The π-bonding

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 order between atoms 1 and 2.                                   [2 marks]

 

 

 

 

(iv) Calculate the total π-bond order 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]

 

 

 

 

 

 

 

 

 

 

  1. (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]

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) Determine the ionisation energy of the bonding molecular orbital in H2 ?            [6 marks]

 

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