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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 » Truhlar</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 the 'Truhlar' Category</h2> <div class="box"> <h2><a href="/blog/archives/2557" rel="bookmark" title="Permanent Link: Large water clusters and DFT performance">Large water clusters and DFT performance</a></h2> <div class="post-content"> Truhlar has made a comparison of binding energies and relative energies of five (H2O)16 clusters.<a href="#16waterRef1">1</a> While technically not organic chemistry, this paper is of interest to the readership of this blog as it compares a very large collection of density functionals on a problem that involves extensive hydrogen bonding, a problem of interest to computational organic chemists. The CCSD(T)/aug-cc-pVTZ//MP2/aug-cc-pVTZ energies of clusters 1-5 (shown in Figure 1) were obtained by Yoo.<a href="#16waterRef2">2</a> These clusters are notable not just for their size but also that they involve multiple water molecules involved in four hydrogen bonds. Truhlar has used these geometries to compute the energies using 73 different density functionals with the jun-cc-pVTZ basis set (see this <a href="/blog/archives/1943">post for a definition of the ‘jun’ basis sets</a>). Binding energies (relative to 16 isolated water molecules) were computed along with the 10 relative energies amongst the 5 different clusters. Combining the results of both types of energies, Truhlar finds that the best overall performance relative to CCSD(T) is obtained with ωB97X-D, a hybrid GGA method with a dispersion correction. The next two best performing functionals are LC-ωPBE-D3 and M05-2x. The best non-hybrid performance is with revPBE-D3 and B97-D. <table align="center" border="0" cellspacing="0" cellpadding="4"> <tr align="center" valign="middle"> <td> <div class="jmol" id="16water1"> <a onclick="return false"> <img src="/blog/wp-content/16water1.jpg" onclick="insertJmol('16water1',300,300,'16water1.xyz')"> </a> </div> 1 (0.0) </td> <td> <div class="jmol" id="16water2"> <a onclick="return false"> <img src="/blog/wp-content/16water2.jpg" onclick="insertJmol('16water2',300,300,'16water2.xyz')"> </a> </div> 2 (0.25) </td> </tr> <tr align="center" valign="middle"> <td> <div class="jmol" id="16water3"> <a onclick="return false"> <img src="/blog/wp-content/16water3.jpg" onclick="insertJmol('16water3',300,300,'16water3.xyz')"> </a> </div> 3 (0.42) </td> <td> <div class="jmol" id="16water4"> <a onclick="return false"> <img src="/blog/wp-content/16water4.jpg" onclick="insertJmol('16water4',300,300,'16water4.xyz')"> </a> </div> 4 (0.51) </td> </tr> <tr align="center" valign="middle"> <td colspan="2"> <div class="jmol" id="16water5"> <a onclick="return false"> <img src="/blog/wp-content/16water5.jpg" onclick="insertJmol('16water5',300,300,'16water5.xyz')"> </a> </div> 5 (0.54) </td> </tr> </table> Figure 1. MP2/aug-cc-pVTZ optimized geometries and relative CCSD(T) energies (kcal mol-1) of (water)16 clusters 1-5. (Don’t forget to click on any of these molecules above to launch Jmol to interactively view the 3-D structure. This feature is true for all molecular structures displayed in all of my blog posts.) While this study can help guide selection of a functional, two words of caution. First, Truhlar notes that the best performing methods for the five (H2O)16 clusters do not do a particularly great job in getting the binding and relative energies of water hexamers, suggesting that no single functional really stands out as best. Second, a better study would also involve geometry optimization using that particular functional. Since this was not done, one can garner little here about what method might be best for use in a typical study where a geometry optimization must also be carried out. <h3>References</h3> <a name="16waterRef1"></a> (1) Leverentz, H. R.; Qi, H. W.; Truhlar, D. G. "Assessing the Accuracy of Density Functional and Semiempirical Wave Function Methods for Water Nanoparticles: Comparing Binding and Relative Energies of (H2O)16 and (H2O)17 to CCSD(T) Results," J. Chem. Theor. Comput. 2013, ASAP, DOI: <a href="http://dx.doi.org/10.1021/ct300848z">10.1021/ct300848z</a>. <a name="16waterRef2"></a> (2) Yoo, S.; Aprà, E.; Zeng, X. C.; Xantheas, S. S. "High-Level Ab Initio Electronic Structure Calculations of Water Clusters (H2O)16 and (H2O)17: A New Global Minimum for (H2O)16," J. Phys. Chem. Lett. 2010, 1, 3122-3127, DOI: <a href="http://dx.doi.org/10.1021/jz101245s">10.1021/jz101245s</a>.  </div> <a href="/blog/archives/category/qm-method/dft" rel="category tag">DFT</a> &<a href="/blog/archives/category/hydrogen-bond" rel="category tag">Hydrogen bond</a> &<a href="/blog/archives/category/authors/truhlar" rel="category tag">Truhlar</a> Steven Bachrach 25 Feb 2013 <a href="/blog/archives/2557#comments">1 Comment</a> </div> <div class="box"> <h2><a href="/blog/archives/2537" rel="bookmark" title="Permanent Link: Benchmarked Dispersion corrected DFT and SM12">Benchmarked Dispersion corrected DFT and SM12</a></h2> <div class="post-content"> This is a short post mainly to bring to the reader’s attention a couple of recent JCTC papers. The first is a benchmark study by Hujo and Grimme of the geometries produced by DFT computations that are corrected for dispersion.<a href="#HujoR1">1</a> They use the S22 and S66 test sets that span a range of compounds expressing weak interactions. Of particular note is that the B3LYP-D3 method provided the best geometries, suggesting that this much (and justly) maligned functional can be significantly improved with just the simple D3 fix. The second paper entails the description of Truhlar and Cramer’s latest iteration on their solvation model, namely SM12.<a href="#JuhoR2">2</a> The main change here is the use of Hirshfeld-based charges, which comprise their Charge Model 5 (CM5). The training set used to obtain the needed parameters is much larger than with previous versions and allows for treating a very broad set of solvents. Performance of the model is excellent. <h3>References</h3> <a href="#HujoR1"></a> (1) Hujo, W.; Grimme, S. "Performance of Non-Local and Atom-Pairwise Dispersion Corrections to DFT for Structural Parameters of Molecules with Noncovalent Interactions," J. Chem. Theor. Comput. 2013, 9, 308-315, DOI: <a href="http://dx.doi.org/10.1021/ct300813c">10.1021/ct300813c</a> <a href="#HujoR2"></a> (2) Marenich, A. V.; Cramer, C. J.; Truhlar, D. G. "Generalized Born Solvation Model SM12," J. Chem. Theor. Comput. 2013, 9, 609-620, DOI: <a href="http://dx.doi.org/10.1021/ct300900e">10.1021/ct300900e</a>  </div> <a href="/blog/archives/category/authors/cramer" rel="category tag">Cramer</a> &<a href="/blog/archives/category/qm-method/dft" rel="category tag">DFT</a> &<a href="/blog/archives/category/authors/grimme" rel="category tag">Grimme</a> &<a href="/blog/archives/category/solvation" rel="category tag">Solvation</a> &<a href="/blog/archives/category/authors/truhlar" rel="category tag">Truhlar</a> Steven Bachrach 14 Jan 2013 <a href="/blog/archives/2537#respond">No Comments</a> </div> <div class="box"> <h2><a href="/blog/archives/1943" rel="bookmark" title="Permanent Link: Diffuse basis sets">Diffuse basis sets</a></h2> <div class="post-content"> How should one add diffuse functions to the basis set? Diffuse functions are known to be critical in describing the electron distribution of anions (as discussed in my book), but they are also quite important in describing weak interactions, like hydrogen bonds, and can be critical in evaluating activation barriers and other properties. The Truhlar group has been active in benchmarking the need of basis functions and their recent review<a href="#calendar">1</a> summarizes their work. In particular, they recommend that for DFT computations a minimally augmented basis set is appropriate for examining barrier heights and weakly bound systems. A minimally augmented basis set would have s and p diffuse functions on heavy atoms for the Pople split-valence basis sets and the Dunning cc-pVxZ basis sets. For wavefunction based computations, they recommend the use of the “jun-“ basis sets. The “jun” basis set is one of the so-called calendar basis set derived from the aug-cc-pVxZ, which includes diffuse functions of all types. So, for C in the aug-cc-pVTZ basis set, there are diffuse s, p, d, and f functions. The “jun-“ basis set omits the diffuse f functions along with all diffuse functions on H. The great advantage of these trimmed basis sets is that they are smaller than the fully augmented sets, leading to faster computations. And since trimming off some diffuse functions leads to little loss in accuracy, one should seriously consider using these types of basis sets. As Truhlar notes, these trimmed basis sets might allow one to use a partially augmented but larger zeta basis set at the same cost of the smaller zeta basis that is fully augmented. <h3>References</h3> <a name="calendar"></a> (1) Papajak, E.; Zheng, J.; Xu, X.; Leverentz, H. R.; Truhlar, D. G., "Perspectives on Basis Sets Beautiful: Seasonal Plantings of Diffuse Basis Functions," J. Chem. Theory Comput., 2011, 7, 3027-3034, DOI: <a href="http://dx.doi.org/10.1021/ct200106a">10.1021/ct200106a</a>  </div> <a href="/blog/archives/category/authors/truhlar" rel="category tag">Truhlar</a> Steven Bachrach 20 Dec 2011 <a href="/blog/archives/1943#comments">5 Comments</a> </div> <div class="box"> <h2><a href="/blog/archives/117" rel="bookmark" title="Permanent Link: Solubility in olive oil">Solubility in olive oil</a></h2> <div class="post-content"> Here’s a nice example of the application of computed solvation energies in non-aqueous studies. Cramer and Truhlar have employed their latest SM8 technique, which is parameterized for organic solvents and for water, to estimate solvation energies in olive oil.<a href="#oliveOil">1</a> Now you may wonder why solvation in olive oil of all things? But the partitioning of molecules between water and olive oil has been shown to be a good predictor of lipophilicity and therefore bioavailability of drugs! The model works reasonably well in reproducing experimental solvation energies and partition coefficients. They do make the case that fluorine substitution which appears to improve solubility in organics,originates not to more favorable solvation in organic solvents (like olive oil) but rather that fluorine substitution dramatically decreases solubility in water. <h3>References</h3> <a name="oliveOil"></a> (1) Chamberlin, A. C.; Levitt, D. G.; Cramer, C. J.; Truhlar, D. G., "Modeling Free Energies of Solvation in Olive Oil," Mol. Pharmaceutics, 2008, 5, 1064-1079, DOI: <a href="http://dx.doi.org/10.1021/mp800059u">10.1021/mp800059u</a>  </div> <a href="/blog/archives/category/authors/cramer" rel="category tag">Cramer</a> &<a href="/blog/archives/category/solvation" rel="category tag">Solvation</a> &<a href="/blog/archives/category/authors/truhlar" rel="category tag">Truhlar</a> Steven Bachrach 17 Feb 2009 <a href="/blog/archives/117#comments">1 Comment</a> </div> <div class="box"> <h2><a href="/blog/archives/94" rel="bookmark" title="Permanent Link: SM8 performance">SM8 performance</a></h2> <div class="post-content"> Cramer and Truhlar have tested their latest solvation model SM8 against a test set of 17 small, drug-like molecules.<a href="#sm8testR1">1</a> Their best result comes with the use of SM8, the MO5-2X functional, the 6-31G(d) basis set and CM4M charge model. This computational model yields a root mean squared error for the solvation free energy of 1.08 kcal mol-1 across this test set. This is the first time these authors have recommended a particular computational model. Another interesting point is that use of solution-phase optimized geometries instead of gas-phase geometries leads to only marginally improved solvation energies, so that the more cost effective use of gas-phase structures is encouraged. These authors note in conclusion that further improvement of solvation prediction rests upon “an infusion of new experimental data for molecules characterized by high degrees of functionality (i.e. druglike)”. <h2>References</h2> <a name="sm8testR1"></a> (1) Chamberlin, A. C.; Cramer, C. J.; Truhlar, D. G., “Performance of SM8 on a Test To Predict Small-Molecule Solvation Free Energies,” J. Phys. Chem. B, 2008, 112, 8651-8655, DOI: <a href="http://dx.doi.org/10.1021/jp8028038">10.1021/jp8028038</a>.  </div> <a href="/blog/archives/category/authors/cramer" rel="category tag">Cramer</a> &<a href="/blog/archives/category/solvation" rel="category tag">Solvation</a> &<a href="/blog/archives/category/authors/truhlar" rel="category tag">Truhlar</a> Steven Bachrach 21 Oct 2008 <a href="/blog/archives/94#respond">No Comments</a> </div> <div class="box"> <h2><a href="/blog/archives/76" rel="bookmark" title="Permanent Link: Review of SM8">Review of SM8</a></h2> <div class="post-content"> Cramer and Truhlar<a href="#sm8rev">1</a> have published a nice review of their SM8 approach to evaluated solvation energy. Besides a quick summary of the theoretical approach behind the model, they detail a few applications. Principle among these is (a) the very strong performance of SM8 relative to some of the standard approaches in the major QM codes (see <a href="http://hackberry.chem.trinity.edu/blog/?p=81">my previous blog post</a>), (b) modeling interfaces, and (c) computing pKa values of organic compounds. <h3>References</h3> <a name="sm8rev"></a> (1) Cramer, C. J.; Truhlar, D. G., "A Universal Approach to Solvation Modeling," Acc. Chem. Res. 2008, 41, 760-768, DOI: <a href="http://dx.doi.org/10.1021/ar800019z">10.1021/ar800019z</a>.  </div> <a href="/blog/archives/category/authors/cramer" rel="category tag">Cramer</a> &<a href="/blog/archives/category/solvation" rel="category tag">Solvation</a> &<a href="/blog/archives/category/authors/truhlar" rel="category tag">Truhlar</a> Steven Bachrach 23 Jul 2008 <a href="/blog/archives/76#respond">No Comments</a> </div> <div class="box"> <h2><a href="/blog/archives/46" rel="bookmark" title="Permanent Link: New solvation model: SM8">New solvation model: SM8</a></h2> <div class="post-content"> Truhlar and Cramer have updated their Solvation Model to SM8.<a href="#sm8ref">1</a> This model allows for any solvent to be utilized (both water and organic solvents) and treats both neutral and charged solutes. While there are some small theoretical changes to the model, the major change is in how the parameters are selected, the number of parameters, and a much more extensive data set is used for the fitting procedure. Of note is how well this new model works. Table 1 compares the errors in solvation free energies computed using the new SM8 model against some other popular continuum methods. Clearly, SM8 provides much better results. As they point out, what is truly discouraging is the performance of the 3PM model against the continuum methods. 3PM stands for “three-parameter model”, where the solvation energies of all the neutral solute in water is set to their average experimental value (-2.99 kcal mol-1), and the same for the neutral solutes in organic solvents (-5.38 kcal mol-1), and for ions (-65.0 kcal mol-1). The 3PM outperforms most of the continuum methods! Table 1. Mean unsigned error (kcal mol-1) for the solvation free energies computed with different methods.<a href="#sm8ref">1</a> <table border="0" cellspacing="0" cellpadding="3" align="center"> <tr> <td colspan="4"> <hr> </td> </tr> <tr> <td> Method </td> <td> Aqueous neutrala </td> <td> Organic neutralsb </td> <td> Ionsc </td> </tr> <tr> <td> SM8d </td> <td> 0.55 </td> <td> 0.61 </td> <td> 4.31 </td> </tr> <tr> <td> IEF-PCM/UA0e </td> <td> 4.87 </td> <td> 5.99 </td> <td> 9.73 </td> </tr> <tr> <td> IEF-PCM/UAHFf </td> <td> 1.18 </td> <td> 3.94 </td> <td> 8.15 </td> </tr> <tr> <td> C-PCM/GAMESSg </td> <td> 1.57 </td> <td> 2.78 </td> <td> 8.39 </td> </tr> <tr> <td> PB/Jaguarh </td> <td> 0.86 </td> <td> 2.28 </td> <td> 6.72 </td> </tr> <tr> <td> 3PM </td> <td> 2.65 </td> <td> 1.49 </td> <td> 8.60 </td> </tr> <tr> <td colspan="4"> <hr> </td> </tr> </table> a274 data points. b666 data points spread among 16 solvents. c332 data points spread among acetonitrile, water, DMSO, and methanol. dUsing mPW1PW/6-31G(d). eUsing mPW1PW/6-31G(d) and the UA0 atomic radii in Gaussian. fUsing mPW1PW/6-31G(d) and the UAHF atomic radii in Gaussian. gUsing B3LYP/6-31G(d) and conductor-PCM in GAMESS. hUsing B3LYP/6-31G(d) and the PB method in Jaguar. <h3>References</h3> <a name="sm8ref"></a> (1) Marenich, A. V.; Olson, R. M.; Kelly, C. P.; Cramer, C. J.; Truhlar, D. G., "Self-Consistent Reaction Field Model for Aqueous and Nonaqueous Solutions Based on Accurate Polarized Partial Charges," J. Chem. Theory Comput., 2007, 3, 2011-2033. DOI: <a href="http://dx.doi.org/10.1021/ct7001418">10.1021/ct7001418</a>.  </div> <a href="/blog/archives/category/authors/cramer" rel="category tag">Cramer</a> &<a href="/blog/archives/category/solvation" rel="category tag">Solvation</a> &<a href="/blog/archives/category/authors/truhlar" rel="category tag">Truhlar</a> Steven Bachrach 19 Nov 2007 <a href="/blog/archives/46#comments">1 Comment</a> </div> <div class="box"> <h2><a href="/blog/archives/15" rel="bookmark" title="Permanent Link: Problems with DFT">Problems with DFT</a></h2> <div class="post-content"> We noted in Chapter 2.1 some serious errors in the prediction of bond dissociation energies using B3LYP. For example, Gilbert examined the C-C bond dissociation energy of some simple branched alkanes.<a href="#DFTref1">1</a> The mean absolute deviation (MAD) for the bond dissociation energy predicted by G3MP2 is 1.7 kcal mol-1 and 2.8 kcal mol-1 using MP2. In contrast, the MAD for the B3LYP predicted values is 13.7 kcal mol-1, with some predictions in error by more than 20 kcal mol-1. Furthermore, the size of the error increases with the size of the molecule. Consistent with this trend, Curtiss and co-workers noted a systematic underestimation of the heat of formation of linear alkanes of nearly 0.7 kcal mol-1 per bond using B3LYP.<a href="#DFTref2">2</a> Further evidence disparaging the general performance of DFT methods (and B3LYP in particular) was presented in a paper by Grimme and in two back-to-back Organic Letters articles, one by Schreiner and one by Schleyer. Grimme<a href="#DFTref3">3</a> noted that the relative Energy of two C8H18 isomers, octane and 2,2,3,3-tetramethylbutane are incorrectly predicted by DFT methods (Table 1). While MP2 and CSC-MP2 (spin-component-scaled MP2) correctly predict that the more branched isomer is more stable, the DFT methods predict the inverse! Grimme attributes this error to a failure of these DFT methods to adequately describe medium-range electron correlation. <table width="75%" align="center"> <tr> <td> <hr> Table 1. Energy (kcal mol-1) of 2,2,3,3-tetramethylbutane relative to octane. <hr> </td> </tr> <tr> <td align="center"> <table cellspacing="2" cellpadding="0" border="0"> <tr> <td> Method </td> <td> ΔE </td> </tr> <tr> <td>Expta </td> <td>1.9 ± 0.5</td> </tr> <tr> <td>MP2b,c </td> <td>4.6</td> </tr> <tr> <td>SCS-MP2b,c </td> <td>1.4</td> </tr> <tr> <td>PBEb,c </td> <td>-5.5</td> </tr> <tr> <td>TPSShb,c </td> <td>-6.3</td> </tr> <tr> <td>B3LYPb,c </td> <td>-8.4</td> </tr> <tr> <td>BLYPb,c </td> <td>-9.9</td> </tr> <tr> <td>M05-2Xd,e </td> <td>2.0</td> </tr> <tr> <td>M05-2Xc,d </td> <td>1.4</td> </tr> </table> </td> </tr> <tr> <td> <hr> aNIST Webbook (<a href="http://webbook.nist.gov/">http://webbook.nist.gov</a>) bRef. <a href="#DFTref3">3</a>. cUsing the cQZV3P basis set and MP2/TZV(d,p) optimized geometries. dRef. <a href="#DFTref4">4</a>. eCalculated at M05-2X/6-311+G(2df,2p). <hr> </td> </tr> </table> Schreiner<a href="#DFTref5">5</a> also compared the energies of hydrocarbon isomers. For example, the three lowest energy isomers of C12H12 are 1-3, whose B3LYP/6-31G(d) structures are shown in Figure 1. What is disturbing is that the relative energies of these three isomers depends strongly upon the computational method (Table 2), especially since these three compounds appear to be quite ordinary hydrocarbons. CCSD(T) predicts that 2 is about 15 kcal mol-1 less stable than 1 and that 3 lies another 10 kcal mol-1 higher in energy. MP2 exaggerates the separation by a few kcal mol-1. HF predicts that 1 and 2 are degenerate. The large HF component within B3LYP leads to this DFT method’s poor performance. B3PW91 does reasonably well in reproducing the CCSD(T) results. <img loading="lazy" width="247" height="89" src="http://hackberry.chem.trinity.edu/blog/files/DFTprob/image002.gif"> <table align="center"> <tr> <td> <hr> Table 2. Energies (kcal mol-1) of 2 and 3 relative to 1. <hr> </td> </tr> <tr> <td align="center"> <table cellspacing="2" cellpadding="2" border="0"> <tr> <td> Method </td> <td> 2 </td> <td> 3 </td> </tr> <tr> <td>CCSD(T)/cc-pVDZ//MP2(fc)/aug-cc-pVDZa </td> <td>14.3</td> <td>25.0</td> </tr> <tr> <td>CCSD(T)/cc-pVDZ//B3LYP/6-31+G(d)a </td> <td>14.9</td> <td>25.0</td> </tr> <tr> <td>MP2(fc)/aug-cc-pVDZa </td> <td>21.6</td> <td>29.1</td> </tr> <tr> <td>MP2(fc)/6-31G(d)a </td> <td>23.0</td> <td>30.0</td> </tr> <tr> <td>HF/6-311+(d) a </td> <td>0.1</td> <td>6.1</td> </tr> <tr> <td>B3LYP/6-31G(d)a </td> <td>4.5</td> <td>7.2</td> </tr> <tr> <td>B3LYP/aug-cc-pvDZa </td> <td>0.4</td> <td>3.1</td> </tr> <tr> <td>B3PW91/6-31+G(d) a </td> <td>17.3</td> <td>23.7</td> </tr> <tr> <td>B3PW91/aug-cc-pVDZa </td> <td>16.8</td> <td>23.5</td> </tr> <tr> <td>KMLYP/6-311+G(d,p)a </td> <td>28.4</td> <td>41.7</td> </tr> <tr> <td>M05-2X/6-311+G(d,p)b </td> <td>16.9</td> <td>25.4</td> </tr> <tr> <td>M05-2X/6-311+G(2df,2p)b </td> <td>14.0</td> <td>21.4</td> </tr> </table> </td> </tr> <tr> <td> <hr> aRef. <a href="#DFTref5">5</a>. bRef. <a href="#DFTref4">4</a>. <hr> </td> </tr> </table> <table cellspacing="0" cellpadding="0" border="0" align="center"> <tr> <td> </td> <td> <div class="jmol" id="DFT1_applet"> <a onclick="return false"><img src="/blog/wp-content/DFTcmpd1.gif" onclick="insertJmol('DFT1_applet',200,200,'DFTcmpd1.xyz')" alt="DFT 1"></a> </div> 1 <a href="http://hackberry.chem.trinity.edu/blog/files/DFTprob/DFTcmpd1.xyz">xyz file</a> </td> <td> <div class="jmol" id="DFT2_applet"> <a onclick="return false"><img src="/blog/wp-content/DFTcmpd2.gif" onclick="insertJmol('DFT2_applet',200,200,'DFTcmpd2.xyz')" alt="DFT 2"></a> </div> 2 <a href="http://hackberry.chem.trinity.edu/blog/files/DFTprob/DFTcmpd2.xyz">xyz file</a> </td> <td> <div class="jmol" id="DFT3_applet"> <a onclick="return false"><img src="/blog/wp-content/DFTcmpd3.gif" onclick="insertJmol('DFT3_applet',200,200,'DFTcmpd3.xyz')" alt="DFT 3"></a> </div> 3 <a href="http://hackberry.chem.trinity.edu/blog/files/DFTprob/DFTcmpd3.xyz">xyz file</a> </td> </tr> </table> Figure 1. Structures of 1-3 at B3LYP/6-31G(d). Another of Schreiner’s examples is the relative energies of the C10H10 isomers; Table 3 compares their relative experimental heats of formation with their computed energies. MP2 adequately reproduces the isomeric energy differences. B3LYP fairs quite poorly in this task. The errors seem to be most egregious for compounds with many single bonds. Schreiner recommends that while DFT-optimized geometries are reasonable, their energies are unreliable and some non-DFT method should be utilized instead. <table width="85%" align="center"> <tr> <td> <hr> Table 3. Relative C10H10 isomer energies (kcal mol-1)<a href="#DFTref5">5</a> <hr> </td> </tr> <tr> <td align="center"> <table cellspacing="1" cellpadding="3" border="0" align="center"> <tr> <td valign="bottom"> Compound </td> <td valign="bottom"> Rel.ΔHf </td> <td valign="bottom"> Rel. E(B3LYP) </td> <td valign="bottom"> Rel. E(MP2) </td> </tr> <tr> <td valign="middle"> <img loading="lazy" width="61" height="55" src="http://hackberry.chem.trinity.edu/blog/files/DFTprob/image007.gif"> </td> <td valign="middle"> 0.0 </td> <td valign="middle"> 0.0 </td> <td valign="middle"> 0.0 </td> </tr> <tr> <td valign="middle"> <img loading="lazy" width="97" height="58" src="http://hackberry.chem.trinity.edu/blog/files/DFTprob/image009.gif"> </td> <td valign="middle"> 5.9 </td> <td valign="middle"> -8.5 </td> <td valign="middle"> 0.2 </td> </tr> <tr> <td valign="middle"> <img loading="lazy" width="81" height="56" src="http://hackberry.chem.trinity.edu/blog/files/DFTprob/image011.gif"> </td> <td valign="middle"> 16.5 </td> <td valign="middle"> 0.7 </td> <td valign="middle"> 10.7 </td> </tr> <tr> <td valign="middle"> <img loading="lazy" width="70" height="41" src="http://hackberry.chem.trinity.edu/blog/files/DFTprob/image013.gif"> </td> <td valign="middle"> 20.5 </td> <td valign="middle"> 3.1 </td> <td valign="middle"> 9.4 </td> </tr> <tr> <td valign="middle"> <img loading="lazy" width="45" height="45" src="http://hackberry.chem.trinity.edu/blog/files/DFTprob/image015.gif"> </td> <td valign="middle"> 26.3 </td> <td valign="middle"> 20.3 </td> <td valign="middle"> 22.6 </td> </tr> <tr> <td valign="middle"> <img loading="lazy" width="69" height="44" src="http://hackberry.chem.trinity.edu/blog/files/DFTprob/image017.gif"> </td> <td valign="middle"> 32.3 </td> <td valign="middle"> 17.6 </td> <td valign="middle"> 31 </td> </tr> <tr> <td valign="middle"> <img loading="lazy" width="118" height="33" src="http://hackberry.chem.trinity.edu/blog/files/DFTprob/image019.gif"> </td> <td valign="middle"> 64.6 </td> <td valign="middle"> 48.8 </td> <td valign="middle"> 61.4 </td> </tr> <tr> <td valign="middle"> <img loading="lazy" width="121" height="25" src="http://hackberry.chem.trinity.edu/blog/files/DFTprob/image021.gif"> </td> <td valign="middle"> 80.8 </td> <td valign="middle"> 71.2 </td> <td valign="middle"> 78.8 </td> </tr> <tr> <td valign="middle"> </td> <td valign="middle"> r2 </td> <td valign="middle"> 0.954a </td> <td valign="middle"> 0.986b </td> </tr> </table> </td> </tr> <tr> <td> <hr> aCorrelation coefficient between Rel. ΔHf and Rel. E(B3LYP). bCorrelation coefficient between Rel. ΔHf and Rel. E(MP2). <hr> </td> </tr> </table> Schleyer’s example of poor DFT performance is in the isodesmic energy of Reaction 1 evaluated for the n-alkanes.<a href="#DFTref6">6</a> The energy of this reaction becomes more positive with increasing chain length, which Schleyer attributes to stabilizing 1,3-interactions between methyl or methylene groups. (Schleyer ascribes the term “protobranching” to this phenomenon.) The stabilization energy of protobranching using experimental heats of formation increases essentially linearly with the length of the chain, as seen in Figure 2. n-CH3(CH2)mCH3 + mCH4 → (m + 1)C2H6         Reaction 1 Schleyer evaluated the protobranching energy using a variety of methods, and these energies are also plotted in Figure 2. As expected, the G3 predictions match the experimental values quite closely. However, all of the DFT methods underestimate the stabilization energy. Most concerning is the poor performance of B3LYP. All three of these papers clearly raise concerns over the continued widespread use of B3LYP as the de facto DFT method. Even the new hybrid meta-GGA functionals fail to adequately predict the protobranching phenomenon, leading Schleyer to conclude: “We hope that Check and Gilbert’s pessimistic admonition that ‘a computational chemist cannot trust a one-type DFT calculation’<a href="#DFTref1">1</a> can be overcome eventually”. These papers provide a clear challenge to developers of new functionals. <img loading="lazy" width="378" height="310" src="http://hackberry.chem.trinity.edu/blog/files/DFTprob/figure2.gif"> Figure 2. Comparison of computed and experimental protobranching stabilization energy (as defined in Reaction 1) vs. m, the number of methylene groups of the n-alkane chain.<a href="#DFTref6">6</a> Truhlar believes that one of his newly developed functionals answers the call for a reliable method. In a recent article,<a href="#DFTref4">4</a> Truhlar demonstrates that the M05-2X<a href="#DFTref7%22">7</a> functional performs very well in all three of the cases discussed here. In the case of the C8H18 isomers (Table 1), M05-2X properly predicts that 2,2,3,3-tetramethylbutane is more stable than octane, and estimates their energy difference within the error limit of the experiment. Second, M05-2X predicts the relative energies of the C12H12 isomers 1-3 within a couple of kcal mol-1 of the CCSD(T) results (see Table 2). Last, in evaluating the isodesmic energy of Reaction 1 for hexane and octane, M05-2X/6-311+G(2df,2p) predicts energies of 11.5 and 17.2 kcal mol-1 respectively. These are in excellent agreement with the experimental values of 13.1 kcal mol-1 for butane and 19.8 kcal mol-1 for octane. Truhlar has also touted the M05-2X functional’s performance in handling noncovalent interactions.<a href="#DFTref8">8</a> For example, the mean unsigned error (MUE) in the prediction of the binding energies of six hydrogen-bonded dimers is 0.20 kcal mol-1. This error is comparable to that from G3 and much better than CCSD(T). With the M05-2X functional already implemented within <a target="_top" href="http://www.emsl.pnl.gov/docs/nwchem/nwchem.html" rel="noopener">NWChem</a> and soon to be released within <a target="_top" href="http://www.gaussian.com/" rel="noopener">Gaussian</a> and <a target="_top" href="http://www.schrodinger.com/ProductDescription.php?mID=6&sID=9&cID=0" rel="noopener">Jaguar</a>, it is likely that M05-2X may supplant B3LYP as the new de facto functional in standard computational chemical practice. Schleyer has now examined the bond separation energies of 72 simple organic molecules computed using a variety of functionals,<a href="#DFTref9">9</a> including the workhorse B3LYP and Truhlar’s new M05-2X. Bond separation energies are defined by reactions of each compound, such as three shown below: <img src="http://hackberry.chem.trinity.edu/blog/wp-content/DFTimg2.gif"> The new M05-2X functional performed the best, with a mean absolute deviation (MAD) from the experimental energy of only 2.13 kcal mol-1. B3LYP performed much worse, with a MAD of 3.96 kcal mol-1. As noted before, B3LYP energies become worse with increasing size of the molecules, but this problem is not observed for the other functionals examined (including PW91, PBE, and mPW1PW91, among others). So while M05-2X overall appears to solve many of the problems noted with common functionals, it too has some notable failures. In particular, the error is the bond separation energies of 4, 5, and 6 is -8.8, -6.8, and -6.0 kcal mol-1, respectively. <h4>References</h4> <a name="DFTref1"></a>(1) Check, C. E.; Gilbert, T. M., “Progressive Systematic Underestimation of Reaction Energies by the B3LYP Model as the Number of C-C Bonds Increases: Why Organic Chemists Should Use Multiple DFT Models for Calculations Involving Polycarbon Hydrocarbons,” J. Org. Chem. 2005, 70, 9828-9834, DOI: <a href="http://dx.doi.org/10.1021/jo051545k">10.1021/jo051545k</a>. <a name="DFTref2"></a>(2) Redfern, P. C.; Zapol, P.; Curtiss, L. A.; Raghavachari, K., “Assessment of Gaussian-3 and Density Functional Theories for Enthalpies of Formation of C1-C16 Alkanes,” J. Phys. Chem. A 2000, 104, 5850-5854, DOI: <a href="http://dx.doi.org/10.1021/jp994429s">10.1021/jp994429s</a>. <a name="DFTref3"></a>(3) Grimme, S., “Seemingly Simple Stereoelectronic Effects in Alkane Isomers and the Implications for Kohn-Sham Density Functional Theory,” Angew. Chem. Int. Ed. 2006, 45, 4460-4464, DOI: <a href="http://dx.doi.org/10.1002/anie.200600448">10.1002/anie.200600448</a> <a name="DFTref4"></a>(4) Zhao, Y.; Truhlar, D. G., “A Density Functional That Accounts for Medium-Range Correlation Energies in Organic Chemistry,” Org. Lett. 2006, 8, 5753-5755, DOI: <a href="http://dx.doi.org/10.1021/ol062318n">10.1021/ol062318n</a> <a name="DFTref5"></a>(5) Schreiner, P. R.; Fokin, A. A.; Pascal, R. A.; deMeijere, A., “Many Density Functional Theory Approaches Fail To Give Reliable Large Hydrocarbon Isomer Energy Differences,” Org. Lett. 2006, 8, 3635-3638, DOI: <a href="http://dx.doi.org/10.1021/ol0610486">10.1021/ol0610486</a> <a name="DFTref6"></a>(6) Wodrich, M. D.; Corminboeuf, C.; Schleyer, P. v. R., “Systematic Errors in Computed Alkane Energies Using B3LYP and Other Popular DFT Functionals,” Org. Lett. 2006, 8, 3631-3634, DOI: <a href="http://dx.doi.org/10.1021/ol061016i">10.1021/ol061016i</a> <a name="DFTref7"></a>(7) Zhao, Y.; Schultz, N. E.; Truhlar, D. G., “Design of Density Functionals by Combining the Method of Constraint Satisfaction with Parametrization for Thermochemistry, Thermochemical Kinetics, and Noncovalent Interactions,” J. Chem. Theory Comput. 2006, 2, 364-382, DOI: <a href="http://dx.doi.org/10.1021/ct0502763">10.1021/ct0502763</a>. <a name="DFTref8"></a><a name="DFTref8"></a>(8) Zhao, Y.; Truhlar, D. G., “Assessment of Model Chemistries for Noncovalent Interactions,” J. Chem. Theory Comput. 2006, 2, 1009-1018, DOI: <a href="http://dx.doi.org/10.1021/ct060044j">10.1021/ct060044j</a>. <a name="DFTref9"></a>(9) Wodrich, M. D.; Corminboeuf, C.; Schreiner, P. R.; Fokin, A. A.; Schleyer, P. v. R., “How Accurate Are DFT Treatments of Organic Energies?,” Org. Lett., 2007, 9, 1851-1854, DOI: <a href="http://dx.doi.org/10.1021/ol070354w">10.1021/ol070354w</a>. <h4>InChI</h4> 1: InChI=1/C11H10/c1-2-5-7-3(1)4(1)8-6(2)10-9(5)11(7,8)10/h1-10H 2: InChI=1/C12H12/c1-2-4-10-6-8-11-7-5-9(3-1)12(10)11/h1-12H 3: InChI=1/C12H12/c1-2-4-8-11(7-3-1)12-9-5-6-10-12/h1-12H 4: InChI=1/C6H6/c1-4-5(2)6(4)3/h1-3H2 5: InChI=1/C8H10/c1-3-7-5-6-8(7)4-2/h3-4H,1-2,5-6H2 6: InChI=1/C10H10/c1-2-8-5-6-9-4-3-7(1)10(8)9/h1-10H  </div> <a href="/blog/archives/category/qm-method/dft" rel="category tag">DFT</a> &<a href="/blog/archives/category/authors/schleyer" rel="category tag">Schleyer</a> &<a href="/blog/archives/category/authors/schreiner" rel="category tag">Schreiner</a> &<a href="/blog/archives/category/authors/truhlar" rel="category tag">Truhlar</a> Steven Bachrach 13 Jul 2007 <a href="/blog/archives/15#comments">5 Comments</a> </div> </div> <div id="sidebar"> <ul> <li class="box"> <h2> Categories </h2> <ul> <li class="cat-item cat-item-25"> <a 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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">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" 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