Dihydrogen Molecule: One more electron goes to bonding orbital * - - PowerPoint PPT Presentation

Dihydrogen Molecule: One more electron goes to bonding orbital

Increased stabilization: Stronger bond!

*

Effective nuclear charge changes the absolute Energy levels and the orbitals! Matching of AO energies needed for LCAO-MO If energies are not close to each other, AOs would not interact to form MOs.

Energies of H2

+, H2, He2 +, He2

He2

+

He2

Matching of AO energies for MO

• Due to large difference in energy of 1s(H) and 1s(F), LCAO-MO for

both 1S is not feasible in HF.

• Rather only 2Pz(F) [NOT 2Px/y(F)] and 1S(H) form a σ-bond.

Both symmetry and energy matching is required for MO Valence electrons are most important for bonding

S=0 S>0

1 1 2 2

c c ϕ ψ ψ

± =

±

PX/Y +s Z-axis PZ + s

Electron Density Maps/Contours

H2 Li2: core 1σ Li2: core 1σ∗ Li2: Valence 2σ Li2: Total

MO Contours electron density maps

O2 molecule Total 2σ and 2σ∗ 3σ and 1π 1π∗

HOMO : Highest Occupied Molecular Orbital LUMO : Lowest Unoccupied Molecular Orbital

Expected MO and Energies for N2

Are these MO and correct energy level diagram for N 2?

There is a problem! Spectroscopy says NO!

Actual MO and Energy Diagram for N2

Mixing of 2S and 2P orbital occur because of small energy gap between them. 2s and 2p electrons feels not so different effective nuclear charge.

Nature 2004 vol 432 867

S-P Mixing in Atomic Orbitals

2S and 2P AOs MIX due to less energy gap  2s and 2p e feels not so different Z eff.  Mixed states can form MOs

1 2 2 2 SPz z

s p

c c ψ ψ ψ

±

= ±

C1 and C2 not equal – In the mix orbital: S and PZ different contributions

s-p Mixing: B2 magnetism confirms it!

Boron is paramagnetic. This can only happen if the two electrons with parallel spin are in the π-orbitals  π-bonding energies lower than σ*?

Incorrect!