Molecular Orbital Theory

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Molecular Orbital Theory
The goal of molecular orbital theory is to describe molecules in a similar way to how we describe atoms, that is, in terms of orbitals, orbital diagrams, and electron configurations.

Atomic Orbitals Orbital Mixing
When atoms share electrons to form a bond, their atomic orbitals mix to form molecular bonds. In order for these orbitals to mix they must: Have similar energy levels. Overlap well. Be close together. This is an example of orbital mixing. The two atoms share one electron each from there outer shell. In this case both 1s orbitals overlap and share their valence electrons.

Molecular Orbitals Sigma Bond Formation

p atomic orbitals overlap to form sigma (s) and pi (p) molecular orbitals

Ethene s and p bonds

Ethyne s and p bonds

Atomic and Molecular Orbitals
In molecule, electrons occupy molecular orbitals which surround the molecule. The two 1s atomic orbitals combine to form two molecular orbitals, one bonding (s) and one antibonding (s*). This is an illustration of molecular orbital diagram of H2. Notice that one electron from each atom is being “shared” to form a covalent bond. This is an example of orbital mixing.

Molecular Orbital Theory
Each line in the diagram represents an orbital. The molecular orbital volume encompasses the whole molecule. The electrons fill the molecular orbitals of molecules like electrons fill atomic orbitals in atoms.

Molecular Orbital and Valence Bond Theory
Electrons go into the lowest energy orbital available. The maximum number of electrons in each molecular orbital is two. One electron goes into orbitals of equal energy, with parallel spin, before they begin to pair up. Aufbau Principle Pauli exclusion principle Hund's Rule

Molecular Orbital Diagram (H2)

Bond Order electrons electrons Bond Order = 2
# bonding - # antibonding electrons electrons Bond Order = 2 The bond order is an indication of bond strength Greater bond order = Greater bond strength The bond order equals the number of bonds formed in the molecule

Predicting Species Stability Using MO Diagrams
PROBLEM: Use MO diagrams to predict whether H2+ and H2- exist. Determine their bond orders and electron configurations. bond order = 1/2(1-0) = 1/2 bond order = 1/2(2-1) = 1/2 s s s s H2- does exist H2+ does exist 1s AO of H 1s AO of H MO of H2- MO of H2+

The paramagnetic properties of O2
Figure 11.21 The paramagnetic properties of O2

MO Diagram for O2

MO vs. VB Atoms or molecules in which the electrons are paired are diamagnetic. Those that have one or more unpaired electrons are paramagnetic, attracted to a magnetic field. Liquid oxygen is attracted to a magnetic field and can actually bridge the gap between the poles of a horseshoe magnet. The molecular orbital model of O2 is therefore superior to the valence-bond model, which cannot explain this property of oxygen.

Molecular Orbital Diagram (HF)

Molecular Orbital Diagram (CH4)
So far, we have only look at molecules with two atoms. MO diagrams can also be used for larger molecules.

Molecular Orbital Diagram (H2O)

MO diagram for He2+ and He2
Figure 11.16 MO diagram for He2+ and He2 Energy s*1s s1s s*1s AO of He 1s AO of He+ 1s AO of He 1s AO of He 1s Energy s1s MO of He+ MO of He2 He2 bond order = 0 He2+ bond order = 1/2 He2 does not exist!

Relative MO energy levels for Period 2 diatomic molecules.
MO energy levels for B2, C2, and N2 MO energy levels for O2, F2, and Ne2

SAMPLE PROBLEM 11.4 Using MO Theory to Explain Bond Properties antibonding e- lost continued N2 N2+ O2 O2+ 2p s2s s2s s2p p2p 2p 2p bonding e- lost 2p 2p 2p s2s s2s bond orders 1/2(8-2)=3 1/2(7-2)=2.5 1/2(8-4)=2 1/2(8-3)=2.5

Bonding in s-block homonuclear diatomic molecules.
s*2s s2s Figure 11.17 s*2s s2s 2s 2s 2s Bonding in s-block homonuclear diatomic molecules. Be2 Li2 Energy 1s s*1s s1s 1s s*1s s1s Li2 bond order = 1 Be2 bond order = 0

Conclusions Bonding electrons are localized between atoms.
Atomic orbitals overlap to form bonds. Two electrons of opposite spin can occupy the overlapping orbitals. Bonding increases the probability of finding electrons in between atoms. It is also possible for atoms to form ionic and metallic bonds.