Understanding Hybrid Orbitals and MO Theory in Chemical Bonding

[eoghan]

Hi,
If 2s orbital and 2p_z orbitals are near enough in energy, then they can mix together to form two sp hybrid orbitals.
But how can I deal with sp^3 or sp^2 hybridization? According to MO only orbitals with the same symmetry species can overlap, so how can an s orbital overlap with a p_x orbital? And the resulting sp^3 orbital won't have the same symmetry of an s orbital, yet the sp^3 orbital will overlap with s orbital as in the methane molecule

 

[DrDu]

Hybridization is a concept of Valence bond theory, not of MO theory.

 

[eoghan]

About the lithium hydride my textbook (Physics of atoms and molecules, Bransden and Joachain) writes:
"It turns out that a lower energy is obtained from the variational method if a linear combination of the 2s and 2p_z atomic orbitals of lithium is used in place of just the 2s orbital. This combination of orbitals corresponding to different values of the angular momentum is called a hybrid orbital (an sp hybrid in the present case) and this phenomenon is called hybridisation."
It writes this in the context of the MO theory...

 

[DrDu]

That's, as I sad, a mixing of concepts. It's ok as long as you know its basics.
But I also see no contradiction to your first post. In a linear molecule, the s and the p_z orbital belong to the same symmetry species. The integral overlap of an s and a p_z on the same center is still zero, but that has no consequences. Both orbitals have an overlap (and a matrix element of the hamiltonian) with e.g. the s-orbital on the other atom which fixes their relative contribution in the MO's.

 

[eoghan]

Ok, so that means that also MO predicts hybrid orbitals?
Let's see if I understand: can we say that hybridization emerges naturally from MO theory because some orbitals of the same atom can overlap with non-zero matrix element, while in Valence bond theory hybridization is just an heuristic argument needed to explain the actual shape of the molecules?

 

[PhaseShifter]

A hybrid orbital is simply a superposition of various (non-hybrid) wavefunctions.
When two or more orbitals are combined to form a set of hybrid orbitals, the result is an equal number of linearly independent wavefunctions.

Molecular orbitals are somewhat different. The electrons in a molecular orbital experience a change in potential due to the presence of additional nuclei and electrons, so the linear combination of atomic orbitals commonly used to represent the resulting molecular orbitals is really only an approximation, as opposed to hybrid orbitals where linear combinations are an exact solution.

 

[DrDu]

Ok, so that means that also MO predicts hybrid orbitals?
Let's see if I understand: can we say that hybridization emerges naturally from MO theory because some orbitals of the same atom can overlap with non-zero matrix element, while in Valence bond theory hybridization is just an heuristic argument needed to explain the actual shape of the molecules?

As I said, hybrid orbitals are a sound concept in VB theory and certainly not heuristic. They can be optimized like you optimize MO's in MO theory.

 

[asheg]

A hybrid orbital is simply a superposition of various (non-hybrid) wavefunctions.
When two or more orbitals are combined to form a set of hybrid orbitals, the result is an equal number of linearly independent wavefunctions.

Molecular orbitals are somewhat different. The electrons in a molecular orbital experience a change in potential due to the presence of additional nuclei and electrons, so the linear combination of atomic orbitals commonly used to represent the resulting molecular orbitals is really only an approximation, as opposed to hybrid orbitals where linear combinations are an exact solution.

Thank you, very nice description.

 

[eoghan]

I guess I have understood (well, I hope ).
Thank you all!