Myśliwiec and Stępień report on a new method for creating buckybowls.¹ The usual way had been to build from the inside outward. They opt instead to build from the outside in and have constructed the heterosubstitued bowl chrysaorole 1.

1

B3LYP/6-31G** optimizations reveal two conformers that are very close in energy: one has the butyl chains outstretched (1a) and one has the butyl arms internal or pendant (1b). These structures are shown in Figure 1. The depth of this bowl (1.96 Å) is quite a bit larger than in corranulene (0.87 Å). The agreement between the computed and experimental ¹³C and ¹H chemical shifts are excellent, supporting the notion that this gas phase geometry is similar to the solution phase structure. Though 1 is strained, 53.4 kcal mol^-1 based on B3LYP/6-31G** energies for Reaction 1 (which uses the parent of 1 – replacing the butyl groups with hydrogens), on a per sp² atom basis, it is no more strained than corranulene.

1a

1b

Figure 1. B3LYP/6-31G** optimized geometries of two conformers of 1.

This new synthetic strategy is likely to afford access to more unusual aromatic structures.

References

(1) Myśliwiec, D.; Stępień, M. "The Fold-In Approach to Bowl-Shaped Aromatic Compounds: Synthesis of Chrysaoroles," Angew. Chem. Int. Ed. 2013, 52, 1713-1717, DOI:10.1002/anie.201208547.

InChI

1: InChI=1S/C54H45N3/c1-4-7-16-55-49-19-31-10-12-33-21-51-45-27-39(33)37(31)25-43(49)44-26-38-32(20-50(44)55)11-13-34-22-52-46(28-40(34)38)48-30-42-36(24-54(48)57(52)18-9-6-3)15-14-35-23-53(47(45)29-41(35)42)56(51)17-8-5-2/h10-15,19-30H,4-9,16-18H2,1-3H3
InChIKey=VUUJVETWVYQACL-UHFFFAOYSA-N

A short note here mainly to call to the reader’s attention a fascinating “trialogue” on the C₂ molecule.¹ Shaik, Danovich, Wu, Su, Rzepa, and Hiberty² recently presented a full CI study of C₂ and concluded that the molecule contains a quadruple bond (see my previous post on this paper). This work was inspired in part by a blog post by Henry Rzepa.

The trialogue¹ is a conversation between Sason Shaik, Henry Rzepa and Roald Hoffmann about the nature of C₂, its 4^th bond, its diradical character, and some historical detours to see how some of our theoretical chemistry ancestors came close to proposing a quadruple bond. The discussion weaves together simple MO pictures, simple VB models, and the need for much more sophisticated analysis to ultimately approach the truth. Very much worth pointing out is the careful analysis of trying to tease out bond dissociation energies, especially analyzing the assumptions made here – including the possibility of errors in the experiments and not just errors in the computations! This is a very enjoyable read, following these three theoreticians as they traipse about the complex C₂ landscape!

References

(1) Shaik, S.; Rzepa, H. S.; Hoffmann, R. "One Molecule, Two Atoms, Three Views, Four Bonds?," Angew. Chem. Int. Ed. 2013, 52, 3020-3033, DOI: 10.1002/anie.201208206.

(2) Shaik, S.; Danovich, D.; Wu, W.; Su, P.; Rzepa, H. S.; Hiberty, P. C. "Quadruple bonding in C2 and analogous eight-valence electron species," Nat. Chem. 2012, 4, 195-200, DOI: 10.1038/nchem.1263.

Truhlar has made a comparison of binding energies and relative energies of five (H₂O)₁₆ clusters.¹ 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.² 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 post for a definition of the ‘jun’ basis sets). 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.

1 (0.0)	2 (0.25)
3 (0.42)	4 (0.51)
5 (0.54)

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.

References

(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: 10.1021/ct300848z.

(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: 10.1021/jz101245s.

I have discussed a few bowl-shaped aromatics in this blog (see for example this and this). Kuo and Wu now report on a few bowls derived from C₇₀-fullerenes.¹ The bowl 1 was synthesized (along with a couple of other derivatives) and its x-ray structure obtained. As anticipated this polyclic aromatic is not planar, but rather a definite bowl, with a bowl depth of 2.28 Å. This is less curved than when the fragment is present in C₇₀-fullerene.

Interestingly, this bowl does not invert through a planar transition state. The fully planar structure 1pl, shown in Figure 1, is 116 kcal mol^-1 above the ground state bowl structure, computed at B3LYP/cc-pVDZ. Rather, the molecule inverts through a twisted S-shaped structure 1TS, also shown in Figure 1. The activation barrier through 1TS is 80 kcal mol^-1. This suggests that 1 is static at room temperature, unlike corranulene which has an inversion barrier, through a planar transition state, of only 11 kcal mol^-1. The much more concave structure of 1 than corranulene leads to the greatly increased strain in its all-planar TS. This implies that properly substituted analogues of 1 will be chiral and configurationally stable. Not remarked upon is that the inversion pathway, which will interchange enantiomers when 1 is properly substituted, follows a fully chiral path, as discussed in this post.

1
1TS	1pl

Figure 1. B3LYP/cc-pVDZ optimized geometries of 1, 1TS, and 1pl.

Reference

(1) Wu, T.-C.; Chen, M.-K.; Lee, Y.-W.; Kuo, M.-Y.; Wu, Y.-T. "Bowl-Shaped Fragments of C₇₀ or Higher Fullerenes: Synthesis, Structural Analysis, and Inversion Dynamics," Angew. Chem. Int. Ed. 2013, 52, 1289-1293, DOI: 10.1002/anie.201208200.

InChIs

1: InChI=1S/C38H14/c1-3-17-21-11-7-15-9-13-23-19-5-2-6-20-24-14-10-16-8-12-22-18(4-1)27(17)33-35-29(21)25(15)31(23)37(35)34(28(19)20)38-32(24)26(16)30(22)36(33)38/h1-14H
InChIKey=KLCLRPVBVWXTPN-UHFFFAOYSA-N

With the recent disclosure of a major security hole in Java, I have been wondering if perhaps my continued use of the Jmol utility for displaying 3-D molecular structures makes sense. Perhaps it is time to consider alternatives. (Right now if you click on a molecule image in one of my blog posts and you are using Firefox, a big warning sign comes up first requiring the user to actively decide to invoke the Jmol viewer. Might this warning be enough to discourage some users?)

In addition, the increasing use of mobile devices, which most often are not Java-enabled, suggests that moving to a new display option is warranted.

So, I am asking the community to participate in a conversation about how we might best address this issue in the (near) future. Is a Javascript widget the way to go? If so, which current program are people happy with? Or should we move to an HTML5 approach? And if this is the way to go, what tools are people suggesting?

If you want to see some fine examples of all three approaches (Java-based: Jmol, Javascipt-based: Chemdoodle, and HTML5-based: GLMol) I strongly encourage you to read Henry Rzepa’s recent brilliant article in Journal of Cheminformatics (DOI: 10.1186/1758-2946-5-6). This is a fantastic article to compare the old-school publication technology (as presented in modern day PDF form) and new-school enabled technology (what Henry calls a datument). First download the pdf version and read it, and then access the HTML version; I guarantee you will be impressed by the difference in the experience.

So, please chime in on what molecular viewers I might adopt for this blog, and perhaps we as a community might be able to encourage the use of and further the development of these enhanced publication technologies.

Nanotubes are currently constructed in ways that offer little control of their size and chirality. The recent synthesis of cycloparaphenylenes (CPP) provides some hope that fully controlled synthesis of nanotubes might be possible in the near future. Jasti has now made an important step forward in preparing dimers of CPP such as 1.¹

They also performed B3LYP-D/6-31G(d,p) computations on 1 and the directly linked dimer 2. The optimized geometries of these two compounds in their cis and trans conformations are shown in Figure 1. Interestingly, both compounds prefer to be in the cis conformation; cis–1 is 10 kcal mol^-1 more stable than trans–1 and cis–2 is 30 kcal mol^-1 more stable than the trans isomer. While a true transition state interconnecting the two isomers was not located, a series of constrained optimizations to map out a reaction surface suggests that the
barrier for 1 is about 13 kcal mol^-1. The authors supply an interesting movie of this pseudo-reaction path (download the movie).

cis–1	trans–1
cis–2	trans–2

Figure 1. B3LYP-D/6-31G(d,p) optimized geometries of the cis and trans conformers of 1 and 2. (Be sure to click on these images to launch a 3-D viewer; these structures come to life in 3-D!)

References

(1) Xia, J.; Golder, M. R.; Foster, M. E.; Wong, B. M.; Jasti, R. "Synthesis, Characterization, and Computational Studies of Cycloparaphenylene Dimers," J. Am. Chem. Soc. 2012, 134, 19709-19715, DOI: 10.1021/ja307373r.

InChIs

1: InChI=1S/C106H82/c1-5-13-79-21-9-17-76-29-37-85(38-30-76)95-59-63-98(64-60-95)103-71-69-101(82(16-8-4)24-12-20-77-27-35-84(36-28-77)90-51-55-94(56-52-90)91-45-41-86(79)42-46-91)73-105(103)99-65-67-100(68-66-99)106-74-102-70-72-104(106)97-61-57-88(58-62-97)81(15-7-3)23-10-18-75-25-33-83(34-26-75)89-49-53-93(54-50-89)92-47-43-87(44-48-92)80(14-6-2)22-11-19-78-31-39-96(102)40-32-78/h5-16,21-74H,1-4,17-20H2/b21-9-,22-11-,23-10-,24-12-,79-13+,80-14+,81-15+,82-16+
InChIKey=WFVBBCVHFBTQRK-VPGVYKRGSA-N

2: InChI=1S/C100H78/c1-5-13-75-21-9-17-72-29-37-81(38-30-72)91-59-63-94(64-60-91)97-67-65-95(78(16-8-4)24-12-20-73-27-35-80(36-28-73)86-51-55-90(56-52-86)87-45-41-82(75)42-46-87)69-99(97)100-70-96-66-68-98(100)93-61-57-84(58-62-93)77(15-7-3)23-10-18-71-25-33-79(34-26-71)85-49-53-89(54-50-85)88-47-43-83(44-48-88)76(14-6-2)22-11-19-74-31-39-92(96)40-32-74/h5-16,21-70H,1-4,17-20H2/b21-9-,22-11-,23-10-,24-12-,75-13+,76-14+,77-15+,78-16+
InChIKey=HOODCSIDKUJYKE-XJQPCHFNSA-N

Basis set superposition error plagues all practical computations. This error results from the use of incomplete basis sets (thus pretty much all computations will suffer from this problem). The primary example of this error is in the formation of a supermolecule AB from the monomers A and B. Superposition occurs when in the computation of the supermolecule, basis functions centered on B are used to supplement the basis set of A, not to describe the bonding or interaction between the two monomers, but simply to better the description of the monomer A itself. Thus, BSSE always serves to increase the binding in the supermolecule. Recently, this concept has been extended to intramolecular BSSE, as discussed in these posts (A and B).

The counterpoise correction proposed by Boys and Bernardi corrects for the superposition by computing the energy of each monomer using the basis sets centered on both monomers, often referred to as ghost orbitals because the functions are used but not the nuclei upon which they are centered. This can overcorrect for superposition but is the only widely utilized approach to treat the problem. A variation on this approach is what has been suggested for the intramolecular
BBSE problem.

A major discouragement for wider use of counterpoise correction is its computational cost. Kruse and Grimme offer a semi-empirical approach that is extremely cost effective and appears to strongly mimic the traditional counterpoise correction.¹

They define the geometric counterpoise scheme (gCP) that provides an energy correction E_gCP that can be added onto the electronic energy. This term is defined as

Eq. (1)

where σ is an empirically fitted scaling term. The atomic contributions are defined as

where e^miss are the errors in the energy of an atom with a particular target basis set, relative to the energy with some large basis set:

(On a technical matter, the atomic terms are computed in an electric field of 0.6a.u. in order to get some population into higher energy orbitals.) The f_dec term is a decay function that relates to the distance between the atoms (R_nm) and the overlap
(S_nm):

where N^virt is the number of virtual orbitals on atom m, and α and β are fit parameters. Lastly, the overlap term comes from the integral of a single Slater orbital with coefficient

where ξ_s and ξ_p are optimized Slater exponents from extended Huckel theory, and η is the last parameter that needs to be fit.

There are four parameters and these need to be fit for each specific combination of method (functional) and basis set. Kruse and Grimme provide parameters for a number of combinations, and suggest that the parameters devised for B3LYP are suitable for other functionals.

So what is this all good for? They demonstrate that for a broad range of benchmark systems involving weak bonds, the that gCP corrected method coupled with the DFT-D3 dispersion correction provides excellent results, even with B3LYP/6-31G*! This allows one to potentially run a computation on very large systems, like proteins, where large basis sets, like TZP or QZP, would be impossible. In a follow-up paper,² they show that the B3LYP/6-31G*-gCP-D3 computations of a few Diels-Alder reactions and computations of strain energies of fullerenes match up very well with computations performed at significantly higher levels.

Once this gCP method and the D3 correction are fully integrated within popular QM programs, this combined methodology should get some serious attention. Even in the absence of this integration, these energy corrections can be obtained using the web service provided by Grimme at http://www.thch.uni-bonn.de/tc/gcpd3.

References

(1) Kruse, H.; Grimme, S. "A geometrical correction for the inter- and intra-molecular basis set superposition error in Hartree-Fock and density functional theory calculations for large systems," J. Chem. Phys 2012, 136, 154101-154116, DOI: 10.1063/1.3700154

(2) Kruse, H.; Goerigk, L.; Grimme, S. "Why the Standard B3LYP/6-31G* Model Chemistry Should Not Be Used in DFT Calculations of Molecular Thermochemistry: Understanding and Correcting the Problem," J. Org. Chem. 2012, 77, 10824-10834, DOI: 10.1021/jo302156p

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.¹ 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 SM12.² 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.

References

(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: 10.1021/ct300813c

(2) Marenich, A. V.; Cramer, C. J.; Truhlar, D. G. "Generalized Born Solvation Model SM12," J. Chem. Theor. Comput. 2013, 9, 609-620, DOI: 10.1021/ct300900e

I have written a number of posts discussing long C-C bonds (here and here). What about very long bonds between carbon and a heteroatom? Well, Mascal and co-workers¹ have computed the structures of some oxonium cations that express some very long C-O bonds. The champion, computed at MP2/6-31+G**, is the oxatriquinane 1, whose C-O bond is predicted to be 1.602 Å! (It is rather disappointing that the optimized structures are not included in the supporting materials!) The long bond is attributed not to dispersion forces, as in the very long C-C bonds (see the other posts), but rather to σ(C-H) or σ(C-C) donation into the σ*(C-O) orbital.

1

Inspired by these computations, they went ahead and synthesized 1 and some related species. They were able to get crystals of 1 as a (CHB₁₁Cl₁₁)^– salt. The experimental C-O bond lengths for the x-ray crystal study are 1.591, 1.593, and 1.622 Å, confirming the computational prediction of long C-O bonds.

As an aside, they also noted many examples of very long C-O distances within the Cambridge
Structural database that are erroneous – a cautionary note to anyone making use of this database to identify unusual structures.

References

(1) Gunbas, G.; Hafezi, N.; Sheppard, W. L.; Olmstead, M. M.; Stoyanova, I. V.; Tham, F. S.; Meyer, M. P.; Mascal, M. "Extreme oxatriquinanes and a record C–O bond length," Nat. Chem. 2012, 4, 1018-1023, DOI: 10.1038/nchem.1502

InChIs

1: InChI=1S/C21H39O/c1-16(2,3)19-10-12-20(17(4,5)6)14-15-21(13-11-19,22(19)20)18(7,8)9/h10-15H2,1-9H3/q+1/t19-,20+,21-
InChIKey=VTBHIDVLNISMTR-WKCHPHFGSA-N

Two interesting questions are addressed in a focal-point computational study of t-butyl radical and the t-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. 2012, 8, 4323-4329, DOI: 10.1021/ct300753d.