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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 » 2008 » June</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 June, 2008</h2> <div class="box"> <h2><a href="/blog/archives/72" rel="bookmark" title="Permanent Link: Heavy atom tunneling">Heavy atom tunneling</a></h2> <div class="post-content"> <p>Wes Borden has been exploring reactions where tunneling is operational. These studies have been inspired by Bill Doering’s<a href="#ctunnel1"><sup>1</sup></a> statement regarding tunneling in 1,5-sigmatropic shifts: “The tunneling effect is likely, in the opinion of some, to remain relegated to the virtual world of calculations”. Borden’s first two papers dealt with the kinetic isotope effects for the [1,5]-H shift in 1,3-cyclopentadiene and 5-methyl-1,3-cyclopentadiene.<a href="#ctunnel2"><sup>2,3</sup></a></p> <p>His latest article examines carbon tunneling,<a href="#ctunnel4"><sup>4</sup></a> which, due to the much heavier mass of the carbon nucleus relative to a proton, is likely to play a minimal role at best. Borden looked at the ring opening of cyclopropylcarbinyl radical <b>1</b> to 3-butene-1-yl radical <b>2</b>, passing through transition state <b>TS1-2</b>. The B3LYP/6-31G(d) optimized structures are shown in Figure 1.</p> <table align="center" border="0" cellspacing="0" cellpadding="2"> <tr> <td valign="middle" align="center"> <p><img src="/blog/wp-content/ctunnel1.gif"><br><b>1</b></p> </td> <td valign="middle" align="center"> <p> </p> </td> <td valign="middle" align="center"> <p><img src="/blog/wp-content/ctunnel2.gif"><br><b>2</b></p> </td> </tr> <tr> <td valign="middle" align="center"> <p></p> <div class="jmol" id="ctun1"> <a onclick="return false"><br> <img src="/blog/wp-content/ctunnel-1.gif" onclick="insertJmol('ctun1',200,200,'ctunnel-1.xyz')"><br> </a> </div> <p><b>1</b></p> </td> <td valign="middle" align="center"> <p></p> <div class="jmol" id="ctun2"> <a onclick="return false"><br> <img src="/blog/wp-content/ctunnel-ts1.gif" onclick="insertJmol('ctun2',200,200,'ctunnel-ts1.xyz')"><br> </a> </div> <p><b>TS1-2</b></p> </td> <td valign="middle" align="center"> <p></p> <div class="jmol" id="ctun3"> <a onclick="return false"><br> <img src="/blog/wp-content/ctunnel-2.gif" onclick="insertJmol('ctun3',200,200,'ctunnel-2.xyz')"><br> </a> </div> <p><b>2</b></p> </td> </tr> </table> <p align="center"><b>Figure 1</b>. B3LYP/6-31G(d) optimized geometries of <b>1</b>, <b>2</b>, and <b>TS1-2</b>.<a href="#ctunnel4"><sup>4</sup></a></p> <p>The predicted rate of the reaction at 298 K using canonical variational transition state theory is increased by about 50% when small-curvature tunneling is included. This predicted rate is a bit smaller than the experimental value. Experiments also shows a linear Arrhenius plot, and Borden’s calculations agree until one reaches very low temperatures. Below 150 K the Arrhenius curve begins to deviate from linearity, and below 20 K the curve is flat – the rate is no longer temperature dependent! Thus, at cryogenic temperatures, the tunneling rate far exceeds traditional crossing of the variational barrier. Borden hopes that experimentalists will reinvestigate this problem (and hopefully confirm his predictions).</p> <h3>References</h3> <p>(1) Doering, W. v. E.; Zhao, X., "Effect on Kinetics by Deuterium in the 1,5-Hydrogen Shift of a Cisoid-Locked 1,3(<i>Z</i>)-Pentadiene, 2-Methyl-10-methylenebicycloJ. Am. Chem. Soc., <b>2006</b>, <i>128</i>, 9080-9085, DOI: <a href="http://dx.doi.org/10.1021/ja057377v">10.1021/ja057377v</a>.</p> <p>(2) Shelton, G. R.; Hrovat, D. A.; Borden, W. T., "Tunneling in the 1,5-Hydrogen Shift Reactions of 1,3-Cyclopentadiene and 5-Methyl-1,3-Cyclopentadiene," <i>J. Am. Chem. Soc.</i>, <b>2007</b>, <i>129</i>, 164-168, DOI: <a href="http://dx.doi.org/10.1021/ja0664279">10.1021/ja0664279</a>.</p> <p>(3) Shelton, G. R.; Hrovat, D. A.; Borden, W. T., "Calculations of the Effect of Tunneling on the Swain-Schaad Exponents (SSEs) for the 1,5-Hydrogen Shift in 5-Methyl-1,3-cyclopentadiene. Can SSEs Be Used to Diagnose the Occurrence of Tunneling?," <i>J. Am. Chem. Soc.</i>, <b>2007</b>, <i>129</i>, 16115-16118, DOI: <a href="http://dx.doi.org/10.1021/ja076132a">10.1021/ja076132a</a>.</p> <p>(4) Datta, A.; Hrovat, D. A.; Borden, W. T., "Calculations Predict Rapid Tunneling by Carbon from the Vibrational Ground State in the Ring Opening of Cyclopropylcarbinyl Radical at Cryogenic Temperatures," <i>J. Am. Chem. Soc.</i>, <b>2008</b>, <i>130</i>, 6684-6685, DOI: <a href="http://dx.doi.org/10.1021/ja801089p">10.1021/ja801089p</a>.</p> <h3>InChIs</h3> <p><b>1</b>: <span class="inchi">InChI=1/C4H7/c1-4-2-3-4/h4H,1-3H2</span></p> <p><b>2</b>: <span class="inchi">InChI=1/C4H7/c1-3-4-2/h3H,1-2,4H2</span></p>  </div> <p class="bottom"> <span class="cat"><a href="/blog/archives/category/authors/borden" rel="category tag">Borden</a> &<a href="/blog/archives/category/qm-method/dft" rel="category tag">DFT</a> &<a href="/blog/archives/category/tunneling" rel="category tag">Tunneling</a></span> <span class="user">Steven Bachrach</span> <span class="date">17 Jun 2008</span> <span class="comments"><a href="/blog/archives/72#comments">2 Comments</a></span> </p> </div> <div class="box"> <h2><a href="/blog/archives/71" rel="bookmark" title="Permanent Link: Electrocyclization of 7-azahepta-1,2,4,6-tetraene">Electrocyclization of 7-azahepta-1,2,4,6-tetraene</a></h2> <div class="post-content"> <p>I concluded the subchapter on pseudopericyclic reaction (Chapter 3.4) with a discussion of the controversy concerning the nature of the electrocyclization of 7-azahepta-1,2,4,6-tetraene <b>1</b>. Quickly summarizing form the book, based on which data one deems important, the reaction can be seen as either pericyclic or pseudopericyclic.</p> <p align="center"><img src="/blog/wp-content/duncan1.gif"></p> <p>However, I offered David Birney’s opinion as perhaps the proper way to interpret this reaction. David suggested that the TS has both pericyclic and pseudopericyclic character. I wrote that “what we have is a continuum from pericyclic to pseudopericyclic character, analogous to the S<sub>N</sub>1 to S<sub>N</sub>2 continuum for nucleophilic substitution”.</p> <p>Duncan has revisited this reaction,<a href="#duncRef1"><sup>1</sup></a> employing both B3LYP and CASSCF(10,9) computations. He concludes that the reaction is “neither purely pericyclic nor pseudopericyclic” – just as Birney had indicated. Duncan does offer the possibility of a secondary orbital interaction involving the nitrogen lone pair. But it is nice to see confirmation of the interpretation that David originated for my book!</p> <h3>References</h3> <p><a name="#duncRef1"></a></p> <p>(1) Duncan, J. A.; Calkins, D. E. G.; Chavarha, M., "Secondary Orbital Effect in the Electrocyclic Ring Closure of 7-Azahepta-1,2,4,6-tetraene – A CASSCF Molecular Orbital Study,", <i>J. Am. Chem. Soc.</i>, <b>2008</b>, <i>130</i>, 6740-6748, DOI: <a href="http://dx.doi.org/10.1021/ja074402j">10.1021/ja074402j</a>.</p> <h3>InChIs</h3> <p><b>1</b>: <span class="inchi">InChI=1/C6H7N/c1-2-3-4-5-6-7/h3-7H,1H2/b5-4-,7-6+</span><br>InChIKey=VCEMZTODUGWAPF-SCFJQAPRBS</p> <p><b>2</b>: <span class="inchi">InChI=1/C6H7N/c1-6-4-2-3-5-7-6/h2-5,7H,1H2</span><br>InChIKey=JGSLKNWXPRDWBA-UHFFFAOYAH</p>  </div> <p class="bottom"> <span class="cat"><a href="/blog/archives/category/reactions/pseudopericyclic" rel="category tag">pseudopericyclic</a></span> <span class="user">Steven Bachrach</span> <span class="date">10 Jun 2008</span> <span class="comments"><a href="/blog/archives/71#comments">1 Comment</a></span> </p> </div> <div class="box"> <h2><a href="/blog/archives/70" rel="bookmark" title="Permanent Link: Hexacoordinate carbon">Hexacoordinate carbon</a></h2> <div class="post-content"> <p>The search for the elusive hypervalent carbon atom took an interesting turn for the positive with the report of the synthesis and characterization of <b>1</b> and especially its dication <b>2</b>.<a href="#hexCref"><sup>1</sup></a> The x-ray structure was obtained for both compounds along with computing their B3PW91/6-31G(d) geometries. These computed geometries are shown in Figure 1.</p> <table border="0" cellspacing="2" cellpadding="2" align="center"> <tr> <td align="center" valign="middle"> <p><img src="/blog/wp-content/hexC1.gif"><br><b>1</b></p> </td> <td align="center" valign="middle"> <p><img src="/blog/wp-content/hexC2.gif"><br><b>2</b></p> </td> </tr> <tr> <td align="center" valign="middle"> <p></p> <div class="jmol" id="hexc1"> <a onclick="return false"><br> <img src="/blog/wp-content/hexC-c1.gif" onclick="insertJmol('hexc1',200,200,'hexC-c1.xyz')"><br> </a> </div> <p><b>1</b></p> </td> <td align="center" valign="middle"> <p></p> <div class="jmol" id="hexc2"> <a onclick="return false"><br> <img src="/blog/wp-content/hexC-c2.gif" onclick="insertJmol('hexc2',200,200,'hexC-c2.xyz')"><br> </a> </div> <p><b>2</b></p> </td> </tr> </table> <p align="center"><b>Figure 1.</b> B3PW91/6-31G(d) optimized geometries of <b>1</b> and <b>2</b>.<a href="#hexCref"><sup>1</sup></a></p> <p>The allene fragment is bent in both structures: 168.5° (169.9° at B3PW91) in <b>1</b> and 166.8° (172.7° at B3PW91) in <b>2</b>. The distances between the central carbon atom of the allene and the four oxygen atoms are 2.66 to 2.82 Å, and computed to be a little longer. Interestingly, these distance contract when the dication <b>2</b> is created; ranging from 2.64 to 2.75 Å (again computed to be a little longer). These distances, while significantly longer than normal covalent C-O bonds, are less than the sum of the C and O van der Waals radii. But are they really bonds?</p> <p>This is not a trivial answer to solve. The authors opt to employ topological electron density analysis (Bader’s atoms-in-molecules approach). Using the electron density from both the high resolution x-ray density map and from the DFT computations, bond paths between the central allene carbon and each oxygen are found, though with, as expected, low values of ρ. The Laplacian of the density at the critical point are positive, indicative of ionic interactions. So according to Bader’s model, the existence of a bond path in a ground state molecule is the necessary and sufficient condition for bonding.</p> <p>The others conclude by proposing that O<sup>…</sup>C intermolecular interactions with separations of around 2.6 to 2.8 Å may also suggest hypervalent cases. They note that about 2000 structures in the Cambridge crystallographic database fit this criterion.</p> <h3>References</h3> <p>(1) Yamaguchi, T.; Yamamoto, Y.; Kinoshita, D.; Akiba, K.-y.; Zhang, Y.; Reed, C. A.; Hashizume, D.; Iwasaki, F., "Synthesis and Structure of a Hexacoordinate<br> Carbon Compound," <i>J. Am. Chem. Soc.</i>, <b>2008</b>, <i>130</i>, 6894-6895, DOI: <a href="http://dx.doi.org/10.1021/ja710423d">10.1021/ja710423d</a>.</p> <h3>InChIs</h3> <p><b>1</b>: <span class="inchi">InChI=1/C31H24O4S2/c1-32-20-9-5-13-24-28(20)18(29-21(33-2)10-6-14-25(29)36-24)17-19-30-22(34-3)11-7-15-26(30)37-27-16-8-12-23(35-4)31(19)27/h5-16H,1-4H3</span><br> InChiKey= RJBVLFYVIBCWKW-UHFFFAOYAD</p> <p><b>2</b>: <span class="inchi">InChI=1/C33H30O4S2/c1-34-22-11-7-15-26-30(22)20(31-23(35-2)12-8-16-27(31)38(26)5)19-21-32-24(36-3)13-9-17-28(32)39(6)29-18-10-14-25(37-4)33(21)29/h7-18H,1-6H3/q+2</span><br> InChIKey= MVHOSIVPHPDYJJ-UHFFFAOYAM</p>  </div> <p class="bottom"> <span class="cat"><a href="/blog/archives/category/qm-method/dft" rel="category tag">DFT</a> &<a href="/blog/archives/category/molecules/non-classical" rel="category tag">non-classical</a></span> <span class="user">Steven Bachrach</span> <span class="date">03 Jun 2008</span> <span class="comments"><a href="/blog/archives/70#comments">3 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href="/blog/archives/category/qm-method/focal-point">focal point</a> (7) </li> <li class="cat-item cat-item-14"> <a href="/blog/archives/category/qm-method/g3">G3</a> (3) </li> <li class="cat-item cat-item-60"> <a href="/blog/archives/category/qm-method/mp">MP</a> (11) </li> </ul> </li> <li class="cat-item cat-item-56"> <a href="/blog/archives/category/reactions">Reactions</a> (83) <ul class="children"> <li 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"> <a 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 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