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zxzj05(½ð±Ò+1):лл»ØÌû½»Á÷ 2010-09-22 10:51:03
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The CASTEP output is as follows. The line

Final energy, E             =  -861.8315373731     eV

gives the Kohn-Sham energy, EKS, which ignores the entropy. However, it is the total Mermin free energy that is minimized by CASTEP and reported in the SCF cycles in the line

Final free energy (E-TS)    =  -861.8315374521     eV

If you were actually interested in the electronic states at some reasonable nonzero temperature, you would smear the Fermi level with a thermal (i.e., Fermi-Dirac) smearing method and the free energy reported by CASTEP would be the value you require.

However, it is often the T = 0 K value that is required and the smearing is necessary to improve the convergence of the numerical algorithm. As the smearing ('temperature') is increased, the TS term increases and the free energy, EKS - TS, goes down. At the same time, as the entropy contributes more and more to the free energy, the electronic minimization pays less attention to the EKS term, so the final EKS increases. Because the dependence of the free energy and the Kohn-Sham energy on the smearing width is the same (to first order), averaging the two values gives a much better approximation to the T = 0 K result:

NB est. 0K energy (E-0.5TS) =  -861.8315374126     eV
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