<div dir="ltr">For a <i>numerical</i> 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.<div><br></div><div>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: <span style="font-family:"Helvetica Neue",Helvetica,Roboto,Arial,sans-serif;font-size:14px"><a href="https://doi.org/10.1103/PhysRevB.54.4519">https://doi.org/10.1103/PhysRevB.54.4519</a></span></div><div><span style="font-family:"Helvetica Neue",Helvetica,Roboto,Arial,sans-serif;font-size:14px"><br></span></div><div><span style="font-family:"Helvetica Neue",Helvetica,Roboto,Arial,sans-serif;font-size:14px">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.</span></div><div><font face="Helvetica Neue, Helvetica, Roboto, Arial, sans-serif"><span style="font-size:14px"><br></span></font></div><div><font face="Helvetica Neue, Helvetica, Roboto, Arial, sans-serif"><span style="font-size:14px"><br></span></font><div class="gmail_extra"><br><div class="gmail_quote">On Wed, Aug 16, 2017 at 2:52 PM, Sunetra Das <span dir="ltr"><<a href="mailto:sunetra.das.88@gmail.com" target="_blank">sunetra.das.88@gmail.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr"><div><br></div><div>Dear Dr. Michael Mehl,</div><div><br></div><div>Quoting you from your reply, "<span style="font-size:12.8px">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." </span></div><div><br></div></div></blockquote></div>-- <br><div class="gmail_signature"><div dir="ltr"><div><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><span><div dir="ltr" style="margin-left:0pt"><span><div dir="ltr" style="margin-left:0pt"><table style="border:none;border-collapse:collapse"><colgroup><col width="73"><col width="240"></colgroup><tbody><tr style="height:0px"><td style="border-width:1px;border-style:solid;border-color:rgb(255,255,255);vertical-align:top;padding:7px"><br><img src="https://lh4.googleusercontent.com/cWahY61df5ZQz3h0L--aoIVBK4j_u5sWfktSfeRgcbi3bi_PKu-Vtt8OPXlJEEX7_J8UVfbP6EYLXroCVHzqegMVgjl4KD3yBpnJZp0zwht66TTfYleiGnAbqPTj7TEwVxNRrdA6" width="57" height="80" style="border: none;" alt="USNA_Gold_Seal.png"></td><td style="border-width:1px;border-style:solid;border-color:rgb(255,255,255);vertical-align:top;padding:7px"><p dir="ltr" style="line-height:1.2;margin-top:0pt;margin-bottom:0pt"><span style="font-size:14.6667px;font-family:Arial;color:rgb(0,0,0);vertical-align:baseline;white-space:pre-wrap;background-color:transparent">Michael J. Mehl, Ph.D.     </span></p><p dir="ltr" style="line-height:1.2;margin-top:0pt;margin-bottom:0pt"><span style="font-size:14.6667px;font-family:Arial;color:rgb(0,0,0);vertical-align:baseline;white-space:pre-wrap;background-color:transparent">Kinnear Chair in Physics</span></p><p dir="ltr" style="line-height:1.2;margin-top:0pt;margin-bottom:0pt"><span style="font-size:14.6667px;font-family:Arial;color:rgb(0,0,0);vertical-align:baseline;white-space:pre-wrap;background-color:transparent">The United States Naval Academy</span></p><p dir="ltr" style="line-height:1.2;margin-top:0pt;margin-bottom:0pt"><span style="font-size:14.6667px;font-family:Arial;color:rgb(0,0,0);vertical-align:baseline;white-space:pre-wrap;background-color:transparent">Mail Stop 9C</span></p><p dir="ltr" style="line-height:1.2;margin-top:0pt;margin-bottom:0pt"><span style="font-size:14.6667px;font-family:Arial;color:rgb(0,0,0);vertical-align:baseline;white-space:pre-wrap;background-color:transparent">572 Holloway Road</span></p><p dir="ltr" style="line-height:1.2;margin-top:0pt;margin-bottom:0pt"><span style="font-size:14.6667px;font-family:Arial;color:rgb(0,0,0);vertical-align:baseline;white-space:pre-wrap;background-color:transparent">Chauvenet Hall 257</span></p><p dir="ltr" style="line-height:1.2;margin-top:0pt;margin-bottom:0pt"><span style="font-size:14.6667px;font-family:Arial;color:rgb(0,0,0);vertical-align:baseline;white-space:pre-wrap;background-color:transparent">Annapolis MD 21402</span></p><p dir="ltr" style="line-height:1.2;margin-top:0pt;margin-bottom:0pt"><span style="font-size:14.6667px;font-family:Arial;color:rgb(0,0,0);vertical-align:baseline;white-space:pre-wrap;background-color:transparent">(410)293-6685</span></p><p dir="ltr" style="line-height:1.2;margin-top:0pt;margin-bottom:0pt"><span style="font-size:14.6667px;font-family:Arial;color:rgb(0,0,0);vertical-align:baseline;white-space:pre-wrap;background-color:transparent"><a href="mailto:mmehl@usna.edu" target="_blank">mmehl@usna.edu</a></span></p><p dir="ltr" style="line-height:1.2;margin-top:0pt;margin-bottom:0pt"><a href="http://aflow.org/CrystalDatabase/" target="_blank">Library of Crystallographic Prototypes</a></p></td></tr></tbody></table></div></span></div></span></div><span><br></span></div></div></div></div></div></div></div>
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