Covalent Bonds: Bonding Orbitals

Great, we know that covalent bonds are sharing their electrons and that these bonds can have a wide array of different properties, but what exactly is going on in a covalent bond.

Orbitals Interact

At a foundational level bonds are simply the interaction of atomic orbitals. That doesn’t sound so simple. Bear with me for a moment. In the quantum, model electrons exist as wave functions or those pesky probability waves. For simplicity’s sake, we are going to treat these like plain old ocean waves.

When two opposing waves meet they cancel out completely in a process called destructive interference. When two perfectly aligned waves meet they amplify one another in a process called constructive interference.

When two electrons with aligned waves meet up they amplify one another. Since these waves are probability functions the electrons are really likely to exist in this space and form a bond. We call these combined orbitals molecular orbitals (MO) and more specifically a bonding MO when the electrons amplify each other. Since these bonding orbitals allow electrons to actually exist we say that they are stable and as a result have lower energy.

If two electrons with opposing waves meet they destructively interfere, but because these are probabilities waves it means the electrons can’t exist in that location. Therefore a bond can’t form and we say that an antibonding MO is formed. Like a punitive dictator, these molecular orbitals are a bit unstable and have much higher energy values.

Sigma, Pi, Oh My

The types of orbitals that end up overlapping determines the type of bond that forms. Chemists, to our benefit, weren’t super creative when naming the bond types and take the greek letter that corresponds to the orbital designations. So when two s-orbitals overlap they form sigma(σ) molecular orbitals and when two p-orbitals overlap they form pi (π) molecular orbitals. Ultimately the names of the bonds will also take the sigma and pi distinction on the basis of which orbitals are involved.

For our high energy antibonding σ MOs we slap on an asterisk as such, σ* to indicate that the orbitals are antibonding. Whereas bonding MOs are simply σ I like to imagine the asterisks as: * note: we aren’t actually binding with one another. The same goes for π MOs too! π* represents a high energy antibonding orbital while π represents a lower energy bonding orbital.

Orbital Hybridization

Understanding the exact particulars of orbital hybridization is ultimately out of the scope of the MCAT. However, we must be able to determine an atom’s orbital hybridization by looking at it. The easiest way to accomplish is by thinking in terms of electron densities. Electron densities consist of either a lone pair or a bond or bonds.

As an example, the carbon in a nitrile only has two electron densities. The triple bond to the nitrogen counts as one density and the single bond to an R group counts as one for a total of two. The nitrogen in the nitrile also has two electron densities. One for its lone pair and one for the triple bond.

Let’s look at another example, a carbonyl, to see how this works in a slightly different scenario. In a carbonyl the carbon has three individual bonded areas and as a result three electron densities. The oxygen only has one bonded area, but two lone pairs so it also has three electron densities.

Densities to sp’s

The number of electron densities directly corresponds to an atom’s orbital hybridization. Where four electron densities correspond to sp3 hybridization. You could memorize what number of electron densities goes with which orbital hybridization, but I prefer to use simple addition to remember them instead. With this method, you count the number of s and p orbitals then distribute the number among the s and p orbitals.

Since atoms only have one s orbital in their valence shell you can only ever have one s then the rest must go into the p orbitals. We use superscripted numbers to demonstrate how many each orbital has. For example if we take the carbon from the carbonyl in our example above we would distribute one density to the s orbital and the remaining two densities to the p orbitals resulting in a sp2 orbital hybridization.

Number of Electron DensitiesOrbital HybridizationAddition Method
4sp3s + p + p + p = 4 things
3sp2s + p + p = 3 things
2sps + p = 2 things

sp Character

The last piece of information we need to know about hybridization is the % character of an atom. Again we could memorize the percentages for each sp, sp2, and sp3, but we can so easily calculate them that it isn’t worth our time. For example, an sp hybridized atom has 50% s character and 50% p character. This makes sense it has two things to choose from one s and one p. Meaning that 50% are s and 50% are p.