Why do electrons in SP3 orbitals need opposite spins in molecular bonding?

[RaduAndrei]

The 3s and 3p orbitals are filled by 4 electrons.A single atom has [Ne]3s2 3p2.But when multiple atoms get together they do so in order to minimize the overall energy.And to minimize the overall energy,the 3s and 3p orbitals hybridize to form 4 tetrahedral SP3 orbitals.And the Si atoms get together by joining their 4 SP3 orbitals.Each SP3 orbital has one electron and is capable of forming a bond with a neighboring atom.So each atom has 4 neighboring atoms.

Am I right?

And when two SP3 orbitals of two atoms join together to form a molecular orbital they do so in order to respect Pauli exclusion principle(the 2 electrons from the 2 SP3 orbitals cannot occupy the same quantum state simultaneously).That is the originial SP3 energy level in 2 energy levels:bonding state and anti-bonding state.And the electrons now occupy the bonding state...one electrons has a spin up and the other a spin down.

So here is my question.Why can't the 2 electrons have different spins in the same molecular orbital,the same original SP3 level?Why must nature split this original level in 2 different energy levels?

 

[DrDu]

Of course electrons can fill the same atomic orbital with different spins. They do so in so called lone pairs, e.g. in NH3 where there are thre bonds between N and H and one lone pair at N.

A bond is formed because the electrons can then move in the potential trough of two nuclei thus lowering their kinetic energy.
Pauli principle is merely a complication.

 

[M Quack]

This is basically the same has Hund's rule. You first fill up all available orbitals with one spin direction, and only when all orbitals are occupied by one electron you add the second electron with opposite spin.

http://en.wikipedia.org/wiki/Hund's_rule
http://en.wikipedia.org/wiki/List_of_Hund's_rules

The reason for this is that electrons different orbitals are less efficiently screened from the nuclear charge and thus have lower energy.