Molecular orbital theory is concerned with the combination of atomic orbitals to form new molecular orbitals. These new orbitals arise from the linear combination of atomic orbitals to form bonding and antibonding orbitals. The bonding orbitals are at a lower energy than the antibonding orbitals, so they are the first to fill up. By figuring out the molecular orbitals, it is easy to calculate bond order.
The valence bond theory is an extension of the Lewis Structures that considers the overlapping of orbitals to create bonds. The valence bond theory is only limited in its use because it does not explain the molecular geometry of molecules very well. This is where hybridization and the molecular orbital theory comes into place.
Hybridization is a simple model that deals with mixing orbitals to from new, hybridized, orbitals. This is part of the valence bond theory and helps explain bonds formed, the length of bonds, and bond energies; however, this does not explain molecular geometry very well.
- sp An example of this is acetylene (C2H2). This combines one s orbital with one p orbital. This means that the s and p characteristics are equal.
- sp2 An example of this is ethylene (C2H4). This is the combination of one s orbital and two p orbitals.
- sp3 An example of this is methane (CH4). This is the combination of one s orbital and three p orbitals.
If you add the exponents of the hybridized orbitals, you get the amount of sigma bonds associated with that bond. The sp2 hybridized orbital has one p orbitals that is not hybridized and so it can form a pi bond. This means that sp2 orbitals allow for the formation of a double bond. Also, sp hybridized orbitals form a triple bond.
Antibonding vs. Bonding Orbitals
Electrons that spend most of their time between the nuclei of two atoms are placed into the bonding orbitals, and electrons that spend most of their time outside the nuclei of two atoms are placed into antibonding orbitals. This is because there is an increasing in electron density between the nuclei in bonding orbitals, and a decreasing in electron density in antibonding orbitals (Chang 459). Placing an electron in the bonding orbital stabilizes the molecule because it is in between the two nuclei. Conversely, placing electrons into the antibonding orbitals will decrease the stability of the molecule. Electrons will fill according to the energy levels of the orbitals. They will first fill the lower energy orbitals, and then they will fill the higher energy orbitals. If a bond order of zero is obtained, that means that the molecule is too unstable and so it will not exist.
Below are a few examples of bonding and antibonding orbitals drawn out:
- Hydrogen Example:
- Oxygen Example (homonuclear):
- See oxygen file below
- Hydrogen Flouride Example (heteronuclear):
- See hydrogen fluoride file below
Bond order is the amount of bonds formed between two atoms. For example, two bonds are formed between oxygen atoms, so the bond order is 2. The following is the equation to find bond order.
1/2(electrons in bonding molecular orbitals - electrons in antibonding molecular orbitals)
Bond order gives information about bond length and strength. Generally, higher bond order correlates to a shorter bond length. This is due to the greater number of bonds between the atoms. In addition, because of the greater number of bonds between the atoms, the strength should also be greater as bond order increases.
- <--- This youtube video is a lecture on Molecular Orbital Theory from the open course website at MIT. It is has a good review of antibonding and bonding orbitals.
- Smith, Derek W. "The Antibonding Effect." J. Chem. Educ. 2000 77 780.
- Chang, Raymond. Physical Chemistry for the Biosciences. University Science Books, 2005.
- Determine if each of the following are paramagnetic or diamagnetic: F2, 02, N2, C2, Ag2.
- Calculate the bond order for each of the following: H2, H2+, H2-. (remember bond order is bonding minus antibonding electrons times one half)
- Draw the molecular orbitals for He2and He2+. Are both of these stable molecules?
- Write out the electron configuration diagram using molecular orbitals and calculate the bond order of HCl, NO-1, and CO. Rank them in order of increasing stability.
Contributors and Attributions
- Mustafa Rupawalla (UCD)