UNIVERISTY of WISCONSIN-MADISON

Department of Chemistry

College of Letters & Science

Hybridization

When thinking of chemical bonds, atoms do not use atomic orbitals to make bonds but rather what are called hybrid orbitals.  Understanding the hybridization of different atoms in a molecule is important in organic chemistry for understanding structure, reactivity, and over properties.  To learn how to find the hybridization of carbon atoms, we will look at the three simplest examples; ethane, ethylene, and acetylene.

Ethane

 

Calculations done at B3LYP/6-311G+(2d,p).  Click on any image above to view the optimized structure.

Ethane, a two carbon molecule with a single-bond between the carbons, is the simplest alkane.  To understand the hybridization, start by thinking about the orbital diagram of the valence electrons of atomic, unhybridized carbon.

Carbon has four valence electrons, two in the 2s orbital and two more in three 2p orbitals (pictured left)  Looking back at ethane above, in this molecule carbon needs to make four single bonds, one to the other carbon atom and three more to the hydrogen atoms.  Single bonds can only be made with s-orbitals or hybrid orbitals, and as it stands carbon can not make four bonds.  To rectify this the atomic orbitals go through a mixing process called hybridization, where the one 2s and the three 2p orbitals are mixed together to make four equivalent sp3hybrid orbitals (pictured right).  Remember, as many hybrid orbitals are made at the end of the mixing process equal to the number of atomic orbitals mixed in.  One s orbital and 3 p-orbitals were used in this case, and the result is a total of four sp3 hybrids.  The four electrons are then distributed equally among them.

Before moving on, a quick refresher on orbital shapes.  Pictured above, there are two types of orbitals with two types of shapes.  Any s type orbital is simply a sphere of electron density around an atom.  Hybrids and s orbitals can make sigma type bonds where the electron density is shared directly between the atoms.  The other type, p-orbitals, have two lobes above and below the plane of the atom.  They are used to make π bonds, which make up double and triple bonds (more on that later).

sp3 hyrbid orbital

Calculations done at B3LYP/6-311G+(2d,p).  Click on any image above to view the NBO output.

Shown above is the sp3 orbital used by the carbon to make the sigma bond with the adjacent carbon.  There are three things to notice:

1) The bulk of the electron density is directly between the two carbon atoms, indicative of a sigma bond.

2) The shape of the hybrid matches what orbitals were used to make it.  For this case, sp3 hybrids are 3 parts p orbitals and 1 part s orbital.  The end result is an orbital that is mostly p shaped but it a little bit lop-sided.

3) sp3 hybrids take a tetrahedral geometry with an angle between them of 109.5 degrees.  Click on one of the ethane pictures above and rotate the 3D image until you can see this geometry.

Ethylene

Using the above process we can also justify the hybridization for the molecule below, ethylene.

Calculations done at B3LYP/6-311G+(2d,p).  Click on any image above to view the optimized structure.

In this case, the carbon atoms have three sigma bonds, and one π bond making up the double bond.  Remember that π bonds, unlike sigma bonds, are made from p-orbitals.

One p-orbital is needed to make the double-bond to the other carbon.  Now when the hybridization happen, there is one less available p-orbtial, and so a total of 1 s orbital and 2 p-orbitals are mixed together to make three sp2 orbitals.  The three hybrids will be used to make the single bonds to the hydrogen atoms and the other carbon.

π bond

sp2 hybrid orbital

Calculations done at B3LYP/6-311G+(2d,p).  Click on any image above to view the NBO output.

The output of the NBO calculation shows the sp2 hybridization of the carbon.  The image on the left is very clearly a π bond, with the electron density between the two carbons shared above and below the plane of the bond.  The image on the right shows a sp2 hybridized orbital making the sigma bond between the carbons.  Notice the shape of the orbital compared to the sp3 hybrid of ethane.  Because sp2 is only two parts p orbital compared to three, its shape is more s like and even more lopsided.

Make sure to click on one of the images above to see and rotate the 3D model of ethylene.  The geometry of sp2 orbitals is planar with 120 degree bond angles, which can be easily seen in the images and 3D models.

Acetylene

To complete the series, let us consider acetylene.

Calculations done at B3LYP/6-311G+(2d,p).  Click on any image above to view the optimized strcuture.

There is a triple bond between the two carbons.  Each carbon has two sigma bonds, one to hydrogen and one to carbon, and two π bonds (the second and third bonds of the triple bond).

Looking at the orbital diagram above, two p-orbitals must be removed from the hybridization pool to make the triple bond.  This leaves one s and one p-orbital, leaving two sp orbitals.

 

π bond

π bond

         sp hybrid orbital

Calculations done at B3LYP/6-311G+(2d,p).  Click on any image above to view the NBO output.

Again using NBO the orbitals described in the orbital diagram can be visualized.  There are two p orbitals that are perpendicular from each other.  This is shown in the left most image above and the center image, which rotates acetylene around from a head-on view to show the other p orbital.  The left image shows the sp orbital between the two carbons.  Having the highest s character of the hybrid orbitals, it looks mostly like a s orbital.

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