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Use hckel theory to calculate the total system energy

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Unformatted text preview: 2ℏ =− = − 36 ℏ = / = 3 18 / ℏ / 2/ − 2 2 3ℏ − 2 2 → 4 9 8ℏ 18ℏ 2 2 3ℏ = 2 2 = ℏ − = / / 3ℏ − 2 2 / / / / 18ℏ 18ℏ 2 / = 12ℏ − 6ℏ =− 12ℏ ℏ 2. Use Hückel theory to calculate the total π system energy and resonance energy of styrene. (Hint: Remember Mathcad!) Solution: The structure of styrene (including the numbering scheme used below) is In the Hückel description, =, = for adjacent C atoms, and atoms. Therefore, the Hückel determinant is = 0 for non-adjacent C − 0 0 0 0= 0 − 0 0 − 0 0 0 0 0 − 0 0 0 − 0 0 0 0 0 0 0 0 0 0 0 0 − 0 0 0 1 − 0 0 − 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 1 0 − 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 = 1 1 Letting − 0 0 = 0 0 0 0 0 0 0 − 1 0 0 0 0 0 0 0 − − − − 1 1 − , 1000100 1 100000 01 10000 001 1000 0= 0001 100 10001 10 000001 1 0000001 The equivalen...
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