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Orbital Hybridization

Introduction

Orbital hybridization is a theory for modeling the shapes of atomic bonding orbitals and predicting molecular geometries.  Orbital Hybridization is an integral part of  valence bond theory, and attempts to explain how bonded atoms adhere to the VSEPR theory.  Hybrid orbitals result from linearly combining the wave equations of atomic orbitals (s, p, and d) of similar energies  Orbital hybridization accurately predicts bond energies for localized bonds of the main group elements, but fails when transition metals are involved.

Hybridization and VSEPR

As mentioned above, orbital hybridization is used to justify how molecules obtain their observed shapes.  VSEPR theory correctly predicts the shape of many molecules, like methane, but does not address how atomic orbitals overlap to produce these structures; this is what orbital hybridization does.

Orbital Hybridization Process

To understand orbital hybridization, we need to to visualize an atom's orbitals in both the unbonded and bonded states.  We will use carbon in methane as an example; thus our first step is to analyze carbon in its unbonded state.  We begin by creating a valid lewis dot structure based on the electronic configuration, 1s22s22p2.  We can see that carbon has four valence electrons.  We draw a simple diagram (figure 1) of an unhybridized carbon by listing each valence orbital seperately, and filling them according to the Aufbau principle, Hund's rule, and Pauli exclusion principle.   We will also draw out a diagram of the orbitals in carbon's unhybridized state (figure 2).  Notice that the only orbitals available for bonding in the unhybridized state are the 2px, 2py, and 2pz orbitals.

Now we will look at carbon as it exists in methane. 
 

Identifying Hydriziation

There are many types of hybridizations, and all result from combining wave equations of orbitals of similar energies.  We will discuss spx, and spdx hybridization by first examining carbon's hybridization in several molecules, and then looking at a coordinated sulfur.  We begin by examining the orbitals and electronic configuartion of an unhybridized atom.

SP Hybridization

Let's look at carbon in CO2.  Drawing out the lewis dot structure, we see that carbon has two sigma bonds, and two pi bonds.  This implies that carbon has two 2p orbitals available for pi bonding, and two hybrid orbitals available for the sigma bonds.  This configuration is called the sp hybridization, and results from taking one P orbital and combining it with the S orbital.  Since two atomic orbitals went into it, we need to get two hybrid orbitals out of it, and there are two sp orbitals in the sp hybridiziation.  The new valence electron diagram for carbon has two hybridized orbitals whose energies are higher than the 2s, but still lower than the 2p.

SP2 Hybridization

Now we are going to explore the sp2 hybridization, which results from taking two p orbitals and combining them with the s orbital.  This leaves one p orbital available for a pi bond, and this is the configuration of carbon in a ketone.  As always, we begin with the lewis dot structure and see that carbon now has three sigma bonds, and one pi bond.  Since we need three hybridized orbitals for the sigma bonds, and one p orbital for the pi bond, we take two P orbitals and combine them with the S to form three sp2 orbitals.  The new valence electron diagram for carbon has three degenerate 2sp2 orbitals whose energies are higher than the S, but lower than the P.  Note that sp2 orbitals are a relatively higher energy than sp orbitals.

SP3 Hybridization

The last hybridization for carbon is SP3.  As you may have noticed, the label of the hybridization tells us everything we need to know about the valence electron configuration: since all the p orbitals have combined with the s orbital, we have four hybrid orbitals, which means there are no p orbitals for pi bonds, hence carbon is limited to four sigma bonds in this configuration, and this is the hybridization of carbon in any alkane.  Drawing out the diagram for the valence electrons, we see that there are four degenerate hybrid orbitals.

**SPD HYBRIDIZATION HERE***

Hybrid Wave Equations

Now that we know why we hybridize orbitals, we will look at how the shapes and energies of these orbitals is determined.  As mentioned above, hybrid orbitals are mathematically defined by linearly combining the wave equations of the orbitals involved.  In sp, we combine the s orbital wave equation with one of the p orbital's.  The sp2 and sp3 are simply the other two p orbitals mixed in.  Intuitively, we can see that the hybrid orbitals are degenerate, but we will discuss the energies later.

Hybrid Orbital Energies

The relative enregies of orbitals is mentioned several times above, but lets take a closer look at it now.  The law of conservation of energy states that energy can neither be created, nor destroyed.  That means, when we combine atomic orbital wave equations to create hybrid orbitals, we need make sure that the energies of both orbitals is acccounted for.  This is the reason why an sp orbital is above the s, but below the sp2, which is below the sp3, which is lower than the p.  The diagram to the right shows the orbitals' relative energies.  Note that the hybridized orbitals are between the s and p energies, but never equal to them.

Problems

  1. What is the hybridization of oxygen in H2O? 
  2. What are the hybridizations of carbon and nitrogen in cyanide(CN-)?
  3. Explain why the hybridization of the oxygens in a deprotonated carboxcylic acid is not fully sp2.

Answers

  1. sp2
  2. Carbon and Nitrogen are both sp.
  3. Since there is a resonance structure, we know that the electrons are delocalized, meaning that they flow through the conjugated system.  This means that both the oxygens must have p orbitals for pi bonding, but they are not full pi bonds.  Experimental evidence has shown that the C to O bond in these molecules is longer than a normal double bond, but shorter than a single bond, which means that the atoms have a hybridization in between sp and sp2.

References

  1. Klein, Douglas J., Trinajstic Nenad. "Valence-Bond Theory and Chemical Structure." Journal of Chemical Education. 67.8 (1990): 633-637. Print. DOI
  2. Chipman, Daniel M., Kirtman, Bernard, Palke, William E.  "Orbital Hybridization." Journal of the American Chemical Society. 99.5 (1977):1305-1307.  Print. DOI

Contributors

  • Donovan K. Hamrick
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Last Modified
10:16, 2 Oct 2013

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