<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2//EN">
<HTML>
<HEAD>
<META HTTP-EQUIV="Content-Type" CONTENT="text/html; charset=US-ASCII">
<META NAME="Generator" CONTENT="MS Exchange Server version 6.5.7226.0">
<TITLE>Relaxation of Cu100 with PBE pseudopotential</TITLE>
</HEAD>
<BODY>
<!-- Converted from text/rtf format -->
<P><FONT SIZE=2 FACE="Arial">Hi,</FONT>
</P>
<P><FONT SIZE=2 FACE="Arial">I was trying to relax Cu100 using 9 p(2x2) layers + 9 vacuum by using PBE pseudopotential provided by pwscf.</FONT>
</P>
<P><FONT SIZE=2 FACE="Arial">First I calculated the lattice constant which turned to be ~ 3.67 A, in good agreement with experiment (3.61, an error less than 2%). Therefore, I proceed to relax the surface and I found these results:</FONT></P>
<P><U><FONT SIZE=2 FACE="Arial">Relaxation of Cu100 with a = 3.67 A</FONT></U>
</P>
<P><FONT SIZE=2 FACE="Arial">ATOMIC_POSITIONS (alat)</FONT>
<BR><FONT SIZE=2 FACE="Arial">Cu 0.500000000 0.500000000 -2.022823825</FONT>
<BR><FONT SIZE=2 FACE="Arial">Cu 0.000000000 0.000000000 -2.022823918</FONT>
<BR><FONT SIZE=2 FACE="Arial">Cu 0.000000000 0.500000000 -1.489744169</FONT>
<BR><FONT SIZE=2 FACE="Arial">Cu 0.500000000 0.000000000 -1.489744169</FONT>
<BR><FONT SIZE=2 FACE="Arial">Cu 0.500000000 0.500000000 -1.000543208</FONT>
<BR><FONT SIZE=2 FACE="Arial">Cu 0.000000000 0.000000000 -1.000543383</FONT>
<BR><FONT SIZE=2 FACE="Arial">Cu 0.000000000 0.500000000 -0.511527906</FONT>
<BR><FONT SIZE=2 FACE="Arial">Cu 0.500000000 0.000000000 -0.511527906</FONT>
<BR><FONT SIZE=2 FACE="Arial">Cu 0.000000000 0.000000000 0.000000000</FONT>
<BR><FONT SIZE=2 FACE="Arial">Cu 0.500000000 0.500000000 0.000000000</FONT>
<BR><FONT SIZE=2 FACE="Arial">Cu 0.500000000 0.000000000 0.511527906</FONT>
<BR><FONT SIZE=2 FACE="Arial">Cu 0.000000000 0.500000000 0.511527906</FONT>
<BR><FONT SIZE=2 FACE="Arial">Cu 0.000000000 0.000000000 1.000543383</FONT>
<BR><FONT SIZE=2 FACE="Arial">Cu 0.500000000 0.500000000 1.000543208</FONT>
<BR><FONT SIZE=2 FACE="Arial">Cu 0.500000000 0.000000000 1.489744169</FONT>
<BR><FONT SIZE=2 FACE="Arial">Cu 0.000000000 0.500000000 1.489744169</FONT>
<BR><FONT SIZE=2 FACE="Arial">Cu 0.000000000 0.000000000 2.022823918</FONT>
<BR><FONT SIZE=2 FACE="Arial">Cu 0.500000000 0.500000000 2.022823825</FONT>
<BR><FONT SIZE=2 FACE="Times New Roman"> </FONT>
<BR><FONT SIZE=2 FACE="Times New Roman"> Forces acting on atoms (Ry/au):</FONT>
</P>
<P><FONT SIZE=2 FACE="Times New Roman"> atom 1 type 1 force = 0.00000000 0.00000000 -0.00067738</FONT>
<BR><FONT SIZE=2 FACE="Times New Roman"> atom 2 type 1 force = 0.00000000 0.00000000 -0.00067707</FONT>
<BR><FONT SIZE=2 FACE="Times New Roman"> atom 3 type 1 force = 0.00000000 0.00000000 -0.00006941</FONT>
<BR><FONT SIZE=2 FACE="Times New Roman"> atom 4 type 1 force = 0.00000000 0.00000000 -0.00006941</FONT>
<BR><FONT SIZE=2 FACE="Times New Roman"> atom 5 type 1 force = 0.00000000 0.00000000 -0.00067574</FONT>
<BR><FONT SIZE=2 FACE="Times New Roman"> atom 6 type 1 force = 0.00000000 0.00000000 -0.00067565</FONT>
<BR><FONT SIZE=2 FACE="Times New Roman"> atom 7 type 1 force = 0.00000000 0.00000000 -0.00063682</FONT>
<BR><FONT SIZE=2 FACE="Times New Roman"> atom 8 type 1 force = 0.00000000 0.00000000 -0.00063682</FONT>
<BR><FONT SIZE=2 FACE="Times New Roman"> atom 9 type 1 force = 0.00000000 0.00000000 0.00000000</FONT>
<BR><FONT SIZE=2 FACE="Times New Roman"> atom 10 type 1 force = 0.00000000 0.00000000 0.00000000</FONT>
<BR><FONT SIZE=2 FACE="Times New Roman"> atom 11 type 1 force = 0.00000000 0.00000000 0.00063682</FONT>
<BR><FONT SIZE=2 FACE="Times New Roman"> atom 12 type 1 force = 0.00000000 0.00000000 0.00063682</FONT>
<BR><FONT SIZE=2 FACE="Times New Roman"> atom 13 type 1 force = 0.00000000 0.00000000 0.00067565</FONT>
<BR><FONT SIZE=2 FACE="Times New Roman"> atom 14 type 1 force = 0.00000000 0.00000000 0.00067574</FONT>
<BR><FONT SIZE=2 FACE="Times New Roman"> atom 15 type 1 force = 0.00000000 0.00000000 0.00006941</FONT>
<BR><FONT SIZE=2 FACE="Times New Roman"> atom 16 type 1 force = 0.00000000 0.00000000 0.00006941</FONT>
<BR><FONT SIZE=2 FACE="Times New Roman"> atom 17 type 1 force = 0.00000000 0.00000000 0.00067707</FONT>
<BR><FONT SIZE=2 FACE="Times New Roman"> atom 18 type 1 force = 0.00000000 0.00000000 0.00067738</FONT>
</P>
<P><FONT SIZE=2 FACE="Times New Roman"> </FONT> <FONT SIZE=2 FACE="Arial">That means that,</FONT>
</P>
<P><FONT COLOR="#FF0000" FACE="Times New Roman">1<SUP>st</SUP> and 2<SUP>nd</SUP> layers separated by ~ + 6.62% </FONT> <FONT COLOR="#FF0000" SIZE=2 FACE="Arial">completely wrong result!!!</FONT>
<BR><FONT COLOR="#FF0000" FACE="Times New Roman">2<SUP>nd</SUP> and 3<SUP>rd</SUP> layers approached by ~ - 2.16% </FONT> <FONT COLOR="#FF0000" SIZE=2 FACE="Arial">completely wrong result!!!</FONT>
</P>
<P><FONT SIZE=2 FACE="Arial">Which is clearly wrong according to the experiment, which predicts:</FONT>
</P>
<P><FONT COLOR="#0000FF" FACE="Times New Roman">1<SUP>st</SUP> and 2<SUP>nd</SUP> layers approach by ~ -2.4 % </FONT>
</P>
<P><FONT COLOR="#0000FF" FACE="Times New Roman">2<SUP>nd</SUP> and 3<SUP>rd</SUP> layers separate by ~ +1.0 % </FONT>
</P>
<P><FONT FACE="Times New Roman">Therefore, I was advised to calculate carefully the lattice constant using the Murnaghan equation of state and repeat the relaxation. But, this time I had to be more careful and calculate the stress too while relaxing the system. </FONT></P>
<P><FONT FACE="Times New Roman">I found a lattice constant<B> just 0.1% larger than the one I had been using before:</B></FONT>
</P>
<P><FONT FACE="Times New Roman">a = 3.6737 A </FONT>
</P>
<P><FONT FACE="Times New Roman">And these were the results I found after relaxing the system:</FONT>
</P>
<P><U><FONT SIZE=2 FACE="Arial">Relaxation of Cu100 with a = 3.6737 A (Murnaghan fitting)</FONT></U>
</P>
<P><FONT SIZE=2 FACE="Arial">ATOMIC_POSITIONS (alat)</FONT>
<BR><FONT SIZE=2 FACE="Arial">Cu 0.500000000 0.500000000 -1.996326571</FONT>
<BR><FONT SIZE=2 FACE="Arial">Cu 0.000000000 0.000000000 -1.996326572</FONT>
<BR><FONT SIZE=2 FACE="Arial">Cu 0.000000000 0.500000000 -1.511684867</FONT>
<BR><FONT SIZE=2 FACE="Arial">Cu 0.500000000 0.000000000 -1.511684867</FONT>
<BR><FONT SIZE=2 FACE="Arial">Cu 0.500000000 0.500000000 -1.009845482</FONT>
<BR><FONT SIZE=2 FACE="Arial">Cu 0.000000000 0.000000000 -1.009845452</FONT>
<BR><FONT SIZE=2 FACE="Arial">Cu 0.000000000 0.500000000 -0.505544119</FONT>
<BR><FONT SIZE=2 FACE="Arial">Cu 0.500000000 0.000000000 -0.505544119</FONT>
<BR><FONT SIZE=2 FACE="Arial">Cu 0.000000000 0.000000000 0.000000000</FONT>
<BR><FONT SIZE=2 FACE="Arial">Cu 0.500000000 0.500000000 0.000000000</FONT>
<BR><FONT SIZE=2 FACE="Arial">Cu 0.500000000 0.000000000 0.505544119</FONT>
<BR><FONT SIZE=2 FACE="Arial">Cu 0.000000000 0.500000000 0.505544119</FONT>
<BR><FONT SIZE=2 FACE="Arial">Cu 0.000000000 0.000000000 1.009845452</FONT>
<BR><FONT SIZE=2 FACE="Arial">Cu 0.500000000 0.500000000 1.009845482</FONT>
<BR><FONT SIZE=2 FACE="Arial">Cu 0.500000000 0.000000000 1.511684867</FONT>
<BR><FONT SIZE=2 FACE="Arial">Cu 0.000000000 0.500000000 1.511684867</FONT>
<BR><FONT SIZE=2 FACE="Arial">Cu 0.000000000 0.000000000 1.996326572</FONT>
<BR><FONT SIZE=2 FACE="Arial">Cu 0.500000000 0.500000000 1.996326571</FONT>
</P>
<P><FONT SIZE=2 FACE="Arial">Forces acting on atoms (Ry/au):</FONT>
</P>
<P><FONT SIZE=2 FACE="Arial"> atom 1 type 1 force = 0.00000000 0.00000000 0.00023390</FONT>
<BR><FONT SIZE=2 FACE="Arial"> atom 2 type 1 force = 0.00000000 0.00000000 0.00023392</FONT>
<BR><FONT SIZE=2 FACE="Arial"> atom 3 type 1 force = 0.00000000 0.00000000 -0.00011805</FONT>
<BR><FONT SIZE=2 FACE="Arial"> atom 4 type 1 force = 0.00000000 0.00000000 -0.00011805</FONT>
<BR><FONT SIZE=2 FACE="Arial"> atom 5 type 1 force = 0.00000000 0.00000000 0.00087029</FONT>
<BR><FONT SIZE=2 FACE="Arial"> atom 6 type 1 force = 0.00000000 0.00000000 0.00087025</FONT>
<BR><FONT SIZE=2 FACE="Arial"> atom 7 type 1 force = 0.00000000 0.00000000 -0.00009007</FONT>
<BR><FONT SIZE=2 FACE="Arial"> atom 8 type 1 force = 0.00000000 0.00000000 -0.00009007</FONT>
<BR><FONT SIZE=2 FACE="Arial"> atom 9 type 1 force = 0.00000000 0.00000000 0.00000000</FONT>
<BR><FONT SIZE=2 FACE="Arial"> atom 10 type 1 force = 0.00000000 0.00000000 0.00000000</FONT>
<BR><FONT SIZE=2 FACE="Arial"> atom 11 type 1 force = 0.00000000 0.00000000 0.00009007</FONT>
<BR><FONT SIZE=2 FACE="Arial"> atom 12 type 1 force = 0.00000000 0.00000000 0.00009007</FONT>
<BR><FONT SIZE=2 FACE="Arial"> atom 13 type 1 force = 0.00000000 0.00000000 -0.00087025</FONT>
<BR><FONT SIZE=2 FACE="Arial"> atom 14 type 1 force = 0.00000000 0.00000000 -0.00087029</FONT>
<BR><FONT SIZE=2 FACE="Arial"> atom 15 type 1 force = 0.00000000 0.00000000 0.00011805</FONT>
<BR><FONT SIZE=2 FACE="Arial"> atom 16 type 1 force = 0.00000000 0.00000000 0.00011805</FONT>
<BR><FONT SIZE=2 FACE="Arial"> atom 17 type 1 force = 0.00000000 0.00000000 -0.00023392</FONT>
<BR><FONT SIZE=2 FACE="Arial"> atom 18 type 1 force = 0.00000000 0.00000000 -0.00023390</FONT>
</P>
<P><FONT SIZE=2 FACE="Arial"> total stress (ryd/bohr**3) (kbar) P= -8.85</FONT>
<BR><FONT SIZE=2 FACE="Arial"> -0.00008010 0.00000000 0.00000000 -11.78 0.00 0.00</FONT>
<BR><FONT SIZE=2 FACE="Arial"> 0.00000000 -0.00008010 0.00000000 0.00 -11.78 0.00</FONT>
<BR><FONT SIZE=2 FACE="Arial"> 0.00000000 0.00000000 -0.00002029 0.00 0.00 -2.99</FONT>
</P>
<P><FONT COLOR="#FF0000" FACE="Times New Roman">1<SUP>st</SUP> and 2<SUP>nd</SUP> layers approached by ~ -3.07 % good agreement with exp</FONT><FONT COLOR="#FF0000" SIZE=2 FACE="Arial">.!!!</FONT><B></B><B></B><B><FONT COLOR="#FF0000" FACE="Times New Roman"></FONT></B>
</P>
<P><FONT COLOR="#FF0000" FACE="Times New Roman">2<SUP>nd</SUP> and 3<SUP>rd</SUP> layers separated by ~ +0.37 % not too bad</FONT><FONT COLOR="#FF0000" SIZE=2 FACE="Arial"> ...</FONT>
</P>
<P><FONT FACE="Times New Roman">We were intrigued by these opposite and inconsistent results under a negligible change in the lattice parameter so, I was advised to</FONT><B><FONT COLOR="#FF0000" FACE="Times New Roman"> repeat the calculation with the old lattice</FONT></B><FONT FACE="Times New Roman"> constant value but, now also calculating the stress, since maybe I had been doing something wrong... </FONT></P>
<P><FONT FACE="Times New Roman">Well, fortunately, I got the same relaxed positions, same small final forces, but what was really amazing was the stress I found:</FONT></P>
<P><FONT SIZE=2 FACE="Times New Roman"> total stress (ryd/bohr**3) (kbar) P= 231.63</FONT>
<BR><FONT SIZE=2 FACE="Times New Roman"> 0.00160923 0.00000000 0.00000000 236.73 0.00 0.00</FONT>
<BR><FONT SIZE=2 FACE="Times New Roman"> 0.00000000 0.00160923 0.00000000 0.00 236.73 0.00</FONT>
<BR><FONT SIZE=2 FACE="Times New Roman"> 0.00000000 0.00000000 0.00150533 0.00 0.00 221.44</FONT>
</P>
<P><FONT SIZE=2 FACE="Arial">That's it, everything is consistent now, the systems wants to expand because we imposed a little bit smaller lattice constant. Our question is, how is it possible that the stress increases so much under such a small change of the lattice constant?, how can we explain that we find completely opposite results under such a small change of the lattice constant?</FONT></P>
<P><FONT SIZE=2 FACE="Arial">We definitely conclude that either I'm missing something or Cu PBE pseudopotentail is dangerously oversensitive so that we cannot trust.</FONT></P>
<P><FONT SIZE=2 FACE="Arial">Please let me know your comments.</FONT>
</P>
<P><FONT SIZE=2 FACE="Arial">Thank you very much.</FONT>
</P>
<P><FONT SIZE=2 FACE="Arial">Best regards.</FONT>
</P>
<P><FONT SIZE=2 FACE="Arial">Marisol Alcantara Ortigoza.</FONT>
</P>
</BODY>
</HTML>