How do atomic orbitals combine to form molecular orbitals?

[CrimpJiggler]

When 2 atoms bond, do all their atomic orbitals combine, or is it just the bonding orbitals that combine? For example when sodium and chlorine bond, do all their orbitals combine or is it just sodiums 3s orbital that combines with chlorines 3p orbital?

 

[Yanick]

When 2 atoms bond, do all their atomic orbitals combine, or is it just the bonding orbitals that combine? For example when sodium and chlorine bond, do all their orbitals combine or is it just sodiums 3s orbital that combines with chlorines 3p orbital?

NaCl is a bad example because the bond is highly ionic (Na⁺ + Cl^-). If you want to talk about molecular orbitals you need to talk about high covalent character bonds. And the answer is that only the valence electrons participate in the bonding. Carbon hybridizes the 2s and the 2p_(x,y,z) orbitals into spⁿ orbitals, where n varies with number of sigma bonds.

IE for methane you get an sp³ where the 2s, 2p_x, 2p_y, 2p_z have hybridized to form 4 molecular orbitals.

 

[CrimpJiggler]

I'm still completely lost. I know how atomic orbital hybridization works. Its molecular orbitals that I'm trying to understand. Heres a diagram for methane:

I like that diagram but I have no idea what the hell I'm looking at. Carbon has 4 sp³ valence orbitals. Hydrogen has a single s orbital. I would have assumed that all these orbitals combine to give 8 identical molecular orbitals. Thats not what I'm seeing on that diagram.

 

[Yanick]

Take a look at: http://www.upei.ca/~chem342/Resources/Reviews/Molecular_Orbital_Tutorial.pdf

Maybe it will help you. MO theory is not something I have a solid grasp on, its one of those topics in Chemistry where you are exposed to bits and pieces as you advance but don't really learn thoroughly until advanced undergrad-graduate level courses (p-chem, inorganic chem, quantum chem).

 

[DrDu]

Carbon has 4 sp³ valence orbitals.

In MO theory, although possible, it is not usual to start from hybrid orbitals which is a concept of valence bond theory. So Carbon has one s and 3 p orbitals which get combined in principle with all other orbitals from all other atoms in the molecule.

 

[CrimpJiggler]

Take a look at: http://www.upei.ca/~chem342/Resources/Reviews/Molecular_Orbital_Tutorial.pdf

Maybe it will help you. MO theory is not something I have a solid grasp on, its one of those topics in Chemistry where you are exposed to bits and pieces as you advance but don't really learn thoroughly until advanced undergrad-graduate level courses (p-chem, inorganic chem, quantum chem).

The reason I'm so determined to get a good grasp of it is because I'm in 3rd year of an applied chem course and I'm coming across various concepts in inorganic, organometallic and quantum chemistry that require (well at least I require it) an understanding of MO theory. For example I want to understand back bonding in CO ligands well but I can't really get my head around the idea that the metal donates pi electrons to the ligands antibonding MO. I get that much but I need to see the big picture. I suspect that MO theory is very incomplete and the only reason its been accepted into mainstream chemistry is because we have no alternative. We don't have a decent model to explain various things that can't be explained by valence bond theory so the MO model is better than nothing.

 

[DrDu]

I suspect that MO theory is very incomplete and the only reason its been accepted into mainstream chemistry is because we have no alternative. We don't have a decent model to explain various things that can't be explained by valence bond theory so the MO model is better than nothing.

No, certainly not. Almost any property of a molecule can be calculated nowadays to almost arbitrary precision starting from either MO or VB calculations + more sophisticated corrections.
However, the MO and VB methods start somehow from different limiting cases to tackle the bonding in molecules. I.e., the MO theory is best when the electrons are rather weakly bound to the atoms, that's why it performs best to describe metals and pi bonding systems. The VB approximation starts out from the isolated atoms and treats bonding as a rather small correction. That's why it performs best in non-metallic compounds.

 

[mcbud]

Going back to the original question, molecular orbitals by definition involve the whole molecule, and all electrons are involved in MO formation, both core and valence electrons. However, how these orbitals are formed depends on the relative energies of the atomic orbitals involved. For example, let's take H₂O. From an atomic orbital perspective, O has two 1s electrons, two 2s electrons, and 4 2p electrons, while H has one 1s electron. When O and H combine to form water, the atomic orbitals of O and H combine to receive the ten electrons (8 from O, 1 from each H). Five of those new molecular orbitals will be occupied by the electrons: 1a₁, 2a₁, 1b₂, 3a₁, and 1b₁ (in ascending order of energy).

The 1a₁ orbital in the water molecule is similar in energy to the 1s orbital of O, hence you can think of it as coming from the core electrons of O (not from the overlap between O and H).

The 2a₁, 1b₂, and 3a₁ orbitals have densities around the O and H nuclei, hence these are the ones mostly responsible for the binding of these two atoms.

The 1b₁ comes from the non-interacting 2p_y O orbital and it is essentially a non-bonding orbital.

Water has also three unoccupied antibonding molecular orbitals of higher energy than the 3a₁ orbital: 4a₁, 2b₂, and 3b₂. It has been reported that the 4a₁ and 2b₂ antibonding orbitals are partially involved in the O-H bond formation, by receiving electrons from the 1b₁ orbital.

In summary, the electronic configuration of water using molecular orbitals can be written as 1a₁² 2a₁² 1b₂² 3a₁² 1b₁². Notice how all atomic orbitals are involved in the formation of the molecular orbitals, even though the origin of the molecular orbital may be from either or both atoms involved in the bonding in this case.

Most MO diagrams show only the valence bonds, so you may get the impression that only the valence electrons are involved in MO formation, when in fact all electrons are involved in MOs, but only the valence electrons are involved in the bonding.

The methane case is discussed here with nice pictures: http://csi.chemie.tu-darmstadt.de/a...mel/tutorials/orbitals/molecular/methane.html

I hope this helps.