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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 » 2016 » February</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 February, 2016</h2> <div class="box"> <h2><a href="/blog/archives/3714" rel="bookmark" title="Permanent Link: Calculating large fullerenes">Calculating large fullerenes</a></h2> <div class="post-content"> <p>What is the size of a molecule that will stretch computational resources today? Chan and co-workers have examined some very large fullerenes<a href="#bigFull1"><sup>1</sup></a> to both answer that question, and also to explore how large a fullerene must be to approach graphene-like properties.</p> <p>They are interested in predicting the heat of formation of large fullerenes. So, they benchmark the heats of formation of C<sub>60</sub> using four different isodesmic reactions (Reaction 1-4), comparing the energies obtained using a variety of different methods and basis sets to those obtained at W1h. The methods include traditional functionals like B3LYP, B3PW91, CAM-B3LYP, PBE1PBE, TPSSh, B98, ωB97X, M06-2X3, and MN12-SX, and supplement them with the D3 dispersion correction. Additionally a number of doubly hybrid methods are tested (again with and without dispersion corrections), such as B2-PLYP, B2GPPLYP, B2K-PLYP, PWP-B95, DSD-PBEPBE, and DSD-B-P86. The cc-pVTZ and cc-pVQZ basis sets were used. Geometries were optimized at B3LYP/6-31G(2df,p).</p> <table align="center" border="0" cellspacing="2" cellpadding="3"> <tr align="center"> <td> <p>C<sub>60</sub> + 10 benzene → 6 corannulene</p> </td> <td> <p>Reaction 1</p> </td> </tr> <tr align="center"> <td> <p>C<sub>60</sub> + 10 naphthalene → 8 corannulene</p> </td> <td> <p>Reaction 2</p> </td> </tr> <tr align="center"> <td> <p>C<sub>60</sub> + 10 phenanthrene → 10 corannulene</p> </td> <td> <p>Reaction 3</p> </td> </tr> <tr align="center"> <td> <p>C<sub>60</sub> + 10 triphenylene → 12 corannulene</p> </td> <td> <p>Reaction 4</p> </td> </tr> </table> <p>Excellent results were obtained with DSD-PBEPBE-D3/cc-pVQZ (an error of only 1.8 kJ/mol), though even a method like BMK-D3/cc-pVTZ had an error of only 9.2 kJ/mol. They next set out to examine large fullerenes, including such behemoths as C<sub>180</sub>, C<sub>240</sub>, and C<sub>320</sub>, whose geometries are shown in Figure 1. Heats of formation were obtained using isodesmic reactions that compare back to smaller fullerenes, such as in Reaction 5-8.</p> <table align="center" border="0" cellspacing="2" cellpadding="3"> <tr align="center"> <td> <p>C<sub>70</sub> + 5 styrene → C60 + 5 naphthalene</p> </td> <td> <p>Reaction 5</p> </td> </tr> <tr align="center"> <td> <p>C<sub>180</sub> → 3 C<sub>60</sub></p> </td> <td> <p>Reaction 6</p> </td> </tr> <tr align="center"> <td> <p>C<sub>320</sub> + 2/3 C<sub>60</sub> → 2 C<sub>180</sub></p> </td> <td> <p>Reaction 7</p> </td> </tr> </table> <table align="center" border="0" cellspacing="0" cellpadding="6"> <tr align="center"> <td> <p></p> <div class="jmol" id="c180"> <a onclick="return false"><br> <img src="/blog/wp-content/c180.jpg" onclick="insertJmol('c180',350,350,'c180.xyz')"></a> </div> <p>C<sub>180</sub></p> </td> </tr> <tr align="center"> <td> <p></p> <div class="jmol" id="c240"> <a onclick="return false"><br> <img src="/blog/wp-content/c240.jpg" onclick="insertJmol('c240',350,350,'c240.xyz')"></a> </div> <p>C<sub>240</sub></p> </td> </tr> <tr align="center"> <td> <p></p> <div class="jmol" id="c320"> <a onclick="return false"><br> <img src="/blog/wp-content/c320.jpg" onclick="insertJmol('c320',350,350,'C320.xyz')"></a> </div> <p>C<sub>320</sub></p> </td> </tr> </table> <p align="center"><b>Figure 1</b>. B3LYP/6-31G(2df,p) optimized geometries of C<sub>180</sub>, C<sub>240</sub>, and C<sub>320</sub>. (Don’t forget that clicking on these images will launch <i>Jmol</i> and allow you to manipulate the molecules in real-time.)</p> <p>Next, taking the heat of formation per C for these fullerenes, using a power law relationship, they were able to extrapolate out the heat of formation per C for truly huge fullerenes, and find the truly massive fullerenes, like C<sub>9680</sub>, still have heats of formation per carbon 1 kJ/mol greater than for graphene itself.</p> <h3>References</h3> <p><a href="#bigFull1"></a></p> <p>(1) Chan, B.; Kawashima, Y.; Katouda, M.; Nakajima, T.; Hirao, K. "From C<sub>60</sub> to Infinity: Large-Scale Quantum Chemistry Calculations of the Heats of Formation of Higher Fullerenes," <i>J. Am. Chem. Soc.</i> <b>2016</b>, <i>138</i>, 1420-1429, DOI: <a href="http://dx.doi.org/10.1021/jacs.5b12518">10.1021/jacs.5b12518</a>.</p>  </div> <p class="bottom"> <span class="cat"><a href="/blog/archives/category/molecules/fullerene" rel="category tag">fullerene</a></span> <span class="user">Steven Bachrach</span> <span class="date">22 Feb 2016</span> <span class="comments"><a href="/blog/archives/3714#comments">4 Comments</a></span> </p> </div> <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/3706" rel="bookmark" title="Permanent Link: QM/MM trajectory of an aqueous Diels-Alder reaction">QM/MM trajectory of an aqueous Diels-Alder reaction</a></h2> <div class="post-content"> <p>I discuss the aqueous Diels-Alder reaction in Chapter 7.1 of my book. A key case is the reaction of methyl vinyl ketone with cyclopentadiene, Reaction 1. The reaction is accelerated by a factor of 740 in water over the rate in isooctane.<a href="#waterDA_1"><sup>1</sup></a> Jorgensen argues that this acceleration is due to stronger hydrogen bonding to the ketone than in the transition state than in the reactants.<a href="#waterDA_2"><sup>2-4</sup></a></p> <table align="center" border="0" cellspacing="0" cellpadding="2"> <tr align="center" valign="middle"> <td> <p><img src="/blog/wp-content/waterDAhouk.png"></p> </td> <td> <p>Rxn 1</p> </td> </tr> </table> <p>Doubleday and Houk<a href="#waterDA_5"><sup>5</sup></a> report a procedure for calculating trajectories including explicit water as the solvent and apply it to Reaction 1. Their process is as follows:</p> <ol> <li>Compute the <i>endo</i> TS at M06-2X/6-31G(d) with a continuum solvent.</li> <li>Equilibrate water for 200ps, defined by the TIP3P model, in a periodic box, with the transition state frozen.</li> <li>Continue the equilibration as in Step 2, and save the coordinates of the water molecules after every addition 5 ps, for a total of typically 25 steps.</li> <li>For each of these solvent configurations, perform an ONIOM computation, keeping the waters fixed and finding a new optimum TS. Call these solvent-perturbed transition states (SPTS).</li> <li>Generate about 10 initial conditions using quasiclassical TS mode sampling for each SPTS.</li> <li>Now for each the initial conditions for each of these SPTSs, run the trajectories in the forward and backward directions, typically about 10 of them, using ONIOM to compute energies and gradients.</li> <li>A few SPTS are also selected and water molecules that are either directly hydrogen bonded to the ketone, or one neighbor away are also included in the QM portion of the ONIOM, and trajectories computed for these select sets.</li> </ol> <p>The trajectory computations confirm the role of hydrogen bonding in stabilizing the TS preferentially over the reactants. Additionally, the trajectories show an increasing asynchronous reactions as the number of explicit water molecules are included in the QM part of the calculation. Despite an increasing time gap between the formation of the first and second C-C bonds, the overwhelming majority of the trajectories indicate a concerted reaction.</p> <h3>References</h3> <p><a href="#waterDA_1"></a></p> <p>(1) Breslow, R.; Guo, T. "Diels-Alder reactions in nonaqueous polar solvents. Kinetic<br> effects of chaotropic and antichaotropic agents and of β-cyclodextrin," <i>J. Am. Chem. Soc.</i> <b>1988</b>, <i>110</i>, 5613-5617, DOI: <a href="http://dx.doi.org/10.1021/ja00225a003">10.1021/ja00225a003</a>.</p> <p><a href="#waterDA_2"></a></p> <p>(2) Blake, J. F.; Lim, D.; Jorgensen, W. L. "Enhanced Hydrogen Bonding of Water to Diels-Alder Transition States. Ab Initio Evidence," <i>J. Org. Chem.</i> <b>1994</b>, <i>59</i>, 803-805, DOI: <a href="http://dx.doi.org/10.1021/jo00083a021">10.1021/jo00083a021</a>.</p> <p>(3) Chandrasekhar, J.; Shariffskul, S.; Jorgensen, W. L. "QM/MM Simulations for Diels-Alder<br> Reactions in Water: Contribution of Enhanced Hydrogen Bonding at the Transition State to the Solvent Effect," <i>J. Phys. Chem. B</i> <b>2002</b>, <i>106</i>, 8078-8085, DOI: <a href="http://dx.doi.org/10.1021/jp020326p">10.1021/jp020326p</a>.</p> <p>(4) Acevedo, O.; Jorgensen, W. L. "Understanding Rate Accelerations for Diels−Alder Reactions in Solution Using Enhanced QM/MM Methodology," <i>J. Chem. Theor. Comput.</i> <b>2007</b>, <i>3</i>, 1412-1419, DOI: <a href="http://dx.doi.org/10.1021/ct700078b">10.1021/ct700078b</a>.</p> <p><a href="#waterDA_5"></a></p> <p>(5) Yang, Z.; Doubleday, C.; Houk, K. N. "QM/MM Protocol for Direct Molecular Dynamics of Chemical Reactions in Solution: The Water-Accelerated Diels–Alder Reaction," <i>J. Chem. Theor. Comput.</i> <b>2015</b>, <i11>, 5606-5612, DOI: <a href="http://dx.doi.org/10.1021/acs.jctc.5b01029">10.1021/acs.jctc.5b01029</a>.</i11></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/authors/houk" rel="category tag">Houk</a> &<a href="/blog/archives/category/solvation" rel="category tag">Solvation</a></span> <span class="user">Steven Bachrach</span> <span class="date">02 Feb 2016</span> <span class="comments"><a href="/blog/archives/3706#comments">1 Comment</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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(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" aria-current="page">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> </div>  <div id="footer"> <p>Copyright © 2021 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