The π-bonding

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CHE204A Quantum Chemistry – Workshop 5 (Week-A11)

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1) Write down the secular determinant for the π-bonding of the butadiene molecule (C₄H₆), ignoring overlap. [2 marks]

2) How many nodes are expected in each of the four π-molecular orbitals (y₁, y₂, y₃, y₄) of butadiene? [2 marks]

3) The coefficients for the linear combination of atomic orbitals for the two lowest

energy π-MOs of butadiene are given below:

	Normalised Coefficients
MO	Atom 1	Atom 2	Atom 3	Atom 4
y₂	+0.6015	+0.3717	–0.3717	–0.6015
y₁	+0.3717	+0.6015	+0.6015	+0.3717

(i) Calculate the total π-electron density on atom 1. [2 marks]

(ii) Calculate the total π-electron density on atom 2. [2 marks]

(iii) Calculate the total π-bond between atoms 1 and 2. [2 marks]

(iv) Calculate the total π-bond between atoms 3 and 4. [2 marks]

(v) Predict the coefficients at each atom for the two highest energy π-MOs (y₃, y₄). [4 marks]

(vi) Present the MO diagram for butadiene, including sketches of each of the four MOs (y₁, y₂, y₃, y₄), clearly indicating the relative size and sign of the atomic orbital contributions at each atom. Justify the signs and sizings of the MOs. [4 marks]

(a) Use the simple one-electron molecular orbital method, including overlap, to calculate the energies of the molecular orbitals of the hydrogen molecule (H₂) in terms of α, β and S? [6 marks]

(b) Calculate b given that a = -13.6 eV, that S = 0.6, and that the lowest UV absorption

energy is 12 eV. [8 marks]

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