<html xmlns:v="urn:schemas-microsoft-com:vml" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:w="urn:schemas-microsoft-com:office:word" xmlns:m="http://schemas.microsoft.com/office/2004/12/omml" xmlns="http://www.w3.org/TR/REC-html40"> <head> <meta http-equiv="Content-Type" content="text/html; charset=utf-8"> <meta name="Generator" content="Microsoft Word 15 (filtered medium)"> <style></style> </head> <body lang="DE" link="blue" vlink="purple" style="word-wrap:break-word"> <div class="WordSection1"> <p class="MsoNormal"><span style="mso-fareast-language:EN-US">Dear Torstein<o:p></o:p></span></p> <p class="MsoNormal"><span style="mso-fareast-language:EN-US"><o:p> </o:p></span></p> <p class="MsoNormal"><span lang="EN-GB" style="mso-fareast-language:EN-US">The Hessian printed after "Hessian in cartesian coordinates" is the Hessian within the Cartesian coordinate system of the input cell. Only the first (maximum) 9 “VIB| Cartesian Low frequencies” are printed for that Hessian. The eigenvalues printed thereafter as well as in the molden file are obtained from the Hessian after rotations and translations have been removed (after transformation with the D matrix). I think that the implementation follows more or less the approach described <a href="https://gaussian.com/vib/">here</a>.<o:p></o:p></span></p> <p class="MsoNormal"><span lang="EN-GB" style="mso-fareast-language:EN-US"><o:p> </o:p></span></p> <p class="MsoNormal"><span lang="EN-GB" style="mso-fareast-language:EN-US">HTH<o:p></o:p></span></p> <p class="MsoNormal"><span lang="EN-GB" style="mso-fareast-language:EN-US"><o:p> </o:p></span></p> <p class="MsoNormal"><span lang="EN-GB" style="mso-fareast-language:EN-US">Matthias<o:p></o:p></span></p> <p class="MsoNormal"><span lang="EN-GB" style="mso-fareast-language:EN-US"><o:p> </o:p></span></p> <div style="border:none;border-top:solid #E1E1E1 1.0pt;padding:3.0pt 0cm 0cm 0cm"> <p class="MsoNormal" style="margin-left:35.4pt"><b>Von:</b> cp...@googlegroups.com <...@googlegroups.com> <b>Im Auftrag von </b>Torstein Fjermestad<br> <b>Gesendet:</b> Samstag, 19. Dezember 2020 22:48<br> <b>An:</b> cp2k <...@googlegroups.com><br> <b>Betreff:</b> [CP2K:14412] Re: Using TAMkin with CP2K - how is CP2K diagonalizing the Hessian matrix?<o:p></o:p></p> </div> <p class="MsoNormal" style="margin-left:35.4pt"><o:p> </o:p></p> <p class="MsoNormal" style="margin-left:35.4pt">Dear all, <o:p></o:p></p> <div> <p class="MsoNormal" style="margin-left:35.4pt"><o:p> </o:p></p> </div> <div> <p class="MsoNormal" style="margin-left:35.4pt">I would like to follow up on this question that I asked on June 10 this year.<o:p></o:p></p> </div> <div> <p class="MsoNormal" style="margin-left:35.4pt">I realize that I might have expressed myself in a very complicated way, and I therefore try to be clearer this time.<o:p></o:p></p> </div> <div> <p class="MsoNormal" style="margin-left:35.4pt"><o:p> </o:p></p> </div> <div> <p class="MsoNormal" style="margin-left:35.4pt">The problem is that when I diagonalize the Hessian printed in the cp2k output file with the following python code (The complete python code is attached)<o:p></o:p></p> </div> <div> <p class="MsoNormal" style="margin-left:35.4pt"><o:p> </o:p></p> </div> <p class="MsoNormal" style="margin-left:35.4pt"><span style="font-family:"Courier New"">from numpy import genfromtxt<br> import numpy as np<br> import sys<br> <br> hessianFile=sys.argv[1]<br> hessian = genfromtxt(hessianFile,delimiter=',')<br> freq = np.linalg.eigvals(hessian)</span><o:p></o:p></p> <div> <p class="MsoNormal" style="margin-left:35.4pt"><o:p> </o:p></p> </div> <div> <p class="MsoNormal" style="margin-left:35.4pt"> <o:p></o:p></p> </div> <div> <p class="MsoNormal" style="margin-left:35.4pt">, I get slightly different frequencies than what is printed in the output file (and the .mol file). The frequencies are compared in the table below.<o:p></o:p></p> </div> <div> <p class="MsoNormal" style="margin-left:35.4pt">Column 2: Frequencies from CP2K output file<o:p></o:p></p> </div> <div> <p class="MsoNormal" style="margin-left:35.4pt">Column 3: Frequencies obtained when diagonalizing the Hessian with numpy<o:p></o:p></p> </div> <div> <p class="MsoNormal" style="margin-left:35.4pt"><o:p> </o:p></p> </div> <div> <p style="margin-left:35.4pt">Table 1: The eight lowest frequencies. There are 48 in total.<o:p></o:p></p> <p class="MsoNormal" style="margin-left:35.4pt"><span style="font-size:12.0pt;font-family:SimSun;mso-fareast-language:ZH-CN"><img border="0" width="214" height="157" style="width:2.2291in;height:1.6319in" id="Bild_x0020_1" src="cid:image002.png@01D6D6DC.AB0096A0"></span><o:p></o:p></p> <p style="margin-left:35.4pt">What am I doing wrong in the diagonalization?<o:p></o:p></p> <p style="margin-left:35.4pt">Thanks a lot for your help.<o:p></o:p></p> <p style="margin-left:35.4pt">Regards,<o:p></o:p></p> <p style="margin-left:35.4pt">Torstein Fjermestad<o:p></o:p></p> <p style="margin-left:35.4pt"><o:p> </o:p></p> <p style="margin-left:35.4pt"><o:p> </o:p></p> <p style="margin-left:35.4pt"><o:p> </o:p></p> <p class="MsoNormal" style="margin-left:35.4pt"><o:p> </o:p></p> </div> <div> <div> <p class="MsoNormal" style="margin-left:35.4pt">onsdag 10. juni 2020 kl. 15:56:53 UTC+2 skrev Torstein Fjermestad:<o:p></o:p></p> </div> <blockquote style="border:none;border-left:solid #CCCCCC 1.0pt;padding:0cm 0cm 0cm 6.0pt;margin-left:4.8pt;margin-right:0cm"> <div> <p class="MsoNormal" style="margin-left:35.4pt">Dear all, <o:p></o:p></p> <div> <p class="MsoNormal" style="margin-left:35.4pt"><o:p> </o:p></p> </div> <div> <p class="MsoNormal" style="margin-left:35.4pt">I would like to use TAMkin (<a href="http://molmod.github.io/tamkin/" target="_blank">http://molmod.github.io/tamkin/</a>) to compute thermodynamic properties from the vibrational frequencies computed with CP2K.<o:p></o:p></p> </div> <div> <p class="MsoNormal" style="margin-left:35.4pt">As I have understood it, the way TAMkin works is to read and diagonalize the Hessian matrix printed in the CP2K output.<o:p></o:p></p> </div> <div> <p class="MsoNormal" style="margin-left:35.4pt">When I compare the frequencies obtained with TAMkin with those obtained with cp2k, the values are not the same (Compare column 2 and 3 in the table below). <o:p></o:p></p> </div> <div> <p class="MsoNormal" style="margin-left:35.4pt"><o:p> </o:p></p> </div> <div> <p class="MsoNormal" style="margin-left:35.4pt">The first task is then to understand how CP2K computes the frequencies. To investigate this, I copied the Hessian matrix from the CP2K output (printed below the string "Hessian in cartesian coordinates") and pasted it into Excel and saved it as a csv file. This file I read into python and diagonalized the Hessian with numpy. The frequencies I get are different from those printed in the cp2k output file (compare column 3 and 4 in the table below). <o:p></o:p></p> </div> <div> <p class="MsoNormal" style="margin-left:35.4pt">I have assumed that the units of the Hessian matrix in the cp2k output file are Ry*bohr-2*kamu-1 (kamu = 1000*amu). This assumption is based on trial and error; it was what got me closest to the cp2k frequencies. <o:p></o:p></p> </div> <div> <p class="MsoNormal" style="margin-left:35.4pt"><o:p> </o:p></p> </div> <div> <p class="MsoNormal" style="margin-left:35.4pt"><o:p> </o:p></p> </div> <div> <p class="MsoNormal" style="margin-left:35.4pt">Table 1: The eight lowest frequencies. There are 48 in total.<o:p></o:p></p> </div> <div> <table class="MsoNormalTable" border="0" cellspacing="0" cellpadding="0" style="margin-left:35.4pt;border-collapse:collapse;border-width:initial"> <tbody> <tr style="height:30.0pt"> <td width="85" nowrap="" valign="top" style="width:63.8pt;border:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt;height:30.0pt"> <p class="MsoNormal" style="mso-margin-top-alt:auto"><span lang="IT">frequencies</span><o:p></o:p></p> </td> <td width="75" nowrap="" valign="top" style="width:56.45pt;border:solid windowtext 1.0pt;border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:30.0pt;border-left-width:initial"> <p class="MsoNormal" style="mso-margin-top-alt:auto"><span lang="IT">TAMkin / <br> cm-1</span><o:p></o:p></p> </td> <td width="76" valign="top" style="width:2.0cm;border:solid windowtext 1.0pt;border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:30.0pt;border-left-width:initial"> <p class="MsoNormal" style="mso-margin-top-alt:auto"><span lang="IT">cp2k / <br> cm-1</span><o:p></o:p></p> </td> <td width="151" valign="top" style="width:4.0cm;border:solid windowtext 1.0pt;border-left:none;padding:0cm 5.4pt 0cm 5.4pt;height:30.0pt;border-left-width:initial"> <p class="MsoNormal" style="mso-margin-top-alt:auto"><span lang="IT">Diag., cp2k Hessian / <br> cm-1</span><o:p></o:p></p> </td> </tr> <tr style="height:15.0pt"> <td width="85" nowrap="" valign="top" style="width:63.8pt;border:solid windowtext 1.0pt;border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:15.0pt;border-top-width:initial"> <p class="MsoNormal" style="mso-margin-top-alt:auto"><span lang="IT">1</span><o:p></o:p></p> </td> <td width="75" nowrap="" valign="top" style="width:56.45pt;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.0pt;border-top-width:initial;border-left-width:initial"> <p class="MsoNormal" style="mso-margin-top-alt:auto"><span lang="IT">31.1</span><o:p></o:p></p> </td> <td width="76" nowrap="" valign="top" style="width:2.0cm;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.0pt;border-top-width:initial;border-left-width:initial"> <p class="MsoNormal" style="mso-margin-top-alt:auto"><span lang="IT">27.3</span><o:p></o:p></p> </td> <td width="151" nowrap="" valign="top" style="width:4.0cm;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.0pt;border-top-width:initial;border-left-width:initial"> <p class="MsoNormal" style="mso-margin-top-alt:auto"><span lang="IT">32.6</span><o:p></o:p></p> </td> </tr> <tr style="height:15.0pt"> <td width="85" nowrap="" valign="top" style="width:63.8pt;border:solid windowtext 1.0pt;border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:15.0pt;border-top-width:initial"> <p class="MsoNormal" style="mso-margin-top-alt:auto"><span lang="IT">2</span><o:p></o:p></p> </td> <td width="75" nowrap="" valign="top" style="width:56.45pt;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.0pt;border-top-width:initial;border-left-width:initial"> <p class="MsoNormal" style="mso-margin-top-alt:auto"><span lang="IT">38.3</span><o:p></o:p></p> </td> <td width="76" nowrap="" valign="top" style="width:2.0cm;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.0pt;border-top-width:initial;border-left-width:initial"> <p class="MsoNormal" style="mso-margin-top-alt:auto"><span lang="IT">40.8</span><o:p></o:p></p> </td> <td width="151" nowrap="" valign="top" style="width:4.0cm;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.0pt;border-top-width:initial;border-left-width:initial"> <p class="MsoNormal" style="mso-margin-top-alt:auto"><span lang="IT">40.1</span><o:p></o:p></p> </td> </tr> <tr style="height:15.0pt"> <td width="85" nowrap="" valign="top" style="width:63.8pt;border:solid windowtext 1.0pt;border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:15.0pt;border-top-width:initial"> <p class="MsoNormal" style="mso-margin-top-alt:auto"><span lang="IT">3</span><o:p></o:p></p> </td> <td width="75" nowrap="" valign="top" style="width:56.45pt;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.0pt;border-top-width:initial;border-left-width:initial"> <p class="MsoNormal" style="mso-margin-top-alt:auto"><span lang="IT">47.7</span><o:p></o:p></p> </td> <td width="76" nowrap="" valign="top" style="width:2.0cm;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.0pt;border-top-width:initial;border-left-width:initial"> <p class="MsoNormal" style="mso-margin-top-alt:auto"><span lang="IT">51.0</span><o:p></o:p></p> </td> <td width="151" nowrap="" valign="top" style="width:4.0cm;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.0pt;border-top-width:initial;border-left-width:initial"> <p class="MsoNormal" style="mso-margin-top-alt:auto"><span lang="IT">50.2</span><o:p></o:p></p> </td> </tr> <tr style="height:15.0pt"> <td width="85" nowrap="" valign="top" style="width:63.8pt;border:solid windowtext 1.0pt;border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:15.0pt;border-top-width:initial"> <p class="MsoNormal" style="mso-margin-top-alt:auto"><span lang="IT">4</span><o:p></o:p></p> </td> <td width="75" nowrap="" valign="top" style="width:56.45pt;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.0pt;border-top-width:initial;border-left-width:initial"> <p class="MsoNormal" style="mso-margin-top-alt:auto"><span lang="IT">74.7</span><o:p></o:p></p> </td> <td width="76" nowrap="" valign="top" style="width:2.0cm;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.0pt;border-top-width:initial;border-left-width:initial"> <p class="MsoNormal" style="mso-margin-top-alt:auto"><span lang="IT">74.0</span><o:p></o:p></p> </td> <td width="151" nowrap="" valign="top" style="width:4.0cm;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.0pt;border-top-width:initial;border-left-width:initial"> <p class="MsoNormal" style="mso-margin-top-alt:auto"><span lang="IT">78.2</span><o:p></o:p></p> </td> </tr> <tr style="height:15.0pt"> <td width="85" nowrap="" valign="top" style="width:63.8pt;border:solid windowtext 1.0pt;border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:15.0pt;border-top-width:initial"> <p class="MsoNormal" style="mso-margin-top-alt:auto"><span lang="IT">5</span><o:p></o:p></p> </td> <td width="75" nowrap="" valign="top" style="width:56.45pt;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.0pt;border-top-width:initial;border-left-width:initial"> <p class="MsoNormal" style="mso-margin-top-alt:auto"><span lang="IT">82.0</span><o:p></o:p></p> </td> <td width="76" nowrap="" valign="top" style="width:2.0cm;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.0pt;border-top-width:initial;border-left-width:initial"> <p class="MsoNormal" style="mso-margin-top-alt:auto"><span lang="IT">80.0</span><o:p></o:p></p> </td> <td width="151" nowrap="" valign="top" style="width:4.0cm;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.0pt;border-top-width:initial;border-left-width:initial"> <p class="MsoNormal" style="mso-margin-top-alt:auto"><span lang="IT">85.8</span><o:p></o:p></p> </td> </tr> <tr style="height:15.0pt"> <td width="85" nowrap="" valign="top" style="width:63.8pt;border:solid windowtext 1.0pt;border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:15.0pt;border-top-width:initial"> <p class="MsoNormal" style="mso-margin-top-alt:auto"><span lang="IT">6</span><o:p></o:p></p> </td> <td width="75" nowrap="" valign="top" style="width:56.45pt;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.0pt;border-top-width:initial;border-left-width:initial"> <p class="MsoNormal" style="mso-margin-top-alt:auto"><span lang="IT">111.0</span><o:p></o:p></p> </td> <td width="76" nowrap="" valign="top" style="width:2.0cm;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.0pt;border-top-width:initial;border-left-width:initial"> <p class="MsoNormal" style="mso-margin-top-alt:auto"><span lang="IT">109.9</span><o:p></o:p></p> </td> <td width="151" nowrap="" valign="top" style="width:4.0cm;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.0pt;border-top-width:initial;border-left-width:initial"> <p class="MsoNormal" style="mso-margin-top-alt:auto"><span lang="IT">116.3</span><o:p></o:p></p> </td> </tr> <tr style="height:15.0pt"> <td width="85" nowrap="" valign="top" style="width:63.8pt;border:solid windowtext 1.0pt;border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:15.0pt;border-top-width:initial"> <p class="MsoNormal" style="mso-margin-top-alt:auto"><span lang="IT">7</span><o:p></o:p></p> </td> <td width="75" nowrap="" valign="top" style="width:56.45pt;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.0pt;border-top-width:initial;border-left-width:initial"> <p class="MsoNormal" style="mso-margin-top-alt:auto"><span lang="IT">223.7</span><o:p></o:p></p> </td> <td width="76" nowrap="" valign="top" style="width:2.0cm;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.0pt;border-top-width:initial;border-left-width:initial"> <p class="MsoNormal" style="mso-margin-top-alt:auto"><span lang="IT">224.1</span><o:p></o:p></p> </td> <td width="151" nowrap="" valign="top" style="width:4.0cm;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.0pt;border-top-width:initial;border-left-width:initial"> <p class="MsoNormal" style="mso-margin-top-alt:auto"><span lang="IT">234.3</span><o:p></o:p></p> </td> </tr> <tr style="height:15.0pt"> <td width="85" nowrap="" valign="top" style="width:63.8pt;border:solid windowtext 1.0pt;border-top:none;padding:0cm 5.4pt 0cm 5.4pt;height:15.0pt;border-top-width:initial"> <p class="MsoNormal" style="mso-margin-top-alt:auto"><span lang="IT">8</span><o:p></o:p></p> </td> <td width="75" nowrap="" valign="top" style="width:56.45pt;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.0pt;border-top-width:initial;border-left-width:initial"> <p class="MsoNormal" style="mso-margin-top-alt:auto"><span lang="IT">245.6</span><o:p></o:p></p> </td> <td width="76" nowrap="" valign="top" style="width:2.0cm;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.0pt;border-top-width:initial;border-left-width:initial"> <p class="MsoNormal" style="mso-margin-top-alt:auto"><span lang="IT">246.3</span><o:p></o:p></p> </td> <td width="151" nowrap="" valign="top" style="width:4.0cm;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt;height:15.0pt;border-top-width:initial;border-left-width:initial"> <p class="MsoNormal" style="mso-margin-top-alt:auto"><span lang="IT">257.3</span><o:p></o:p></p> </td> </tr> </tbody> </table> </div> <div> <p class="MsoNormal" style="margin-left:35.4pt"><o:p> </o:p></p> </div> <div> <p class="MsoNormal" style="margin-left:35.4pt">What is wrong with my calculation?<o:p></o:p></p> </div> <div> <p class="MsoNormal" style="margin-left:35.4pt">What steps should be done to go from the Hessian to the frequencies?<o:p></o:p></p> </div> <div> <p class="MsoNormal" style="margin-left:35.4pt"><o:p> </o:p></p> </div> <div> <p class="MsoNormal" style="margin-left:35.4pt">The Hessian in csv format, the python script and the cp2k output file are attached. <o:p></o:p></p> </div> <div> <p class="MsoNormal" style="margin-left:35.4pt"><o:p> </o:p></p> </div> <div> <p class="MsoNormal" style="margin-left:35.4pt">Thanks a lot for your help.<o:p></o:p></p> </div> <div> <p class="MsoNormal" style="margin-left:35.4pt"><o:p> </o:p></p> </div> <div> <p class="MsoNormal" style="margin-left:35.4pt">Regards,<o:p></o:p></p> </div> <div> <p class="MsoNormal" style="margin-left:35.4pt">Torstein Fjermestad<o:p></o:p></p> </div> <div> <p class="MsoNormal" style="margin-left:35.4pt"> <o:p></o:p></p> </div> <div> <p class="MsoNormal" style="margin-left:35.4pt"><o:p> </o:p></p> </div> <div> <p class="MsoNormal" style="margin-left:35.4pt"><o:p> </o:p></p> </div> </div> </blockquote> </div> <p class="MsoNormal" style="margin-left:35.4pt">-- <br> You received this message because you are subscribed to the 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