Molecular Orbital Diagram (MO Diagram) of methane (CH4) - Chemical Bonding & Molecular Structures

Methane is a pentatomic, tetrahedral molecule. It is formed by combination of one carbon atom with 4 hydrogen atoms. In the molecule of methane, the carbon atom is at the centre and four hydrogen atoms are at the four corners of a regular tetrahedron. Hence carbon atom is taken as central atom with four hydrogen atoms as peripheral atoms.
The shape of methane molecule is tetrahedral, so we can imagine a cube with the carbon atom at the center of cube and 4 hydrogen atoms at alternate corners of the cube. This is the simplest representation of tetrahedral geometry. Now we can label all four hydrogen atoms as H1, H2 H3 and H4.
So when wave function of all 4 hydrogen atoms are same say positive the group orbital can be formed by combining wave functions of all hydrogen atoms, I.e. psi 1 become psi 1s of first hydrogen + psi 1s of 2nd hydrogen + psi 1s of third hydrogen and psi 1s of 4th hydrogen.
As all the lobes of hydrogen atoms are of same sign, this can easily match with the symmetry of 2s orbital of carbon atom because 2s orbital is spherical, and can have positive or negative sign, so when it is positive bonding molecular orbital is formed and when it is negative anti bonding molecular orbital can be formed.
Similarly Psi 2 can be formed when sign of waves of two hydrogen atoms are opposite. e.g Hydrogen 3 and hydrogen 4. This group orbital is similar to the 2pz orbital of the carbon atom, so they can overlap to form bonding and anti bonding molecular orbitals depending upon the sign of the lobes of 2pz orbitals.
Psi 3 can be formed when sign of waves of hydrogen 2 and hydrogen 3 are opposite. This group orbital have matching symmetry with 2px orbital of carbon. And can overlap with 2px orbital of carbon atom.
And finally Psi 4 can be formed when sign of waves of hydrogen 2 and 4 are opposite which is having matching symmetry with 2py orbitals. In this way we have total 4 group orbitals formed by overlap of 4 atomic orbitals of hydrogen atoms represented by psi 1, psi 2, psi 3 and psi 4. Now lets try to combine these group orbitals with the matching atomic orbitals from the carbon atom.
On the basis of symmetry adapted linear combinations (SALCs), the four group orbitals combine with the matching orbitals of central carbon atom. The group orbitals psi 1 combines with their matching 2s orbital of carbon atom forming sigma s bonding molecular orbital and sigma star s antibonding molecular orbital.
The combination of 2pz, 2px, and 2py, orbitals of carbon with the group orbitals psi 2, psi 3 and psi 4, respectively produce three bonding (sigma pz, sigma px, sign py) and three antibonding (sigma star pz, sigma star px, sign star py) molecular orbitals. The character of overlapping of 2pz, 2px, 2py, orbitals of carbon atom with 1s orbitals of hydrogen atoms is the same. Hence the three bonding molecular orbitals have same energy, i.e., they are triply degenerate.
Similarly, the three antibonding molecular orbitals also are triply degenerate. Thus in CH, molecule in all eight molecular orbitals are formed which are delocalised over all the five atoms.
The eight molecular orbitals formed may be shown in molecular orbital diagram as follows:
On the right hand side we have represented 4 group orbitals formed by overlap of 4 atomic orbitals. And on the left atomic orbitals of carbon atom is shown. The electrons can be filled as per the electronic configuration of these atoms. Now psi 1 overlaps with 2s orbital forming sigma s and sigma star s orbitals, and psi 2, psi 3 and psi 4 overlaps with 2pz, 2px and 2py respectively to form 3 sigma bonding and 3 anti bonding molecular orbitals. As the energy of these orbitals are same, they are shown on the same level.
The eight available electrons (four from carbon and four from four hydrogen atoms) are distributed in four bonding molecular orbitals from the lowest energy level. Hence the electronic configuration of methane, molecule is diamagnetic.
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[@rkraman78]

very elegant pictorial representation

[@Edmerls]

Thanks

[@kaushikumarihami1982]

very useful video. what a great teacher you are!!!!

[@Edmerls]

Thank you! 😃

[@hrushikeshpatel9146]

2pz and 2py are pi orbitals since they antisymmetrical spins

[@lumaineje]

Sending love from the Philippines

[@yeshvanths3327]

Sir in carbon sp mixing will take place know

[@reynanfielsuyom1415]

What about CH3+

[@nathanrmn]

thank you from brasil

[@Edmerls]

Your welcome

[@tarangmungushmare5668]

Thank you

[@Edmerls]

You're welcome!!

[@rahimchemist6033]

Very nice sir

[@Edmerls]

Thanks and welcome

[@bhupendra5846]

Sir how to decide energy level of carbon atomic orbital and group orbitals of Hydrogen

[@Edmerls]

They are calculated experimentally

[@AbdulRAUF-xu1ty]

Thank you very much.

[@Edmerls]

You are welcome!

[@boogaooga3118]

very helpful! Can you upload the mo diagram of SF6 and PH5 please sir

[@pullaajay9415]

Sir provide a video on Correlation diagram for AnHn type Molecules

[@Edmerls]

Will try

[@muhammadfaizan2909]

Sir upload MOT structure of water

[@Edmerls]

kzbin.info/www/bejne/oJ_NoniPq56hn6M

[@amanadleshorts7429]

Nice explanation

[@Edmerls]

Thanks and welcome

[@anupamaghata8738]

Nice explanation