ABINIT Discussion Forums

Hi,

I'm interested in how anaddb deals with imaginary phonon frequencies to calculate the phonon free energy because
\[
F_vib = k_BT int_0^{\infty} ln {2 sinh [\frac {\hbar \omega}{2k_B T}]} g (\omega) d \omega
\]
can only be used for real frequencies. How can one take imaginary frequencies into account?

Thanks for your help!

Is it even a well-defined concept, to compute the free energy in this case? Don't imaginary frequencies imply an unstable configuration, therefore out of equilibrium, therefore standard formula for F not applicable?

finally I came to the conclusion that this concept is not applicable in case of imaginary frequencies. I hoped that there was a solution implemented in anaddb but to my knowledge there's no way to calculate the free energy with unstable phonons within the harmonic approximation since these imaginary frequencies occur due to the neglection of anharmonic terms...