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MO Theory

Naming orbitals

S and P orbitals are simple:

D orbitals are slightly different

  • For orbitals with lobes off the axis/nodes on the axis
    • They are named after the axis which they sit across
    • \(3d_{xy}\),\(3d_{xz}\), and \(3d_{xy}\)
  • For orbitals whose nodes lie on the axis
    • They are named after the axis in which they are on (squared)
    • \(3d_{z^2}\) and \(3d_{x^2−y^2}\)

When d orbitals collide

  • Dealing with planar interacting d orbitals, we introduce the δ bond
  • These are found in quadruple bonded species such as \(\ce{Re2Cl8}\)

S-P gap

  • As you progress along the periodic table, the gap in energies between s orbitals and p orbitals within an individual atom increases
  • This is also why atoms Z<8 have their π orbitals first


Fragment Orbital (FO) energy difference

  • The energy of the bond is \(E=\Delta E_s+\Delta E_d\). The bond is stabilised by the energy drop from the atoms to the occupied bonds
  • The bond is destabilised by the energy increase of the antibonding from the atomic orbitals
  • The bond energy is the difference between these two

This energy depends on the amount of orbital overlap, so the difference is greater when there is a greater overlap, as the resulting orbitals interact more greatly

  • Splitting energy: \(\sigma>\pi>\delta\)

\(\sigma\) orbitals have greater overlap and thus greater splitting energy than \(\pi\) orbitals (as shown in the MO diagram)

Orbital Hybridisation

When hybridisation occurs, the result is a series of degenerate orbitals. This process occurs before the actual bonding (in terms of drawing the MO diagram) and any unhybridised orbitals will remain a the same energy level as the original orbital.

Frontier MO (FMO) theory

  • FMO theory describes the integration of nucleophilic and electrophilic species with HOMO and LUMO electron density, rather than with curvy arrows
  • The notion here is that sites in the HOMO with higher electron density will be more likely to react with nucleophilic species
  • Likewise, electrophilic reactions will likely happen where the LUMO is the most dense, as it’s the next location on the molecule that wants electrons