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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> <html xmlns="http://www.w3.org/1999/xhtml"> <head profile="http://gmpg.org/xfn/1"> <title>Computational Organic Chemistry » Stereochemistry</title> <meta name="google-site-verification" content="g1Myv4tUVAmqRbwZeBi7IPuSZpP64RWjVJ6itIoouCo"> <meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> <style type="text/css" media="screen">@import url( /blog/wp-content/themes/comporg/style.css);</style> <link rel="stylesheet" id="wp-block-library-css" href="/blog/wp-includes/css/dist/block-library/style.min.css?ver=5.6.1" type="text/css" media="all"> <script type="text/javascript">  </script> </head> <body> <div id="header"> <div id="header_img"></div> </div> <div id="link_section"> <div style="float:left"> <a href="/blog/about">About this Blog</a> | <a href="/">Book Homepage</a> | <a href="http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471713422.html">Purchase the Book</a> </div> </div> <div id="after_links"></div> <div id="content"> <div id="main"> <h2 class="post-title">Archive for the 'Stereochemistry' Category</h2> <div class="box"> <h2><a href="/blog/archives/3698" rel="bookmark" title="Permanent Link: Atropisomerization within a cyclic compound">Atropisomerization within a cyclic compound</a></h2> <div class="post-content"> <p>Atropisomers are stereoisomer that differ by axial symmetry, such as in substituted biphenyls or allenes. These acyclic systems have received a fair amount of attention, but now Buevich has looked at atropisomerization that occurs in a ring system.<a href="#atropism1"><sup>1</sup></a> <b>1</b> has a biphenyl as part of the eight-member ring, and the biphenyl can exist in either an <i>M</i> or <i>P</i> orientation. Since C3 is chiral (<i>S</i>), the two isomers are (<i>M,S</i>)-<b>1</b> and (<i>P,S</i>)-<b>1</b>. Variable temperature NMR analysis concludes that (<i>P,S</i>)-<b>1</b> is 1.19 kcal mol<sup>-1</sup> more stable than (<i>M,S</i>)-<b>1</b>, and the barrier for the interchange (<i>P,S</i>)-<b>1</b> → (<i>M,S</i>)-<b>1</b> is 26.77 kcal mol<sup>-1</sup>.</p> <p align="center"><img src="/blog/wp-content/atropImg.png"></p> <p>To identify the process for this atropisomerization process, he utilized B3LYP/6-31G(d) computations of the model system <b>2</b>. A variety of different techniques were used to identify the local energy minimum conformations of both (<i>M,S</i>)-<b>2</b> and (<i>P,S</i>)-<b>2</b>, and the lowest energy conformers (<b>M1</b> for (<i>P,S</i>)-<b>2</b> and <b>M4</b> for (<i>M,S</i>)-<b>2</b>) are shown in Figure 1. He then produced a series of 2-D potential energy surfaces varying two of the dihedral angles defining the eight-member ring to help identify potential initial geometries for searching for transition states. (As an aside, this procedure ended up identifying a few additional local energy minima not identified in the initial conformational search – and these all have <i>trans</i> amide groups instead of the <i>cis</i> relationship found initially. These <i>trans</i> isomer are considerably higher in energy than the conformers.) With this model and this computational level, (<i>P,S</i>)-<b>2</b> is 0.76 kcal mol<sup>-1</sup> lower in energy than (<i>M,S</i>)-<b>2</b>.</p> <table align="center" border="0" cellspacing="0" cellpadding="3"> <tr align="center" valign="bottom"> <td> <p></p> <div class="jmol" id="atropM1"> <a onclick="return false"><br> <img src="/blog/wp-content/atropM1.jpg" onclick="insertJmol('atropM1',250,250,'atropM1.xyz')"></a> </div> <p><b>M1</b><br>0.0</p> </td> <td> <p></p> <div class="jmol" id="atropTS1"> <a onclick="return false"><br> <img src="/blog/wp-content/atropTS1.jpg" onclick="insertJmol('atropTS1',250,250,'atropTS1.xyz')"></a><br> <br><b>TS1</b><br>3.54 </div> </td> </tr> <tr align="center" valign="bottom"> <td> <p></p> <div class="jmol" id="atropM2"> <a onclick="return false"><br> <img src="/blog/wp-content/atropM2.jpg" onclick="insertJmol('atropM2',250,250,'atropM2.xyz')"></a><br> <br><b>M2</b><br>2.21 </div> </td> <td> <p></p> <div class="jmol" id="atropTS4"> <a onclick="return false"><br> <img src="/blog/wp-content/atropTS4.jpg" onclick="insertJmol('atropTS4',250,250,'atropTS4.xyz')"></a><br> <br><b>TS4</b><br>25.83 </div> </td> </tr> <tr align="center" valign="bottom"> <td> <p></p> <div class="jmol" id="atropM4"> <a onclick="return false"><br> <img src="/blog/wp-content/atropM4.jpg" onclick="insertJmol('atropM4',250,250,'atropM4.xyz')"></a><br> <br><b>M4</b><br>0.76 </div> </td> <td> <p> </p> </td> </tr> </table> <p align="center"><b>Table 1</b>. B3LYP/6-31G(d) optimized geometries and relative free energies of some critical points along the lowest energy pathway taking (<i>P,S</i>)-<b>2</b> → (<i>M,S</i>)-<b>2</b>.</p> <p>A number of transition states were identified, and the lowest energy pathway that takes <b>M1</b> into <b>M4</b> first crosses <b>TS1</b> to make the minimum <b>M2</b>, which than passes a high barrier (25.8 kcal mol<sup>-1</sup>) to go to <b>M4</b>. This barrier is in reasonable agreement with the experimental barrier for <b>1</b>. These TSs are also shown in Figure 1.</p> <p>Buevich analyzes the conformational process by examination of the changes in the ring dihedral angles following this reaction path. As expected, crossing the highest barrier requires a combination of torsional rotations, but essentially one at a time moving clockwise about the ring.</p> <h3>References</h3> <p><a name="atropism1"></a></p> <p>(1) Buevich, A. V. "Atropisomerization of 8-Membered Dibenzolactam: Experimental NMR and Theoretical DFT Study," <i>J. Org. Chem.</i> <b>2016</b>, <i>81</i>, 485–501 DOI: <a href="http://dx.doi.org/10.1021/acs.joc.5b02321">10.1021/acs.joc.5b02321</a>.</p> <h3>InChIs</h3> <p><b>1</b>: InChI=1S/C27H26N2O/c1-3-12-26-27(30)29(20-21-13-6-5-7-14-21)25-18-11-9-16-23(25)22-15-8-10-17-24(22)28(26)19-4-2/h3-11,13-18,26H,1-2,12,19-20H2/t26-/m0/s1<br>InChIKey=IYYACMIVKDJSJD-SANMLTNESA-N</p> <p><b>2</b>: InChI=1S/C17H18N2O/c1-12-17(20)19(3)16-11-7-5-9-14(16)13-8-4-6-10-15(13)18(12)2/h4-12H,1-3H3/t12-/m0/s1<br>InChIKey=NIBPKKMKNFOPRM-LBPRGKRZSA-N</p>  </div> <p class="bottom"> <span class="cat"><a href="/blog/archives/category/stereochemistry" rel="category tag">Stereochemistry</a></span> <span class="user">Steven Bachrach</span> <span class="date">10 Feb 2016</span> <span class="comments"><a href="/blog/archives/3698#comments">1 Comment</a></span> </p> </div> <div class="box"> <h2><a href="/blog/archives/1849" rel="bookmark" title="Permanent Link: [6]Saddlequat – the ruber glove inversion">[6]Saddlequat – the ruber glove inversion</a></h2> <div class="post-content"> <p>In 1955 Mislow<a href="#saddleR1"><sup>1</sup></a> discussed the possibility of enatiomers interchanging via a path that was entirely chiral, never passing through an achiral structure. His analogy is the inversion of a rubber glove, taking a right hand rubber glove and pulling it inside out creates a left hand glove (its mirror image) but never passing through an achiral glove. Well, now a helicene with this type of stereochemistry has been developed, with a stable chiral intermediate.<a href="#saddleR2"><sup>2</sup></a></p> <p>Helicenes typically interchange (<i>P</i> → <i>M</i> → <i>P</i>) through an achiral saddle-like structure. But larger helicenes can have high-lying intermediates along this pathway. Helquat <b><i>P-1</i></b> interchanges to <b><i>M</i>-1</b> through the intermediate <b>2</b>, which is an achiral structure and can be isolated.</p> <p align="center"><img src="/blog/wp-content/saddleImg1.gif"></p> <p>Computations at B3LYP/def2-TZVP//PBE/def2-SV(P) with dispersion corrections (and PCM simulating DMSO) of the inversion process identified a number of intermediates and transition states along the stereoinversion pathway. The intermediate <b>2</b> lies 18.4 kJ mol<sup>-1</sup> above <b>1</b>. These structures are shown in Figure 1. The highest lying TS between <b>2</b> and <b><i>P</i>-1</b> (labeled <b>TSP</b> in Figure 1) is 119 kJ mol<sup>-1</sup> above <b>2</b>. The highest lying TS on the path from <b>2</b> to <b><i>M</i>-1 </b>(labeled <b>TSM</b> in Figure 1) is 138 kJ mol<sup>-1</sup> above <b>2</b>. Note that going from <b>2</b> to <b><i>P</i>-1</b> is not the mirror image path of going from <b>2</b> to <b><i>M</i>-1</b>.</p> <table align="center" border="0" cellspacing="0" cellpadding="4"> <tr align="center"> <td> <p></p> <div class="jmol" id="sadTSP"> <a onclick="return false"><br> <img src="/blog/wp-content/saddleTSP.jpg" onclick="insertJmol('sadTSP',250,250,'saddleTSP.xyz')"><br> </a> </div> <p><b>TSP</b></p> </td> <td> <p></p> <div class="jmol" id="sadTSM"> <a onclick="return false"><br> <img src="/blog/wp-content/saddleTSM.jpg" onclick="insertJmol('sadTSM',250,250,'saddleTSM.xyz')"><br> </a> </div> <p><b>TSM</b></p> </td> </tr> </table> <table align="center" border="0" cellspacing="0" cellpadding="4"> <tr align="center"> <td> <p></p> <div class="jmol" id="sadP5"> <a onclick="return false"><br> <img src="/blog/wp-content/saddleP5.jpg" onclick="insertJmol('sadP5',250,250,'saddleP5.xyz')"><br> </a> </div> <p><b><i>P</i>-1</b></p> </td> <td> <p></p> <div class="jmol" id="sadSR4"> <a onclick="return false"><br> <img src="/blog/wp-content/saddleSR4.jpg" onclick="insertJmol('sadSR4',250,250,'saddleSR4.xyz')"><br> </a> </div> <p><b>2</b></p> </td> <td> <p></p> <div class="jmol" id="sadM5"> <a onclick="return false"><br> <img src="/blog/wp-content/saddleM5.jpg" onclick="insertJmol('sadM5',250,250,'saddleM5.xyz')"><br> </a> </div> <p><b><i>M</i>-1</b></p> </td> </tr> </table> <p align="center"><b>Figure 1</b>. Optimized structures of <b>1</b>, <b>2</b>, and the highest transition states interconverting them.</p> <p>Heating racemic <b>2</b> and following the conversion to <b>1</b> with NMR gives the activation barrier of 119 kJ mol<sup>-1</sup>, in excellent agreement with the computation.</p> <p>Racemic <b>2</b> was resolved through differential crystallization and its x-ray structure indicates it is (+)-[<i>S<sub>a</sub></i>,R<sub>a</sub>]. Heating it does give just <b><i>P</i>-1</b>, as predicted by the computations. Then heating <b><i>P</i>-1</b> to 180 °C does racemize it, with an experimental barrier of 157.7 kJ mol<sup>-1</sup>. The computations predict a barrier of 156.6 kJ mol<sup>-1</sup>, again in fine agreement with experiment. Overall, a nice piece showing experiment and computation working together to provide an understanding of an interesting chemical system!</p> <h3>References</h3> <p><a name="saddleR1"></a></p> <p>(1) Mislow, K.; Bolstad, R., "Molecular Dissymmetry and Optical Inactivity," <i>J. Am. Chem. Soc.</i>, <b>1955</b>, <i>77</i>, 6712-6713, DOI: <a href="http://dx.doi.org/10.1021/ja01629a131">10.1021/ja01629a131</a></p> <p><a name="saddleR2"></a></p> <p>(2) Adriaenssens, L.; Severa, L.; Koval, D.; Cisarova, I.; Belmonte, M. M.; Escudero-Adan, E. C.; Novotna, P.; Sazelova, P.; Vavra, J.; Pohl, R.; Saman, D.; Urbanova, M.; Kasicka, V.; Teply, F., "[6]Saddlequat: a [6]helquat captured on its racemization pathway," <i>Chem. Sci.</i> <b>2011</b>, ASAP, DOI: <a href="http://dx.doi.org/10.1039/C1SC00468A">10.1039/C1SC00468A</a></p> <h3>InChIs</h3> <p><b>1</b>: InChI=1/C27H26N2/c1-2-11-23-20(8-1)15-19-29-18-7-10-22-14-13-21-9-3-5-16-28-17-6-4-12-24(28)25(21)26(22)27(23)29/h1-2,4,6,8,11-15,17,19H,3,5,7,9-10,16,18H2/q+2<br>InChIKey=YVVUWUZXUZDMQS-UHFFFAOYAP</p>  </div> <p class="bottom"> <span class="cat"><a href="/blog/archives/category/stereochemistry" rel="category tag">Stereochemistry</a></span> <span class="user">Steven Bachrach</span> <span class="date">18 Oct 2011</span> <span class="comments"><a href="/blog/archives/1849#comments">2 Comments</a></span> </p> </div> <p align="center"></p> </div> <div id="sidebar"> <ul> <li class="box"> <h2> Categories </h2> <ul> <li class="cat-item cat-item-25"> <a href="/blog/archives/category/acidity">Acidity</a> (12) </li> <li class="cat-item cat-item-3"> <a href="/blog/archives/category/aromaticity">Aromaticity</a> (91) </li> <li class="cat-item cat-item-53"> <a 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class="cat-item cat-item-13"> <a href="/blog/archives/category/reactions/12-addition">1,2-addition</a> (1) </li> <li class="cat-item cat-item-35"> <a href="/blog/archives/category/reactions/aldol">aldol</a> (4) </li> <li class="cat-item cat-item-32"> <a href="/blog/archives/category/reactions/bergman-cyclization">Bergman cyclization</a> (6) </li> <li class="cat-item cat-item-44"> <a href="/blog/archives/category/reactions/claisen-rearrangement">Claisen rearrangement</a> (2) </li> <li class="cat-item cat-item-10"> <a href="/blog/archives/category/reactions/cope-rearrangement">Cope Rearrangement</a> (5) </li> <li class="cat-item cat-item-69"> <a href="/blog/archives/category/reactions/cycloadditions">cycloadditions</a> (12) </li> <li class="cat-item cat-item-23"> <a href="/blog/archives/category/reactions/diels-alder">Diels-Alder</a> (26) </li> <li class="cat-item cat-item-47"> <a href="/blog/archives/category/reactions/electrocyclization">electrocyclization</a> (11) </li> <li class="cat-item cat-item-76"> <a href="/blog/archives/category/reactions/electrophilic-aromatic-substitution">electrophilic aromatic substitution</a> (1) </li> <li class="cat-item cat-item-5"> <a href="/blog/archives/category/reactions/ene-reaction">ene reaction</a> (1) </li> <li class="cat-item cat-item-52"> <a href="/blog/archives/category/reactions/hajos-parrish-reaction">Hajos-Parrish Reaction</a> (1) </li> <li class="cat-item cat-item-61"> <a href="/blog/archives/category/reactions/mannich">Mannich</a> (2) </li> <li class="cat-item cat-item-64"> <a href="/blog/archives/category/reactions/michael-addition">Michael addition</a> (5) </li> <li class="cat-item cat-item-40"> <a href="/blog/archives/category/reactions/ozonolysis">ozonolysis</a> (1) </li> <li class="cat-item cat-item-43"> <a href="/blog/archives/category/reactions/proton-transfer">proton transfer</a> (1) </li> <li class="cat-item cat-item-38"> <a href="/blog/archives/category/reactions/pseudopericyclic">pseudopericyclic</a> (4) </li> <li class="cat-item cat-item-63"> <a href="/blog/archives/category/reactions/strecker">Strecker</a> (1) </li> <li class="cat-item cat-item-24"> <a href="/blog/archives/category/reactions/substitution">Substitution</a> (6) </li> <li class="cat-item cat-item-93"> <a href="/blog/archives/category/reactions/wittig">Wittig</a> (1) </li> </ul> </li> <li class="cat-item cat-item-87"> <a href="/blog/archives/category/second-edition">Second Edition</a> (3) </li> <li class="cat-item cat-item-11"> <a href="/blog/archives/category/solvation">Solvation</a> (17) </li> <li class="cat-item cat-item-77 current-cat"> <a aria-current="page" href="/blog/archives/category/stereochemistry">Stereochemistry</a> (2) </li> <li class="cat-item cat-item-68"> <a href="/blog/archives/category/stereoinduction">stereoinduction</a> (4) </li> <li class="cat-item cat-item-71"> <a href="/blog/archives/category/tunneling">Tunneling</a> (26) </li> <li class="cat-item cat-item-1"> <a href="/blog/archives/category/uncategorized">Uncategorized</a> (57) </li> <li class="cat-item cat-item-82"> <a href="/blog/archives/category/vibrational-frequencies">vibrational frequencies</a> (3) </li> </ul> </li> <li class="box"> <h2> Monthly </h2> <ul> <li><a href="/blog/archives/date/2019/06">June 2019</a></li> <li><a href="/blog/archives/date/2019/04">April 2019</a></li> <li><a href="/blog/archives/date/2019/03">March 2019</a></li> <li><a href="/blog/archives/date/2019/02">February 2019</a></li> <li><a href="/blog/archives/date/2019/01">January 2019</a></li> <li><a href="/blog/archives/date/2018/12">December 2018</a></li> <li><a href="/blog/archives/date/2018/11">November 2018</a></li> <li><a href="/blog/archives/date/2018/10">October 2018</a></li> <li><a href="/blog/archives/date/2018/09">September 2018</a></li> <li><a href="/blog/archives/date/2018/08">August 2018</a></li> <li><a href="/blog/archives/date/2018/07">July 2018</a></li> <li><a href="/blog/archives/date/2018/06">June 2018</a></li> <li><a href="/blog/archives/date/2018/05">May 2018</a></li> <li><a href="/blog/archives/date/2018/04">April 2018</a></li> <li><a href="/blog/archives/date/2018/03">March 2018</a></li> <li><a href="/blog/archives/date/2018/02">February 2018</a></li> <li><a href="/blog/archives/date/2018/01">January 2018</a></li> <li><a href="/blog/archives/date/2017/12">December 2017</a></li> <li><a href="/blog/archives/date/2017/11">November 2017</a></li> <li><a href="/blog/archives/date/2017/10">October 2017</a></li> <li><a href="/blog/archives/date/2017/09">September 2017</a></li> <li><a href="/blog/archives/date/2017/08">August 2017</a></li> <li><a href="/blog/archives/date/2017/07">July 2017</a></li> <li><a href="/blog/archives/date/2017/06">June 2017</a></li> <li><a href="/blog/archives/date/2017/05">May 2017</a></li> <li><a href="/blog/archives/date/2017/04">April 2017</a></li> <li><a href="/blog/archives/date/2017/03">March 2017</a></li> <li><a href="/blog/archives/date/2017/02">February 2017</a></li> <li><a href="/blog/archives/date/2017/01">January 2017</a></li> <li><a href="/blog/archives/date/2016/12">December 2016</a></li> <li><a href="/blog/archives/date/2016/11">November 2016</a></li> <li><a href="/blog/archives/date/2016/10">October 2016</a></li> <li><a href="/blog/archives/date/2016/09">September 2016</a></li> <li><a href="/blog/archives/date/2016/08">August 2016</a></li> <li><a href="/blog/archives/date/2016/07">July 2016</a></li> <li><a href="/blog/archives/date/2016/06">June 2016</a></li> <li><a href="/blog/archives/date/2016/05">May 2016</a></li> <li><a href="/blog/archives/date/2016/04">April 2016</a></li> <li><a href="/blog/archives/date/2016/03">March 2016</a></li> <li><a href="/blog/archives/date/2016/02">February 2016</a></li> <li><a href="/blog/archives/date/2016/01">January 2016</a></li> <li><a href="/blog/archives/date/2015/12">December 2015</a></li> <li><a href="/blog/archives/date/2015/11">November 2015</a></li> <li><a href="/blog/archives/date/2015/10">October 2015</a></li> <li><a href="/blog/archives/date/2015/09">September 2015</a></li> <li><a href="/blog/archives/date/2015/08">August 2015</a></li> <li><a href="/blog/archives/date/2015/07">July 2015</a></li> <li><a href="/blog/archives/date/2015/06">June 2015</a></li> <li><a href="/blog/archives/date/2015/05">May 2015</a></li> <li><a href="/blog/archives/date/2015/04">April 2015</a></li> <li><a href="/blog/archives/date/2015/03">March 2015</a></li> <li><a href="/blog/archives/date/2015/02">February 2015</a></li> <li><a href="/blog/archives/date/2015/01">January 2015</a></li> <li><a href="/blog/archives/date/2014/12">December 2014</a></li> <li><a href="/blog/archives/date/2014/11">November 2014</a></li> <li><a href="/blog/archives/date/2014/10">October 2014</a></li> <li><a href="/blog/archives/date/2014/09">September 2014</a></li> <li><a href="/blog/archives/date/2014/08">August 2014</a></li> <li><a href="/blog/archives/date/2014/07">July 2014</a></li> <li><a href="/blog/archives/date/2014/06">June 2014</a></li> <li><a href="/blog/archives/date/2014/05">May 2014</a></li> <li><a href="/blog/archives/date/2014/04">April 2014</a></li> <li><a href="/blog/archives/date/2014/03">March 2014</a></li> <li><a href="/blog/archives/date/2014/02">February 2014</a></li> <li><a href="/blog/archives/date/2014/01">January 2014</a></li> <li><a href="/blog/archives/date/2013/12">December 2013</a></li> <li><a href="/blog/archives/date/2013/11">November 2013</a></li> <li><a href="/blog/archives/date/2013/10">October 2013</a></li> <li><a href="/blog/archives/date/2013/09">September 2013</a></li> <li><a href="/blog/archives/date/2013/08">August 2013</a></li> <li><a href="/blog/archives/date/2013/07">July 2013</a></li> <li><a href="/blog/archives/date/2013/06">June 2013</a></li> <li><a href="/blog/archives/date/2013/05">May 2013</a></li> <li><a href="/blog/archives/date/2013/04">April 2013</a></li> <li><a href="/blog/archives/date/2013/03">March 2013</a></li> <li><a href="/blog/archives/date/2013/02">February 2013</a></li> <li><a href="/blog/archives/date/2013/01">January 2013</a></li> <li><a href="/blog/archives/date/2012/12">December 2012</a></li> <li><a href="/blog/archives/date/2012/11">November 2012</a></li> <li><a href="/blog/archives/date/2012/10">October 2012</a></li> <li><a href="/blog/archives/date/2012/09">September 2012</a></li> <li><a href="/blog/archives/date/2012/08">August 2012</a></li> <li><a href="/blog/archives/date/2012/07">July 2012</a></li> <li><a href="/blog/archives/date/2012/06">June 2012</a></li> <li><a href="/blog/archives/date/2012/05">May 2012</a></li> <li><a href="/blog/archives/date/2012/04">April 2012</a></li> <li><a href="/blog/archives/date/2012/03">March 2012</a></li> <li><a href="/blog/archives/date/2012/02">February 2012</a></li> <li><a href="/blog/archives/date/2012/01">January 2012</a></li> <li><a href="/blog/archives/date/2011/12">December 2011</a></li> <li><a href="/blog/archives/date/2011/11">November 2011</a></li> <li><a href="/blog/archives/date/2011/10">October 2011</a></li> <li><a href="/blog/archives/date/2011/09">September 2011</a></li> <li><a href="/blog/archives/date/2011/08">August 2011</a></li> <li><a href="/blog/archives/date/2011/07">July 2011</a></li> <li><a href="/blog/archives/date/2011/06">June 2011</a></li> <li><a href="/blog/archives/date/2011/05">May 2011</a></li> <li><a href="/blog/archives/date/2011/04">April 2011</a></li> <li><a href="/blog/archives/date/2011/03">March 2011</a></li> <li><a href="/blog/archives/date/2011/02">February 2011</a></li> <li><a href="/blog/archives/date/2011/01">January 2011</a></li> <li><a href="/blog/archives/date/2010/12">December 2010</a></li> <li><a href="/blog/archives/date/2010/11">November 2010</a></li> <li><a href="/blog/archives/date/2010/10">October 2010</a></li> <li><a href="/blog/archives/date/2010/09">September 2010</a></li> <li><a href="/blog/archives/date/2010/08">August 2010</a></li> <li><a href="/blog/archives/date/2010/07">July 2010</a></li> <li><a href="/blog/archives/date/2010/06">June 2010</a></li> <li><a href="/blog/archives/date/2010/05">May 2010</a></li> <li><a href="/blog/archives/date/2010/04">April 2010</a></li> <li><a href="/blog/archives/date/2010/03">March 2010</a></li> <li><a href="/blog/archives/date/2010/02">February 2010</a></li> <li><a href="/blog/archives/date/2010/01">January 2010</a></li> <li><a href="/blog/archives/date/2009/12">December 2009</a></li> <li><a href="/blog/archives/date/2009/11">November 2009</a></li> <li><a href="/blog/archives/date/2009/10">October 2009</a></li> <li><a href="/blog/archives/date/2009/09">September 2009</a></li> <li><a href="/blog/archives/date/2009/08">August 2009</a></li> <li><a href="/blog/archives/date/2009/07">July 2009</a></li> <li><a href="/blog/archives/date/2009/06">June 2009</a></li> <li><a href="/blog/archives/date/2009/05">May 2009</a></li> <li><a href="/blog/archives/date/2009/04">April 2009</a></li> <li><a href="/blog/archives/date/2009/03">March 2009</a></li> <li><a href="/blog/archives/date/2009/02">February 2009</a></li> <li><a href="/blog/archives/date/2009/01">January 2009</a></li> <li><a href="/blog/archives/date/2008/12">December 2008</a></li> <li><a href="/blog/archives/date/2008/11">November 2008</a></li> <li><a href="/blog/archives/date/2008/10">October 2008</a></li> <li><a href="/blog/archives/date/2008/09">September 2008</a></li> <li><a href="/blog/archives/date/2008/08">August 2008</a></li> <li><a href="/blog/archives/date/2008/07">July 2008</a></li> <li><a href="/blog/archives/date/2008/06">June 2008</a></li> <li><a href="/blog/archives/date/2008/05">May 2008</a></li> <li><a href="/blog/archives/date/2008/04">April 2008</a></li> <li><a href="/blog/archives/date/2008/03">March 2008</a></li> <li><a href="/blog/archives/date/2008/02">February 2008</a></li> <li><a href="/blog/archives/date/2008/01">January 2008</a></li> <li><a href="/blog/archives/date/2007/12">December 2007</a></li> <li><a href="/blog/archives/date/2007/11">November 2007</a></li> <li><a href="/blog/archives/date/2007/10">October 2007</a></li> <li><a href="/blog/archives/date/2007/09">September 2007</a></li> <li><a href="/blog/archives/date/2007/08">August 2007</a></li> <li><a href="/blog/archives/date/2007/07">July 2007</a></li> </ul> </li> </ul> <a rel="license" href="https://creativecommons.org/licenses/by-nd/3.0/"> <img alt="Creative Commons License" style="border-width:0" src="https://i.creativecommons.org/l/by-nd/3.0/88x31.png"> </a> <br>This work is licensed under a <a rel="license" href="https://creativecommons.org/licenses/by-nd/3.0/">Creative Commons Attribution-No Derivative Works 3.0 Unported License</a>. </div>  <div class="clear"></div> 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