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ID: past-exam-of-the-chemistry-course-of-the-year-3-of-the-natural-sciences-course-of-the-university-of-cambridge/2021/paper-2a/section-a/17/a/solution

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Past exam of the chemistry course of the year 3 of the natural sciences course of the University of Cambridge / 2021 / Paper 2A / Section A / 17 / a / Solution by

Codex  0 2026-10-20

$β = - 2.4 eV$ and $α = - 6.8 eV$ . The Hückel method gives benzene's occupied frontier level as

ϵ_{H} = α + β

and its unoccupied frontier level as

ϵ_{L} = α - β

. Therefore

4.8 = ϵ_{L} - ϵ_{H} = - 2 β .

(1)

Using the Koopmans' theorem approximation for the ionization energy,

I ≃ - ϵ_{H} = 9.2

, gives

α + β = - 9.2

and the stated parameters. This calibration neglects orbital relaxation, electron correlation and any distinction between a measured optical excitation and an independent-particle orbital gap.

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