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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 » 2009 » October</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 October, 2009</h2> <div class="box"> <h2><a href="/blog/archives/470" rel="bookmark" title="Permanent Link: TD-DFT benchmark study">TD-DFT benchmark study</a></h2> <div class="post-content"> Here’s another extensive benchmarking study – this time on the use of TD-DFT to predict excitation energies.<a href="#TDDFT1">1</a> This study looks at the performance of 28 different functionals, and compares the TD-DFT excitation energies against a data set of (a) computed vertical energies and (b) experimental energies. The performance is generally about the same for both data sets, with many functionals (especially the hybrid functionals) giving errors of about 0.3 eV. Performance can be a bit better when examining subclasses of compounds. For example, PBE0 and mPW1PW91 have a mean unsigned error of only 0.14 eV for a set of organic dyes. <h3>References</h3> (1) Jacquemin, D.; Wathelet, V.; Perpete, E. A.; Adamo, C., "Extensive TD-DFT Benchmark: Singlet-Excited States of Organic Molecules," J. Chem. Theory Comput., 2009, 5, 2420-2435, DOI: <a href="http://dx.doi.org/10.1021/ct900298e">10.1021/ct900298e</a>  </div> <a href="/blog/archives/category/qm-method/dft" rel="category tag">DFT</a> Steven Bachrach 28 Oct 2009 <a href="/blog/archives/470#respond">No Comments</a> </div> <div class="box"> <h2><a href="/blog/archives/441" rel="bookmark" title="Permanent Link: Higher-order Möbius Annulenes">Higher-order Möbius Annulenes</a></h2> <div class="post-content"> An emerging theme in this blog is Möbius systems, ones that can be aromatic or antiaromatic. Rzepa has led the way here, especially in examining <a href="/blog/archives/95">annulenes with a twisted structure</a>. Along with Schleyer and Schaefer, they have now explored a series of Möbius annulenes.<a href="#mobAnnR1">1</a> The particularly novel aspect of this new work is the examination of higher-order Möbius systems. In the commonly held notion of the <a href="http://en.wikipedia.org/wiki/Mobius_strip">Möbius strip</a>, the strip contains a single half twist. Rzepa points out that the notion of twist must be considered as two parts, a part due to torsions and a part due to writhe.<a href="#mobAnnR2">2</a> We can think of the Möbius strip as formed by a ladder where the ends are connect such that the left bottom post connects with the top right post and the bottom right post connects with the top left post. Let’s now consider the circle created by joining the midpoints of each rug of the ladder. If this circle lies in a plane, then the torsion is π/N where N is the number of rungs in the ladder. But, the collection of midpoints does not have to lie in a plane, and if these points distort out of plane, that’s writhe and allows for less torsion in the strip.The sum of these two parts is called Lk and it will be an integral multiple of π. So the common Möbius strip has Lk = 1. An example of a molecular analogue of the common Möbius strip is the annulene C9H9+ (1) – see figure 1. But Möbius strips can have more than one twist. Rzepa, Schleyer, and Schaefer have found examples with Lk = 2, 3, or 4. Examples are C14H14 (2) with one full twist (Lk = 2, two half twists), C16H162- (3) with three half twists, and C20H202+ (4) with four half twists. <table align="center" border="0" cellspacing="0" cellpadding="3"> <tr> <td valign="middle" align="center"> <div class="jmol" id="MobAnn1"> <a onclick="return false"> <img src="/blog/wp-content/MobAnn1.gif" onclick="insertJmol('MobAnn1',200,200,'MobAnn1.xyz')"> </a> </div> 1 </td> <td> <div class="jmol" id="MobAnn2"> <a onclick="return false"> <img src="/blog/wp-content/MobAnn2.gif" onclick="insertJmol('MobAnn2',200,200,'MobAnn2.xyz')"> </a> </div> 2 </td> </tr> <tr> <td valign="middle" align="center"> <div class="jmol" id="MobAnn3"> <a onclick="return false"> <img src="/blog/wp-content/MobAnn3.gif" onclick="insertJmol('MobAnn3',200,200,'MobAnn3.xyz')"> </a> </div> 3 </td> <td valign="middle" align="center"> <div class="jmol" id="MobAnn4"> <a onclick="return false"> <img src="/blog/wp-content/MobAnn4.gif" onclick="insertJmol('MobAnn4',200,200,'MobAnn4.xyz')"> </a> </div> 4 </td> </tr> </table> Figure 1. Structures of annulenes 1-4. These annulenes with higher-order twisting, namely 2-4, are aromatic, as determined by a variety of measures. For example, all express negative NICS values, all have positive diagmagnetic exaltations, and all express positive isomerization stabilization energies (which are a measure of aromatic stabilization energy). <h3>References</h3> <a name="mobAnnR2"></a> (1) Wannere, C. S.; Rzepa, H. S.; Rinderspacher, B. C.; Paul, A.; Allan, C. S. M.; Schaefer Iii, H. F.; Schleyer, P. v. R., "The Geometry and Electronic Topology of Higher-Order Charged M&oml;bius Annulenes" J. Phys. Chem. A 2009, ASAP, DOI: <a href="http://dx.doi.org/10.1021/jp902176a">10.1021/jp902176a</a> (2) Fowler, P. W.; Rzepa, H. S., "Aromaticity rules for cycles with arbitrary numbers of half-twists," Phys. Chem. Chem. Phys. 2006, 8, 1775-1777, DOI: <a href="http://dx.doi.org/10.1039/b601655c">10.1039/b601655c</a>.  </div> <a href="/blog/archives/category/molecules/annulenes" rel="category tag">annulenes</a> &<a href="/blog/archives/category/aromaticity" rel="category tag">Aromaticity</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> Steven Bachrach 20 Oct 2009 <a href="/blog/archives/441#comments">1 Comment</a> </div> <div class="box"> <h2><a href="/blog/archives/462" rel="bookmark" title="Permanent Link: Intramolecular basis set superposition error">Intramolecular basis set superposition error</a></h2> <div class="post-content"> As mentioned in Chapter 2 of my book, many post-HF methods predict that planar benzene has an imaginary frequency, whereby out-of-plane bending leads to a lower energy structure.<a href="#intraBSSE1">1</a> This anomaly was suggested to result from intramolecular basis set incompleteness. Asturiol, Duran and Salvador provide more evidence that the root cause is intramolecular basis set superposition error.<a href="#intraBSSE2">2</a> They propose an extension of the standard counterpoise correction, which has been widely applied to interacting molecules. They divide the molecule into small fragments and apply the counterpoise correction to these fragments. For benzene, they use C-H or (CH)2 fragments. With this counterpoise correction, the imaginary frequency corresponding to an out-of-plane distortion is removed for all combinations of either MP2 or CISD with the 6-31+G*, 6-311G or 6-311++G basis sets. The planar indenyl anion, which is found to have 4 imaginary frequencies at MP2/6-311G, has no imaginary frequencies when the counterpoise correction is used. These authors have now shown that nucleic acid bases suffer from the same intramolecular superposition error.<a href="#intraBSSE3">3</a> Uracil, thymine and guanine suffer from spurious imaginary frequencies with certain combinations of MP2 and Pople basis sets. However, all of these out-of-plane imaginary frequencies become real when the counterpoise correction is applied. The take-home message is to carefully mate the post-HF method and basis set combination – or else make the counterpoise correction! <h3>References</h3> <a name="intraBSSE1"></a> (1) Moran, D.; Simmonett, A. C.; Leach, F. E.; Allen, W. D.; Schleyer, P. v. R.; Schaefer, H. F., III, "Popular Theoretical Methods Predict Benzene and Arenes To Be Nonplanar," J. Am. Chem. Soc. 2006, 128, 9342-9343, DOI: <a href="http://dx.doi.org/10.1021/ja0630285">10.1021/ja0630285</a> <a name="intraBSSE2"></a> (2) Asturiol, D.; Duran, M.; Salvador, P., "Intramolecular basis set superposition error effects on the planarity of benzene and other aromatic molecules: A solution to the problem," J. Chem. Phys. 2008, 128, 144108, DOI: <a href="http://dx.doi.org/10.1063/1.2902974">10.1063/1.2902974</a> <a name="intraBSSE3"></a> (3) Asturiol, D.; Duran, M.; Salvador, P., "Intramolecular Basis Set Superposition Error Effects on the Planarity of DNA and RNA Nucleobases," J. Chem. Theory Comput. 2009, 5, 2574-2581, DOI: <a href="http://dx.doi.org/10.1021/ct900056u">10.1021/ct900056u</a>  </div> <a href="/blog/archives/category/uncategorized" rel="category tag">Uncategorized</a> Steven Bachrach 15 Oct 2009 <a href="/blog/archives/462#comments">2 Comments</a> </div> <div class="box"> <h2><a href="/blog/archives/419" rel="bookmark" title="Permanent Link: Benzene dimer once again">Benzene dimer once again</a></h2> <div class="post-content"> Once more into the benzene dimer (see these previous posts: “<a href="/blog/archives/161">Benzene dimer again</a>“, “<a href="/blog/archives/110">Benzene dimer</a>“, “<a href="/blog/archives/88">π-π stacking (part 2)</a>“, “<a href="/blog/archives/68">π-π stacking</a>“)! Sherrill has published a detailed and impressive benchmark study of the benzene dimer in its three most important configurations: the D6h stacked arrangement (1), the T-shaped arrangement (2) and the parallel displaced arrangement (3). <a href="#sherrill">1</a> <img src="/blog/wp-content/sherrillFig1.gif"> First, they performed a careful extrapolation study to obtain accurate binding energies based on CCSD(T) with large basis sets. Then they compared the potential energy curves of the three configurations of benzene dimer obtained with this accurate method with those obtained with less computationally expensive methods. These alternates include RI-MP2, SCS-MP2 and a variety of different density functional. Their results are summarized in Table 1. The upshot is that the SCS-MP2 results are very similar to the much more expensive CCDS(T) values. And while the errors are a bit larger with the DFT methods, their performance is really quite good, especially given their dramatically lower costs. (Note that the “-D” indicates inclusion of Grimme’s dispersion correction term.) Particularly worth mentioning is the very fine performance of the MO6-2X functional. Table 1. Binding energies (kcal mol-1) of the three benzene dimers with different computational methods. <table align="center" border="0" cellspacing="0" cellpadding="4"> <tr> <td colspan="4"></td> </tr> <tr> <td> Method </td> <td> 1 </td> <td> 2 </td> <td> 3 </td> </tr> <tr> <td> CCSD(T) </td> <td> -1.65 </td> <td> -2.69 </td> <td> -2.67 </td> </tr> <tr> <td> SCS-MP2 </td> <td> -1.87 </td> <td> -2.47 </td> <td> -2.87 </td> </tr> <tr> <td> MO6-2X </td> <td> -0.95 </td> <td> -2,42 </td> <td> -2.54 </td> </tr> <tr> <td> B3LYP-D </td> <td> -1.20 </td> <td> -3.03 </td> <td> -2.51 </td> </tr> <tr> <td> PBE-D </td> <td> -1.51 </td> <td> -3.02 </td> <td> -2.63 </td> </tr> <tr> <td colspan="4"></td> </tr> </table> <h3>References</h3> <a name="sherrill"></a> (1) Sherrill, C. D.; Takatani, T.; Hohenstein, E. G., "An Assessment of Theoretical Methods for Nonbonded Interactions: Comparison to Complete Basis Set Limit Coupled-Cluster Potential Energy Curves for the Benzene Dimer, the Methane Dimer, Benzene-Methane, and Benzene-H2S" J. Phys. Chem. A 2009, ASAP, DOI: <a href="http://dx.doi.org/10.1021/jp9034375">10.1021/jp9034375</a>  </div> <a href="/blog/archives/category/aromaticity" rel="category tag">Aromaticity</a> Steven Bachrach 12 Oct 2009 <a href="/blog/archives/419#respond">No Comments</a> </div> <div class="box"> <h2><a href="/blog/archives/412" rel="bookmark" title="Permanent Link: Gaunine tautomers">Gaunine tautomers</a></h2> <div class="post-content"> Here’s another fine paper from the Alonso group employing laser ablation molecular beam Fourier transform microwave spectroscopy coupled with computation to discern molecular structure. In this work they examine the low-energy tautomers of guanine.<a href="#guanineR1">1</a> The four lowest energy guanine tautomers are shown in Figure 1. (Unfortunately, Alonso does not include the optimized coordinates of these structures in the supporting information – we need to more vigorously police this during the review process!) These tautomers are predicted to be very close in energy (MP2/6-311++G(d,p), and so one might expect to see multiple signals in the microwave originating from all four tautomers. In fact, they discern all four, and the agreement between the computed and experimental rotational constants are excellent (Table 1), especially if one applies a scaling factor of 1.004. Once again, this group shows the power of combined experiment and computations! <table align="center" border="0" cellspacing="0" cellpadding="3"> <tr> <td align="center"> <img src="/blog/wp-content/guanine1.gif"> 1 (0.0) </td> <td align="center"> <img src="/blog/wp-content/guanine2.gif"> 2 (0.28) </td> </tr> <tr> <td align="center"> <img src="/blog/wp-content/guanine3.gif"> 3 (0.40) </td> <td align="center"> <img src="/blog/wp-content/guanine4.gif"> 4 (0.99) </td> </tr> </table> Figure 1. Four lowest energy (kcal mol-1, MP2/6-311++G(d,p)) tautomers of guanine. Table 1. Experimental and computed rotational constants (MHz) of the four guanine tautomers. <table align="center" border="0" cellspacing="0" cellpadding="3"> <tr> <td align="center">   </td> <td align="center" colspan="2"> 1 </td> <td align="center" colspan="2"> 2 </td> <td align="center" colspan="2"> 3 </td> <td align="center" colspan="2"> 4 </td> </tr> <tr> <td align="center">   </td> <td align="center"> Exp </td> <td align="center"> Comp </td> <td align="center"> Exp </td> <td align="center"> Comp </td> <td align="center"> Exp </td> <td align="center"> Comp </td> <td align="center"> Exp </td> <td align="center"> Comp </td> </tr> <tr> <td align="center"> A </td> <td align="center"> 19.22155 </td> <td align="center"> 1909.0 </td> <td align="center"> 19.222780 </td> <td align="center"> 1909.7 </td> <td align="center"> 1916.080 </td> <td align="center"> 1908.6 </td> <td align="center"> 1923.460 </td> <td align="center"> 1915.6 </td> </tr> <tr> <td align="center"> B </td> <td align="center"> 1121.6840 </td> <td align="center"> 119.2 </td> <td align="center"> 1116.6710 </td> <td align="center"> 1113.5 </td> <td align="center"> 1132.360 </td> <td align="center"> 1128.2 </td> <td align="center"> 1136.040 </td> <td align="center"> 1131.9 </td> </tr> <tr> <td align="center"> C </td> <td align="center"> 709.0079 </td> <td align="center"> 706.6 </td> <td align="center"> 706.8580 </td> <td align="center"> 704.2 </td> <td align="center"> 712.1950 </td> <td align="center"> 709.5 </td> <td align="center"> 714.7000 </td> <td align="center"> 712.0 </td> </tr> </table> <h3>References</h3> <a name="guanineR1"></a> (1) Alonso, J. L.; Peña, I.; López, J. C.; Vaquero, V., "Rotational Spectral Signatures of Four Tautomers of Guanine," Angew. Chem. Int. Ed. 2009, 48, 6141-6143, DOI: <a href="http://dx.doi.org/10.1002/anie.200901462">10.1002/anie.200901462</a> <h3>InChIs</h3> Guanine: InChI=1/C5H5N5O/c6-5-9-3-2(4(11)10-5)7-1-8-3/h1H,(H4,6,7,8,9,10,11)/f/h8,10H,6H2 InChIKey=UYTPUPDQBNUYGX-GSQBSFCVCX  </div> <a href="/blog/archives/category/qm-method/mp" rel="category tag">MP</a> &<a href="/blog/archives/category/molecules/nucleic-acids" rel="category tag">nucleic acids</a> Steven Bachrach 05 Oct 2009 <a href="/blog/archives/412#comments">3 Comments</a> </div> </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 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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">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" aria-current="page">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> 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"> Copyright © 2021 Computational Organic Chemistry. </div> </body> </html>