MOLECULAR ORBITAL THEORY

Instead of making bonds one at a time by overlapping pairs of atomic or hybridized orbitals we just take all the available atomic orbitals and mix them in. This procedure is called the Linear Combination of Atomic Orbitals (LCAO), and it simply means that we use "fractions" of atomic orbitals to make new mixtures (Molecular Orbitals). We have to use each atomic orbital completely, we have to generate normalized molecular orbitals (MOs), and the number of MOs must be equal to the number of atomic orbitals that we have started with.  Again, it is like making drinks (see hybridization), but now we mix orbitals of all atoms (instead of just one atom).

Since many atomic orbitals participate in the "mixture" to form the molecular orbitals, the volumes of these new orbitals encompass many atoms, sometimes even the whole molecule. The formed MOs do not any longer correspond to specific bonds (as they were in VB theory).  In fact, they can be bonding between some pairs of atoms and antibonding between other pairs of atoms, and sometimes they will have a node at a given atom (like in the allyl system). On some occasions the MO and VB orbitals will "look" exactly the same. For example, we may  find such cases in isolated π bonds, or orbitals containing lone pairs that are not adjacent to π systems.

This separation is the consequence of symmetry. π bonds are usually perpendicular to σ bonds, i.e. they cannot mix (because the overlap is zero).  In many cases this arrangement simply means that π and σ networks do not interact and can be treated separately. This situation simplifies the analysis.  For example, look at benzene: its σ and π networks are essentially independent; when we analyze benzene (and aromaticity) we talk exclusively about π electrons. Of course, there are exceptions. There are many situations where σ bonds are in geometry that allows for overlap with a π system.  One such exception is called hyperconjugation. In fact, the concept is (again) derived from the VB theory to account for the delocalization of electrons from the σ bond to the π system. And like resonance (= conjugation) it is a fix of our model, and not the problem of molecular structure. In MO theory, the hyperconjugation shows naturally: the appropriate, mostly π-type MO shows contributions from some atomic orbitals (s or p) of adjacent atoms that are properly aligned with the π system (but would not be, in the VB language, considered a part of it).

Each MO has energy associated with it (see above). All available electrons (from all participating atoms) are placed (two per orbital) in the molecular orbitals, starting at the bottom of the energy scale and moving up,  until no more electrons are left. What counts is not whether the orbital is bonding or antibonding between specific atoms within the molecule, but what is the energy of the orbital.

This ordering is very qualitative, but at the same time very useful in deciding about the nature of certain especially important molecular orbitals (see below), i.e. those that lay very close to the line separating the occupied and empty molecular orbitals.

Predicting the ordering of the energy levels of the orbitals that are farther removed from the line dividing the occupied and unoccupied orbitals is more difficult, short of performing calculations. But we rarely need it anyway.  On the other hand, it is useful to know that the energy of each type of orbital (σ or π) increases with the number of nodes. Here, we want to count the nodes that result in antibonding interaction between atoms that are directly bonded in the molecule. The more nodes (nodal planes) of this type the higher the energy of the orbital. So, although we cannot order the σ and π orbitals relative to each other, we can arrange the π orbitals according to their energy and decide easily (for example) which is the highest occupied (see below).

The situation here is slightly complicated. The size of the lobe of the atomic orbital participating in a given molecular orbital depends on the energy of that orbital and its size (these two are of course related, see above).   The bonding molecular orbital will have larger contributions from the lower energy (i.e. more electronegative) atoms, and the antibonding orbitals will have larger contributions from the higher energy (i.e. less electronegative) atoms.  This usually works well for atoms from the same row of periodic table, but "exception" can be expected from atoms belonging to different rows (compare for example the size of the p orbitals of oxygen and sulfur in the table in Part I).

The energy of the specific molecular structure depends on energy of its electrons in occupied molecular orbitals. Different structures (i.e. molecular geometries) will have different energies of their molecular orbitals. Thus, all electrons will influence the structure (remember the compromises discussed above). But from the point of view of reactivity some electrons and some orbitals are more important than others. The electrons of the highest energy are the ones that the molecule would like to "dump", and empty orbitals of the lowest energy (in the reaction partner) are the best "dumping grounds".  In some chemical reactions (for example electron-transfer reactions) this is exactly what takes place, in others the interactions between the HOMO (occupied) and the LUMO (unoccupied) lead to reorganization of bonding of both reacting partners.

This is just the consequence of orbital ordering discussed in p. 5.  A minor complication (not really) is when a π system incorporates lone pair orbitals. Well... then the whole thing is the π system: end of complications.

Since interaction between filled (occupied) orbitals does not result in net bonding (electron-electron repulsion), and interaction between empty (unoccupied) orbitals cannot contribute to bonding (no electrons to be shared) only the interaction between occupied and unoccupied will provide the initial impetus for the reorganization of existing bonding. Of course the highest energy electrons (HOMO) and the lowest energy empty orbitals (LUMO) will interact the strongest (they are closest in energy, see above). Essentially all chemical reactions are dependent on these HOMO-LUMO interactions.