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Using SIESTA for bulk Si (not optimized, downloaded from materialsproject.org), I am trying to optimize the DZP basis set using the PAO.EnergyShift parameter. SIESTA official documentation mentions that one should minimize the "BASIS_ENTHALPY" instead of the total energy when performing basis optimization. The following is a plot of both the "Total Energy" and the "Basis Enthalpy" as a function of EnergyShift. The pseudopotential is obtained from "pseudodojo.com" (Norm conserving, scalar relativistic).

Basis Enthalpy and total Energy vs EnergyShift

The difference in energy shift that minimizes both the enthalpy and the total energy is large. The same behavior appeared also for Si slabs. So what should be considered as a good energy shift?

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