How Do Orbital Interactions and Sigma Bonds Work in Methane?

[Watari]

Hello all

I have an exam coming up this week but there's something that I don't understand:

Let's take methane, for example.
If I understand it correctly, the bonding orbitals of carbon are all hybridized to sp³ orbitals and overlap with the 1s orbital of four H atoms.
Does the orbital of hydrogen also change in any way?

And the bonds involved here are all sigma bonds. Do the shared electrons of carbon and hydrogen follow a common sigma orbital, or do the orbitals simply overlap but still follow their own distinct paths? If the latter is the case, then what exactly is the definition of a sigma orbital?

Thanks

 

[Quantum Defect]

Hello all

I have an exam coming up this week but there's something that I don't understand:

Let's take methane, for example.
If I understand it correctly, the bonding orbitals of carbon are all hybridized to sp³ orbitals and overlap with the 1s orbital of four H atoms.
Does the orbital of hydrogen also change in any way?

And the bonds involved here are all sigma bonds. Do the shared electrons of carbon and hydrogen follow a common sigma orbital, or do the orbitals simply overlap but still follow their own distinct paths? If the latter is the case, then what exactly is the definition of a sigma orbital?

Thanks

Reality is more complex than the simple pictures.

For Valence Bond Theory (which is implied in the language you use above) sigma bonds are bonds that have cylindrical symmetry about the bond axis. Pi bonds have a nodal plane along the bond axis. For this level of discussion, the carbon atom has sp^3 hybrid orbitals and the H atom has 1s orbitals. These orbitals overlap to give you the sigma bond. The electrons are not following "their own distinct path".

In simple Molecular Orbital Theory, you would come up with molecular orbitals by taking linear combinations of atomic orbitals (or some other basis functions) to come up with orbitals that would be de-localized (to a greater or lesser extent) over the whole molecule. In the simple picture, you would plop electrons in (two-per orbital) until you accounted for all of the electrons.

To get better numbers for energies, etc. you need to do fancier stuff. Look at e.g. Levine "Quantum Chemistry" to get a fuller description of how people do this.