Diborane Exercises

These questions make reference to the 3D rotatable molecular orbitals of diborane. They were produced using a density functional theory calculation; each time you bring up an MO according to the instructions on the web page, information about the symmetry and calculated energy of that MO will be displayed at the upper left hand corner of the applet.
  1. Which of the six valence molecular orbitals of diborane appear to contain boron-boron bonding character? Interestingly, the calculated boron-boron bond order in diborane is approximately 0.8.
  2. Which of the six valence molecular orbitals of diborane have identically zero contribution from the four terminal hydrogens?
  3. Which of the six valence molecular orbitals of diborane have identically zero contribution from the two bridging hydrogens?
  4. The valence orbital ionization energies for boron are as follows: 2s, 14.0 eV; 2p, 8.3 eV. This means that the boron 2s orbital is lower in energy than the boron 2p manifold by 5.7 eV. Which of the six valence molecular orbitals appear to have the most boron 2s character, and where do these rank in order of ascending energy? Explain.
  5. In principle, each of the six valence molecular orbitals of diborane could give rise to a unique peak in the photoelectron spectrum of the molecule. In practise, only five peaks were observed. From your reading, which peak is missing?
  6. A molecular orbital energy level diagram for a molecule may be summarized by writing e.g. (2ag)2(2b1u)2... and so on representing all the filled valence orbitals in order of ascending energy from left to right. Complete this notation representing the ground state configuration for the diborane molecule.
  7. Consider the pentaborane-9 molecule. Take the four-fold rotation axis to be the z axis, and take the x and y axes to be running through the basal four boron atoms. How many sets of symmetry-related hydrogen atoms are present? Use each set as the basis for a reducible representation, reduce it to irreducible components using REDUCE, and thereby obtain the symmetry species (Mulliken symbols) for nine of the molecular orbitals.
  8. How many valence electrons does pentaborane-9 have?
  9. Based on inspection of the appropriate character table, is it likely that pentaborane-9 will exhibit any MO degeneracies? Explain.
  10. How many filled molecular orbitals does pentaborane-9 have, assuming all its electrons are spin-paired?