 Solution

ID: past-exam-of-the-chemistry-course-of-the-year-3-of-the-natural-sciences-course-of-the-university-of-cambridge/2022/paper-2b/section-b/36/a/iii/solution

α

β

on each adjacent pair, zero interaction across a diagonal, and the identity overlap matrix. In site order

(1, 2, 3, 4)

H = α β 0 β β α β 0 0 β α β β 0 β α .

E_{A_{1 g}} = α + 2 β, E_{E_{u}} = α (twice), E_{B_{1 g}} = α - 2 β .

For the conventional bonding sign

β < 0

, the all-in-phase combination is lowest and the alternating combination is highest. The

E_{u}

combinations have canceling nearest-neighbour interactions and are nonbonding within this model.

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