Dear Devyesh Rana,
the mechanical properties your are referring to are best calculated by your own
post-processing tools based on static CP2K calculations and as such, in my
opinion, not matter of the electronic structure core itself.
Even though the same holds also for the calculation of thermal and electric
conductivities, they are indeed much more subtle. The former can be computed
via the time-integral of the autocorrelation function of the heat flux. Alternatively,
non-equilibrium MD techniques can be used for faster convergence, but do have
their own problems.
Please have a look e.g. at Donadio & Galli, Phys. Rev. Lett. 99, 255502 (2007)
and references therein for a particular instructive treatment on the matter.
Very recently, we have devised a novel approach, which appears to be very
fast converging, but have only demonstrated that for the electric conductivity
(thermal conductivity should be analog and is matter of current investigations)
in solids, which only requires the calculation of the density matrix within CP2K:
Greetings,
Thomas Kühne