Do electron clouds overlap when hybridization occurs?

First of all, electron clouds CAN overlap, and they must, to form chemical bonds in the first place!

The attraction of nucleus #A# to the electrons in atom #B# balance out with the repulsion of the two negatively-charged electron clouds and of the two positively-charged nuclei when bonds form at the potential energy minimum.

And so, they must be able to overlap to form hybridized atomic orbitals in a linear combination.

Take the #sp^3# for example:

#Psi_(sp^3) = c_1psi_(s) + c_2psi_(p_x) + c_3psi_(p_y) + c_4psi_(p_z)#

where each wave function #psi# represents a given pure atomic orbital, with weighted contributions given by #c_i#. As a result, #Psi_(sp^3)# represents the #sp^3#-hybridized orbital.

All that the above equation says is that hybridized orbitals form by the overlap of pure atomic orbitals.

They achieve an intermediate energy between the original orbitals, so that all the hybridized orbitals are:

• the same energy
• the same look/symmetry

So, in #"CH"_4#, carbon would hybridize its #2s# and #2p_(x//y//z)# as follows:

This then allows the orbitals to align themselves along the internuclear axes, and bond by head-on overlap (meaning, #sigma# overlap) with outer atoms.

You can see more info on this here.