For a heteronuclear diatomic molecule (general formula AB) the MO changes
somewhat: Source: Shriver & Atkins, Inorganic Chemistry, 3rd ed., Freeman,
1999.
5. Molecular Orbital Theory Related Textbook Reading: Chapter 2, Sections 2.7 – 2.12 •
MO theory considers the entire molecule at once – not isolated electron pairs. Consequence: An electron pair can be bonding/non-bonding/anti-bonding over more than two nuclei!
•
Electrons are described as a standing matter wave in the potential field set up by all the nuclei that make up the molecule.
•
These standing matter waves can only assume certain shapes (determined by symmetry considerations!!!) and are called molecular orbitals.
•
Mathematically these orbitals are represented by wavefunctions, which can be approximated by the Linear Combination of Atomic Orbitals (LCAO):
•
The total number n of MO’s = total number of contributing AO’s.
•
Need to know two things to describe a molecule: 1) Shape of the orbitals (→ symmetry considerations) 2) Relative energies of the orbitals (→ quantum mechanical calculations)
5.1. Review of diatomic molecules (cf. CHEM 206) Simplest case: H2(g)
Source: Miessler & Tarr, Inorganic Chemistry, Prentice-Hall, 1998.
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For a heteronuclear diatomic molecule (general formula AB) the MO changes somewhat:
Source: Shriver & Atkins, Inorganic Chemistry, 3rd ed., Freeman, 1999. •
In this case the bonding orbital will have more φA character and the antibonding orbital more φB character. The AO closer in energy to an MO contributes more to the MO, its coefficient is larger.
•
General rule: If two orbitals are more than 12 eV apart in energy, they do not interact to form an MO.
The MO diagram for a generic diatomic molecule (E2) is:
Source: Shriver & Atkins, Inorganic Chemistry, 3rd ed. , Freeman, 1999. Note on the above diagram: •
It is ONLY appropriate for diatomics in which the valence s and p orbitals are roughly 12 eV (or more) apart in energy!! USEFUL FOR O2 AND F2 (but not N2!)
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For diatomics wherein the valence s and p orbitals are closer in energy (Li2 through N2), the energetic ordering of the MO’s is modified by symmetry allowed orbital mixing: The σ type MO’s arise from mixing of BOTH s and pz orbitals!
•
Mixing results in a change-over of the energetic ordering of the HOMO/LUMO between N2 and O2.
Source: Shriver & Atkins, Inorganic Chemistry, 3rd ed. , Freeman, 1999. •
Mixing is more pronounced for the lighter atoms: ΔZeff between 2s and 2p smaller → Mixing energetically more favoured for lighter atoms.
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In the above examples, there are σ and π bonds. MO’s can of also be formed by dorbitals giving rise to σ, π and δ (delta) bonds.
… to be covered in more detail in CHEM 365.
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For heteronuclear diatomics of type HX (X is a halogen, e.g., F), the atomic orbitals of X are significantly lower in energy than the 1s orbital of H. Consequence: The 1s orbital of F is too low to mix…instead, the 2s orbital and the 2pz orbital are of appropriate energy and symmetry and can both mix with the H 1s orbital to generate MO’s of σ-symmetry. CONCEPTS: •
Mixing 3 AO’s gives rise to 3 MO’s.
•
We can still rationalize the three lone pairs on HF, including their directionality.
•
We need to specify a coordinate system in order to determine which p orbital mixes.
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CO: 1σ2 1σ*2 2σ2 2σ*2 1π4 3σ2 Carbon Monoxide as an example of a heteronuclear diatomic and an important ligand. 2σ mostly O in character, 2σ* roughly equal C and O Mixing of 2σ/3σ and 2σ*/3σ* causes lowering in energy of 2σ/2σ* and raising of 3σ/3σ* → 3σ is the HOMO for CO The HOMO has mostly C character! a) Experimental evidence: CO binds to M and BH3 through carbon only: M – CO b) Calculations (figure on the left) reveal a large lobe on C for 3σ The LUMO is 1π*. This also has mostly C character! C is the “business end”! Source: Miessler & Tarr, Inorganic Chemistry, Prentice-Hall, 1998. •
So why does CO bind through carbon?
3σ and 3σ* are linear combinations of
… and at the same time: … while C(pz) is too far away in energy (>12 eV) to contribute to 2σ*.
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Consequences: →
O(pz) contributes to 3 MO’s
→
C(pz) contributes to only 2 MO’s
→
The coefficient c2 is so small that the 3σ MO is dominated by the C(pz) AO contribution and the chemistry of CO occurs predominantly at carbon.
Correlation of VB Lewis diagrams with bond orders from MO theory: • •
Bond order = ½ (nbonding electrons – nantibonding electrons) NOTE: non-bonding electrons don’t count!! (Exclude 2σ* and 3σ in CO.)
•
Bond order correlates with bond strength and bond distance
Source: Shriver & Atkins, Inorganic Chemistry, 3rd ed. , Freeman, 1999. •
The bond order concept breaks down in larger molecules, where (anti/non)-bonding MOs can stretch over more than two atoms.
Related Textbook Exercises 2.14 – 2.19
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