MO theory considers the entire molecule at once not isolated electron pairs.

Transcription

1 5. Molecular Orbital Theory READING: Chapter 2, Sections 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: H 2 (g) Source: Miessler & Tarr, Inorganic Chemistry, Prentice-Hall, For a heteronuclear diatomic molecule (general formula AB) the MO changes somewhat: 108

2 Source: Shriver & Atkins, Inorganic Chemistry, 3 rd ed., Freeman, In this case the bonding orbital will have more φ A character and the antibonding orbital more φ B 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 (E 2 ) is: Source: Shriver & Atkins, Inorganic Chemistry, 3 rd ed., Freeman, 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 O 2 AND F 2 (but not N 2!) 109

3 For diatomics wherein the valence s and p orbitals are closer in energy (Li 2 through N 2 ), 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 p z orbitals! Mixing results in a change-over of the energetic ordering of the HOMO/LUMO between N 2 and O 2. Source: Shriver & Atkins, Inorganic Chemistry, 3 rd ed., Freeman, Mixing is more pronounced for the lighter atoms: ΔZ eff between 2s and 2p smaller Mixing energetically more favoured for lighter atoms. 110

4 In the above examples, there are σ and π bonds. MO s can of also be formed by d- orbitals giving rise to σ, π and δ (delta) bonds. to be covered in more detail in CHEM

5 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 2p z 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. 112

6 CO: 1σ 2 1σ* 2 2σ 2 2σ* 2 1π 4 3σ 2 Carbon Monoxide as an example of a heteronuclear diatomic and an important ligand. Source: Miessler & Tarr, Inorganic Chemistry, Prentice-Hall, So why does CO bind through carbon? 3σ and 3σ * are linear combinations of 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 BH 3 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! and at the same time: while C(p z ) is too far away in energy (>12 ev) to contribute to 2σ *. 113

7 Consequences: O(p z ) contributes to 3 MO s C(p z ) contributes to only 2 MO s The coefficient c 2 is so small that the 3σ MO is dominated by the C(p z ) 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 (n bonding electrons n antibonding 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, 3 rd ed., Freeman, The bond order concept breaks down in larger molecules, where (anti/non)-bonding MOs can stretch over more than two atoms. HOMEWORK: Exercises