Molecular Orbitals of Heteronuclear Diatomics

The molecular orbitals of heteronuclear diatomics (HF, CO, CN-, etc.) can be predicted using the same principles that we used to construct the molecular orbitals of homonuclear diatomics:

i) Ignore the core electrons

ii) Remember that the total number of MOs = total number of AOs

iii) Only AOs of similar energy combine.

iv) Only AOs of compatible symmetry combine.

ie. -type AOs (s and pz orbitals) make MOs-type AOs (px and py orbitals) make MOs

Molecular Orbitals for HFValence Atomic Orbitals of Isolated H and F

Molecular Orbitals for HF

2pz

2px, 2py

Valence Atomic Orbitals of H next to F along the z-axis

1

2

1

3 *

Bonding in HF

Localized on F

Localized on F

Bonding MO

Anti-bonding MO

Non-bonding

Non-bonding2s(F)

2pz(F) + 1s(H)

2px(F)2py(F)

- 2pz(F) + 1s(H)

1

2

1

3 *

Bonding in HF

LP

BP

LP

H-F:

::

LUMO

HOMO

NB B NB

LP LP

LP

LPBP

122214

1LP 1BP 2LP’s1

2

1

3 *

Molecular Orbitals for CO

2s

2pz

2s

2pxy2pz

2pxy

2s(O) 1

Core 1s(C) & 1s(O)Not MO’s but AO’s

Valence AO’s for C and O aligned along the z-axis

Molecular Orbitals for CO

2s

2pz

2s

2pxy2pz

2pxy

2s(O) 1Core

2px(C) + 2 px(O)2py(C) + 2 py(O)

11

1s(C) & 1s(O)Not MO’s but AO’s

Valence AO’s for C and O aligned along the z-axis

2px(C) - 2 px(O)2py(C) - 2 py(O)

22

Molecular Orbitals for CO

2s

2pz

2s

2pxy2pz

2pxy

2s(O) 11s(C) & 1s(O)Core

2px(C) + 2 px(O)2py(C) + 2 py(O)

11

2s(C) + 2pz 2

2pz(C) - 2 pz(O) 3

Not MO’s but AO’s

Valence AO’s for C and O aligned along the z-axis2pz(C) + 2 pz(O) 4

2px(C) - 2 px(O)2py(C) - 2 py(O)

22

9

1

2

1

2

3

Molecular Orbitals for CO

2pz2pz

4

10

1

2*

1

2* ?

3

4* ?

Molecular Orbitals for CO

2 s

2 s

2 pxy

2 pz

2 pxy

2 pz

12221432LP LP 2BP 1BP

C O: :

Actual Molecular Orbitals for CO from Hyperchem

2s(O)

2s(C)+2pz(O)

2px(C)+2px(O)2py(C)+2py(O)

2pz(C)-2pz(O)

2px(C)-2px(O)2py(C)-2py(C)

2pz(C)+2pz(O)

Node = *

Bond = BMO

Bond =

Bond =

Node = *

Node = *

Node = *

Bond =

B

AB

BB

B

122*21432 C O: :

3 Sets of Bonding Pairs

LP LP 2BP’s BP

1

2 *

1

3

2 *

4 *

B

AB AB

ABElectron Configurationfor CO using MO

3

1*

4*

1

2*

1

Electron Configuration of N2

122*21432

N N: :

LP LP 2BP’s BP

14

Computating MOsAb initio calculations :“from the beginning” and refers to calculations made from first principles.

1) consider all electrons in a molecule. (core & valence)2) considers all interactions. (n-e, e-e & n-n)3) Uses Born-Oppenheimer Approximation.4) Simplifies e-e interactions to make the equations solvable.

Semi-empirical calculations 1) Consider only the valence electrons, replacing the nucleus and core electrons with a “core potential” which represents their effect on the valence electrons. 2) Valence MO’s are calculated just as in Ab-initio methods where the core potential is added along with the Coulombic interactions.

Faster than ab initio calculations and give relatively reliable molecular geometries.

MO diagrams are less accurate than ab initio, but the MOs are typically in the correct order with the right separations.

Predicted geometries can be verified by X-ray crystallography (and other techniques) and the energies can be verified by spectroscopy.