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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.

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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.

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Molecular Orbitals Sigma Bond Formation

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

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Ethene and bonds

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Ethyne and bonds

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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 ( ) and one antibonding ( *). This is an illustration of molecular orbital diagram of H 2. Notice that one electron from each atom is being “shared” to form a covalent bond. This is an example of orbital mixing.

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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.

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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

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Molecular Orbital Diagram (H 2 )

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Bond Order # bonding -# antibonding 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

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

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Figure The paramagnetic properties of O 2

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MO Diagram for O 2

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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 O 2 is therefore superior to the valence-bond model, which cannot explain this property of oxygen.

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Molecular Orbital Diagram (HF)

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Molecular Orbital Diagram (CH 4 ) So far, we have only look at molecules with two atoms. MO diagrams can also be used for larger molecules.

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Molecular Orbital Diagram (H 2 O)

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

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Relative MO energy levels for Period 2 diatomic molecules. MO energy levels for O 2, F 2, and Ne 2 MO energy levels for B 2, C 2, and N 2

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SAMPLE PROBLEM 11.4Using MO Theory to Explain Bond Properties continued 2s 2s 2p 2p 2p 2p N2N2 N2+N2+ O2O2 O2+O2+ bond orders 1/2(8-2)=31/2(7-2)=2.51/2(8-4)=21/2(8-3)=2.5 2s 2s 2p 2p 2p 2p bonding e - lost antibonding e - lost

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* 2s 2s 2s 1s * 1s 1s 1s Figure s * 1s 1s 1s 2s * 2s 2s Li 2 bond order = 1Be 2 bond order = 0 Bonding in s-block homonuclear diatomic molecules. Energy Li 2 Be 2

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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.

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