# 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