[xshadow]

Why  is  :CH₂   foundamental state a triplet ?

My textbook speaks about a hund's rule for stabilty...I have to put the electrons in different orbital with parallel spin

But here  I have an electron on a  sp2 orbital and  the other  on a p orbital at different energy

Isn't  Hund's rule  for orbital at the same energy level?

Thanks

[mjc123]

Simplistically, yes, but when orbitals are close together you have to consider the energy balance between promoting an electron to a higher orbital and pairing the spins.
If the energy difference between the orbitals is E_O, and the spin-pairing energy is E_P, then the difference between the singlet and triplet states is E_O - E_P. Whether this is positive or negative depends on the relative magnitudes of E_O and E_P.  Evidently in carbene this balance favours the triplet.

[hollytara]

And don't forget that hybridization is a construct invented to make it easier for us to visualize bonding but the experimental evidence is that it does not occur.  So your idea that triplet CH2 has one electron in a p orbital and one in a sp2 orbital is not accurate. 

Experimentally the ground state is triplet, but not by much (~38 kJ/mol kcal/mol).  There have been a lot of calculations on this simple system trying to understand why triplet is below singlet.  Triplet has wider bond angles (>125 degrees) than the singlet (~105 degrees).  At typical temperatures, there is a small but significant population of the singlet state.

Any pi donor substituents push the singlet state lower than the triplet.