Hi Ashis,

calculating E(T) is generally nontrivial and requires specific techniques such as thermodynamic integration (TI). TI requires equilibrium simulations at different temperatures, so that one has to use molecular dynamics or Monte Carlo to sample dynamic trajectories. 

DFT is typically restricted to 0K calculations so you cannot perform finite temperature simulations with it. Then you need to make some approximations to calculate free energies, such as the quasiharmonic approximation where one calculates the eigenfrequencies of the system and assumes that these do not change with temperature.

I believe you are talking about the Free energy G. There are two ways to calculate the G (Gibbs free energy) at certain temperature.

The first is to follow the equation:

G(T) = H(T) - TS(T) = H + Hcorrection at T + TS(T) = E + ZPE + Hcorrection at T + TS(T)

You can get E from standard DFT calculation (at 0K). ZPE, Hcorrection and S can be calculated from statistical thermodynamics (e.g. using vibrational frequencies).

The second way to do molecular dynamics at the desired T (and even solvent density). As I heard, the metadynamics in CPMD works very well for this purpose.

Hope this help.

Hi Ashis,

You can refer following document regarding your query

http://www.gaussian.com/g_whitepap/thermo.htm