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GATE 2020 CY – Question 23

Physical Chemistry · Molecular Structure and Chemical Bonding: Born-Oppenheimer approximation; Valence bond theory treatment for hydrogen molecule and linear combination of atomic orbitals – molecular orbitals (LCAO-MO) theory. Concept of hybridization and hybrid orbitals. Applications of LCAO-MO theory to H2+, H2; Molecular orbital theory (MOT) of homo- and heteronuclear diatomic molecules. Hückel theory, applications to simple molecules, small conjugated π-electron systems. · 1 mark · Multiple choice

Which atomic-orbital combination represents the lowest unoccupied π molecular orbital of butadiene?

  1. $\Psi=-0.372\phi_1+0.602\phi_2-0.602\phi_3+0.372\phi_4$
  2. $\Psi=0.602\phi_1-0.372\phi_2-0.372\phi_3+0.602\phi_4$
  3. $\Psi=0.602\phi_1+0.372\phi_2-0.372\phi_3-0.602\phi_4$
  4. $\Psi=0.372\phi_1+0.602\phi_2+0.602\phi_3+0.372\phi_4$

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Correct answer: (B) $\Psi=0.602\phi_1-0.372\phi_2-0.372\phi_3+0.602\phi_4$

Explanation

Butadiene has four π electrons occupying the two lowest π orbitals. Its LUMO is therefore ψ₃, which has two sign changes along the chain. Hückel coefficients are proportional to $\sin(3j\pi/5)$ for j = 1,…,4, giving the pattern + − − + and normalized magnitudes 0.602,0.372,0.372,0.602. This is B; a global sign reversal would describe the same orbital.

More Molecular Structure and Chemical Bonding: Born-Oppenheimer approximation; Valence bond theory treatment for hydrogen molecule and linear combination of atomic orbitals – molecular orbitals (LCAO-MO) theory. Concept of hybridization and hybrid orbitals. Applications of LCAO-MO theory to H2+, H2; Molecular orbital theory (MOT) of homo- and heteronuclear diatomic molecules. Hückel theory, applications to simple molecules, small conjugated π-electron systems. questions

All Molecular Structure and Chemical Bonding: Born-Oppenheimer approximation; Valence bond theory treatment for hydrogen molecule and linear combination of atomic orbitals – molecular orbitals (LCAO-MO) theory. Concept of hybridization and hybrid orbitals. Applications of LCAO-MO theory to H2+, H2; Molecular orbital theory (MOT) of homo- and heteronuclear diatomic molecules. Hückel theory, applications to simple molecules, small conjugated π-electron systems. questions →