In amine inversion, there is a planar $sp^2$ intermediate.
The electron pair transferred from the blue lobe to the red one during the inversion. It is natural to assume, for a layman like me, that in the planar intermediate the electron pair is present in both lobes- one electron in each. That would impart paramagnetic character to the molecule. Does this really happen? I couldn't find any such phenomenon on internet.
Picture: http://chemistryjee.blogspot.in/2015/02/amines.html