Sigma & Pi Bonding

What are Sigma and Pi bonds?

Many of us are already aware of the definition of a sigma bond from our teachers, text books or from many of the websites online. However, if you are still not aware of what these two bonds are, then here is a basic definition of the two:

Sigma bond: A covalent bond resulting from the formation of a molecular orbital by the end-to-end overlap of atomic orbitals, denoted by the symbol σ.

Now have a look at this illustration to see how this end-to-end overlapping occures:


Fig 1: Formation of a Sigma bond

Misconception: many students in the Pacific may have this worng notion that a sigma

Pi bond: A covalent bond resulting from the formation of a molecular orbital by side-to-side overlap of atomic orbitals along a plane perpendicular to a line connecting the nuclei of the atoms, denoted by the symbol π.

Here's another illustration showing how the side-to-side overlapping occurs:


Fig 2: Formation of a Pi bond

It is important to note that different sources use different terms to define what a sigma and pi bond is. However, once examined carefully, it will be evident that they all try to explain the same thing.


Misconception: many students in the Pacific may have this wrong notion that a sigma bond is the result of the overlapping of s orbitals and a pi bond is the result of the overlapping of p orbitals because they may relate the 's' to 'sigma' and the 'p' to 'pi'. However, it is seen that sigma bonds can be formed by the overlapping of both the s and p orbitals and not just s orbital.


You may have noticed that in order to understand these definitions it is obvious that we must know what an s and p orbital is.

Please click here to learn more about Atomic Orbitals if you are unfamiliar with the concept.


Note: A single bond such as (C-H) has one sigma bond whereas a double (C=C) and triple (C≡C) bond has one sigma bond with remaining being pi bonds.

Bond type

No. of σ bond

No. of π bonds

Single (C-H)

1

0

Double (C=C)

1

1

Triple (C≡C)

1

2


Sigma (σ) Bonding:

To understand Sigma bonding let us look at the simple molecule of methane (CH4).

Methane, CH4

We may all be familiar with drawing methane using electron dot diagrams, which would look something like this:


Fig 3: Covalent bonding in Methane


Misconception: many students after drawing such electron dot diagrams fail to appreciate that in reality molecules exist as a 3D system and not as a two dimensional system as shown above. These diagrams are drawn for simplicity and should not be viewed as an exact representation of what a molecule looks like.


For now, let us ignore the Hydrogen and concentrate on the central Carbon atom. We know that it is the valence electrons that are responsible for covalent bonding and we must know the electron configuration of an element from the periodic table to know how many valence electron it has.

Please click here to learn more about Electron Configuration if you are unfamiliar with the concept.

Now, when we look at the carbon atom from our Methane, we see that its electron configuration is 1s2 2s2 2p2. However, from this electron configuration we can see that carbon has only two unpaired electrons (2p2) in its valence shell which can be used to form bonds with two hydrogen atoms. You can see this more clearly in the electrons-in-boxes notation below.


Fig 3: Energy diagram for Carbon

So why is methane written as CH4 and not CH2? Well the answer to this lies in something know as hybridization.

Please click here to learn more about hybridization if you are unfamiliar with the concept.

Forming the bonds

Now that we have hybridized the s and p orbitals of carbon to form four identical sp3 hybrid orbitals, it is time to bring in the Hydrogens that we ignored earlier. It is easy to see that the the four Hydrogens that will bond with the carbon all have a single 1s orbital with a single unpaired electron in each. This makes it very easy for it to bond with the carbon.

Fig 4: Sigma bonding in Methane. Source osxs.ch.liv.ac.uk
At this point it is important that we notice how the 1s orbital of each of the four hydrogen comes together with the sp3 orbital of the central carbon. The two types of orbitals overlap in an end-to-end manner and form four single bonds which are referred to as sigma bonds giving us our methane molecule. Now remember the energy that the carbon atom gained to promote one of its electrons from the 2s to the 2pz orbital during hybridisation? Well once the carbon bonds with the hydrogens to form the CH4 molecule, it loses far more energy compared to this gain which eventually makes the molecule very stable and this is what is would look like:


Fig 5: 3D animation of methane molecule. Source: iws.collin.edu website

Ethane, C2H6

Now lets try to recap what we have learnt using the ethane C2H6 molecule.

  1. First we isolate the two Carbons and get their electron configuration which is 1s2 2s2 2p2
  2. Since the electron configuration shows only two unpaired electrons available for bonding and we know that each carbon can form four bonds (3 bonds with hydrogen and 1 with the other carbon in this case), it is obvious that hybridization is needed to make four unpaired electrons available for this bonding.
  3. Hybridization results in four sp3 hybrid orbitals
  4. Now three of these sp3 hybrid orbitals form sigma bonds by overlapping with three 1s orbitals of the three hydrogens and the remaining sp3 hybrid orbital forms a sigma bond by overlapping with the sp3 hybrid orbital of the other carbon which also has three Hydrogens bonded to it in the similar manner.
  5. When all these sigma bonds have formed, we get a molecule with a total of 7 sigma bonds. Have a look at the illustration of how the orbitals come together to form the bond and eventually the ethane molecule:
Fig 6: Sigma & Pi bonding in Ethane molecule. Source: chem1 virtual textbook home page

pi (π) bonds

To understand pi bonding lets have a look at the simple molecule of Ethene C2H4.

You may have drawn the ethane molecule many times in your classrooms and we are all aware of how the atoms and bonds are drawn to represent this molecule. Usually is would look something like this:


Fig 7: Structure of Ethene

In the case of Ethene, there is a difference from methane or ethane, because each carbon is only joining to three other atoms rather than four. When the carbon atoms hybridise their outer orbitals before forming bonds, this time they only hybridise three of the orbitals rather than all four. They use the 2s electron and two of the 2p electrons, but leave the other 2p electron unchanged.


Fig 8: sp2 hybridisation
The new orbitals formed are called sp2 hybrids, because they are made by an s orbital and two p orbitals which have reorganised themselves. sp2 orbitals look much like sp3 orbitals that you have already come across in the bonding in methane. The three sp2 hybrid orbitals arrange themselves as far apart as possible, which is at 120° relative to each other in a plane and remaining p orbital is at right angles to them.

The two carbon atoms and four hydrogen atoms would look like this before they joined together:

Fig 9: 1s and sp2 hybrid orbitals

The various atomic orbitals which are pointing towards each other now merge to give molecular orbitals, each containing a bonding pair of electrons. These are sigma bonds - just like those formed by end-to-end overlap of atomic orbitals that we saw in methane and ethane

The p orbitals on each carbon aren't pointing towards each other, are overlapping sideways.

This sideways overlap also creates a molecular orbital, but of a different kind. In this one the electrons aren't held on the line between the two nuclei, but above and below the plane of the molecule. A bond formed in this way is called a pi bond. Look at this illustration and notice how the orbitals have arranged themselves to form the pi bonds:

Fig 10: Sigma and pi bonding in Ethene. Source: andromeda.rutgers.edu website

misconception:
  • It is also important to note that this sort of overlapping is represented by drawing a single line to show the bond. However this is just for clarity and it does no mean that the electrons in a pi bond are present in the same region as the electrons in the sigma bond as the structural diagram would suggest.
  • A pi bond would still have a pair of electrons. Many students may think that due to the orientation of the p orbitals that come together to form the pi bond, it would have four electrons (two above the plane and two below the plane) but this is not true.  
Reference:

Clark, J 2010, Helping you to understand Chemistry. Chemguide, Retrieved September 12, 2010 from, http://www.chemguide.co.uk/index.html#top