[nj_bartel]

Can someone explain to me why a carbene with a lone pair is sp² hybridized and a carbene with 2 lone electrons is sp hybridized?  I understand that the triplet methylene exists due to Pauli Exclusion, but why do the spin unpaired electrons belong in p orbitals?  Why can't they be hybridized?

[azmanam]

Think of your MO diagrams.  2 p orbitals will be degenerate, but an sp² and a p orbital will have different energies.  It is the difference between placing one electron in each of 2 degenerate orbitals or one electron in a lower energy orbital and one electron in a higher energy orbital.  That being said, the H-C-H angle in methylene (CH₂) has been determined to be ~135^o.  I'll leave you with two quotes.  One from my advanced organic text (Carey and Sundberg, Advanced Organic Chemistry: B) and one from a 'Google book' I found through a Google search (Moss, Platz & Jones, Reactive Intermediate Chemistry):

Carey & Sundberg:

The bonds in the corresponding triplet carbene structure are formed from sp orbitals, with the unpaired electrons being in two orthogonal p orbitals.  A linear structure would be predicted for this bonding arrangement.

Both theoretical and experimental studies have provided more detailed information about carbene structure.  MO calculations lead to the prediction of H-C-H angles for methylene of ~135^o for the triplet and ~105^o for the singlet.  The triplet is calculated to be about 8 kcal/mol lower in energy than the singlet.  Experimental determinations of the geometry of CH₂ tend to confirm the theoretical results.  The H-C-H angle of the triplet state, as determined from the electron paramagnetic resonance (EPR) spectrum, is 125-140^o.  The H-C-H angle of the singlet state is found to be 102^o by electronic spectroscopy.

Moss, Platz & Jones:

To understand the difference between the singlet and the triplet state, let us consider a prototypal carbene.  The carbon atom can be either linear or bent, each geometry is describable by a specific hybridization.  The linear geometry implies an sp hybridized carbene center with two non bonding degenerate orbitals (p_x p_y).  Bending the molecule breaks this degeneracy and the carbon atom adopts an sp²-type hybridization: the p_y orbital remains almost unchanged (it is usually called p_z), while the orbital that starts as a pure p_x orbital is stabilized because it acquires some s character (it is therefore called σ).  The carbene ground-state multiplicity is related to the relative energy of the σ and p_x orbitals.  The singlet ground state is favored by a large σ-p_x separation.

[nj_bartel]

Took me a while, but I believe that makes sense; thanks