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Localized Bonding

Chemical bonds are formed when two nuclei share a pair of electrons between them. These bonds are considered combinations of overlapping one-electron atomic orbitals. The bond is strongest when the two electrons are confined to a region between the two nuclei. This type of bond is described as a localized bond. One of the limitations of valence bond theory is that it assumes all bonds are localized bonds. As we will see, this is not a valid assumption.


What the valence bond theory introduces is the the notion that orbitals with one electron overlap other orbitals also containing one electron of opposite spin to create an area of increased electron probability density, or a chemical bond.

How do the Atomic Orbitals overlap?

If we recall when we learned about wavefunctions, waves can either have constructive or destructive interfere. Every orbital has a corresponding wave function which represents the probability that an electron can be found within it. Constructive interference of these wavefunctions occur when the two waves that come together are "in-phase;" destructive interference occurs when the two waves are out of phase.  The two wave functions have constructive interfere in a chemical bond which creates a new wavefunction for the area of orbital overlap.  The valence bond theory is a localized electron theory.  Electrons are constrained to the same orbital locations that they were in the individual atoms, and orbital themselves keep the same location.


Why do the Atomic Orbitals overlap?

As mentioned before, when two atomic orbitals come together, they form an area of increased electron probability.  This overlap area is attracted to the nucleus much more than the two individual oribtals were.  The electrons in the overlap are thus in a lower energy state which is the cause for the chemical bond.  If this concept is hard to grasp, think back to the Bohr Atom representation of electron orbitals.  The Bohr model says that the electron orbitals that come closer to the nucleus are attracted greatly to the nucleus and are thus in a lower energy state than orbitals further from the nucleus.  If we apply this concept to the valence bond theory, we can say that areas of increased electron density probability are also much more attracted to the nucleus than areas of lesser electron density probability so are in a lower, more stable energy state. 

What are Pi and Sigma Bonds?

Sigma Bonds

Among the covalent bonds, the bond with the most strength is considered the sigma bond because of its high stabilization between bonding orbitals. Sigma bonds are formed on the internuclear axis, are able to rotate and are considered symmetrical. Sigma bonds typically involve s-orbitals due to the single dimensional restraints of the s-orbitals. However, sigma bonds can also arise for an internuclear bond between two p-orbitals.

π Bonds

In contrast to sigma bonds, π bonds involve p-orbitals and are not symmetrical around the axis and therefore cannot be rotated. π bonds are in most cases bonded along with sigma bonds. π bonds also have less strength than sigma bonds because the atomic orbitals have smaller overlaps.

Pi Bond formed from the overlap of two P orbitals.

  • Single Bonds - Single bonds involve one sigma bond.
  • Double Bonds - Double bonds have one sigma bond and one π bond. Although it may seem like a π bond includes two bonds in itself, that is not true because the two overlaps occur within a single pi orbital. The reason for the two overlaps is that fact the p-orbitals include two phases seperated by a nodal plane. 
  • Triple Bonds - Triple bonds include one sigma bond and two pi bonds. The two π bonds are perpendicular to each other so if you were to rotate the internuclear axis by 90o, the two π bonds would seemingly switch places.

Limitations of the Valence Bond Theory

When the bonding scheme of certain polyatomic molecules is discussed, our simple valence bond theory fails to accurately describe what is going on. Methane is one of these molecules where we must expand upon our valence bond theory. The 2s orbital is filled with two electrons and the 2py orbital has no electrons for use in bonding. This leaves only the 2px and the 2pz orbitals as the orbitals that can participate in bonding. We know however, that in CH4, four hydrogen atoms must make four bonds with the central carbon atom. 

What happens is that the carbon atom promotes one of its 2s electrons to the 2py oribital. This leaves one electron in the 2s orbital and one electron in the 2py orbital. All together, the central carbon now has four unpaired valence electrons to bond to each of the four hydrogen atoms. This is called hybridization and is covered in another module.

To learn more about hybridization, click here

Another one of the shortcomings of the Valence Bond Theory is the inability to predict molecular geometries. If we take a look at the bonding orbitals of H2S, only two of the p orbitals of sulfur bond with a 1s orbital from H. The molecular geometry predicted by these two bonding orbitals is 90o. This is obviosuly incorrect because the valence bond theory does not take into account the lone pair electrons on the central S atom.  The two lone pair electrons create a angle of 104.5o between the two hydrogen atoms. To learn more about electron geometries, click here. The following video is might help you to better understand the valence bond theory.

Implications of the Valence Bond Theory

The valence bond theory can provide some essential insight into many of the chemical properties we observe. For example, the H-H bond strength in H2 is one of the strongest bonds because of the sigma bond between the hydrogen molecules. As we learned before sigma bonds are significantly stronger than pi bonds. Additionally, the involvment of only s-orbitals and increased overlap increases the bond strength. The F-F bond in F2 is significantly weaker due to the nature of the p-orbital bonds. There are many chemical properties such as bond strength and bond length that we can derive from analysis of the valence bonds that we would not be able to get from just lewis structures.


  Bond Dissociation Energy
H2 104.2 kcal/mol
F2 36.6 kcal/mol


Figure showing the s-orbital overlap of the H2 molecule. Figure by Parmveer Hansra.


  1. Petrucci, Ralph, William S. Harwood, F. Geoffrey Herring, and Jeffrey D. Madura. General Chemistry. 9th ed. Upper Saddle River, New Jersey: Pearson Prentice Hall, 1993. Print.
  2. Kotz, Treichel, and Townsend. Chemistry and Chemical Reactivity. 7th ed. Belmont, Ca: Thomson Higher Education, 2006. Web. 30 Nov. 2009
  3. Drennan, Catherine, and Elizabeth Vogel Taylor. 5.111 Principles of Chemical Science, Fall 2008. (Massachusetts Institute of Technology: MIT OpenCourseWare), (Accessed 21 Nov, 2010). License: Creative Commons BY-NC-SA


1. How does a chemical bond form in terms of a valence bond method?

a) Two electrons with the same spin overlap and the corresponding wavelengths constructively interfere.

b) Electrons join together to create an area of high electron density probability.

c) Two electrons of opposing spin overlap and the corresponding wavelengths constructively interfere.

d) The internuclear forces share protons to for a chemical bond.

e) Electron orbitals destructively interfere to form a chemical bond.

2. Describe the molecular geometry of H2O suggested by each of the following methods:

(a) Lewis theory

(b) valence-bond method using simple atomic orbitals (not hybridized);

3. What is the difference between a sigma bond and a pi bond?  Compare and constrast the two.

4. Represent bonding in the CO2 molecule by

a) Lewis structure

b) The valence bond method

c) The orbital overlap

5. How many pi and sigma bonds does O2 have?  What kind of a bond is this?


1. C is correct

A is incorrect because of Pauli's exclusion principal.

B is incorrect because electrons don't join together.

D is incorrect because protons aren't involved in bonds.

E is incorrect because chemical bonds are formed with constructive interference.

2. a. There is a single bond between each hydrogen atom and the oxygen atom.

- There are two lone pairs attached to the Oxygen atom because its electron configuration is [He] 2s22p4 creating a 104.5o bond angle.

b. the bond results from the overlapping of 1s orbital with a 2p orbital on O creating a 90o bond angle.

3.  Sigma bonds are formed on the internuclear axis and are symmetrical if rotated.  Pi bonds are not symmetrical.  Typically sigma bonds are stronger than pi bonds due to the greater orbital overlap and resistance to rotation.


 a. Lewis dot structure of CO2 CO2.jpg

 b. Molecule is linear, and is a straight line with 180 degree angle. C is the central atom.

 c. sp2 orbitals overlap each other.


5. O2 consists of 1 sigma bond and 1 pi bond.  This is a double bond.


  • Parmveer Hansra (UCD)