[Rutherford]

Why can phosphorus and sulfur atoms be chiral, but not nitrogen (except in rigid structures)? Is it related to tunneling?

[discodermolide]

What is the definition of chirality?

[Rutherford]

No plane or center of symmetry. An atom is a stereogenic center when it has four different groups. I know all that. Nitrogen with four different groups (counting the electron pair) isn't chiral, while phosphorus and sulfur are even though they also have an electron pair, but R/S doesn't exchange rapidly, why? Is it because tunneling is less probable in their case?

[discodermolide]

The definition is the compound must be non-superimposable on it's mirror image, nothing to do with 4 different groups. Nitrogen can be chiral.
The interconversion of enantiomers in the case of S & P means they must proceed through some sort of quasi planar intermediate, the barrier to inversion is high. I'm not quite sure what tunnelling has to do with it!
Carbon R & S do not interconvert either.

[Rutherford]

Why would it be so easy for nitrogen to interconvert but not for the rest?

[rwiew]

Ok, so let's think about what has to happen for inversion to occur. As discodermolide said, you have to go through some sort of a quasi planar intermediate (e.g. trigonal planar for N/P) to get to the other enantiomer - can you draw molecular orbital diagrams for both cases (i.e. tetrahedral and trigonal planar). In a nutshell, my reasoning would be this: as you go down a group, the s/p gap increases and s/p mixing and hence hybridization decrease in extent. For nitrogen it is fairly easy to change shape as the s/p mixing is strong and it can go from sp3 to sp2 and again to sp3 with little effort. However, bonding in P is determined more by the intrinsic angles between px, py and pz orbitals than by tetrahedral sp3 mixing (see the experimental bond angles trends as you go down a group for confirmation of this). Hence a change of shape would actually require some s/p mixing to occur, as deviation from the atomic inter-p angles is not possible (or very highly energetically unfavorable) otherwise. This however is much harder than in N, because of the s/p gap. Does this make sense?

[Rutherford]

Yes, but I don't quite understand what you meant.

For nitrogen it is fairly easy to change shape as the s/p mixing is strong and it can go from sp3 to sp2 and again to sp3 with little effort.

I don't see the logic behind this. Why would strong s/p mixing make sp3 to sp2 transition easier?

[rwiew]

What I am saying is that the transitions are different - nitrogen goes sp3 to sp2, phosphorous more like 3 unhybridized p's via for example sp2 to 3 unhybridized p's - the change between the ground state and the 'transition state' is much higher for phosphorous = large activation energy for this process. Essentially having an s orbital which has a spherical symmetry to mix with the p orbitals allows you to play around with geometry much more, 'isolated' p orbitals are more or less stuck in their positions.