Problem in understanding of 2nd and 3rd derivative in Slater exchange in xc dirac.F file.

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Hi all,

I don't understand 2nd and 3rd derivative of the Dirac exchange functional. Usually, to calculate exchange potential we have to take the functional derivative of exchange energy with respect to density i.e. one-time derivative. 
Can anyone please help me why the 2nd and third derivative are taken in the xc_dirac.F file?


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