Creating p Molecular Orbitals

OK, let's start at the beginning, with something you learned in general chemistry. This is a p atomic orbital.

Atomic orbitals come from treating electrons with the mathematics of waves, so orbitals have phase signs, like waves.

A p orbital, as shown, consists of two parts, usually called lobes. The two parts have opposite phase signs; which is positive and which negative is irrelevant. All that is significant is that they are opposite.

The place where the phase signs change is called a node.

When atoms combine into molecules, their atomic orbitals (AOs) combine into molecular orbitals (MOs), which extend over two or more atoms.

In general, we can make two kinds of MOs from p orbitals. If we interact the AOs in an "end on" orientation, we get an MO that is symmetrical to rotation around a line connecting the nuclei.

Orbitals of this symmetry are called s MOs.

We also can make MOs from p orbitals by pushing them together sideways, as shown in the next picture. Here we introduce a convenient convention: instead of trying to draw the actual shape of the MO, we picture it by drawing the AOs from which it was made, in a way that illustrates the properties the MO will have.

Once again, if each atomic orbital contributes a single electron, as in ethylene (CH2=CH2), we can place both electrons in the bonding orbital, lowering their energy relative to what it was in the AOs.

It is hard to visualize how we might combine three AOs to make s-MOs, and indeed, three or more atom s-MOs are quite rare.

However, it is very easy to combine more than two p orbitals to make p-MOs; in fact, it is possible to imagine pushing an unlimited number of p orbitals together. Let's stay simple and use three, such as in allyl, CH2=CHCH2. Systems with three or more p orbitals on adjacent carbons are called conjugated.

Here we have viewed creating a set of three p-orbitals from three p AOs by taking the two p-MOs created above, and adding one more p.

If the system is the allyl cation, CH2=CHCH2+, the only electrons are the ones from the double bond in the Lewis structure.

If we add one electron, we get the allyl free radical.

A second additional electron produces the allyl anion. Again, the electron must go into the nonbonding orbital, and does not contribute to stabilizing the ion.

A little more nomenclature here: look at the allyl cation, with two electrons in the lowest energy orbital and the other two orbitals unoccupied.

Finally, here are the MOs for a system built from four p-orbitals: butadiene, CH2=CH-CH=CH2.

I am deliberately not showing the mode of formation of these orbitals. You should work this out for yourself, using either a scheme in which ethylene p and p* orbitals are added together together, or inserting one set between the p orbitals of the other. Note that I have marked the nodes with a yellow bar.

Butadiene has four p electrons. Two go in the lowest MO, and two in the next. All electrons thus occupy orbitals lower in energy than individual p orbitals, and thus the molecule is stabilized by the interaction of the two double bonds.

We shall only rarely need p-orbitals for more than a four-atom system. However, if we do, the easiest way in which to derive them is to look at the generalities found in our first three cases: