Molecular Orbital

Molecular Orbital Theory (MO)
  • A molecular orbital is a Schrodinger's orbital which can include several but usually only 2 nuclei.
  • The molecular orbital theory is a method for determining the molecular structure in which electrons are not assigned to individual bonds between atoms, but are moving under the influence of the nuclei in the whole molecule.
  • An orbital is the region where there is a 95% probability of locating an electron in a free atom.
  • There are mainly 4 types of orbitals (s,p,d and f) and each orbital can hold a maximum of 2 electrons.
  • These orbitals contain different numbers of subshells and have different energy level (s-1 , p-3 , d-5 and f-7).
  • There are 3 main rules in this theory:
  • 1)The molecular orbitals are filled in a way that yields the lowest potential energy for the molecule. In other words the electrons must fill up 1s before 2s and 2s before 2p.
  • 2)Each orbital can only contain 2 electrons(which i mentioned above)
  • 3)Orbitals of equal energy are half filled with parallel spin before they begin to pair up which means that electrons are half-filled(the arrow pointing up) before they can pair up with the other electron(the arrow pointing down). (Refer to diagram below for example)
  • Lets look a O2 and O as an example:

  • Note that the ones with the asterisk(*) represents anti-bonding molecular orbitals
Bonding order
  • A bonding order is basically the number of bonds formed
  • The bonding order tells us the stability of the molecule and whether it is diamagnetic or paramagnetic
  • Diamagnetic basically means that all of the electrons that are being shared forms a pair and is basically stable
  • On the other hand paramagnetic means that one or more electrons is unpaired and the molecule is unstable
  • We can calculate the bonding order of molecules by the formula, bond order = 1/2(number of bonding molecular orbitals - number of anti-bonding molecular orbitals)
  • Lets look at O2 as an example:

  • From this diagram we can see that there are 10 bonding MOs and 6 anti-bonding MOs (1 spin represents 1 bonding or anti-bonding MO)
  • Therefore the bond order of O2 = 1/2(10-6) = 2
  • We can see that O2 has 2 unpaired electrons and we can tell that O2 is paramagnetic
  • Another example would be H2:
  • I know its kind of hard to see but basically there are 2 bonding MOs and zero anti-bonding MOs
  • Therefore the bond order = 1/2(2-0) = 1
  • We can see that there are 2 unpaired electrons and this tells us that H2 is paramagnetic
  • Lastly we have F2 (I couldnt find a nice picture for N2 so i replaced it with F2 however the blog apparently won't accept gif images so i will just link the picture D;)
  • From the diagram we can see that there are 10 bonding MOs and 8 anti-bonding MOs
  • So the bond order = 1/2(10-8) = 1
  • We can also see that there are no unpaired electrons, or spins, therefore we can say that F2 is diamagnetic
  • All in all there is actually a simpler way of counting the bond order which is taking the total number of shared electrons divide by 2 :P.

The different types of molecular orbitals
  • The molecular orbital theory uses a Linear Combination of Atomic Orbitals(LCAO) to form molecular orbitals which cover the whole molecule
  • These molecular orbitals are divided into bonding orbitals , anti-bonding orbitals and non-bonding orbitals
  • So today we will only touch on the bonding and anti-bonding orbitals.
  • If the orbital is the type which the electrons present in the orbital have a higher chance to be found between the nuclei, then this is said to be a bonding orbital as it will tend to hold the nuclei together.
  • However if the orbital is the type which the electrons present in the orbital have a higher chance to be found elsewhere other than between the nuclei, then this is said to be an anti-bonding orbital and the bond will be weaker.
  • In order to understand the anti-bonding orbital, we must first know what is the Linear Combination of Atomic Orbital.
  • This model follows these assumptions made:
  • 1)Molecular orbitals are formed by 2 overlapping atomic orbitals
  • 2)Only atomic orbitals with almost the same energy level can react to a certain point
  • 3)When 2 atomic orbitals they react in 2 very different ways and form both bonding and anti-bonding orbitals
The in-phase reaction
  • Where the atomic orbitals overlap, the in-phase interaction leads to an increase in the intensity of the negative charge in the region where they overlap.
  • This creates an increase in negative charge between the nuclei and an increase in the attraction between the electron and the nuclei for the atoms.
  • The greater attraction leads to lower potential energy and because electrons in the molecular orbital are of lower potential energy than in separate atomic orbitals, energy would be required to shift the electrons back into the 1s orbitals of separate atoms.
  • This keeps the atoms together in the molecule, so we call this orbital a bonding molecular orbital.
The out-of-phase reaction
  • Where the atomic orbitals overlap, the out-of-phase interaction leads to a decrease in the intensity of the negative charge.
  • This creates a decrease in negative charge between the nuclei and a decrease in the attraction between the electron charge and the nuclei for the atoms in the bond.
  • The lesser attraction leads to higher potential energy and the electrons are more stable in the 1s atomic orbitals of separate atoms, so electrons in this type of molecular orbital destabilizes the bond between atoms.
The following diagram shows the bonding and antibonding molecular orbitals formed from the interaction of two 1s atomic orbitals.



The above example shows how the 1s orbital overlaps and thus having 2 different kinds of reactions. However for the 2p orbitals (and subsequently 3p , 3d , 4p , 4d , 4f and so on), there will be more scenarios as they can overlap differently.

  • The p atomic orbitals of the two atoms can interact in two different ways, parallel or end-on. The molecular orbitals are different for each type of interaction.




  • There is less overlap for the parallel atomic orbitals and when the interaction is in-phase, less overlap leads to less electron charge enhancement between the nuclei.
  • This leads to less electron charge between the nuclei for the pi bonding molecular orbital than for the sigma bonding molecular orbital.
  • Less electron character between the nuclei means less attraction, less stabilization, and higher potential energy for the pi bonding molecular orbital compared to the sigma bonding molecular orbital.
  • When the interaction is out-of-phase, less overlap leads to less shift of electron charge from between the nuclei.
  • This leads to more electron charge between the nuclei for the pi anti-bonding molecular orbital than for the sigma anti-bonding molecular orbital.
  • More electron charge between the nuclei means more attraction and lower potential energy for the pi anti-bonding molecular orbital compared to the sigma anti-bonding molecular orbital.
In a nutshell:
  • Molecular orbitals are formed by 2 overlapping atomic orbitals.
  • There are 4 orbitals (s,p,d and f) and all orbitals can only contain 2 electrons
  • In orbitals, electrons must be filled from the lowest energy level and lose from the highest energy level.
  • In all orbitals with the same energy level, all of them must be filled with half-spin before they can be paired up with another electron.
  • There are 3 molecular orbitals (bonding orbital, anti-bonding orbital and non-bonding orbital).
  • When 2 atomic orbitals overlap they react in 2 different forms, the in-phase or out-of-phase form with in turns lead to the bonding orbital or anti-bonding orbital
  • If the bonding interactions outnumber the anti-bonding interactions, the molecular orbital is said to be "bonding," while if the anti-bonding interactions outnumber the bonding interactions, the molecular orbital is said to be "anti-bonding"
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