Transcription of MO Diagrams for More Complex Molecules
1 MO Diagrams for More Complex MoleculesChapter 5 Friday, October 16, 20152s:A1 E (y)E (x)BF3- Projection Operator Method2py:A1 E (y)E (x)2px:A2 E (y)E (x)2pz:A2 E (y)E (x)boron orbitalsA1 A2 E (y)E (x)2s:A1 E (y)E (x)BF3- Projection Operator Method2py:A1 E (y)E (x)2px:A2 E (y)E (x)2pz:A2 E (y)E (x)boron orbitalsA1 A2 E (y)E (x)little overlapF 2sis very deep in energy and won t interact with eV eV eV eVBoron trifluoride *Boron Trifluoride nbnb * *a1 e a2 a2 A1 A2 E Energy eV eVA1 + E A1 + E A2 + E A2 +E eV eVdorbitals l= 2, so there are 2l+ 1 = 5 d- orbitals per shell, enough room for 10 electrons. This is why there are 10 elements in each row of the d-block. MOs for Octahedral Complexes1. Point group Oh2. The six ligands can interact with the metal in a sigma or pi fashion. Let s consider only sigma interactions for 3. Make reducible reps for sigma bond vectors MOs for Octahedral Complexes4.
2 This reduces to: = A1g+ Eg+ T1usix GOs in total MOs for Octahedral Complexes = A1g+ Eg+ T1uReading off the character table, we see that the group orbitals match the metal sorbital (A1g), the metal porbitals (T1u), and the dz2and dx2-y2 metal dorbitals (Eg). We expect bonding/antibonding remaining three metal dorbitals are T2gand Find symmetry matches with central atom. MOs for Octahedral ComplexesWe canuse the projection operator method to deduce the shape of the ligand group orbitals , but let s skip to the results:L6 SALC symmetry label 1+ 2+ 3+ 4+ 5+ 6A1g(non-degenerate) 1- 3, 2- 4, 5- 6T1u(triply degenerate) 1- 2+ 3- 4, 2 6+ 2 5- 1- 2- 3- 4Eg(doubly degenerate)123456 MOs for Octahedral ComplexesThere is no combination of ligand orbitals with the symmetry of the metal T2gorbitals, so these do not participate in +T2gorbitals cannot form sigma bonds with the = non-bonding MOs for Octahedral Complexes6.
3 Here is the general MO diagram for bonding in Ohcomplexes:SummaryMO Theory MO Diagrams can be built from group orbitals and central atom orbitals by considering orbital symmetries and energies. The symmetry of group orbitals is determined by reducing a reducible representation of the orbitals in question. This approach is used only when the group orbitals are not obvious by inspection. The wavefunctions of properly-formed group orbitals can be deduced using the projection operator method. We showed the following examples: homonuclear diatomics, HF, CO, H3+, FHF-, CO2, H2O, BF3, and -ML6
