Resonance, Formal Charge, etc.

Some molecules can't quite completely satify all of the requirements that Lewis thought all molecules wanted to have.

Consider a very interesting and important allotrope of oxygen, ozone. This molecule is known to be bent but not an equiliateral triangle. It is also known that it is symmetric with repect to the O-O bonds. (It does in fact have a two-fold symmetry axis, and two perpendicular symmetry planes, i.e. C2V symmetry) The simplest Lewis theory cannot predict this without a 'fix' called resonance.

I have also shown the 'Formal Charge' on these structures, where this is defined as the number of valence electrons minus the number of lone pair electrons minus one half of the bonding electrons. Usually formal charges are not found in Lewis structures, but some molecules require them. Formal charges do not always occur in molecules with resonance structures, as is the most famous case of benzene. The resonance stabilization of benzene and its analogs is sometimes called 'aromatic' stabilization.
What is the state of hybridization of the carbon atoms in benzene?

Sometimes the formal charges can help one decide between the relative importance of non-equivalent resonance structures. The best structure has the fewest formal charges and has the negative charge on the highest electronegativity atom, as can be seen in the cyanate anion

What is the 'best' structure for the cyanate anion, above? The worst?

The nitrate anion is symmetric, so either an incomplete octet, or three equivalent resonance structures can predict this. Resonance is the preferred explanation.

What are the formal charges on the structures above?
Molecular Orbitals and DiOxygen
We have no difficulty writing a perfectly reasonable Lewis structure for O2 that has all of the electrons paired, a double bond and complete octets:

But, as we can see in this movie, oxygen molecules are paramagnetic, which means that this structure cannot be correct! This means we have to think a little more carefully about the orbitals that are involved in chemical bonding.

The orbitals that electrons are in when they exist in molecules are actually different from even the most 'hybridized' or perturbed atomic orbitals. How molecular orbitals for stems from how waves interefer with one another and the concept of Phase. Adding orbitals 'in phase' or 'out of phase' can make two different shapes, usually one that is 'bonding' and one that is 'antibonding'. Antibonding orbitals have a new node between the atoms and perpendicular to the bond axis.

Molecular orbitals arising from p orbitals can have two types of nodes: A node containing the bond axis (makes a pi bond) or a node perpendicular the the bond axis (making and antibonding orbital). Orbitals that have no nodes containing the bond axis are called sigma orbitals (Greek for s). Orbitals that have one nodes containing the bond axis are called pi orbitals (Greek for p). Orbitals that have two nodes containing the bond axis are called delta orbitals (Greek for d), etc.
The energy level diagram for the lowest-lying molecular orbitals of a homonuclear diatomic molecule look like this:

Including the p orbitals complicates matters considerably.

Molecular 'aufbau' can now predict the correct nature of DiOxygen (and DiBoron)!

Careful examination of electron-electron repulsion in these systems shows an inversion of the MO energies between N2 and O2
Heteronuclear Diatomics of the second period elements have less symmetric molecular orbitals because of the uneven nuclear charge. Below are the orbitals of Carbon Monoxide, which is isoelectronic with N2

Polyatomic Molecular Orbitals explain many properties that "simple" Lewis or Valence Bond theories cannot. One such property is the energetics of Bond Rotation, which has a low barrier (easy) for single bonds, such as in ethane:

Bond rotation is restricted in multiple bonds because the nature of the p (pi) - bond, which has a node containing the bond axis, and must be 'broken' for rotation about the bond axis to occur. An example of a p (pi) - bond is in that of ethylene (ethene):

Here is an animation of the structure of the MO's in ethylene.

There are two p (pi) - bonds in acetylene (ethyne) but the bond rotation issue is moot since because the molecule is linear.

Molecular orbitals also describe the actual nature of molecules that appear to have 'resonance structures' in their Lewis dot description.

Here is an animation of the structure of the MO's in benzene.

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