[lviorel]

Hello,

could someone answer me this question, please?
Why is the number of molecular orbitals (in molecular orbital theory) equal to the number the atomic orbitals included in the linear expansion?

[renge ishyo]

It's easier to see this if you consider the old hybridization theory of orbitals, and then extrapolate the idea to the MO theory. For instance, the bonds between carbon and chloride in CCl₄ are sp3 hybridized...the s-orbital mixes with each of the three p orbitals to form four orbitals with some s character and p character in each. This idea is consistent with the pauli exclusion principle which states that only 2 electrons maximum are allowed in each orbital. For unhybridized carbon you can fit 2 e's in the s orbital and 6 e's (potentially) in the three p-orbitals. When you combine these orbitals in bonds with another molecule (as you would with an LCAO) you now have 4 orbitals each on carbon with a certain percentage of s and p character, but you can still fit a maximum of 8 electrons into these hybridized orbitals; the numbers of electrons you can fit doesn't change whether the orbitals are mixed/hybridized or unmixed/unhybridized, and therefore the overall number of distinct orbitals must remain the same before and after. This principle can also be shown as a consequence from the raw quantum calculations themselves, but the idea must be solidified long before that point.