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Covalent bonding results from the overlap of atomic orbitals to form a new bonding orbital. The shared electron pair is contained within the bonding orbital. The example of the covalent bond in H_2 is shown in Figure 1. When hydrogen exists as a free atom its 1s atomic orbital houses its lone electron. When two hydrogen atoms come together, their 1s orbitals overlap, forming a new orbital that houses the shared pair of electrons.

The plot in Figure 2 should look familiar, as we saw one like it in earlier. Like before, this graph is plotting energy versus the distance between a pair of hydrogen nuclei. As the two atoms come closer together their orbitals begin to overlap, enabling the sharing of electrons, leading to a decrease in energy. Beyond some point, however, energy increases with decreasing distance. At some point in between, however, energy is minimized. The distance that minimizes energy is the bond distance.

We can divide covalent bonds into two categories: sigma (σ) bonds and pi (π) bonds. Sigma bonds form from the head-on overlap of a pair of orbitals. In other words, there is only one region of overlap in a sigma bond. A couple of examples are shown in Figure 3. We already saw the example of two s orbitals overlapping in H_2 , but you could also imagine an s orbital overlapping with a p orbital (pictured as H and F as in b) or a pair of p orbitals overlapping in a head-to-head arrangement (pictured as Cl and Cl in c). We’ll soon see that the orbital overlap in H-F and Cl-Cl is a bit more complicated than we’re suggesting here, but this should still give you a good idea of what it means to be a sigma bond. Another key point is that the electron density in a sigma bond is symmetric about the internuclear axis. In other words, if you look down along a straight line connecting the nuclei in these examples, you’ll see a symmetric distribution of electron density (i.e., it would look like a circle if you viewed it from the side). This symmetry allows sigma bonds to rotate without interfering with orbital overlap.

In contrast to sigma bonds, pi bonds feature two regions of overlap, and they result from the side-to-side overlap of two p orbitals (Figure 4). In contrast to sigma bonds, pi bonds are not symmetric if viewed down the length of the internuclear axis. Instead, you would observe two regions of electron density on either side of the internuclear axis. As a consequence of this, it is not possible for pi bonds to rotate without disrupting the overlap between the two p orbitals.

You’ll also notice that in the figure we show p orbitals as being shaded with two different colors. These colors represent the sign of the orbital’s wave function in that region of space. Bonding can only take place when orbital regions with the same wave function sign overlap.