Chem-­‐601, Problems Set 6 Due: Friday, November 22, 2013 Instructor: Efrain E. Rodriguez Total points: 20 1. (5 points) Construct the molecular orbital diagram for the diatomic (CN)− molecule and label the resulting MO’s with their appropriate Mulliken symbols. a. Which MO’s behave as the lone pair of electrons? b. Which MO’s behave as the bonding orbitals? c. Label the HOMO and LUMO on the diagram. 2. (5 points) In problem set 4, we constructed the dsp2 hybrid orbitals of the tetracyanonickelate anion [Ni(CN)4]2-­‐. In this complex, Ni(II) is bonded to four (CN)− ligands in a square planar geometry. Use the coordinate system below to answer the following questions. a.) How do each of the 3d, 4s, and 4p orbitals of Ni transform in the group of this molecule (i.e. list the atomic orbitals and the irreducible representation to which they belong) ? b.) For sigma type bonding of CN-­‐ to the central Ni, write out a reducible representation ΓSALC , and decompose it into its component species. Note: you will use only the HOMO from problem 1. c.) Which d-­‐orbitals are allowed to combine with these SALC’s? d.) Which other orbitals are allowed to combine with these SALC’s? 3. (10 points) Use the projection operator to y
construct the SALC’s of the CN-­‐ pendant atoms in [Ni(CN)4]2-­‐. Make sure to demonstrate that they are orthogonal, and approximate them as φA
s-­‐orbitals. φD
a.) Sketch the bonding MO’s for the combination of the Ni 3d-­‐orbitals to x
Ni
the pendant SALC’s . φB
b.) Write out the corresponding MO wavefunctions. c.) Repeat parts a.) and b.) for the φC
bonding MO’s combining the SALC’s to the other Ni orbitals.