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Let \(\phi_{x}^{C}\) and \(\phi_{z}^{C}\) denote the wavefunctions of the 2px and 2pz orbitals of carbon, respectively, and \(\phi_{x}^{O}\) and \(\phi_{z}^{O}\) represent the wavefunctions of the 2px and 2pz orbitals of oxygen, respectively. If \(c_{1}\) and \(c_{2}\) are constants used in linear combinations and the CO molecule is oriented along the z axis, then, according to molecular orbital theory, the π-bonding molecular orbital has a wavefunction given by

  • A.\(c_{1}\phi_{z}^{C} + c_{2}\phi_{x}^{O}\)
  • B.\(c_{1}\phi_{z}^{C} + c_{2}\phi_{z}^{O}\)
  • C.\(c_{1}\phi_{x}^{C} + c_{2}\phi_{z}^{O}\)
  • D.\(c_{1}\phi_{x}^{C} + c_{2}\phi_{x}^{O}\)

Answer: D

The π-bonding orbital is \(c_{1}\phi_{x}^{C} + c_{2}\phi_{x}^{O}\).

With the molecule along the z axis, a π orbital is built from p orbitals perpendicular to the bond, that is, 2px (or 2py), and only orbitals of the same symmetry about the axis can combine. So the π MO combines 2px on carbon with 2px on oxygen, in phase for the bonding combination.

2pz on carbon with 2pz on oxygen point along the bond and give a σ orbital, not a π orbital. A 2pz with a 2px on the other atom has zero net overlap by symmetry: one is symmetric and the other antisymmetric under reflection through the yz plane, so the two mixed options describe no bond at all.

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