eg

t1u

6B 2pz symmetry adapted atomic orbitals

a1g

(2pz) (1s)

a1g(2s)

1a1g

2a1g

3a1g

Note that only one of the six 2pz boron group orbitals, namely a1g, is bonding

Six 2s and six 2pz 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)

a1g(2s+2pz)2a1g(2s-2pz)

1a1g(2s+2pz+1s)3a1g(2s+2pz-1s)

+

6) Molecular Orbitals of closo-B6H62-. “Tangential” group orbitals

• Remaining twelve 2px and 2py boron orbitals form four sets of triply degenerate “tangential” group orbitals of t1g, t2g, t1u and t2u symmetry.

• Only two of these sets , t2g and t1u, are suitable for B-B -bonding in closo-B6H62-. They

form six -bonding MO’s (B-B -bonds).

t1u

Bonding and antibonding 6B 2py and 2px symmetry adapted group orbitals

t2g

t2u

t1g

...

...

7) B-B and B-H bonding MO’s of closo-B6H62-

• closo-B6H62- has 7 core bonding orbitals, 6 of them are - (t1u & t2g) and one is -MO

(a1g).

• 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-.

t2g1.9 eV

-1.1 eV 2t1u

eg

2a1g

1a1g

1t1u

-4.4 eV

-5.0 eV

-7.3 eV

-15.3 eV B6-core -orbital

B6-core -orbitals

BH bond orbitals

BH bond orbitals

BH bond orbital

B6-core -orbitals