For a *numerical* differentiation you need E(V) at least at three separate volumes. The reason we use equations of state is that no one wants to do numerical derivatives if they don't have to. I suggested the numerical differentiation as a check on the bulk modulus you get from the equation of state.
As for the rest, I said in my experience the bulk modulus isn't off that much. Long ago we did this for various elements within the LDA: https://doi.org/10.1103/PhysRevB.54.4519 But I realized there is an important question we didn't ask: what system are you looking at. For some elements, especially the alkali metals, DFT is difficult. On Wed, Aug 16, 2017 at 2:52 PM, Sunetra Das <[email protected]> wrote: > > Dear Dr. Michael Mehl, > > Quoting you from your reply, "You must have minimum energy structure for > your crystal structure at that volume. This means minimizing the energy > with respect to all atomic positions and all lattice parameters: b/a, c/a, > etc., while keeping the volume fixed." > > -- [image: USNA_Gold_Seal.png] Michael J. Mehl, Ph.D. Kinnear Chair in Physics The United States Naval Academy Mail Stop 9C 572 Holloway Road Chauvenet Hall 257 Annapolis MD 21402 (410)293-6685 [email protected] Library of Crystallographic Prototypes <http://aflow.org/CrystalDatabase/>
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