The following pages have been developed to help you understand molecular orbitals. There are a number of theories in chemistry that attempt to rationalize the electronic structure and / or geometry observed in molecules. The ones you should already be familiar with are Lewis, VSEPR and Valence Bond Theory, review these as required. Keep in mind the "best" theory is the one which can explain the greatest amount of experimental data, and has the fewest number of exceptions. The great success of MO theory is that it can explain more physical and chemical properties of more molecules than other theories, and with fewer or no exceptions. MO theory can explain the paramagnetism of O2, electronic spectra and the concept of delocalization (i.e. resonance) very well, things other theories do not account for adequately.
Note: some of the orbital files are quite large and the download time maybe significant, especially on a dial-up line.In contrast to Valence Bond (VB) Theory, Molecular Orbital (MO) Theory uses a very delocalized concept of bonding. The bonding in a molecule arises from the interaction of atomic orbitals (AOs) on all atoms in the molecule. The "molecular orbitals" (Ψ, MOs) results from a "Linear Combination of Atomic Orbitals" (LCAO, φ) of all the atoms in the molecule.
i.e. Ψ = c1φ1 + c2φ2 + c3φ3 + ... where ci is the coefficient for atomic orbital φiSo how do you determine which atomic orbitals are used?
- AOs which are close in energy interact the strongest.
- The combination of AOs must be consistent with the symmetry of the molecule.
- Possible 2s - 2p mixing.
- The total number of MOs must be the same as the total number of AOs from all atoms.
- The AOs combine by both "in-phase" additions to produce a bonding MO, and "out-of-phase" subtractions to produce an anti-bonding (or virtual) MO (review bonding?). In general the stabilization (lowering of the MO's energy) in less for bonding MOs than the destabilization (raising of energy) of the anti-bonding MOs (see point 1).
- It is possible for the atomic orbitals not to combine to form MOs. This can occur if the energy difference is too large (see point 1) or the orbital overlap is symmetry forbidden (see point 2). Either case produces non-bonding orbitals which are either isolated on a single atom (i.e. "lone pair electrons") or the orbital spans several atoms, but none of them adjacent to one another (thus the electrons are not "shared" between adjacent atoms to produce a bond).
- Only occupied MOs will have an effect on the energy of the molecule, virtual MOs are empty (review bonding?).
- The most important MOs in chemical reactions are the HOMO (Highest Occupied MO) which acts as a Lewis base (electron donor), and the LUMO (Lowest Unoccupied MO) which acts as a Lewis acid (electron acceptor).
In MO theory the terms σ or π bonds are no longer necessarily correct since the MO can span every atom in the molecule.
The concept can get quite complex very quickly so we will use the homo diatomics as examples along with HF, water and benzene (as an example of extended π systems, delocalized bonding that requires resonance in a VB explanation). All of the data and MO images were generated using Gaussian 03. The geometry optimizations were done at the G3 level, a very high level calculation that attempts reproduce experimental data exactly.
I assume you have already reviewed the materials on waves and bond formation.
H2 He2 Li2 Be2 B2 C2 N2 O2 F2 Ne2 HF H2O H2CO C6H6 Summary for Diatomics Points to watch for:
- correlation between bond order and bond length: as the bond order increases the bond length decreases
- orbitals:
- equivalent AOs and MOs all have the same "shape" in the homonuclear diatomics
- equivalent AOs and MOs decrease in size as the atomic number increases (due to increasing electron - nucleus attraction)
- equivalent AOs and MOs energy decreases as the atomic number increases