<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
<style type="text/css" style="display:none;"> P {margin-top:0;margin-bottom:0;} </style>
</head>
<body dir="ltr">
<div class="elementToProof" style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
Dear Dr. Lorenzo,</div>
<div class="elementToProof" style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
<br>
</div>
<div class="elementToProof" style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
Thank you for your reply and the code. I am not familiar with Fortran. I need to calculate the total force constant of the atom numbered 205 (Mg). I can understand that each pair of atoms has a force constant matrix with 9 elements, and for my case, for one
supercell, there are a total of {(205*2)*9}=3690 values of matrix elements only related to the 205<sup>th</sup> atom. I need the addition of all of these from each pair of root mean square values. Is there any direct way or any calculation in QE itself to
find this?<br>
<br>
Thanks,</div>
<div class="elementToProof" style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
Chirantan</div>
<div style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
<br>
</div>
<div id="Signature">
<div style="font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
<span style="font-family: garamond, "times new roman", serif;">Chirantan Pramanik<br>
Postdoctoral Researcher<br>
Dept. of Earth and Planetary Sciences<br>
Weizmann Institute of Science<br>
Rehovot, Israel</span><br>
</div>
</div>
<div id="appendonsend"></div>
<hr style="display:inline-block;width:98%" tabindex="-1">
<div id="divRplyFwdMsg" dir="ltr"><font face="Calibri, sans-serif" style="font-size:11pt" color="#000000"><b>From:</b> users <users-bounces@lists.quantum-espresso.org> on behalf of Lorenzo Paulatto <lorenzo.paulatto@cnrs.fr><br>
<b>Sent:</b> Tuesday, May 6, 2025 11:09 AM<br>
<b>To:</b> users@lists.quantum-espresso.org <users@lists.quantum-espresso.org><br>
<b>Subject:</b> Re: [QE-users] Format of the interatomic force constant .fc file</font>
<div> </div>
</div>
<div style="padding-bottom:1px"><span style="font-family:verdana,arial,sans-serif; font-size:13px; background-color:#FFFF99"><strong>Caution: External Sender. Do not click on links or open attachments unless you recognize the sender.</strong></span><br>
<span> </span>
<p><br>
</p>
<div class="x_moz-cite-prefix">On 05/05/2025 12:52, Chirantan Pramanik wrote:<br>
</div>
<blockquote type="cite"><style type="text/css" style="display:none">
<!--
p
{margin-top:0;
margin-bottom:0}
-->
</style>
<div class="x_elementToProof" style="font-family:Aptos,Aptos_EmbeddedFont,Aptos_MSFontService,Calibri,Helvetica,sans-serif; font-size:12pt; color:rgb(0,0,0)">
Dear All, </div>
<div class="x_elementToProof" style="font-family:Aptos,Aptos_EmbeddedFont,Aptos_MSFontService,Calibri,Helvetica,sans-serif; font-size:12pt; color:rgb(0,0,0)">
<br>
</div>
<div class="x_elementToProof" style="font-family:Aptos,Aptos_EmbeddedFont,Aptos_MSFontService,Calibri,Helvetica,sans-serif; font-size:12pt; color:rgb(0,0,0)">
I am stuck with the format of the interatomic force constant file obtained by the q2r.x code. Below is a preview of the .fc file. Please help me to understand the entries. I need the interatomic force constant, suppose, only for the atom '205'.</div>
</blockquote>
<p>Hello,</p>
<p>please note that force constants always act between two atoms, assuming you know what you are doing, here is the subroutine that reads the force constants stripped of all the parallel distribution and ssafety checks, it is only a couple dozen liens of code.
The subroutine reads the force constants for a supercell of size nr1×nr2×nr3, because of translational invariance, the first atom (i,na) is always in the first unit cell (i.e. that with coordinates 0,0,0) while the second atom (j,nb) is in cell (nr1-1)*a1
+ (nr2-1)*a2 + (nr3-1)*a3. (Or maybe it is the second atom which is in cell 0,0,0, I never remember).</p>
<p>Because in your case the cell is 1×1×1, it won't make any difference.</p>
<p><br>
</p>
<p>hth<br>
</p>
<p><br>
</p>
<br>
<p><br>
</p>
<div style="color:#333333; background-color:#ffffff; font-family:'Nimbus Mono L','Droid Sans Mono','monospace',monospace,'Droid Sans Fallback','Droid Sans Mono','monospace',monospace; font-weight:normal; font-size:14px; line-height:19px; white-space:pre">
<div><span style="color:#008000">!-----------------------------------------------------------------------</span></div>
<div><span style="color:#0000ff">SUBROUTINE</span><span style="color:#333333"> </span>
<span style="color:#795e26">readfc</span><span style="color:#333333"> ( </span><span style="color:#001080">flfrc</span><span style="color:#333333">,
</span><span style="color:#001080">nr1</span><span style="color:#333333">, </span>
<span style="color:#001080">nr2</span><span style="color:#333333">, </span><span style="color:#001080">nr3</span><span style="color:#333333">,
</span><span style="color:#001080">epsil</span><span style="color:#333333">, </span>
<span style="color:#001080">nat</span><span style="color:#333333">, </span><span style="color:#000000">&</span></div>
<div><span style="color:#333333"></span><span style="color:#001080">ibrav</span><span style="color:#333333">,
</span><span style="color:#001080">alat</span><span style="color:#333333">, </span>
<span style="color:#001080">at</span><span style="color:#333333">, </span><span style="color:#001080">ntyp</span><span style="color:#333333">,
</span><span style="color:#001080">amass</span><span style="color:#333333">, </span>
<span style="color:#001080">omega</span><span style="color:#333333">, </span><span style="color:#000000">&</span></div>
<div><span style="color:#333333"></span><span style="color:#001080">has_zstar</span><span style="color:#333333">,
</span><span style="color:#001080">alph</span><span style="color:#333333">, </span>
<span style="color:#001080">read_lr</span><span style="color:#333333"> )</span></div>
<div><span style="color:#333333"></span><span style="color:#008000">!-----------------------------------------------------------------------</span></div>
<div><span style="color:#333333"></span><span style="color:#008000">!</span></div>
<div><span style="color:#333333"></span><span style="color:#0000ff">IMPLICIT</span><span style="color:#333333">
</span><span style="color:#0000ff">NONE</span></div>
<div><span style="color:#333333"></span><span style="color:#008000">! I/O variable</span></div>
<div><span style="color:#333333"></span><span style="color:#0000ff">CHARACTER</span><span style="color:#333333">(</span><span style="color:#001080">LEN</span><span style="color:#000000">=</span><span style="color:#098658">256</span><span style="color:#333333">)
</span><span style="color:#000000">::</span><span style="color:#333333"> flfrc</span></div>
<div><span style="color:#333333"></span><span style="color:#0000ff">CHARACTER</span><span style="color:#333333">(</span><span style="color:#001080">LEN</span><span style="color:#000000">=</span><span style="color:#098658">80</span><span style="color:#333333">)
</span><span style="color:#000000">::</span><span style="color:#333333"> line</span></div>
<div><span style="color:#333333"></span><span style="color:#0000ff">INTEGER</span><span style="color:#333333">
</span><span style="color:#000000">::</span><span style="color:#333333"> ibrav, nr1,nr2,nr3,nat, ntyp</span></div>
<div><span style="color:#333333"></span><span style="color:#0000ff">REAL</span><span style="color:#333333">(DP)
</span><span style="color:#000000">::</span><span style="color:#333333"> alat, at(</span><span style="color:#098658">3</span><span style="color:#333333">,</span><span style="color:#098658">3</span><span style="color:#333333">), epsil(</span><span style="color:#098658">3</span><span style="color:#333333">,</span><span style="color:#098658">3</span><span style="color:#333333">),
alph</span></div>
<div><span style="color:#333333"></span><span style="color:#0000ff">LOGICAL</span><span style="color:#333333">
</span><span style="color:#000000">::</span><span style="color:#333333"> has_zstar, read_lr</span></div>
<div><span style="color:#333333"></span><span style="color:#008000">! local variables</span></div>
<div><span style="color:#333333"></span><span style="color:#0000ff">INTEGER</span><span style="color:#333333">
</span><span style="color:#000000">::</span><span style="color:#333333"> i, j, na, nb, m1,m2,m3</span></div>
<div><span style="color:#333333"></span><span style="color:#0000ff">INTEGER</span><span style="color:#333333">
</span><span style="color:#000000">::</span><span style="color:#333333"> ios, ibid, jbid, nabid, nbbid, m1bid,m2bid,m3bid</span></div>
<div><span style="color:#333333"></span><span style="color:#0000ff">REAL</span><span style="color:#333333">(DP)
</span><span style="color:#000000">::</span><span style="color:#333333"> amass(ntyp), amass_from_file, omega</span></div>
<div><span style="color:#333333"></span><span style="color:#0000ff">INTEGER</span><span style="color:#333333">
</span><span style="color:#000000">::</span><span style="color:#333333"> nt</span></div>
<div><span style="color:#333333"></span><span style="color:#008000">!</span></div>
<div>
<div style="color:#333333; background-color:#ffffff; font-family:'Nimbus Mono L','Droid Sans Mono','monospace',monospace,'Droid Sans Fallback','Droid Sans Mono','monospace',monospace; font-weight:normal; font-size:14px; line-height:19px; white-space:pre">
<div><span style="color:#af00db">OPEN</span><span style="color:#333333"> (</span><span style="color:#001080">unit</span><span style="color:#000000">=</span><span style="color:#098658">1</span><span style="color:#333333">,</span><span style="color:#001080">file</span><span style="color:#000000">=</span><span style="color:#333333">flfrc,</span><span style="color:#001080">status</span><span style="color:#000000">=</span><span style="color:#a31515">'old'</span><span style="color:#333333">,</span><span style="color:#001080">form</span><span style="color:#000000">=</span><span style="color:#a31515">'formatted'</span><span style="color:#333333">)</span></div>
<div><span style="color:#333333">!</span></div>
<div><span style="color:#333333"></span><span style="color:#008000">! Read cell parameters</span><span style="color:#333333"></span></div>
</div>
</div>
<div><span style="color:#333333"></span><span style="color:#af00db">READ</span><span style="color:#333333">(</span><span style="color:#098658">1</span><span style="color:#333333">,</span><span style="color:#000000">*</span><span style="color:#333333">) ntyp,nat,ibrav,(celldm(i),i</span><span style="color:#000000">=</span><span style="color:#098658">1</span><span style="color:#333333">,</span><span style="color:#098658">6</span><span style="color:#333333">)</span></div>
<div><span style="color:#333333"></span><span style="color:#af00db">if</span><span style="color:#333333"> (ibrav</span><span style="color:#0000ff">==</span><span style="color:#098658">0</span><span style="color:#333333">)
</span><span style="color:#af00db">then</span></div>
<div><span style="color:#333333"></span><span style="color:#af00db">read</span><span style="color:#333333">(</span><span style="color:#098658">1</span><span style="color:#333333">,</span><span style="color:#000000">*</span><span style="color:#333333">) ((at(i,j),i</span><span style="color:#000000">=</span><span style="color:#098658">1</span><span style="color:#333333">,</span><span style="color:#098658">3</span><span style="color:#333333">),</span><span style="color:#001080">j</span><span style="color:#000000">=</span><span style="color:#098658">1</span><span style="color:#333333">,</span><span style="color:#098658">3</span><span style="color:#333333">)</span></div>
<div><span style="color:#333333"></span><span style="color:#af00db">end if</span></div>
<div><span style="color:#333333"></span><span style="color:#008000">!</span></div>
<div><span style="color:#333333"></span><span style="color:#af00db">CALL</span><span style="color:#333333">
</span><span style="color:#795e26">latgen</span><span style="color:#333333">(ibrav,celldm,at(</span><span style="color:#098658">1</span><span style="color:#333333">,</span><span style="color:#098658">1</span><span style="color:#333333">),at(</span><span style="color:#098658">1</span><span style="color:#333333">,</span><span style="color:#098658">2</span><span style="color:#333333">),at(</span><span style="color:#098658">1</span><span style="color:#333333">,</span><span style="color:#098658">3</span><span style="color:#333333">),omega)</span></div>
<div><span style="color:#333333">alat </span><span style="color:#000000">=</span><span style="color:#333333"> celldm(</span><span style="color:#098658">1</span><span style="color:#333333">)</span></div>
<div><span style="color:#333333">at </span><span style="color:#000000">=</span><span style="color:#333333"> at / alat
</span><span style="color:#008000">! bring at in units of alat</span></div>
<div><span style="color:#333333"></span><span style="color:#af00db">CALL</span><span style="color:#333333">
</span><span style="color:#795e26">volume</span><span style="color:#333333">(alat,at(</span><span style="color:#098658">1</span><span style="color:#333333">,</span><span style="color:#098658">1</span><span style="color:#333333">),at(</span><span style="color:#098658">1</span><span style="color:#333333">,</span><span style="color:#098658">2</span><span style="color:#333333">),at(</span><span style="color:#098658">1</span><span style="color:#333333">,</span><span style="color:#098658">3</span><span style="color:#333333">),omega)</span></div>
<div><span style="color:#333333"></span><span style="color:#008000">!</span></div>
<div><span style="color:#333333"></span><span style="color:#008000">! read atomic types, positions and masses</span></div>
<div><span style="color:#333333"></span><span style="color:#008000">!</span></div>
<div><span style="color:#333333"></span><span style="color:#af00db">ALLOCATE</span><span style="color:#333333"> (atm(ntyp))</span></div>
<div><span style="color:#333333"></span><span style="color:#af00db">DO</span><span style="color:#333333"> nt
</span><span style="color:#000000">=</span><span style="color:#333333"> </span><span style="color:#098658">1</span><span style="color:#333333">,ntyp</span></div>
<div><span style="color:#333333"></span><span style="color:#af00db">READ</span><span style="color:#333333">(</span><span style="color:#098658">1</span><span style="color:#333333">,</span><span style="color:#000000">*</span><span style="color:#333333">) i,atm(nt),amass_from_file
! type and mass</span></div>
<div><span style="color:#333333"></span><span style="color:#af00db">END DO</span></div>
<div><span style="color:#333333"></span><span style="color:#008000">!</span></div>
<div><span style="color:#333333"></span><span style="color:#af00db">ALLOCATE</span><span style="color:#333333"> (tau(</span><span style="color:#098658">3</span><span style="color:#333333">,nat), ityp(nat), zeu(</span><span style="color:#098658">3</span><span style="color:#333333">,</span><span style="color:#098658">3</span><span style="color:#333333">,nat))</span></div>
<div><span style="color:#333333"></span><span style="color:#008000">!</span></div>
<div><span style="color:#333333"></span><span style="color:#af00db">DO</span><span style="color:#333333"> na</span><span style="color:#000000">=</span><span style="color:#098658">1</span><span style="color:#333333">,nat</span></div>
<div><span style="color:#333333"></span><span style="color:#af00db">READ</span><span style="color:#333333">(</span><span style="color:#098658">1</span><span style="color:#333333">,</span><span style="color:#000000">*</span><span style="color:#333333">) i,ityp(na),(tau(j,na),j</span><span style="color:#000000">=</span><span style="color:#098658">1</span><span style="color:#333333">,</span><span style="color:#098658">3</span><span style="color:#333333">)
! positions of atoms in the cell</span></div>
<div><span style="color:#333333"></span><span style="color:#af00db">END DO</span></div>
<div><span style="color:#333333"></span><span style="color:#008000">!</span></div>
<div><span style="color:#333333"></span><span style="color:#008000">! read macroscopic variables</span></div>
<div><span style="color:#008000">! (dielectric constant and effective charges) </span>
</div>
<div><span style="color:#333333"></span><span style="color:#008000">!</span></div>
<div><span style="color:#333333">alph </span><span style="color:#000000">=</span><span style="color:#333333">
</span><span style="color:#098658">1.0_dp</span></div>
<div><span style="color:#333333"></span><span style="color:#af00db">READ</span><span style="color:#333333"> (</span><span style="color:#098658">1</span><span style="color:#333333">,</span><span style="color:#a31515">'(a)'</span><span style="color:#333333">)
line</span></div>
<div><span style="color:#333333"></span><span style="color:#af00db">READ</span><span style="color:#333333">(line,</span><span style="color:#000000">*</span><span style="color:#333333">,</span><span style="color:#001080">iostat</span><span style="color:#000000">=</span><span style="color:#333333">ios)
has_zstar, alph</span></div>
<div><span style="color:#333333"></span><span style="color:#008000">!</span></div>
<div><span style="color:#333333"></span><span style="color:#af00db">IF</span><span style="color:#333333"> (has_zstar)
</span><span style="color:#af00db">THEN</span></div>
<div><span style="color:#333333"></span><span style="color:#af00db">READ</span><span style="color:#333333">(</span><span style="color:#098658">1</span><span style="color:#333333">,</span><span style="color:#000000">*</span><span style="color:#333333">) ((epsil(i,j),j</span><span style="color:#000000">=</span><span style="color:#098658">1</span><span style="color:#333333">,</span><span style="color:#098658">3</span><span style="color:#333333">),</span><span style="color:#001080">i</span><span style="color:#000000">=</span><span style="color:#098658">1</span><span style="color:#333333">,</span><span style="color:#098658">3</span><span style="color:#333333">)</span></div>
<div><span style="color:#333333"></span><span style="color:#af00db">DO</span><span style="color:#333333"> na</span><span style="color:#000000">=</span><span style="color:#098658">1</span><span style="color:#333333">,nat</span></div>
<div><span style="color:#333333"></span><span style="color:#af00db">READ</span><span style="color:#333333">(</span><span style="color:#098658">1</span><span style="color:#333333">,</span><span style="color:#000000">*</span><span style="color:#333333">)</span></div>
<div><span style="color:#333333"></span><span style="color:#af00db">READ</span><span style="color:#333333">(</span><span style="color:#098658">1</span><span style="color:#333333">,</span><span style="color:#000000">*</span><span style="color:#333333">) ((zeu(i,j,na),j</span><span style="color:#000000">=</span><span style="color:#098658">1</span><span style="color:#333333">,</span><span style="color:#098658">3</span><span style="color:#333333">),</span><span style="color:#001080">i</span><span style="color:#000000">=</span><span style="color:#098658">1</span><span style="color:#333333">,</span><span style="color:#098658">3</span><span style="color:#333333">)</span></div>
<div><span style="color:#333333"></span><span style="color:#af00db">END DO</span></div>
<div><span style="color:#333333"></span><span style="color:#af00db">ELSE</span></div>
<div><span style="color:#333333">zeu (:,:,:) </span><span style="color:#000000">=</span><span style="color:#333333">
</span><span style="color:#098658">0.d0</span></div>
<div><span style="color:#333333">epsil(:,:) </span><span style="color:#000000">=</span><span style="color:#333333">
</span><span style="color:#098658">0.d0</span></div>
<div><span style="color:#333333"></span><span style="color:#af00db">END IF</span></div>
<div><span style="color:#333333"></span><span style="color:#008000">!</span></div>
<div><span style="color:#333333"></span><span style="color:#af00db">READ</span><span style="color:#333333"> (</span><span style="color:#098658">1</span><span style="color:#333333">,</span><span style="color:#000000">*</span><span style="color:#333333">) nr1,nr2,nr3</span></div>
<div><span style="color:#333333"></span><span style="color:#008000">!</span></div>
<div><span style="color:#333333"></span><span style="color:#008000">! read real-space interatomic force constants</span></div>
<div><span style="color:#333333"></span><span style="color:#008000">!</span></div>
<div><span style="color:#333333"></span><span style="color:#af00db">ALLOCATE</span><span style="color:#333333"> ( frc(nr1,nr2,nr3,</span><span style="color:#098658">3</span><span style="color:#333333">,</span><span style="color:#098658">3</span><span style="color:#333333">,nat,nat)
)</span></div>
<div><span style="color:#333333">frc(:,:,:,:,:,:,:) </span><span style="color:#000000">=</span><span style="color:#333333">
</span><span style="color:#098658">0.d0</span></div>
<div><span style="color:#333333"></span><span style="color:#af00db">ALLOCATE</span><span style="color:#333333"> ( frc_lr(nr1,nr2,nr3,</span><span style="color:#098658">3</span><span style="color:#333333">,</span><span style="color:#098658">3</span><span style="color:#333333">,nat,nat)
)</span></div>
<div><span style="color:#333333">frc_lr(:,:,:,:,:,:,:) </span><span style="color:#000000">=</span><span style="color:#333333">
</span><span style="color:#098658">0.d0</span></div>
<div><span style="color:#333333"></span><span style="color:#af00db">DO</span><span style="color:#333333"> i</span><span style="color:#000000">=</span><span style="color:#098658">1</span><span style="color:#333333">,</span><span style="color:#098658">3</span></div>
<div><span style="color:#333333"></span><span style="color:#af00db">DO</span><span style="color:#333333"> j</span><span style="color:#000000">=</span><span style="color:#098658">1</span><span style="color:#333333">,</span><span style="color:#098658">3</span></div>
<div><span style="color:#333333"></span><span style="color:#af00db">DO</span><span style="color:#333333"> na</span><span style="color:#000000">=</span><span style="color:#098658">1</span><span style="color:#333333">,nat</span></div>
<div><span style="color:#333333"></span><span style="color:#af00db">DO</span><span style="color:#333333"> nb</span><span style="color:#000000">=</span><span style="color:#098658">1</span><span style="color:#333333">,nat</span></div>
<div><span style="color:#333333"></span><span style="color:#333333"></span><span style="color:#af00db">READ</span><span style="color:#333333"> (</span><span style="color:#098658">1</span><span style="color:#333333">,</span><span style="color:#000000">*</span><span style="color:#333333">)
ibid, jbid, nabid, nbbid</span></div>
<div><span style="color:#333333"></span><span style="color:#af00db">READ</span><span style="color:#333333"> (</span><span style="color:#098658">1</span><span style="color:#333333">,</span><span style="color:#000000">*</span><span style="color:#333333">) (((m1bid,
m2bid, m3bid, </span><span style="color:#000000">&</span></div>
<div><span style="color:#333333">frc(m1,m2,m3,i,j,na,nb), </span><span style="color:#000000">&</span></div>
<div><span style="color:#333333">m1</span><span style="color:#000000">=</span><span style="color:#098658">1</span><span style="color:#333333">,nr1),m2</span><span style="color:#000000">=</span><span style="color:#098658">1</span><span style="color:#333333">,nr2),</span><span style="color:#001080">m3</span><span style="color:#000000">=</span><span style="color:#098658">1</span><span style="color:#333333">,nr3)</span></div>
<div><span style="color:#333333"></span><span style="color:#af00db">END IF</span></div>
<div><span style="color:#333333"></span><span style="color:#af00db">END DO</span></div>
<div><span style="color:#333333"></span><span style="color:#af00db">END DO</span></div>
<div><span style="color:#333333"></span><span style="color:#af00db">END DO</span></div>
<div><span style="color:#333333"></span><span style="color:#af00db">END DO</span></div>
<div><span style="color:#333333"></span><span style="color:#008000">!</span></div>
<div><span style="color:#333333"></span><span style="color:#af00db">CLOSE</span><span style="color:#333333">(</span><span style="color:#001080">unit</span><span style="color:#000000">=</span><span style="color:#098658">1</span><span style="color:#333333">)</span></div>
<div><span style="color:#333333"></span><span style="color:#008000">!</span></div>
<div><span style="color:#333333"></span><span style="color:#af00db">RETURN</span></div>
<div><span style="color:#0000ff">END SUBROUTINE</span><span style="color:#333333">
</span><span style="color:#795e26">readfc</span></div>
</div>
<p><br>
</p>
<br>
<div class="x_moz-signature">-- <br>
<small>Dr. Lorenzo Paulatto<br>
IdR @ IMPMC - CNRS UMR 7590 & Sorbonne Université<br>
phone: +33 (0)1 442 79822 / skype: paulatz<br>
<a href="http://people.impmc.fr/lpaulatto/" class="x_moz-txt-link-freetext">http://people.impmc.fr/lpaulatto/</a> -
<a href="https://anharmonic.github.io/" class="x_moz-txt-link-freetext">https://anharmonic.github.io/</a><br>
23-24/423 B115, 4 place Jussieu 75252 Paris CX 05</small></div>
</div>
</body>
</html>