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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 » 2011 » September</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 September, 2011</h2> <div class="box"> <h2><a href="/blog/archives/1757" rel="bookmark" title="Permanent Link: Electrophilic aromatic substitution is really addition-elimination">Electrophilic aromatic substitution is really addition-elimination</a></h2> <div class="post-content"> <p>We have all learned about aromatic substitution as proceeding via the following mechanism</p> <p align="center"><img src="/blog/wp-content/aromSubimg1.gif"></p> <p>(Worse yet – many of us have taught this for years!) Well, Galabov, Zou, Schaefer and Schleyer pour a whole lot of cold water on this notion in their recent <i>Angewandte</i> article.<a href="#AromSub"><sup>1</sup></a> Modeling the reaction of benzene with Br<sub>2</sub> and using B3LYP/6-311+G(2d,2p) for both the gas phase and PCM simulating a CCl<sub>4</sub> solvent, attempts to locate this standard intermediate led instead to a concerted substitution transition state <b>TS1</b> (see Figure 1).</p> <table align="center" border="0" cellspacing="0" cellpadding="0"> <tr align="center"> <td> <p></p> <div class="jmol" id="aromSubTS1"> <a onclick="return false"><br> <img src="/blog/wp-content/aromSubTS1.jpg" onclick="insertJmol('aromSubTS1',225,225,'aromSubTS1.xyz')"><br> </a> </div> <p><b>TS1</b></p> </td> </tr> </table> <p align="center"><b>Figure 1</b>. PCM/B3LYP/6-311+G(2d,2p) optimized transitin state along the concerted pathway</p> <p>However, this is not the lowest energy pathway for substitution. Rather and addition-elimination pathway is kinetically preferred. In the first step Br<sub>2</sub> adds in either a 1,2 or 1,4 fashion to form an intermediate. The lower energy path is the 1,4 addition, leading to <b>P3</b>. This intermediate then undergoes a syn,anti-isomerization to give <b>P5</b>. The last step is the elimination of HBr from <b>P5</b> to give the product, bromobenzene. This mechanism is shown in Scheme 2 and the critical points are shown in Figure 3.</p> <p align="center"><b>Scheme 1</b></p> <p align="center"><img src="/blog/wp-content/aromSubimg2.gif"></p> <table align="center" border="0" cellspacing="0" cellpadding="4"> <tr align="center"> <td> <p></p> <div class="jmol" id="aromSubTS3"> <a onclick="return false"><br> <img src="/blog/wp-content/aromSubTS3.jpg" onclick="insertJmol('aromSubTS3',225,225,'aromSubTS3.xyz')"><br> </a> </div> <p><b>TS3</b></p> </td> <td> <p></p> <div class="jmol" id="aromSubP3"> <a onclick="return false"><br> <img src="/blog/wp-content/aromSubP3.jpg" onclick="insertJmol('aromSubP3',225,225,'aromSubP3.xyz')"><br> </a> </div> <p><b>P3</b></p> </td> </tr> <tr align="center"> <td> <p></p> <div class="jmol" id="aromSubTS6"> <a onclick="return false"><br> <img src="/blog/wp-content/aromSubTS6.jpg" onclick="insertJmol('aromSubTS6',225,225,'aromSubTS6.xyz')"><br> </a> </div> <p><b>TS6</b></p> </td> <td> <p></p> <div class="jmol" id="aromSubP5"> <a onclick="return false"><br> <img src="/blog/wp-content/aromSubP5.jpg" onclick="insertJmol('aromSubP5',225,225,'aromSubP5.xyz')"><br> </a> </div> <p><b>P5</b></p> </td> </tr> <tr align="center"> <td> <p></p> <div class="jmol" id="aromSubTS9"> <a onclick="return false"><br> <img src="/blog/wp-content/aromSubTS9.jpg" onclick="insertJmol('aromSubTS9',225,225,'aromSubTS9.xyz')"><br> </a> </div> <p><b>TS9</b></p> </td> <td> <p> </p> </td> </tr> </table> <p align="center"><b>Figure 2</b>. PCM/B3LYP/6-311+G(2d,2p) optimized critical points along the addition-elimination pathway</p> <p>The barrier for the concerted substitution process through <b>TS1 </b>is 41.8 kcal mol<sup>-1</sup> (in CCl<sub>4</sub>) while the highest barrier for the addition-elimination process is through <b>TS3</b> of 39.4 kcal mol<sup>-1</sup>.</p> <p>Now a bit of saving grace is that in polar solvents, acidic solvents and/or with Lewis acid catalysts, the intermediate of the standard textbook mechanism may be competitive. </p> <p>Textbook authors – please be aware!</p> <h3>References</h3> <p><a name="AromSub"></a></p> <p>(1) Kong, J.; Galabov, B.; Koleva, G.; Zou, J.-J.; Schaefer, H. F.; Schleyer, P. v. R., "The Inherent Competition between Addition and Substitution Reactions of Br<sub>2</sub> with Benzene and Arenes," <i>Angew. Chem. Int. Ed.</i> <b>2011</b>, <i>50</i>, 6809-6813, DOI: <a href="http://dx.doi.org/10.1002/anie.201101852">10.1002/anie.201101852</a></p>  </div> <p class="bottom"> <span class="cat"><a href="/blog/archives/category/reactions/electrophilic-aromatic-substitution" rel="category tag">electrophilic aromatic substitution</a> &<a href="/blog/archives/category/authors/schaefer" rel="category tag">Schaefer</a> &<a href="/blog/archives/category/authors/schleyer" rel="category tag">Schleyer</a></span> <span class="user">Steven Bachrach</span> <span class="date">27 Sep 2011</span> <span class="comments"><a href="/blog/archives/1757#comments">4 Comments</a></span> </p> </div> <div class="box"> <h2><a href="/blog/archives/1726" rel="bookmark" title="Permanent Link: Structure of 1-Methyl-Piperidone">Structure of 1-Methyl-Piperidone</a></h2> <div class="post-content"> <p>The combined supersonic jet expansion and Fourier transform microwave spectroscopy provides an excellent opportunity for the synergistic workings of experiments and computations. This is nicely demonstrated in the study of 1-methyl-4-piperidone.<a href="#piperidone1"><sup>1</sup></a></p> <p align="center"><img src="/blog/wp-content/mePiperidone.gif"></p> <p>The careful microwave study allows for the full structural characterization of the equatorial form <b>1e</b> along with obtaining a good deal of information concerning the axial form <b>1a</b>. To help evaluate the experimental data, the authors have optimized the structure of the two isomers at MP2, B3LYP and M06-2x using the 6-311++G(d,p) basis set.</p> <p>The rotational parameters computed with the three methods are in very fine agreement with the experimental values. Of particular note is that the three computations predict a different sign for the nuclear quadrupole coupling tensor elements χ<sub>aa</sub> and χ<sub>bb</sub>, and this is observed in the experiment as well. It is perhaps the critical identifier of the axial isomer. The computed and experimental geometries of <b>1e</b> are in fine agreement, with the largest deviation of a few degrees in the dihedral angle of the carbonyl to the ring. The experiment suggests an energy difference of 11.9 kJ mol<sup>-1</sup>, which is corroborated by MP2, B3LYP and M06-2x computations. In fact, these first two methods predict an enthalpy difference within a kJ of the experimental value.</p> <h3>References</h3> <p><a name="piperidone1"></a></p> <p>(1) Evangelisti, L.; Lesarri, A.; Jahn, M. K.; Cocinero, E. J.; Caminati, W.; Grabow, J.-U., "N-Methyl Inversion and Structure of Six-Membered Heterocyclic Rings: Rotational Spectrum of 1-Methyl-4-piperidone," <i>J. Phys. Chem. A</i>, <b>2011</b>,<br> <i>115</i>, 9545–9551, DOI: <a href="http://dx.doi.org/10.1021/jp112425w">10.1021/jp112425w</a></p> <h3>InChIs</h3> <p><b>1</b>: InChI=1/C6H11NO/c1-7-4-2-6(8)3-5-7/h2-5H2,1H3<br>InChIKey=HUUPVABNAQUEJW-UHFFFAOYAT</p>  </div> <p class="bottom"> <span class="cat"><a href="/blog/archives/category/uncategorized" rel="category tag">Uncategorized</a></span> <span class="user">Steven Bachrach</span> <span class="date">20 Sep 2011</span> <span class="comments"><a href="/blog/archives/1726#respond">No Comments</a></span> </p> </div> <div class="box"> <h2><a href="/blog/archives/1819" rel="bookmark" title="Permanent Link: Fantastic host-guest complex">Fantastic host-guest complex</a></h2> <div class="post-content"> <p>Check out this an incredibly cool host guest complex: the [10]-cycloparaphenylene ([10]CPP) hoop encapsulating C<sub>60</sub>!<a href="#10cppc60"><sup>1</sup></a></p> <p align="center"> </p> <div align="center" class="jmol" id="10cppc60"> <a onclick="return false"><br> <img src="/blog/wp-content/10cppc60.jpg" onclick="insertJmol('10cppc60',340,340,'10cppc60.xyz')"><br> </a> </div> <p>(Be sure to click on this image to bring up the 3-D interactive structure – as with all structures in my blog!)</p> <p><sup>1</sup>H and <sup>13</sup>C NMR and fluorescence quenching spectrometry clearly indicate that this complex is formed when [10]CPP is mixed with C<sub>60</sub> in toluene. In fact, when C<sub>60</sub> is mixed with a mixture of nanohoops ranging from 8 to 12 phenyl ring, only the [10]CPP hoop complexes with the fullerene. The experimental binding energy is between 38 and 59 kJ mol<sup>-1</sup>.</p> <p>M06-2x/6-31G* computations give the structure shown above. The computed binding energy is 173 kJ mol<sup>-1</sup>, but the computations do not include solvent. So this overestimation might be somewhat due to the difference in gas phase vs. solution complexation.</p> <p>(Check out <a href="/blog/archives/1561">this post for other interesting nanohoops</a>.)</p> <h3>References</h3> <p><a name="10cppc60"></a></p> <p>(1) Iwamoto, T.; Watanabe, Y.; Sadahiro, T.; Haino, T.; Yamago, S., "Size-Selective Encapsulation of C<sub>60</sub> by [10]Cycloparaphenylene: Formation of the Shortest Fullerene-Peapod," <i>Angew. Chem. Int. Ed.</i>, <b>2011</b>, <i>50</i>, 8342-8344, DOI: <a href="http://dx.doi.org/10.1002/anie.201102302">10.1002/anie.201102302</a></p>  </div> <p class="bottom"> <span class="cat"><a href="/blog/archives/category/molecules/nanohoops" rel="category tag">nanohoops</a></span> <span class="user">Steven Bachrach</span> <span class="date">13 Sep 2011</span> <span class="comments"><a href="/blog/archives/1819#comments">3 Comments</a></span> </p> </div> <div class="box"> <h2><a href="/blog/archives/1709" rel="bookmark" title="Permanent Link: <i>trans</i>-Cyclooctene as a Click Alternative"><i>trans</i>-Cyclooctene as a Click Alternative</a></h2> <div class="post-content"> <p>The click reaction, the copper-assisted cycloaddition of an azide with an alkyne, has been extended to biological systems by use of a strained alkyne (cyclooctyne) thereby eliminating the need of the toxic copper agent.<a href="#tCyoctR1"><sup>1</sup></a> Fox has extended this analogy with the reaction of strained <i>trans</i>-cyclooctene <b>1</b> with tetrazine <b>2</b>.<a href="#tCyoctR2"><sup>2</sup></a></p> <p align="center"><img src="/blog/wp-content/tCyoctImg1.gif"></p> <p>The interesting new twist here is to add more strain to <i>trans</i>-cyclooctene to perhaps make the cycloaddition even faster. Bach<a href="#tCyoctR3"><sup>3</sup></a> had pointed out that the half chair conformation of <b>1</b> is almost 6 kcal mol<sup>-1</sup> higher in energy than the ground state (Figure 1). Fox suggests that fusing a cyclopropyl ring to the eight-member ring would create a ring in the half chair <b>3</b>. Since <b>3</b> would be even more strained than <b>1</b>, it should undergo a faster cycloaddition reaction.</p> <table align="center" border="0" cellspacing="0" cellpadding="4"> <tr align="center"> <td> <p></p> <div class="jmol" id="tCyoct1"> <a onclick="return false"><br> <img src="/blog/wp-content/tCyoct1.jpg" onclick="insertJmol('tCyoct1',300,300,'tCyoct1.xyz')"><br> </a> </div> <p><b>1</b></p> </td> <td> <p></p> <div class="jmol" id="tCyoct1b"> <a onclick="return false"><br> <img src="/blog/wp-content/tCyoct1b.jpg" onclick="insertJmol('tCyoct1b',300,300,'tCyoct1b.xyz')"><br> </a> </div> <p><b>1 (half chair)</b></p> </td> </tr> <tr align="center"> <td colspan="2"> <p></p> <div class="jmol" id="tCyoct3"> <a onclick="return false"><br> <img src="/blog/wp-content/tCyoct3.jpg" onclick="insertJmol('tCyoct3',300,300,'tCyoct3.xyz')"><br> </a> </div> <p><b>3</b></p> </td> </tr> </table> <p><align><b>Figure 1</b>. M06L/6-311+G(d,p) optimized structures of <b>1</b> and <b>3</b>.</align></p> <p>Though Fox did not estimate the strain of <b>3</b>, I have computed the structure of <b>1</b> constrained to the geometry of <b>3</b>, with the two hydrogens that replace the bonds to the cyclopropyl carbon allowed to optimize. This restricted geometry is in fact 6.1 kcal mol<sup>-1</sup> (M06L/6-311+G(d,p)) higher in energy than <b>1</b> – so the fusion of the 3-member ring does net the strain increase expected by Bach.</p> <p>Fox reports estimates of the free energy of activation (at M06L/6-311+G(d,p)) for the reaction of <b>1</b>or <b>3</b> with <b>2</b>. The barrier for the raction with <i>trans</i>-cyclooctene <b>1</b> is 8.92 kcal mol<sup>-1</sup>, while the barrier for the reaction with <b>3</b> is 6.95 kcal mol<sup>-1</sup>. A methylenehydroxyl derivative of <b>3</b> was synthesized and it does react 180 times faster than the reaction with <b>1</b>. Furthermore, the differences in the experimental free energies of activation is 3.0 kcal mol<sup>-1</sup>, in excellent agreement with the computed difference.</p> <h3>References</h3> <p><a name="tCyoctR1"></a></p> <p>(1) Agard, N. J.; Prescher, J. A.; Bertozzi, C. R., "A Strain-Promoted [3 + 2] Azide-Alkyne Cycloaddition for Covalent Modification of Biomolecules in Living Systems," <i>J. Am. Chem. Soc.</i>, <b>2004</b>, <i>126</i>, 15046-15047, DOI: <a href="http://dx.doi.org/10.1021/ja044996f">10.1021/ja044996f</a></p> <p><a name="tCyoctR2"></a></p> <p>(2) Taylor, M. T.; Blackman, M. L.; Dmitrenko, O.; Fox, J. M., "Design and Synthesis of Highly Reactive Dienophiles for the Tetrazine-<i>trans</i>-Cyclooctene Ligation," <i>J. Am. Chem. Soc.</i>, <b>2011</b>, <i>133</i>, 9646-9649, DOI: <a href="http://dx.doi.org/10.1021/ja201844c">10.1021/ja201844c</a></p> <p><a name="tCyoctR3"></a></p> <p>(3) Bach, R. D., "Ring Strain Energy in the Cyclooctyl System. The Effect of Strain Energy on [3 + 2] Cycloaddition Reactions with Azides," <i>J. Am. Chem. Soc.</i>, <b>2009</b>, <i>131</i>, 5233-5243, DOI: <a href="http://dx.doi.org/10.1021/ja8094137">10.1021/ja8094137</a></p> <h3>InChIs</h3> <p><b>1</b>: InChI=1/C8H14/c1-2-4-6-8-7-5-3-1/h1-2HInChIKey </p> <p><b>2</b>: InChI=1/C12H8N6/c1-3-7-13-9(5-1)11-15-17-12(18-16-11)10-6-2-4-8-14-10/h1-8H<br>InChIKey=JFBIRMIEJBPDTQ-UHFFFAOYAE</p> <p><b>3</b>: InChI=1/C9H14/c1-2-4-6-9-7-8(9)5-3-1/h1-2,8-9H,3-7H2/b2-1+/t8-,9+<br>InChIKey=YWIJRSGCJZLJNV-YLSDFIPEBO</p>  </div> <p class="bottom"> <span class="cat"><a href="/blog/archives/category/reactions/cycloadditions" rel="category tag">cycloadditions</a></span> <span class="user">Steven Bachrach</span> <span class="date">07 Sep 2011</span> <span class="comments"><a href="/blog/archives/1709#respond">No 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 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class="cat-item cat-item-39"> <a href="/blog/archives/category/molecules/diradicals">diradicals</a> (8) </li> <li class="cat-item cat-item-59"> <a href="/blog/archives/category/molecules/ephedrine">ephedrine</a> (1) </li> <li class="cat-item cat-item-37"> <a href="/blog/archives/category/molecules/ethyl-cation">ethyl cation</a> (2) </li> <li class="cat-item cat-item-90"> <a href="/blog/archives/category/molecules/fullerene">fullerene</a> (6) </li> <li class="cat-item cat-item-51"> <a href="/blog/archives/category/molecules/fulvalenes">fulvalenes</a> (1) </li> <li class="cat-item cat-item-21"> <a href="/blog/archives/category/molecules/hexacyclinol">hexacyclinol</a> (2) </li> <li class="cat-item cat-item-78"> <a href="/blog/archives/category/molecules/nanohoops">nanohoops</a> (4) </li> <li class="cat-item cat-item-41"> <a href="/blog/archives/category/molecules/non-classical">non-classical</a> (4) </li> <li class="cat-item cat-item-34"> <a href="/blog/archives/category/molecules/norbornyl-cation">norbornyl cation</a> (2) </li> <li class="cat-item cat-item-49"> <a href="/blog/archives/category/molecules/nucleic-acids">nucleic acids</a> (4) </li> <li class="cat-item cat-item-36"> <a href="/blog/archives/category/molecules/oximes">oximes</a> (1) </li> <li class="cat-item cat-item-75"> <a href="/blog/archives/category/molecules/phenyloxenium">phenyloxenium</a> (1) </li> <li class="cat-item cat-item-8"> <a href="/blog/archives/category/molecules/polycyclic-aromatics">polycyclic aromatics</a> (7) </li> <li class="cat-item cat-item-50"> <a href="/blog/archives/category/molecules/propellane">propellane</a> (2) </li> <li class="cat-item cat-item-79"> <a href="/blog/archives/category/molecules/stilbene">stilbene</a> (1) </li> <li class="cat-item cat-item-80"> <a href="/blog/archives/category/molecules/sugars">sugars</a> (5) </li> <li class="cat-item cat-item-85"> <a href="/blog/archives/category/molecules/terpenes">terpenes</a> (2) </li> <li class="cat-item cat-item-89"> <a href="/blog/archives/category/molecules/twistane">twistane</a> (1) </li> </ul> </li> <li class="cat-item cat-item-22"> <a href="/blog/archives/category/nmr">NMR</a> (40) </li> <li class="cat-item cat-item-31"> <a href="/blog/archives/category/optical-rotation">Optical Rotation</a> (16) </li> <li class="cat-item cat-item-28"> <a href="/blog/archives/category/qm-method">QM Method</a> (96) <ul class="children"> <li class="cat-item cat-item-20"> <a href="/blog/archives/category/qm-method/caspt2">CASPT2</a> (1) </li> <li class="cat-item cat-item-7"> <a href="/blog/archives/category/qm-method/dft">DFT</a> (71) </li> <li class="cat-item cat-item-45"> <a 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" aria-current="page">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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