## Wednesday, December 26, 2012

### Popular Highlights of 2012

Computational Chemistry Highlights received nearly 21,000 pageviews in 2012.

A total of 62 highlights were published in 2012 and the five most viewed highlights are

1. Chemical Networks (Triple Header!) highlighted by Robert Paton in July

2. Steric Crowding Can Stabilize a Labile Molecule: Solving the Hexaphenyethane Riddle highlighted by Shason Shaik in April

3. A Paramagnetic Bonding Mechanism for Diatomics in Strong Magnetic Fields highlighted by Grant Hill in July

4. Hydrogen-bond stabilization in oxyanion holes: grand jeté to three dimensions highlighted by Robert Paton in April

5. Benchmarking Semiempirical Methods for Thermochemistry, Kinetics, and Noncovalent Interactions: OMx Methods Are Almost As Accurate and Robust As DFT-GGA Methods for Organic Molecules highlighted by Jan Jensen in November

The most popular entries within the last 30 days can as always be found on the right hand side of this page.

The are many ways to stay updated on the latest CCH highlights

## Tuesday, December 18, 2012

### Characterization of the t-Butyl Radical and Its Elusive Anion

Sokolov, A. Y.; Mittal, S.; Simmonett, A. C.; Schaefer, H. F. J. Chem. Theory Comput. 2012, 8, 4323
Contributed by Steven Bachrach.
Reposted from Computational Organic Chemistry with permission

Two interesting questions are addressed in a focal-point computational study of t-butyl radical and thet-butyl anion from the Schaefer group.1 First, is the radical planar? EPR and PES studies from the 1970s indicate a pyramidal structure, with an inversion barrier of only 0.64 kcal mol-1. The CCSD(T)/cc-pCVTZ optimized structure of t-butyl radical shows it to be pyramidal with the out-of-plane angle formed by one methyl group and the other three carbons of 22.9°, much less than the 54.7° of a perfect tetrahedron. Focal point analysis give the inversion barrier 0.74 kcal mol-1, in outstanding agreement with experiment.

Second, what is the electron affinity (EA) of the t-butyl radical? Schleyer raised the concern that the alkyl anions may be unbound, and suggested that the electron affinity of t-butyl radical was -9.6 kcal mol-1; in other words, the anion is thermodynamically unstable. This focal-point study shows just how sensitive the EA is to computational method. The HF/CBS value of the EA is -39.59 kcal mol-1 (unbound anion), but the MP2/CBS value is +41.57 kcal mol-1 (bound anion!). The CCSD/aug-cc-pVQZ value is -8.92 while the CCSD(T)/aug-cc-pVQZ value is +4.79 kcal mol-1. The estimated EA at CCSDT(Q)/CBS is -1.88 kcal mol-1, and inclusion of correction terms (including ZPE and relativistic effect) gives a final estimate of the EA as -0.48 kcal mol-1, or a very weakly unbound t-butyl anion. It is somewhat disconcerting that such high-level computations are truly needed for some relatively simple questions about small molecules.

### References

(1) Sokolov, A. Y.; Mittal, S.; Simmonett, A. C.; Schaefer, H. F. "Characterization of the t-Butyl Radical and Its Elusive Anion," J. Chem. Theory Comput. 20128, 4323-4329, DOI: 10.1021/ct300753d.

## Tuesday, December 11, 2012

### Basis Set Recommendations for DFT Calculations of Gas-Phase Optical Rotation at Different Wavelengths

Hedegård, E. D.; Jensen, F.; Kongsted, J. J. Chem. Theory Comput. 2012, 8, 4425
Contributed by Steven Bachrach.
Reposted from Computational Organic Chemistry with permission

What is the appropriate basis set to use for computing optical rotations? Hedgård, Jensen, and Kongsted examined the optical rotation of 1-6 using B3LYP and CAM-B3LYP at two different wavelengths.1 They examined a series of different basis sets, including the aug-pCS sets2 (developed for NMR computations), the aug-cc-pVXZ series and 6-311++G(3df,3pd). They compared the computed optical rotation with the different basis sets with the value obtained from an extrapolated basis set computation. The mean absolute deviation using either B3LYP or CAM-B3LYP at the two different basis sets are listed in Table 1. The bottom line is that aug-pcS-2 is the preferred method, but this basis set is rather large and computations of big molecules will be difficult. The aug-pcS-1 set is the best choice for large molecules. Errors with the extensive Pople basis set and the aug-cc-pVXZ sets are quite sizable and of concern (especially at the shorter wavelength). It should also be mentioned that even with the largest aug-pcS basis sets extrapolated to the CBS limit, the computed value of the optical rotation of 3 has the wrong sign! Clearly, basis set choice is not the only issue of concern. We remain in need of a robust methodology for computing optical activity.
Table 1. Mean absolute deviation of the optical activities of 1-6 evaluated at two wavelengths.
 589.3 nm 355.0 nm Basis set B3LYP CAM-B3LYP B3LYP CAM-B3LYP aug-pcS-1 4.5 2.2 20.8 15.3 aug-pcS-2 1.4 1.1 4.0 1.5 aug-cc-pVDZ 15.6 13.6 62.2 144.1 aug-cc-pVTZ 3.9 6.3 9.2 37.0 6-311++G(3df,3pd) 6.4 10.3 20.5 40.7

### References

(1) Hedegård, E. D.; Jensen, F.; Kongsted, J. "Basis Set Recommendations for DFT Calculations of Gas-Phase Optical Rotation at Different Wavelengths," J. Chem. Theory Comput. 20128, 4425-4433, DOI:10.1021/ct300359s
(2) Jensen, F. "Basis Set Convergence of Nuclear Magnetic Shielding Constants Calculated by Density Functional Methods," J. Chem. Theory Comput. 20084, 719-727, DOI: 10.1021/ct800013z

## Monday, December 10, 2012

### Calculation of Host-Guest Binding Affinities Using a Quantum-Mechanical Energy Model

Hari S. Muddana and Michael K. Gilson J. Chem. Theory Comput. 2012, 8, 2023 (Paywall)
Contributed by Jan Jensen

This paper presents absolute binding energies for 29 ligands complexed with cucurbit[7]uril (CB7) computed using PM6-DH+ and the COSMO solvation model.

This is a great model system for studying binding: CB7 is a macrocyclic molecule made of seven fused-ring monomers and has only one conformational minimum.  Many of the 29 ligands for which binding free energies have been measure experimentally are also conformationally restricted, and the binding free energies span a wide range: -5.3 to -21.5 kcal/mol.

Because of this a fairly exhaustive conformational search was feasible and the number of conformations per complex ranged from 5 to 300 depending on the flexibility of the guest.  The conformational search was done using the OPLS-2005 all-atom force field and a low-mode conformational search algorithm implemented in the Schrodinger software suite.

These structures where then used as a starting point for PM6-DH+/COSMO energy minimizations and subsequent vibrational analysis.  Given the number of conformations and ligands this paper represents a significant investment of CPU time even at a semiempirical level of theory.  The COSMO solvation energy is augmented by a non-polar solvation term that depends on the molecular surface area.  Though not explicitly stated this must have been done as a single point correction.

The computed binding energies correlate well ($R^2$=0.79) with the experimental results, but the root-mean-square error (RMSE) is high (11.4 kcal/mol) suggesting a systematic error.  To address this a three parameter fit was made involving the COSMO and non-polar solvation energy plus an off-set, which led to a $R^2$=0.91 and RMSE of 1.9 kcal/mol, excluding one outlier.  This analysis suggests that the COSMO solvation energies are overestimated by 4%, consistent with a similar analysis performed on 367 solvation energies for small neutral molecules.

The off-set was found to be -5.83 kcal/mol, i.e. the predicted binding energies are systematically underestimated by nearly 6 kcal/mol.  Interestingly, a recent analysis of explicit solvation thermodynamics of CB7, by Gilson and co-workers, "suggests that the water molecules in the CB7 cavity are unstable relative to bulk ...  If so, then treating the water in the cavity as a bulk dielectric might lead to a significant overestimation of the host’s solvation free energy and hence the underestimations of binding affinities observed here."  Furthermore, very recently  Rogers et al. was able to compute an absolute binding energy for one of the ligands to CB7 using thermodynamic integration and explicit solvent that was in excellent agreement with experiment.

The paper also provides a useful outline of how the thermodynamical aspects should be handled and analyzed, including a nice analysis of the conformational entropy change.  For example, the translational entropy must be computed using a volume of 1 L rather than that of an ideal gas a 1 bar, and that one should compute the Helmholtz, rather than the Gibbs, free energy change since the change in volume of the solution upon binding is negligible in the condensed phase.  There is also a reference to a real gem of a paper by Zhou and Gilson that reconciles the rigid rotor-harmonic oscillator approach to thermodynamics used here with that used in molecular dynamics studies.

While the agreement with experiment is impressive there is some room for improvement and this system provides a great model system for testing all aspects of the binding energy including ab initio calculations of the interaction energy and new continuum solvation methods.

## Thursday, December 6, 2012

### The Correct Structure of Aquatolide—Experimental Validation of a Theoretically-Predicted Structural Revision

Lodewyk, M. W.; Soldi, C.; Jones, P. B.; Olmstead, M. M.; Rita, J.; Shaw, J. T.; Tantillo, D. J. J. Am. Chem. Soc. 2012
Contributed by Steven Bachrach.
Reposted from Computational Organic Chemistry with permission

The natural product aquatolide has the proposed structure 1.1 Before starting to investigate this rather unusual structure – the 2[ladderane] component is rare and likely to be a synthetic challenge – Shaw and Tantillo opted to reassure themselves that the structure is correct.2 They computed the chemical shifts of this structure at mPW1PW91/6-311+G(2d,p)//B3LYP/6-31+G(d,p) including PCM to model chloroform. Surprisingly, the mean absolute deviation of the computed 13C NMR shifts of 1 with the experimental values is 7.23 ppm, with the largest deviation of 24.3 ppm. The largest deviation between1 and the experimental 1H NMR shifts is 1.31 ppm. These large errors suggested that the structure is wrong. Surveying some 60 different possible alternative structures, largely based on other related compounds found in the same plant, they landed on 2. Here the mean absolute deviation of the computed 13C chemical shifts is only 1.37 ppm, with a maximum deviation of only 4.3 ppm. Similar dramatic improvement is also seen with the proton chemical shifts. Excellent agreement is also seen in the computed 1H-1H coupling constants between those computed for 2 and the experimental spectrum. Crystallization of aquatolide and subsequent determination of the structure using x-ray diffraction confirms that the actual structure of aquatolide is 2.
 1 2

### References

(1) San Feliciano, A.; Medarde, M.; Miguel del Corral, J. M.; Aramburu, A.; Gordaliza, M.; Barrero, A. F. "Aquatolide. A new type of humulane-related sesquiterpene lactone," Tetrahedron Lett. 1989, 30, 2851-2854, DOI: 10.1016/s0040-4039(00)99142-1

(2) Lodewyk, M. W.; Soldi, C.; Jones, P. B.; Olmstead, M. M.; Rita, J.; Shaw, J. T.; Tantillo, D. J. "The Correct Structure of Aquatolide—Experimental Validation of a Theoretically-Predicted Structural Revision," J. Am. Chem. Soc. 2012, DOI: 10.1021/ja3089394

InChIs
1: InChI=1S/C15H18O3/c1-7-5-4-6-15-9(11(7)16)8-10(15)12(14(8,2)3)18-13(15)17/h5,8-10,12H,4,6H2,1-3H3/t8-,9+,10+,12+,15+/m1/s1
InChIKey=JGSDEQLPLHCECO-NIDGLEHPSA-N
2: InChI=1S/C15H18O3/c1-7-5-4-6-15-9-8(10(7)16)11(15)14(2,3)12(9)18-13(15)17/h5,8-9,11-12H,4,6H2,1-3H3/b7-5-/t8-,9-,11+,12-,15+/m0/s1
InChIKey=OKZHLNWYFSWUMD-AETBLWMGSA-N

## Thursday, November 29, 2012

### A Hierarchy of Methods for the Energetically Accurate Modeling of Isomerism in Monosaccharides

Sameera, W. M. C.; Pantazis, D. A. J. Chem. Theory Comput. 2012, 8, 2630-2645 (Paywall)
Contributed by Steven Bachrach.
Reposted from Computational Organic Chemistry with permission

A comprehensive evaluation of how different computational methods perform in predicting the energies of monosaccharides comes to some very interesting conclusions. Sameera and Pantazis1 have examined the eight different aldohexoses (allose, alltrose, glucose, mannose, gulose, idose, galactose and talose), specifically looking at different rotomers of the hydroxymethyl group, α- vs. β-anomers, pyranose vs. furanose isomers, ring conformations (1C4 vs skew boat forms), and ring vs. open chain isomers. In total, 58 different structures were examined. The benchmark computations are CCSD(T)/CBS single point energies using the SCS-MP2/def2-TZVPP optimized geometries. The RMS deviation from these benchmark energies for some of the many different methods examined are listed in Table 1.
Table 1. Average RMS errors (kJ mol-1) of the 58 different monosaccharide structures for
different computational methods.
 method average RMS error LPNO-CEPA 0.71 MP2 1.27 SCS-MP2 1.55 mPW2PLYP-D 2.02 M06-2x 2.03 PBE0 3.62 TPSS 4.78 B3LYP-D 4.79 B3LYP 5.06 HF 6.69 B97D 7.66
Perhaps the most interesting take-home message is that CEPA, MP2, the double hybrid methods and M06-2x all do a very good job at evaluating the energies of the carbohydrates. Given the significant computational advantage of M06-2x over these other methods, this seems to be the functional of choice! The poorer performance of the DFT methods over the ab initio methods is primarily in the relative energies of the open-chain isomers, where errors can be on the order of 10-20 kJ mol-1 with most of the functionals; even the best overall methods (M06-2x and the double hybrids) have errors in the relative energies of the open-chain isomers of 7 kJ mol-1. This might be an area of further functional development to probe better treatment of the open-chain aldehydes vs. the ring hemiacetals.

### References

(1) Sameera, W. M. C.; Pantazis, D. A. "A Hierarchy of Methods for the Energetically Accurate Modeling of Isomerism in Monosaccharides," J. Chem. Theory Comput. 20128, 2630-2645, DOI:10.1021/ct3002305

## Tuesday, November 27, 2012

### Polyoxometalates are cationic, not anionic

N.V. Izarova, N. Vankova, A. Banerjee, G.B. Jameson, T. Heine, F. Schinle, O. Hampe, U. Kortz, Angewandte Chemie International Edition 2010, 49, 7807-7811 (Paywall)
Contributed by Marcel Swart

Polyoxometalates are clusters of metals connected together through oxygens, and can be giant molecules such as {(MoVI)MoVI5O21}12(MoV2O4)30]12- (also known as Mo132) as shown by Bo and Miró in Dalton Transactions recently[1]. These clusters bear a total anionic charge, for instance -12 in the aforementioned example. However, this is not the complete picture.

Ulrich Kortz (Univ. Bremen) visited Girona a couple of months ago and reported an interesting example of how theory can be useful. His group was working on a "A Noble-Metalate Bowl", and when trying to reproduce the 51V NMR spectrum computationally, it was impossible to get good agreement. By introducing Na/K cations they did get more and more reasonable results, and only obtained good agreement after having introduced 7 potassiums (or alternatively 6 potassiums and 1 sodium).

At first, the experimental people did not believe the calculations, because they had their mind set on the fact that polyoxometalates carry a large negative charge, and not a positive one. However, after doing electrospray mass spectrometry, indeed they observed mainly two peaks:

1) a singly charged molecular cation {K7[Pd7V6O24(OH)2]}+ (with seven potassiums)
2) a singly charged molecular cation {Na1K6[Pd7V6O24(OH)2]}+ (with six potassiums)

Therefore, contrary to popular belief, polyoxometalates are cationic!

[1] C. Bo, P. Miró, Dalton Trans. 2012, 41, 9984-9988

## Sunday, November 25, 2012

### Predicting pKa of Amines for CO2 Capture: Computer versus Pencil-and-Paper

K Z. Sumon, A. Henni, and Allan L. L. East. Industrial & Engineering Chemistry Research 2012 51 (37), 11924-11930
Contributed by Thomas Cundari

I tell my students, as was told tome, that the title is the shortest abstract for a paper. The title should becarefully chosen to be as succinct as possible, and also to catch the reader'sattention and make them want to read the rest of the paper. I mention this inconnection with a recent paper[1]by Sumon, Henni and East of the University of Regina, entitled"Predicting pKa of Aminesfor CO2 Capture: Computer versus Pencil-and-Paper."  This title has three factors to recommend it - an important andpopular application (carbon dioxide capture), one of the most fundamental concepts in chemistry (pKa andhence Brønsted acidity), and the title itselfinvokes images of a titanic struggle between a giant pencil and a multi-headedLinux cluster beast, perhaps akin to the Leviathans from recent Avengers movie.

Thus, suitably intrigued, I read on.The authors reported a new pKa calculational method, entitled SHE - one assumes thatthe abbreviation denotes theauthor's last names. The rationale for the various energetic contributionsneeded for ab initio computed pKavalues like the free energy of the proton in aqueous solution were given. Themethod was then applied to organic amines of interest in carbon capture, morespecifically the amines used to strip carbon dioxide from power plant effluent.

The underlying electronic energiesneeded to compute thedifference in free energy between an amine base (B) and its Brønsted conjugate acid (BH+)were computed at the MP2/6-31G(d) level of theory. The basis set settled uponby the authors was compared to larger basis sets - triple zeta, withpolarization functions on H, inclusion of diffusion functions, etc. - and the smaller basis setreproduced a larger, extended basis set reasonably well for a subset ofprimary, secondary, tertiary and cyclic amines. Moreover, I assumed that anydifferences introduced by the use of a less complete basis set could be accounted for with theempirical constant C (more about that below). Obviously, smaller basis setswill permit access to larger amines, as the authors pointed out.

For the ab initio calculations, the authors also investigated the role ofthe atomic radii (used in the continuum solvation calculations) as well as the impactof conformational flexibility. The latter issue is also one of the majordifficulties in developing and applying paper-and-pencil methods, in that thefunctional groups of a molecule are the same whether or not it is in a low orhigh energy conformation, and thus so-called 2D methods cannot distinguish onefrom the other, and both would thus be predicted to have identical properties.

Interestingly, only electronic energies (thusobviating the need for a potentially expensive Hessian calculation) wereutilized as current and previous analyses by the author indicated that the zeropoint, enthalpic and entropic corrections to convert electronic energiesto free energies were nearconstant given the chemical similarity of the conjugate acid-base pairs (B andBH+ or B-OH2 and BH+-OH2) that makeup the amine systems of interest. For the latter conjugate pair, an extra watermolecule was added to the continuum solvent cavity to mimic what some mightrefer to as microsolvation (Model II in the author's jargon).

An empirical constant of 1.7 pKaunits for cyclic amines and 0.7 pKa units for acyclic amines was subtracted toput computed values into better correspondence with experimentalvalues for a test set of 32 molecules, and presumably to account for some ofthe uncertainty and approximations made elsewhere in the SHE procedure.

Hence, the authors presented acompact, computationally efficient procedure for computing the pKa's of amines.Arrayed against this approach is a more old school, parametric method. For those of us old enoughto remember the days before computers were all powerful, the use of parametricmethods for estimating important quantities was a popular researchendeavor for understanding and estimating important physicalquantities of novel materials. Benson's rules for predicting heats offormation,[2]and Drago's EC model for acid-base reaction enthalpies,[3]are but two examples of parametric methods. Today, the parametric approach is embodied in QSPR and QSARanalyses, many of which have at their heart an assumption of group additivity,which assumes that the whole (molecule) is the sum of its parts (functionalgroups).

The pencil-and-paper method utilizedby the authors was the PDS (Perrin-Dempsey-Sarjeant) technique. Not requiringany MP2 computations,the method is, ofcourse, much faster than "computer" methods. Like all methods, it islimited by the functional group approximation. Therefore, if one would like touse PDS to estimate thepKa of a new material, which contains a functional group not in the originalparameterization, then one is faced with the daunting task of extending theparameterization to the new functional group. Of course, any attempts to go “outsidethe box,” will always going to suffer from the uncertainty that arises fromextrapolation versus interpolation, which has always been a problem forparametric methods.

The authors presented an updated PDSmethod by introducing new base values and functional group corrections, whichessentially halved the RMS error for amines of interest in carbon dioxidecapture.

Finally, with this framework, theepic battle between computer and paper/pencil was on! And, it was a true battleroyale, with parametric and computational methods squaring off among themselvesand with each other. The old and new PDS methods were compared for a test setof 32 amines, and the latter, as alluded to above, outperformed the former by afactor of two. The new PDS method yielded a pKa error of only 0.18 pKa units.The SHE method had an RMS error of 0.28, hence only marginally higher. Theinclusion of the C empirical constant reduced the error in the SHE method bynearly 1 pKa unit. At the end of the struggle, the SHE method stood alone inthe ring. It had an RMS error less than the other approaches investigated bythe authors in this paper, and given the attention the authors put into makingit as computationally efficient as possible, one would expect this recipe tohave significant upside for larger organic amines. However, the updated PDSmethod fought valiantly, and would seem to be an interesting candidate for furtherresearch to diversify it to alarger functional grouplibrary.

Likewise, it would also be ofinterest to diversify the SHE method in a similar manner to investigate a greater range of possible CO2sorbents. Other possible extensions include assessing the impact of lessexpensive abs initio methods likeHartree-Fock (yes, good old Hartree-Fock!) or perhaps DFT, instead of MP2, tobring the SHE method to larger and more complex organics amines and indeed evennon-amines.

[1]      Predicting pKa of Amines for CO2 Capture: Computer versusPencil-and-Paper.  K Z. Sumon, A. Henni, and Allan L. L. East. Industrial& Engineering Chemistry Research 2012 51 (37),11924-11930
[2]      Estimation of heats of formation of organic compounds by additivitymethods. N. Cohen and S. W.Benson. Chemical Reviews 1993 93 (7), 2419-2438
[3]      A Double-Scale Equation for Correlating Enthalpies of Lewis Acid-BaseInteractions. R. S. Dragoand B. B. Wayland. Journal of the American Chemical Society 1965 87(16), 3571-3577