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<DIV><BR> </DIV></BLOCKQUOTE>It is *NOT* any free energy of any physical system. It can be interpreted as the free energy of a system of electrons in the field of clamped nuclei, at the *fictitious* temperature corresponding to the smearing you use. The reason why this concept is useful is that the free energy is variational, while the internal energy is not. That's why Hellman-Feynman forces are derivatives of the free energy, but not of the internal energy.</DIV>
<DIV><BR>Thanks Stefano. So, if we want to get the real physical free energy, we should do something else. As far as i know, it is difficult to estimate the free energy. There are several methods calculating it, one of which is from the phonon density of states. But i did not sure this method can be used at high temperature, because the anhormanic effect is important here.<BR>
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<DIV>Furthermore, how to get the internal energy here? The kinetic energy is easy to calculate, but how about the potential energy?<BR></DIV></BLOCKQUOTE>
<DIV><BR></DIV>You do not need any internal energy. what you may actually want to estimate is the T->0 extrapolation of both the free and internal energies (which coincide in the T->0 limit). I think that some estimate of this are available in the pw output, but others may know more than me about this.</DIV>
<DIV><BR>Yes, what you said is what i want. Maybe from the scf calculation, we can get something useful, cause scf gives out more information about energies. So, could some experts can said a little about this problem?<BR><BR>Thank all.<BR><BR>Jiayu<BR></DIV><BR>----------------<BR>-------------------------------------------<BR>Jiayu Dai<BR>Department of Physics<BR>National University of Defense Technology, <BR>Changsha, 410073, P R China<BR>-----------------------------------------