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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 » 2010 » April</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 April, 2010</h2> <div class="box"> <h2><a href="/blog/archives/835" rel="bookmark" title="Permanent Link: More dynamic effects in Diels-Alder reactions">More dynamic effects in Diels-Alder reactions</a></h2> <div class="post-content"> <p>Dynamic effects rear up yet again in a seemingly simple reaction. Singleton has examined the Diels-Alder cycloaddition of acrolein with methyl vinyl ketone to give two cross products <b>1</b> and <b>2</b>.<a href="#singleton2"><sup>1</sup></a> Upon heating the product mixture, <b>1</b> is essentially the only observed species. The retro-Diels-Alder is much slower than the conversion of <b>2</b> into <b>1</b>. Using a variety of rate data, the best estimate for the relative formation of <b>1:2</b> is 2.5.</p> <p align="center"><img src="/blog/wp-content/singleton2fig1.gif"></p> <p>The eight possible transition states for this reaction were computed with a variety of methodologies, all providing very similar results. The lowest energy TS is <b>TS3</b>. A TS of type <b>TS4</b> could not be found; all attempts to optimize it collapsed to <b>TS3</b>.</p> <p align="center"><img src="/blog/wp-content/singleton2fig2.gif"></p> <p> IRC computations indicate the <b>TS3</b> leads to <b>1</b>. The lowest energy TS that leads to <b>2</b> is <b>TS6</b>, but a second TS (<b>TS5</b>) lower in energy than <b>TS6</b> also leads to <b>1</b>. The other TS are still higher in energy. A Cope-type TS that interconverts <b>1</b> and <b>2</b> (<b>TS7</b>) was also located. The geometries of these TSs are shown in Figure 1.</p> <table align="center" border="0" cellspacing="0" cellpadding="3"> <tr align="center" valign="bottom"> <td> <p></p> <div class="jmol" id="singleton2TS3"> <a onclick="return false"><br> <img src="/blog/wp-content/singleton2TS3.jpg" onclick="insertJmol('singleton2TS3',200,200,'singleton2TS3.xyz')"><br> </a> </div> <p><b>TS3</b><br>(0.0)</p> </td> <td> <p></p> <div class="jmol" id="singleton2TS5"> <a onclick="return false"><br> <img src="/blog/wp-content/singleton2TS5.jpg" onclick="insertJmol('singleton2TS5',200,200,'singleton2TS5.xyz')"><br> </a> </div> <p><b>TS5</b><br>(4.2)</p> </td> </tr> <tr align="center" valign="bottom"> <td> <p></p> <div class="jmol" id="singleton2TS6"> <a onclick="return false"><br> <img src="/blog/wp-content/singleton2TS6.jpg" onclick="insertJmol('singleton2TS6',200,200,'singleton2TS6.xyz')"><br> </a> </div> <p><b>TS6</b><br>(5.2)</p> </td> <td> <p></p> <div class="jmol" id="singleton2TS7"> <a onclick="return false"><br> <img src="/blog/wp-content/singleton2TS7.jpg" onclick="insertJmol('singleton2TS7',200,200,'singleton2TS7.xyz')"><br> </a> </div> <p><b>TS7</b><br>(-0.4)</p> </td> </tr> </table> <p align="center"><b>Figure 1</b>. MP2/6-311+G** optimized geometries and relative energies (kcal mol<sup>-1</sup>) of <b>TS3-TS7</b>.<a href="#singleton2"><sup>1</sup></a></p> <p>Ordinary transition state theory cannot explain the experimental results – the energy difference between the lowest barrier to <b>1</b> (<b>TS3</b>) and to <b>2</b> (<b>TS6</b>) suggests a rate preference of over 700:1 for <b>1:2</b>. But the shape of the potential energy surface is reminiscent of others that have been discussed in both my book (Chapter 7) and this blog (see my posts on <a href="/blog/archives/category/dynamics">dynamics</a>) – a surface where trajectories cross a single TS but then bifurcate into two product wells.</p> <p>To address the chemical selectivity on a surface like this, one must resort to molecular dynamics and examine trajectories. In their MD study of the 296 trajectories that begin at <b>TS3</b> with motion towards product, 89 end at <b>1</b> and 33 end at <b>2</b>, an amazingly good reproduction of experimental results! Interestingly, 174 trajectories recross the transition state and head back towards reactants. These recrossing trajectories result from “bouncing off” the potential energy wall of the forming C<sub>4</sub>-C<sub>5</sub> bond.</p> <p>In previous work, selectivity in on these types of surfaces was argued in terms of which well the TS was closer to. But analysis of the trajectories in this case revealed that a strong correlation exists between the initial direction and velocity in the 98 cm<sup>-1</sup> vibration – the vibration that corresponds to the closing of the second σ bond, the one between C<sub>6</sub>-O<sub>1</sub> (forming <b>1</b>), in the negative direction, and closing the C<sub>3</sub>-O<sub>8</sub> bond (forming <b>2</b>) in the positive direction. Singleton argues that this is a type of dynamic matching, and it might be more prevalent that previously recognized.</p> <h3>References</h3> <p><a name="singleton2"></a></p> <p>(1) Wang, Z.; Hirschi, J. S.; Singleton, D. A., "Recrossing and Dynamic Matching Effects on Selectivity in a Diels-Alder Reaction," <i>Angew. Chem. Int. Ed.</i>, <b>2009</b>, <i>48</i>, 9156-9159, DOI: <a href="http://dx.doi.org/10.1002/anie.200903293">10.1002/anie.200903293</a></p> <h3>InChIs</h3> <p><b>1</b>: InChI=1/C7H10O2/c1-6(8)7-4-2-3-5-9-7/h3,5,7H,2,4H2,1H3<br>InChIKey=AOFHZPHBPUYLAG-UHFFFAOYAJ</p> <p><b>2</b>: InChI=1/C7H10O2/c1-6-3-2-4-7(5-8)9-6/h3,5,7H,2,4H2,1H3<br>InChIKey=PLZQHPPETMMEED-UHFFFAOYAD</p>  </div> <p class="bottom"> <span class="cat"><a href="/blog/archives/category/reactions/diels-alder" rel="category tag">Diels-Alder</a> &<a href="/blog/archives/category/dynamics" rel="category tag">Dynamics</a> &<a href="/blog/archives/category/authors/singleton" rel="category tag">Singleton</a></span> <span class="user">Steven Bachrach</span> <span class="date">27 Apr 2010</span> <span class="comments"><a href="/blog/archives/835#respond">No Comments</a></span> </p> </div> <div class="box"> <h2><a href="/blog/archives/830" rel="bookmark" title="Permanent Link: Dynamics in 1,3-dipolar cycloadditions (2)">Dynamics in 1,3-dipolar cycloadditions (2)</a></h2> <div class="post-content"> <p>Houk and Doubleday have a nice follow-up study<a href="#doubleday2r1"><sup>1</sup></a> to their previous MD study<a href="#doubleday2r2"><sup>2</sup></a> of 1,3-dipolar cycloadditions, which I posted on <a href="/blog/archives/154">here</a>. They report on the cycloaddition of either acetylene or ethylene to 9 different 1,3-dipoles. Continuing on Houk’s recent thread of looking at distortion energies to attain the TS, they note that a sizable fraction (often over 50%) of the distortion energy is associated with bending the X-Y-Z bond of the dipole, consistent with their earlier work suggesting the importance of this vibration in attaining and crossing the TS. What’s new in this paper is the extensive MD studies, with trajectory studies of all 18 reactions. These revealed again the importance of vibrational energy in this X-Y-Z bending mode in crossing the TS. They also noted the role of translational energy, and the relationship between translational vs. vibrational energy depending on the early/late nature of the TS. Their final point was that the lifetime of any diradical or diradical-like intermediate is so short, less than the time of a bond vibration, so that one can discount any diradical participation. The reaction is concerted.</p> <h3>References</h3> <p><a name="doubleday2r1"></a></p> <p>(1) Xu, L.; Doubleday, C. E.; Houk, K. N., "Dynamics of 1,3-Dipolar Cycloadditions: Energy Partitioning of Reactants and Quantitation of Synchronicity," <i>J. Am. Chem. Soc.</i>, <b>2010</b>, ASAP, DOI: <a href="http://dx.doi.org/10.1021/ja909372f">/10.1021/ja909372f</a></p> <p><a name="doubleday2r2"></a></p> <p>(2) Xu, L.; Doubleday, C. E.; Houk, K. N., "Dynamics of 1,3-Dipolar Cycloaddition Reactions of Diazonium Betaines to Acetylene and Ethylene: Bending Vibrations Facilitate Reaction," <i>Angew. Chem. Int. Ed.</i>, <b>2009</b>, <i>48</i>, 2746-2748, DOI: <a href="http://dx.doi.org/10.1002/anie.200805906">10.1002/anie.200805906</a></p>  </div> <p class="bottom"> <span class="cat"><a href="/blog/archives/category/dynamics" rel="category tag">Dynamics</a> &<a href="/blog/archives/category/authors/houk" rel="category tag">Houk</a></span> <span class="user">Steven Bachrach</span> <span class="date">21 Apr 2010</span> <span class="comments"><a href="/blog/archives/830#comments">1 Comment</a></span> </p> </div> <div class="box"> <h2><a href="/blog/archives/821" rel="bookmark" title="Permanent Link: Protobranching once again!">Protobranching once again!</a></h2> <div class="post-content"> <p>An interesting little discussion on the meaning of “protobranching” appears in a comment<a href="#protoDebate1"><sup>1</sup></a> and reply<a href="#protoDebate2"><sup>2</sup></a> in <i>J. Phys. Chem. A</i>. Fishtik<a href="#protoDebate1"><sup>1</sup></a> calls out the concept of protobranching on three counts:</p> <ol> <li>It is inconsistent to count a single protobranch for propane, but then not have three protobranches in cyclopropane</li> <li>It is inappropriate to utilize methane as a reference species.</li> <li>Group additivities work well.</li> </ol> <p>I tend to side more with Schleyer<a href="#protoDebate2"><sup>2</sup></a> in his rebuttal of these charges, and so will present from this perspective. First off, Schleyer argues that he can define protobranch anyway he wants! (He in fact cites a quote of Humpty Dumpty from Lewis Carroll to support this stance!) Schleyer is of course correct. Fishtik should really have argued “Does Schleyer’s definition of protobranch add to our understanding of strain?” So Fishtik claims that there is an internal inconsistency in Schleyer’s definition – taking the view point that the C-(C)<sub>2</sub>(H)<sub>2</sub> group is identical to the protobranch. Schleyer counters that no, the protobranch is this group <i>along</i> with the caveat that the two terminal carbons are not connected, like they are in cyclopropane. I really prefer Gronert’s approach here – where he argues for just what are the implications of Schleyer’s definition (see this <a href="/blog/archives/143">post</a>).</p> <p>Fishtik refuses to use methane as a reference since it is a unique molecule. Again, if one takes the group-centric view, then methane possesses a group that no other compound has. But Schleyer counters that one is free to choose whatever reference one thinks is appropriate, just be sure to understand what properties are conserved or not conserved when using that reference selection. To me, this is really the key for the entire discussion: choose one’s references in such a way as to minimize differences between your reference compound(s) and the molecule(s) you are trying to explore to just the property of interest. So, if one is interested in quantifying ring strain, the reference compounds should be not only be strain-free but they should differ in <i>no other way</i> from the cyclic molecule other than the presence of the ring! Unfortunately, there is no <i>unique or non-arbitrary way to do this!</i> Schleyer’s approach and Fishtik’s approach differ in just what properties they believe are important to conserve and which properties they are going to lump into the concept “ring strain”.</p> <p>Fishtik shows a whole slew of reactions that demonstrate the consistency of group additivity methods. Schleyer correctly points out that these examples are really intimately related and represent only one type of definition. Again, there is really no <i>unique</i> set of references, and many, many different models have been developed, all of which can match experimental data quite well – like for example heats of formation. The key is what these models say in terms of interpreting, say, these heats of formation. Can one rationalize trends and make predictions with the model? If so, then it has utility. If not, then the model should be discarded. Ultimately, Fishtik’s argument is that the protobranching model does not assist us in understanding strain – Schleyer would obviously beg to differ!</p> <h3>References</h3> <p><a name="protoDebate1"></a></p> <p>(1) Fishtik, I., "Comment on "The Concept of Protobranching and Its Many Paradigm Shifting Implications for Energy Evaluations"," <i>J. Phys. Chem. A</i>, <b>2010</b>, ASAP, DOI: <a href="http://dx.doi.org/10.1021/jp908894q">10.1021/jp908894q</a></p> <p><a name="protoDebate2"></a></p> <p>(2) Schleyer, P. v. R.; McKee, W. C., "Reply to the "Comment on ‘The Concept of Protobranching and Its Many Paradigm Shifting Implications for Energy Evaluations’"," <i>J. Phys. Chem. A</i>, <b>2010</b>, ASAP, DOI: <a href="http://dx.doi.org/10.1021/jp909910f">10.1021/jp909910f</a></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">13 Apr 2010</span> <span class="comments"><a href="/blog/archives/821#comments">3 Comments</a></span> </p> </div> <div class="box"> <h2><a href="/blog/archives/707" rel="bookmark" title="Permanent Link: Cycloadditions of cyclodienes with ketenes">Cycloadditions of cyclodienes with ketenes</a></h2> <div class="post-content"> <p>One more study of cyclodiene reactions with ketenes that suggest the occurrence of dynamic effects.<a href="#MartanR1"><sup>1</sup></a> The reaction of cyclopentadiene with <i>t</i>-butylcyanoketene <b>1</b> gives cyclobutanone <b>2</b> solely. In contrast, the reaction of 1,3-cyclophexadiene with <b>1</b> gives the cyclobutanone <b>3</b> and a small amount (less than 25%) of the ether <b>4</b>. Warming the reaction from -20 °C to 20 °C leads to loss of <b>3</b> and an increase in <b>4</b>. This is in distinct contrast with the reaction of cyclopentadiene with diphenylketene,<a href="#MartanR2"><sup>2</sup></a> where the ether product is the major product and the cyclobutenone is the minor product (see Chapter 7.3.5.2 in my book).</p> <p align="center"><img src="/blog/wp-content/Martan1.gif"></p> <p>To help understand this situation, the authors optimized the structures of the critical points on the surface of the cyclohexadiene reaction at MPWB1K/6-31+G(d,p) – though once again, there are no supporting materials so I cannot supply the 3-D structures in the blog! <b>4</b> is predicted to be 3.4 kcal mol<sup>-1</sup> more stable than <b>3</b>, which accounts for it being the thermodynamic product, consistent with experiment. Only two transition states are found. The first TS, with a barrier of 23.2 kcal mol<sup>-1</sup>, connects reactants with <b>3</b>. The second transition state corresponds to the oxy-Cope rearrangement that takes <b>3</b> into <b>4</b>. This surface is reminiscent of many others that display dynamic effects (again see my book and also these <a href="/blog/archives/category/dynamics">posts</a>). Unfortunately, the authors have not performed any trajectory calculation. But one might expect that most trajectories cross the first transition state and fall into the well associated with <b>3</b>. Some of these molecules then go on to cross the second barrier to form <b>4</b>. But some trajectories cross the first TS and then veer off into the slightly lower well associated with <b>4</b>, being directly formed from reactant. This would be a manifestation of dynamic effects, and is worth further study.</p> <h3>References</h3> <p><a name="MartanR1"></a></p> <p>(1) Marton, A.; Pârvulescu, L.; Draghici, C.; Varga, R. A.; Gheorghiu, M. D., "Reaction of Moore’s ketene (tert-butylcyanoketene) with 1,3-cyclopentadiene and 1,3-cyclohexadiene. Is periselectivity controlled by the dynamic of trajectories at the bifurcation point?," <i>Tetrahedron</i>, <b>2009</b>, <i>65</i>, 7504-7509, DOI: <a href="http://dx.doi.org/10.1016/j.tet.2009.07.020">10.1016/j.tet.2009.07.020</a>.</p> <p><a name="MartanR2"></a></p> <p>(2) Ussing, B. R.; Hang, C.; Singleton, D. A., "Dynamic Effects on the Periselectivity, Rate, Isotope Effects, and Mechanism of Cycloadditions of Ketenes with Cyclopentadiene," <i>J. Am. Chem. Soc.</i>, <b>2006</b>, <i>128</i>, 7594-7607, DOI: <a href="http://dx.doi.org/10.1021/ja0606024">10.1021/ja0606024</a>.</p>  </div> <p class="bottom"> <span class="cat"><a href="/blog/archives/category/dynamics" rel="category tag">Dynamics</a></span> <span class="user">Steven Bachrach</span> <span class="date">06 Apr 2010</span> <span class="comments"><a href="/blog/archives/707#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 cat-item-3"> <a href="/blog/archives/category/aromaticity">Aromaticity</a> (91) </li> <li class="cat-item cat-item-53"> <a href="/blog/archives/category/authors">Authors</a> (153) <ul class="children"> <li class="cat-item cat-item-42"> <a href="/blog/archives/category/authors/borden">Borden</a> (12) </li> <li class="cat-item cat-item-12"> <a 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</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">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" aria-current="page">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> </div>  <div id="footer"> <p>Copyright © 2021 <strong>Computational Organic Chemistry</strong>. </p> </div> </body> </html>