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Valence bond theory - hybrid orbitals
Let’s consider two hybrid orbitals: h3 = s – px + py – pz and h4 = s + px – py – pz.
(a) Normalize the hybrid orbital h4.
(b) Show that the hybrid orbitals h4 and h3 are orthogonal.
(c) Argue for an angle between the hybrid orbitals h4 and h3.
Molecular orbital theory – symmetry
You may have had trouble appreciating the three-dimensional symmetry in class
using pictures on two-dimensional paper, so we’ll treat symmetry more rigorously
here. Consider the function 𝑓(𝑥, 𝑦, 𝑧) = 𝑥𝑒
−(𝑥
2+𝑦
2+𝑧
2
)
.
(a) Is this function even, odd, or does it lack symmetry along the x-axis?
(b) Is this function even, odd, or does it lack symmetry along the y-axis?
(c) Is this function even, odd, or does it lack symmetry along the z-axis?
(a) Is this function gerade, ungerade, or does it lack symmetry in three dimensions?
Molecular orbital theory – diatomic molecules 1
Consider the hypothetical diatomic molecule BC made from boron and carbon.
(a) Draw a molecular orbital energy diagram for this molecule and label each orbital
according to its symmetry.
(b) Determine the bond order for BC, BC+, and BC
.
(c) Rank BC, BC+, and BC according to their bond length.
(d) Rank BC, BC+, and BC according to their bond strength.
Molecular orbital theory – Huckel theory 1
(a) Number the carbon atoms in the substituted benzene ring shown below left.
(b) Write the Hamiltonian matrix [H] for this molecule in a way that agrees with the
numbers in (a).
(c) Explain why you write but not symbols like 11, 12, 6, 3, etc. in [H] for (b).
(d) Explain why you write but not symbols like 22, 34, 1, 5, etc. in [H] for (b).

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