[Heisenberg97]

Why is PF4(CH3) fluxional whereas PF3(CH3)2 isn't?

Attempt - Methyl groups prefer to occupy equatorial sites because the dz^2 orbital of p donates electron density to the electronegative F axially, contracting the dz^2 orbital, and lowers the energy of the molecule (makes it more stable). In PF3(CH3)2, the lowest energy form is where the 2 fluorines are axial. CH3 groups are bulky and will make rotation difficult due to steric strain. Lots more energy is required to make PF3(CH3)2 fluxional

[Flatbutterfly]

The NMR spectra (both F-19 and P-31) of the molecules PF(5-n)Me(n) (n= 0,1, 2) were first carried out by Muetterties and coworkers in 1963.  They found that the F atoms always occupied the axial sites in the Me cmpds (easily determined by IR that has a much faster time-scale than NMR).  Both PF5 and PF4Me were highly fluxional on the NMR time-scale with the pairwise axial-equatorial exchange presumed to occur by the Berry mechanism; on the other hand PF3Me2 was rigid.  Because PH2F3 is also rigid the increased barrier in the dimethyl molecule is probably not due to steric factors.  The barrier was rationalized in terms of an isomer with a Me group in an axial position being at a much higher energy to those isomers with F atoms in axial sites.  In my day this was rationalized by postulating that the trigonal bipyramidal configuration comprised of s,px,py bonding to the substituents in the equatorial plane and pz, dz^2 to the axial substituents, and that the F p AO had better overlap with the axial AOs leading to stabilization of the PFax forms.  You might look up Bent’s Rule that states more electronegative substituents prefer AOs with more p-character.  It was initially an empirical rule but was later put on more sound footing by using MO theory.
I was initially going to work through the latest papers on the subject but I’ll leave that to you!
(If you don’t have access to these refs then contact me privately.)
Key references:
Westheimer, F. H. Acc. Chem. Res. 1968, 1, 70.  (Early NMR studies)
Moreland, C. G.  et al J. Am. Chem. Soc.1976, 98, 2161. (More detailed NMR studies)
Wasada, H.; Hirao, K.  J. Am. Chem. Soc.1992, 114, 16. (Theoretical studies)