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Molecular Orbital Theory
LCAO-MO = linear combination of atomic orbitals
ψ 1 = c 1 φ1 + c 2 φ2
ψ 2 = c 1 φ1 - c 2 φ2
Add and subtract amplitudes of atomic orbitals to make molecular orbitals
Just like making hybrid orbitals, but AO’s come from different atoms
Bonding orbitals: Electrons have high probability of being between nuclei (lower
Orbital overlap determines bonding energy
Weak overlap => weak interaction (bonding & antibonding MO energy same as AO’s
Strong overlap => lowers energy of bonding MO, raises energy of antibonding MO
Bonding and antibonding orbital energies in H2
We typically draw MO energy level diagrams at the equilibrium bond distance
MO energy level diagram for H2 (H2+, HHe, He2, …)
α = Coulomb integral => ionization energy of electron in atomic orbital, e.g., H1s
β = Exchange integral => energy difference between AO and bonding orbital
S = Overlap integral, S12 = ∫φ1*φ2dτ
MO diagram for a polar bond (e.g., in HCl)
α values are different because of electronegativity difference between H and Cl
Larger difference between bonding and antibonding orbital energies
Bonding orbital closer in energy to Cl 3pz AO = > bond has more “Cl character”
MO diagram for an ionic bond (e.g., in Na+F-)
Larger energy difference
Bonding electron pair is localized on the F atom
Excited state is Na0F0
Summary of MO theory so far:
• Add and subtract AO wavefunctions to make MOs. # of
AOs = # of MOs.
• More nodes → higher energy MO
• Bond order = ½ ( # of bonding electrons - # of antibonding
• Bond polarity emerges in the MO picture as orbital
• AOs that are far apart in energy do not interact much
when they combine to make MOs.
Orbital Symmetry
AO’s of different symmetries (in the point group of the molecule) do not interact
Greatly simplifies the problem of constructing MO’s for complex molecules
MO diagram for HCl molecule
Cl 2px and 2py orbitals have π symmetry – no interaction with σ symmetry orbitals
Cl 3s is too low in energy to interact => nonbonding electron pair
8 electrons => 1 bond + 3 lone pairs (same result as valence bond picture)
σ, π, and δ orbitals in inorganic compounds
Face-to-face overlap of
d-orbitals => δ bond
e.g., in [Re2Cl8]2−
σ and π bonding in metal d-orbital complexes
Early transition metal
Empty d-orbital
Late transition metal
Filled d-orbital
Ligand acts as a σ donor (= Lewis base), empty d-orbital is σ acceptor (Lewis acid)
Ligands can also act as π donors or π acceptors
MO diagram for 2nd row diatomic molecules
Li2, Be2, B2, C2, N2
O2, F2
Fill up MOs in Aufbau order
O2 = 12 e = double bond, 2 unpaired electrons (paramagnetic)
B2, C2?
O2 MO diagram & orbitals
π-bonding: 2nd row vs. 3rd (4th, 5th, 6th) rows
Ethylene: Stable molecule, doesn't polymerize
without a catalyst.
Silylene: Never isolated, spontaneously polymerizes.
The large Ne core of Si atoms inhibits sideways overlap of
3p orbitals → weak π-bond
N can make π-bonds, so N2 has a very strong triple
bond and is a relatively inert diatomic gas
“RTV” silicone polymer (4 single bonds to Si)
vs. acetone (C=O double bond)