The fluorine doesn't pass through carbon. It passes between two neighboring carbons through a C-C gap of 2.64 Å at the transition state. This is pyramidal inversion — the same mechanism as ammonia (NH₃), but with a 4.6 eV barrier instead of 0.25 eV. The transition state geometry is computed and verified with one imaginary frequency.

> with one imaginary frequency

Technical note, because it's jargon:

"Real" means position = A * sin(w * t)

"Imaginary" means position = A * expt(w * t)

(because expt(w * i * t) = cos(w * t) + i * sin(w * t))

If you calculate in a computer an ammonia molecule with all the atom is a plane z = 0 (instead of the usual piramidal shape), then the N in the center is in an inestable equilibrium and the N does not make small vibrations like z = expt(w * t).

It makes a big "imaginary" vibration like z = expt(w * t) that is exponential for a short time while z is almost 0, and then the approximations don't apply and it reach the z of the usual shape at equilibrium.