Polyhedral Borane Exercises

Some of these questions make reference to the 3D rotatable molecular orbitals of B6H6 dianion. 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. Examine the calculated HOMO of B6H6 dianion. What is its symmetry (Mulliken symbol)? Does it represent one of the (n+1) skeletal electron pairs?
  2. Explain what is the relationship between MO numbers 17 and 18 to that of the HOMO.
  3. What are the symmetries of MO numbers 12 and 13?
  4. Do MO numbers 12 and 13 correspond to any of the skeletal electron pairs?
  5. Consider a set of five d orbitals located at the origin of the same coordinate system used for B6H6. Which d orbitals are of the same symmetry type as MO numbers 12 and 13 of B6H6?
  6. What is the MO number of B6H6 dianion that corresponds to the totally symmetric skeletal electron pair?
  7. To what do MO numbers 1-6 correspond?
  8. Take the six hydrogen 1s atomic orbitals of B6H6 dianion as the basis for a reducible representation and reduce it using REDUCE or another method of your choice.
  9. How many valence electrons does the B6H6 dianion have?
  10. Provide an interpretation of the 11B NMR spectrum of decaborane(14). For reference see the assigned paper on 11B NMR.
  11. Optional extra credit: construct a model of B12H12 dianion according to the method of the assigned paper.

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