 Solution

ID: past-exam-of-the-chemistry-course-of-the-year-3-of-the-natural-sciences-course-of-the-university-of-cambridge/2022/paper-2a/section-b/23/c/solution

β_{OO} = - 2.0

and

β_{CC} = - 2.5 eV

. The oxygen HOMO is pi-antibonding, whereas the ethene HOMO is pi-bonding. The frozen-orbital Koopmans estimate therefore gives

α_{O} - β_{OO} ≃ - 12.1, α_{C} + β_{CC} ≃ - 10.5.

Consequently $α_{O} ≃ - 14.1 eV$ and $α_{C} ≃ - 8.0 eV$ . These Hückel Coulomb parameters are effective parameters of this spectroscopically calibrated model. Real ionization energies include relaxation and correlation, so they are not exact matrix elements of an isolated-atom Hamiltonian.

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