How to calculate the vibrational entropy of a certain substance at some temperature?

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tssunrise · #1 Post by **tssunrise** » Mon Aug 30, 2010 2:37 am

I wonder how to get the phonon contribution to the energy of a certain substance at T after I have done the phonon calculation using IBROIN=5.
Thanks!

forsdan · #2 Post by **forsdan** » Mon Aug 30, 2010 9:30 am

Given that you only have the force constants at q = 0 (which VASP provides you with):

1. Set up the dynamical matrix at a number of q-points and diagonalize it to obtain the frequencies.
2. Integrate over the Brillouin zone to obtain the phonon-DOS.
3. Evaluate the free energy from the harmonic approximation.

If you don't want to these steps by yourself there is a free software (which reads the VASP output) that can do it for you:

http://phonopy.sourceforge.net/

Cheers,
/Dan

tssunrise · #3 Post by **tssunrise** » Tue Aug 31, 2010 1:48 am

Thank you for your reply.I have another question after reading your answer.
What is the relationship between the frequencies got from PHONOPY and obtained using IBROIN=5?Can I calculate the free energy using the result got from IBROIN=5?

forsdan · #4 Post by **forsdan** » Tue Aug 31, 2010 9:20 am

The basic relationships between the real-space force constants (which you obtain from VASP), the dynamical matrices and the free energy are outlined/commented on in many textbooks on condensed matter physics. So I would recommend you to revisit your old undergraduate literature. See e.g. Ashcroft/Mermin or Michael Marder, Condensed Matter Physics.

For more elaborate theory on thermal properties I also recommend to consider reading e.g. Thermophysical Properties of Materials By GÃ¶ran Grimvall.

Cheers,
/Dan