x y z (1s + 1s) σ

(1s - 1s) sσ*

(2pz + pz) 2pσ

(pz - pz) 2pσ*

(2px + 2px) 2pπ

(2px - 2px) 2pπ*

(2py + 2py) 2pπ

(2py - 2py) π*

1sσ* 1sσ (1sσ)2 (1sσ*)2

H2+ 1sσ* ↑ 1sσ (1sσ)2 (1sσ*)2

H2 1sσ* ↑ ↓ 1sσ (1sσ)2 (1sσ*)2

He2+ 1sσ* ↑ ↑ ↓ 1sσ (1sσ)2 (1sσ*)2

He2+ H2– 1sσ* ↑ ↑ ↓ 1sσ (1sσ)2 (1sσ*)2

He2 1sσ* ↑ ↓ ↑ ↓ 1sσ) (1sσ)2 (1sσ*)2

2sσ 1sσ* 1sσ) (1sσ)2 (1sσ*)2 (2sσ)2 (2pσ)2 (2pπ)4 (2pπ*)4 (2pσ*)2 (2sσ*)2

2sσ* 2sσ 1sσ* 1sσ) (1sσ)2 (1sσ*)2 (2sσ)2 (2pσ)2 (2pπ)4 (2pπ*)4 (2pσ*)2 (2sσ*)2

2p 2pσ 2sσ* 2sσ 1sσ* 1sσ) (1sσ)2 (1sσ*)2 (2sσ)2 (2pσ)2 (2pπ)4 (2pπ*)4 (2pσ*)2 (2sσ*)2

2pσ* 2p 2pσ 2sσ* 2sσ 1sσ* 1sσ) (1sσ)2 (1sσ*)2 (2sσ)2 (2pσ)2 (2pπ)4 (2pπ*)4 (2pσ*)2 (2sσ*)2

2pσ* 2pπ 2pσ 2sσ* 2sσ 1sσ* 1sσ) (1sσ)2 (1sσ*)2 (2sσ)2 (2pσ)2 (2pπ)4 (2pπ*)4 (2pσ*)2 (2sσ*)2

2pσ* 2pπ* 2pπ 2pσ 2sσ* 2sσ 1sσ* 1sσ) (1sσ)2 (1sσ*)2 (2sσ)2 (2pσ)2 (2pπ)4 (2pπ*)4 (2pσ*)2 (2sσ*)2

2pσ* 2pπ* 2pπ 2pσ 2sσ* 2sσ 1sσ* 1sσ) (1sσ)2 (1sσ*)2 (2sσ)2 (2pσ)2 (2pπ)4 (2pπ*)4 (2pσ*)2 (2sσ*)2

O2 2pσ* 2pπ* 2pπ 2pσ 2pπ 2pσ 2sσ* 2sσ 1sσ* 1sσ) (1sσ)2 (1sσ*)2 (2sσ)2 (2pσ)2 (2pπ)4 (2pπ*)4 (2pσ*)2 (2sσ*)2

(1sσ)2 (1sσ*)2 (2sσ)2 (2pσ)2 (2pπ)4 (2pπ*)4 (2pσ*)2 (2sσ*)2 ↑ ↑ ↑ ↓ 2pσ ↑ ↓ ↑ ↓ 2pπ ↑ ↓ 2sσ* 2sσ ↑ ↓ 1sσ* ↑ ↓ ↑ ↓ 1sσ) (1sσ)2 (1sσ*)2 (2sσ)2 (2pσ)2 (2pπ)4 (2pπ*)4 (2pσ*)2 (2sσ*)2

O2 2pσ* 2pπ* 2pπ 2pσ 2sσ* 2sσ 1sσ* 1sσ) (1sσ)2 (1sσ*)2 (2sσ)2 (2pσ)2 (2pπ)4 (2pπ*)4 (2pσ*)2 (2sσ*)2

O2 2pσ* 2pπ* 2pσ 2pπ 2sσ* 2sσ 1sσ* 1sσ) ↑ ↑ ↑ ↓ 2pσ ↑ ↓ ↑ ↓ 2pπ ↑ ↓ 2sσ* 2sσ ↑ ↓ 1sσ* ↑ ↓ ↑ ↓ 1sσ) (1sσ)2 (1sσ*)2 (2sσ)2 (2pσ)2 (2pπ)4 (2pπ*)4 (2pσ*)2 (2sσ*)2

O2 2pσ* 2pπ* 2pσ 2pπ 2sσ* 2sσ 1sσ* 1sσ) ↑ ↑ ↑ ↓ 2pσ ↑ ↓ ↑ ↓ 2pπ ↑ ↓ 2sσ* 2sσ ↑ ↓ 1sσ* ↑ ↓ ↑ ↓ 1sσ) (1sσ)2 (1sσ*)2 (2sσ)2 (2pσ)2 (2pπ)4 (2pπ*)4 (2pσ*)2 (2sσ*)2

O2 2pσ* 2pπ* 2pπ 2pσ 2sσ* 2sσ 1sσ* 1sσ) ↑ ↑ 2pπ ↑ ↓ ↑ ↓ ↑ ↓ 2pσ ↑ ↓ 2sσ* 2sσ ↑ ↓ 1sσ* ↑ ↓ ↑ ↓ 1sσ) (1sσ)2 (1sσ*)2 (2sσ)2 (2pσ)2 (2pπ)4 (2pπ*)4 (2pσ*)2 (2sσ*)2

O2 2pσ* 2pπ* 2pπ 2pσ 2sσ* 2sσ 1sσ* 1sσ) ↑ ↑ 2pπ ↑ ↓ ↑ ↓ ↑ ↓ 2pσ ↑ ↓ 2sσ* 2sσ ↑ ↓ 1sσ* ↑ ↓ ↑ ↓ 1sσ) (1sσ)2 (1sσ*)2 (2sσ)2 (2pσ)2 (2pπ)4 (2pπ*)4 (2pσ*)2 (2sσ*)2

O2 2pσ* 2pπ* 2pπ 2pσ 2sσ* 2sσ 1sσ* 1sσ) ↑ ↑ 2pπ ↑ ↓ ↑ ↓ ↑ ↓ 2pσ ↑ ↓ 2sσ* 2sσ ↑ ↓ 1sσ* ↑ ↓ ↑ ↓ 1sσ) (1sσ)2 (1sσ*)2 (2sσ)2 (2pσ)2 (2pπ)4 (2pπ*)4 (2pσ*)2 (2sσ*)2

Separate atoms ↑ ↑

At the bond separation the bonding and antibonding orbitals split apart in energy ↑ ↑

The electrons pair up in the lower level – energy is gained - relative to the separate atoms and a stable molecule is formed σ* ↑ ↑ ↓↑ σ

σ* E = α - β ↓↑ σ E = α + β

Note β the stabilisation energy is –ve ↓↑ E = α + β Note β the stabilisation energy is –ve

↑ σ* ↑ σ

↓↑ σ* σ

H2+ σ* ↑ σ

The wave function is usually represented by ψ

The electron density is given by ψ2

probability = ψ2 Electron Density Radius r