The Hückel molecular orbital of benzene that is degenerate with the molecular orbital 1/2 (χ₂+χ₃-χ₅-χ₆) · ABC26PH0177

Subject: Physical Chemistry · Chapter: Quantum Chemistry · Topic: Huckel MO Theory · Exam: CSIR NET 2019 · Marks: 2 · Difficulty: Medium

The Hückel molecular orbital of benzene that is degenerate with the molecular orbital $\frac{1}{2}\left(\chi_{2}+\chi_{3}-\chi_{5}-\chi_{6}\right)$
(a)$\frac{1}{\sqrt{12}}\left(2 \chi_{1}+\chi_{2}-\chi_{3}-\chi_{5}+\chi_{6}\right)$
(b)$\frac{1}{2}\left(\chi_{2}-\chi_{3}+\chi_{5}-\chi_{6}\right)$
(c)$\frac{1}{\sqrt{12}}\left(2 \chi_{1}-\chi_{2}-\chi_{3}+2 \chi_{4}-\chi_{5}-\chi_{6}\right)$
(d)$\frac{1}{\sqrt{6}}\left(\chi_{1}-\chi_{2}+\chi_{3}-\chi_{4}+\chi_{5}-\chi_{6}\right)$
Answer
Answer: A ✓ checked by 4AB · confidence medium
Explanation
½(χ₂ + χ₃ − χ₅ − χ₆) is one of the bonding e₁g pair. Its partner is (1/√12)(2χ₁ + χ₂ − χ₃ − 2χ₄ − χ₅ + χ₆); option (a) is this function with the −2χ₄ term misprinted. (b) and (c) belong to the antibonding e₂u pair (a).

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