I think there is an error in the original paper of the barostat in the formula for the damping parameter gamma (equation 4):
Instead of
,
gamma should be given by
.
If this is true, we should change the code accordingly (line 402 in src/standalone/sliding_p.f90). I might be wrong though.
Here's my reasoning:
The equation of motion for the damped harmonic oscillator (equation 2 in the paper) without external force and vanishing F_int is given by

Critical damping occurs here for the condition (see e.g. wikpedia and I also checked the standard textbook Demtröder 1 )

yielding the expression above.