# Solutions

1. Calculate the CFSE for both high spin and low spin octahedral complexes of Co(gly)_{6}^{3-}. Which is preferred?

**10Dq = 21476 cm ^{-1}, P = 23,625 cm^{-1}, d^{6} complex.**

H.S. CFSE = 4Dq - P = - 15034.6 cm^{-1} | L.S. CFSE = 24Dq - 3P = -19332.6 cm^{-1} |

H.S. preferred, as expected when comparing 10Dq with P |

2. Determine whether the Co^{+2} complex with phenanthroline will prefer to be octahedral or tetrahedral based on CFSE.

**d ^{7} complex, 10Dq_{Oh} = 12060 cm^{-1}, P = 20800 cm^{-1}: complex will be H.S.**

**Oh CFSE = 8Dq - 2P = -31952 cm**

^{-1}**10Dq _{Td} = 5360 cm^{-1}**

**Td CFSE = 12Dq - 2P = - 35168 cm**

^{-1}**Oh preferred**

3. Draw the M.O. diagram for an octahedral complex with six sigma donor ligands. Draw the electrons for a d^{5} high spin complex. **see class notes**

4. What are Jahn-Teller distortions? Where do they come from? Show 'z - in' and 'z-out' configurations. Which is preferred for a d^{9} configuration?

**Tetragonal distortions arising from a) different distances for the ligands, b) ligands of different field strength, and c) to remove degeneracy.**

**d ^{9} prefers z - out**

5. Draw the expected splitting for a Cu(ox)_{3}^{4-} complex. Would the splitting pattern change if two of the Cu-O bond lengths were longer than the other four?

**Cu ^{+2}, d^{9} complex**

6. Using the Tanabe-Sugano diagrams, give the ground states for the free metal, high spin and low spin d^{5} complexes. What are the first excited state for each of these? List all possible transitions. Draw the microstates of the ground state for each of the three species.

Ground State | 1st Excited State | |

Free metal ion | ^{6}S | ^{4}G |

H.S. | ^{6}A_{1g} | ^{4}T_{1g} (below 2Dq/B), ^{2}T_{2g} (above 2Dq/B) |

L.S. | ^{2}T_{2g} | ^{6}A_{1g} (below 3.6Dq/B), ^{4}T_{1g} (above 3.6Dq/B) |

**Transitions:**

**H.S. - none**

**L.S. - 7 possible transitions**

^{2}T_{2g}- ^{2}A_{2g}

^{2}T_{2g}- ^{2}T_{1g}

^{2}T_{2g}- ^{2}E_{g}

^{2}T_{2g}- ^{2}T_{2g}

^{2}T_{2g}- ^{2}T_{1g}

^{2}T_{2g}- ^{2}A_{1g}

^{2}T_{2g}- ^{2}A_{1g}

7. Determine the spin state for each of the following:

a) Fe(OH_{2})_{6}^{3+} | d^{5} H.S., 10Dq < P |

b) V(CN)_{6}^{3-} | d^{2} neither |

c) CuI_{4}^{2-} | d^{9} neither, even though Td always H.S, only one way to do diagram |

d) RuCl_{6}^{4-} | Ru^{+2} d^{6} 2nd row transition metal, always L.S. |

8. Draw the expected splitting of the d orbitals for a trigonal bipyramidal geometry

9. Draw the high spin and low spin configurations for a d^{4} ion in a tetrahedral field. Which is preferred and why?

**H.S. always perferred for Td geometry since 10Dq _{Td} is small compared to pairing energies.**

10. Determine the CFSE for the tetrahedral Co^{+2} complex with methylamine.

**10Dq _{Oh} = 10530 cm^{-1}, 10Dq_{Td} = 4680 cm^{-1}, P = 20800 cm^{-1},**

**CFSE = 12Dq - 2P = -35984 cm**

^{-1}