Capturing buckyballs involves molecular design based on non-covalent interactions. This poses interesting challenges for both the designer and the computational chemist. The curved surface of the buckyball demands a sequestering agent with a complementary curved surface, likely an aromatic curved surface to facilitate π-π stacking interactions. For the computational chemist, weak interactions, like dispersion and π-π stacking demand special attention, particularly density functionals designed to account for these interactions.

Two very intriguing new buckycatchers were recently prepared in the Sygula lab, and also examined by DFT.¹ Compounds 1 and 2 make use of the scaffold developed by Klärner.² In these two buckycatchers, the tongs are corranulenes, providing a curved aromatic surface to match the C₆₀ and C₇₀ surface. They differ in the length of the connector unit.

B97-D/TZVP computations of the complex of 1 and 2 with C₆₀ were carried out. The optimized structures are shown in Figure 1. The binding energies (computed at B97-D/QZVP*//B97-D/TZVP) of these two complexes are really quite large. The binding energy for 1:C₆₀ is 33.6 kcal mol^-1, comparable to some previous Buckycatchers, but the binding energy of 2:C₆₀ is 50.0 kcal mol^-1, larger than any predicted before.

1

2

Figure 1. B97-D/TZVP optimized geometries of 1:C₆₀and 2:C₆₀.

Measurement of the binding energy using NMR was complicated by a competition for one or two molecules of 2 binding to buckyballs. Nonetheless, the experimental data show 2 binds to C₆₀ and C₇₀ more effectively than any previous host. They were also able to obtain a crystal structure of 2:C₆₀.

References

(1) Abeyratne Kuragama, P. L.; Fronczek, F. R.; Sygula, A. "Bis-corannulene Receptors for Fullerenes Based on Klärner’s Tethers: Reaching the Affinity Limits," Org. Lett. 2015, ASAP, DOI: 10.1021/acs.orglett.5b02666.

(2) Klärner, F.-G.; Schrader, T. "Aromatic Interactions by Molecular Tweezers and Clips in Chemical and Biological Systems," Acc. Chem. Res. 2013, 46, 967-978, DOI: 10.1021/ar300061c.

InChIs

1: InChI=1S/C62H34O2/c1-63-61-57-43-23-45(41-21-37-33-17-13-29-9-5-25-3-7-27-11-15-31(35(37)19-39(41)43)53-49(27)47(25)51(29)55(33)53)59(57)62(64-2)60-46-24-44(58(60)61)40-20-36-32-16-12-28-8-4-26-6-10-30-14-18-34(38(36)22-42(40)46)56-52(30)48(26)50(28)54(32)56/h3-22,43-46H,23-24H2,1-2H3/t43-,44+,45+,46-
InChIKey=RLOJCVYXCBOUQB-RYSLUOGPSA-N

2: InChI=1S/C66H36O2/c1-67-65-51-24-45-43-23-44(42-20-38-34-16-12-30-8-4-27-3-7-29-11-15-33(37(38)19-41(42)43)59-55(29)53(27)56(30)60(34)59)46(45)25-52(51)66(68-2)64-50-26-49(63(64)65)47-21-39-35-17-13-31-9-5-28-6-10-32-14-18-36(40(39)22-48(47)50)62-58(32)54(28)57(31)61(35)62/h3-22,24-25,43-44,49-50H,23,26H2,1-2H3/t43-,44+,49+,50-
InChIKey=JAUUHTKCNSNBMD-NETXOKAWSA-N

Feng, Müller and co-workers have prepared a bistetracene analogue 1.¹ This molecule displays some interesting features. While a closed shell Kekule structure can be written, a biradical structure results in more closed Clar rings, suggesting that perhaps the molecule is a ground state singlet biradical. The loss of NMR signals with increasing temperature along with an EPR signal that increases with temperature both support the notion of a ground state singlet biradical with a triplet excited state. The EPR measurement suggest as singlet-triplet gap of 3.4 kcal mol^-1.

The optimized B3LYP/6-31G(d,p) geometries of the biradical singlet and triplet states are shown in Figure 1. The singlet is lower in energy by 6.7 kcal mol^-1. The largest spin densities are on the carbons that carry the lone electron within the diradical-type Kekule structures.

singlet 1

triplet 1

Figure 1. B3LYP/6-31G(d,p) optimized geometries of the biradical singlet and triplet states of 1.

References

(1) Liu, J.; Ravat, P.; Wagner, M.; Baumgarten, M.; Feng, X.; Müllen, K. "Tetrabenzo[a,f,j,o]perylene: A Polycyclic Aromatic Hydrocarbon With An Open-Shell Singlet Biradical Ground State," Angew. Chem. Int. Ed. 2015, 54, 12442-12446, DOI: 10.1002/anie.201502657.

InChIs

1: InChI=1S/C62H56/c1-33-25-35(3)51(36(4)26-33)53-45-17-13-15-19-47(45)57-56-44-24-22-42(62(10,11)12)30-40(44)32-50-54(52-37(5)27-34(2)28-38(52)6)46-18-14-16-20-48(46)58(60(50)56)55-43-23-21-41(61(7,8)9)29-39(43)31-49(53)59(55)57/h13-32H,1-12H3
InChIKey=LPRMROONCKWUEJ-UHFFFAOYSA-N

Cramer, Hoye, Kuwata and coworkers have examined the intramolecular cyclization of an alkyne with a diyne.¹ Their model system is 1, which can cyclize through a concerted transition state TSC togive the benzyne product 2, or it can proceed through a stepwise pathway, first going through TS1 to form the intermediate INT¸ before traversing through a second transition state TS2 and on to product 2. Using both computations and experiments, they examined a series of compounds with
differing substituents at the ends of the two yne moieties.

The experiments show almost the exact same rate of reaction regardless of the terminal substituents. This includes the parent case where the terminal substituents are hydrogens and also the case where the terminal substituents (which end up on adjacent centers on the benzyne ring) are bulky TMS groups. And though there is no real rate effect due to changes in solvent or the presence of light or triplet oxygen, which suggest a concerted reaction, these substituent effects argue for a step wise reaction.

SMD(o-dichlorobenzene)/B3LYP-D3BJ/6-311+G-(d,p)//M06-2X/6-311+G(d,p)
computations help explain these observations. Shown in Figure 1 are the optimized geometries and relative energies of the critical points on the reaction surface for the conversion of 1 into 2, and these results are similar with the other substituents as well.

1 (0.0)	2 (-56.9)
TSC (31.5)
TS1 (25.5)	INT (18.8)
TS2 (18.1)

Figure 1. SMD(o-dichlorobenzene)/B3LYP-D3BJ/6-311+G-(d,p)//M06-2X/6-311+G(d,p) optimized geometries and relative energies (kcal mol^-1).

The first thing to note is that the concerted TSC is higher in energy than the stepwise TS1. The wavefunction for TSC unstable towards moving from a restricted to unrestricted formalism. Reoptimization of some of these concerted TSs actually led to the stepwise TS.

The next item of note is that TS2 for this case is actually lower in energy than the intermediate (this is a true TS on the energy surface, but when zero-point energy and other thermal corrections are included, it becomes lower in energy than INT). For some of the cases the second TS lies above the intermediate, but typically by a small amount.

Therefore, the mechanism of this reaction is stepwise, but the second step might have such a small barrier (or even no barrier) that one might consider this to be concerted, though highly asymmetric and really bearing little resemblance to more traditional concerted pericyclic reactions.

The authors obliquely hinted at some potential interesting dynamics. I suspect that molecular dynamics calculations will show no effect of that second TS, and one might observe some interesting dynamics, which could be seen in kinetic isotope experiments.

References

(1)  Marell, D. J.; Furan, L. R.; Woods, B. P.; Lei, X.; Bendelsmith, A. J.; Cramer, C. J.; Hoye, T. R.; Kuwata, K. T. "Mechanism of the Intramolecular Hexadehydro-Diels–Alder Reaction," J. Org. Chem. 2015 ASAP, DOI: 10.1021/acs.joc.5b01356.

InChIs

1: InChI=1S/C8H4O2/c1-3-5-6-7-10-8(9)4-2/h1-2H,7H2
InChIKey=MGXDIFXPYGGQLF-UHFFFAOYSA-N

2: InChI=1S/C8H4O2/c9-8-7-4-2-1-3-6(7)5-10-8/h2,4H,5H2
InChIKey=MYFORDRJCVOBTH-UHFFFAOYSA-N

I want to update my discussion of m-benzyne, which I present in my book in Chapter 5.5.3. The interesting question concerning m-benzyne concerns its structure: is it a single ring structure 1a or a bicyclic structure 1b? Single configuration methods including closed-shell DFT methods predict the bicylic structure, but multi-configuration methods and unrestricted DFT predict it to be 1a. Experiments support the single ring structure 1a.

The key measurement distinguishing these two structure type is the C₁-C₃ distance. Table 1 updates Table 5.11 from my book with the computed value of this distance using some new methods. In particular, the state-specific multireference coupled cluster Mk-MRCCSD method¹ with the cc-pCVTZ basis set indicates a distance of 2.014 Å.² The density cumulant functional theory³ ODC-12⁴ with the cc-pCVTZ basis set also predicts the single ring structure with a distance of 2.101 Å.⁵

Table 1. C₁-C₃ distance (Å) with different computational methods using the cc-pCVTZ basis set

References

(1) Evangelista, F. A.; Allen, W. D.; Schaefer III, H. F. "Coupling term derivation and general implementation of state-specific multireference coupled cluster theories," J. Chem. Phys 2007, 127, 024102-024117, DOI: 10.1063/1.2743014.

(2) Jagau, T.-C.; Prochnow, E.; Evangelista, F. A.; Gauss, J. "Analytic gradients for Mukherjee’s multireference coupled-cluster method using two-configurational self-consistent-field orbitals," J. Chem. Phys. 2010, 132, 144110, DOI: 10.1063/1.3370847.

(3) Kutzelnigg, W. "Density-cumulant functional theory," J. Chem. Phys. 2006, 125, 171101, DOI: 10.1063/1.2387955.

(4) Sokolov, A. Y.; Schaefer, H. F. "Orbital-optimized density cumulant functional theory," J. Chem. Phys. 2013, 139, 204110, DOI: 10.1063/1.4833138.

(5) Mullinax, J. W.; Sokolov, A. Y.; Schaefer, H. F. "Can Density Cumulant Functional Theory Describe Static Correlation Effects?," J. Chem. Theor. Comput. 2015, 11, 2487-2495, DOI: 10.1021/acs.jctc.5b00346.

InChIs

1a: InChI=1S/C6H4/c1-2-4-6-5-3-1/h1-3,6H

To advance our understanding of why ribose takes on the furanose form, rather than the pyranose form, in RNA, Alonso and co-workers have examined the structure of uridine 1 in the gas phase.¹

1

Uridine is sensitive to temperature, and so the laser-ablation method long used by the Alonso group is ideal for examining uridine. The microwave spectrum is quite complicated due to the presence of many photofragments. Careful analysis lead to the identification of a number of lines and hyperfine structure that could be definitively assigned to uridine, leading to experimental values of the rotational constants and the diagonal elements of the ¹⁴N nuclear quadrupole coupling tensor for each nitrogen. These values are listed in Table 1.

Table 1. Experimental and calculated rotational constants (MHz), quadrupole coupling constants (MHz) and relative energy (kcal mol^-1).

In order to assign a 3-D structure to these experimental values, they examined the PES of uridine with molecular mechanics and semi-empirical methods, before reoptimizing the structure of the lowest 5 energy structures at MP2/6-311++G(d,p). Then, comparison of the resulting rotational constants and ¹⁴N nuclear quadrupole coupling constants of these computed structures (see Table 1) led to identification of the lowest energy structure (anti/C2’-endo-g+, see Figure 1) in best agreement with the experiment. Once again, the Alonso group has demonstrated the value of the synergy between experiment and computation in structure identification.

Figure 1. MP2/6-311++G(d,p) optimized structure of 1 (anti/C2’-endo-g+).

References

(1) Peña, I.; Cabezas, C.; Alonso, J. L. "The Nucleoside Uridine Isolated in the Gas Phase," Angew. Chem. Int. Ed. 2015, 54, 2991-2994, DOI: 10.1002/anie.201412460.

Inchis:

1: Inchi=1S/C9H12N2O6/c12-3-4-6(14)7(15)8(17-4)11-2-1-5(13)10-9(11)16/h1-2,4,6-8,12,14-15H,3H2,(H,10,13,16)/t4-,6-,7-,8-/m1/s1
InChiKey=DRTQHJPVMGBUCF-XVFCMESISA-N

The Alonso group has yet again (see these posts) determined the gas-phase structure of an important, biologically significant molecule using a combination of exquisite microwave spectroscopy and quantum computations. This time they examine the structure of histidine.¹

They optimized four conformations of histidine, as its neutral tautomer, at MP2/6-311++G(d,p). These are schematically drawn in Figure 1. Conformer 1a is the lowest in free energy, likely due to the two internal hydrogen bonds. Its structure is shown in Figure 2.

Figure 1. The four conformers of histidine. The relative free energy (MP2/6-311++G(d,p)) in kcal mol^-1 are also indicated.

Figure 2. MP2/6-311++G(d,p) optimized geometry of 1a.

The initial experimental rotation constants were only able to eliminate 1b from consideration. So they then determined the quadrupole coupling constants for the ¹⁴N nuclei. These values strongly implicated 1a as the only structure in the gas phase. The agreement between the experimental values and the computed values at MP2/6-311++G(d,p) was a concern, so they rotated the amine group to try to match the experimental values. This lead to a change in the NHCC dihedral value of -16° to -23° Reoptimization of the structure at MP2/cc-pVTZ led to a dihedral of -21° and overall excellent agreement between the experimental spectral parameters and the computed values.

It is somewhat disappointing the supporting materials does not include the structures of the other three isomers, nor the optimized geometry at MP2/cc-pVTZ.

References

1) Bermúdez, C.; Mata, S.; Cabezas, C.; Alonso, J. L. "Tautomerism in Neutral Histidine," Angew. Chem. Int. Ed. 2014, 53, 11015-11018, DOI: 10.1002/anie.201405347.

InChIs

Histidine: InChI=1S/C6H9N3O2/c7-5(6(10)11)1-4-2-8-3-9-4/h2-3,5H,1,7H2,(H,8,9)(H,10,11)/t5-/m0/s1
InChIKey=HNDVDQJCIGZPNO-YFKPBYRVSA-N

Comparing S_N2 and S_N1 reactions using computational methods is often quite difficult. The problem is that the heterolytic cleavage in the S_N1 reaction leads to an ion pair, and in the gas phase this is a highly endothermic process. Optimization of the ion pair in the gas phase invariably leads to recombination. This is disturbingly the result even when one uses PCM to mimic the solvent, which one might have hoped would be sufficient to stabilize the ions.

The computational study of the glycoside cleavage by Hosoya and colleagues offers some guidance towards dealing with this problem.¹ They examined the cleavage of triflate from 2,3,4,6-tetra-O-methyl-α-D-glucopyranosyl triflate 1.

Benchmarking the dissociation energy for the cleavage of 1 and considering computational performance, they settled on M06-2X/BS-III//M06-2X/BS-I, where BS-III is aug-cc-pVTZ basis set for O, F, and Cl and cc-pVTZ for H, C, and S and BS-I is 6-31G(d,p) basis sets were employed for H, C, and S, and 6-31+G(d) for O, F, and Cl. Solvent (dichloromethane) was included through PCM.

Attempted optimization of the contact ion pair formed from cleavage of 1 invariably led back to the covalent bound 1. PCM is not capable of properly stabilizing these types of ions in proximity. To solve this problem, they incorporated four explicit dichloromethane molecules. A minor drawback to their approach is that they did not sample much of configuration space and so their best geometries may not be the lowest energy configurations. Nonetheless, with four solvent molecules, they were able to locate contact ion pairs and solvent-separated ion pairs. Representative examples are shown in Figure 1. This method of explicit incorporation of a few solvent molecules seems to be the direction we must take to treat ions or even highly polar molecules in solution.

1 0.0	1-CIP 8.5
1-SSIPa 8.4	1-SSIPb 11.1

Figure 1. Representative examples of microsolvated 1, its contact ion pair (CIP) and solvent separated ion pair (SSIP) computed at M06-2X/BS-III//M06-2X/BS-I, and relative energies (kcal mol^-1)

References

(1) Hosoya, T.; Takano, T.; Kosma, P.; Rosenau, T. "Theoretical Foundation for the Presence of Oxacarbenium Ions in Chemical Glycoside Synthesis," J. Org. Chem. 2014, 79, 7889-7894, DOI: 10.1021/jo501012s.

InChIs

1: InChI=1S/C11H19F3O8S/c1-17-5-6-7(18-2)8(19-3)9(20-4)10(21-6)22-23(15,16)11(12,13)14/h6-10H,5H2,1-4H3/t6-,7-,8+,9-,10-/m1/s1
InChIKey=RPZNYYCDDYUPJR-HOTMZDKISA-N

Diels-Alder reaction involving fullerenes have been known for some time. They occur across the [6,6] double bond of C₆₀, the one between two fused 6-member rings. Houk and Briseno report on the Diels-Alder reaction of C₆₀ with pentacene 1 and bistetracene 2 and compare their computations with experiments.¹

Pentacene and bistetracene ring numbering convention

Computations were performed for the reaction of 1 and 2 with C₆₀ at M06-2x/6-31G(d)//M062x-3-21G*. The reaction can occur with the dienophile being either ring 1, 2, or 3 of pentacene and ring 1, 2, 3, or 4 of bistetracene. They located TSs and products for all of these possibilities. Select TSs and products are shown in Figure 1.

For the reaction of 1a, the lowest energy TS is for the reaction at the central ring (ring 3), and the resulting product is the lowest energy product. The transition state (PT_TS3) is shown in Figure 1. This TS has the least distortion energy of the three possibilities, because reacting at this central ring destroys the least amount of aromaticity of pentacene. For the reaction of 1b, the lowest barrier is again for reaction of ring 3 (through TMSPT_TS3). However, the product from the reaction with ring 2 (TMSPT_P2) is lower in free energy than TMSPT­_P3, likely caused by steric interactions with the silyl substituents. This actually matches up with experiments which indicate that an analogue of TMSPT_P2 is the kinetic product but TMSPT_P3 is the thermodynamic product.

PT_TS3
TMSPT_­TS3
TMSPT_P2	TMSPT_P3
BT_TS2	BT_P2

Figure 1. M06-2x/3-21G* optimized geometries.
(Once again a reminder that clicking on any of these structures will launch JMol and you’ll be able to visualize and manipulate this structure in 3-D.)

The computations involving the Diels-Alder reaction of C₆₀ with either 2a or 2b come to the same conclusion. In both cases, the lowest barrier is for the reaction at ring 2, and the product of the reaction at this same ring is the only one that is endoergonic. The geometries of BT_TS2 and BT_P2 are shown in Figure 1. More importantly, the barrier for the Diels-Alder reaction involving 2a and 2b are at least 6 kcal mol^-1 higher than the barriers for the reaction of 1a and 1b, in complete agreement with experiments that show little reaction involving analogues of 2b with C₆₀, while analogues of 1b are reasonably rapid.

References

(1) Cao, Y.; Liang, Y.; Zhang, L.; Osuna, S.; Hoyt, A.-L. M.; Briseno, A. L.; Houk, K. N. "Why Bistetracenes Are Much Less Reactive Than Pentacenes in Diels–Alder Reactions with Fullerenes," J. Am. Chem. Soc. 2014, 136, 10743-10751, DOI: 10.1021/ja505240e.

Clark and co-workers have examined small fullerene clusters for their ability to capture electrons.¹ They first looked at the fullerene dimer, comparing the electron affinity of the dimer having a C-C bond between the two cages (about 1.6-1.7 Å between the two cages) 1 and where the two cages are interacting only through van der Waals attractions (around 2.6 Å) 2. The structures and their radical anions were computed at RI-BP86/TZV. The structures of the two radical anions are shown in Figure 1. Interestingly, the radical anion of 2 is actually lower in energy that the radical anion of 1. Comparisons with some other methods are discussed, including a CASSPT2(5,4)/ANO-L-VDZ, computation, that support this result.

1	2
3	4

Figure 1. RI-BP86/TZV optimized geometries of the radical anions of 1-4.
(Be sure to click on these images to be able to manipulate these structures in 3-D!)

This suggests that the added electron is being held between the cages, in an interstitial region. That suggested looking at the trimer and tetramer structures 3 and 4. The radical anions of these two oligomers are also shown in Figure 1. These oligomers show electron affinities of 1 eV greater than for fullerene itself, along with the ability to stabilize the dianion and even the trianion, what the authors call “deep electron traps”.

References

(1) Shubina, T. E.; Sharapa, D. I.; Schubert, C.; Zahn, D.; Halik, M.; Keller, P. A.; Pyne, S. G.; Jennepalli, S.; Guldi, D. M.; Clark, T. "Fullerene Van der Waals Oligomers as Electron Traps," J. Am. Chem. Soc. 2014, 136, 10890-10893, DOI: 10.1021/ja505949m.

Carbenes remain an active area of interest for computational chemists, as seen in Chapter 5 of my book. For many carbenes, the triplet is the ground state, and that is true of diphenylcarbene 1. Can solvent play a role in the stability of carbene spin states? Surprisingly, the answer, provided in a recent paper by Sander,¹ is yes!

In the gas phase, the singlet-triplet gap of 1 is computed to be 5.62 kcal mol^-1 at (U)B3LYP/6-311++G(d,p) (and this reduces to 5.06 at (U)B3LYP+D3/6-311++G(d,p)) with the ground state as a triplet. If a single methanol molecules is allowed to approach 1, then the complex involving the singlet has a short hydrogen bond distance of 1.97 Å but the triplet has a much longer distance of 2.33 Å. These structures are shown in Figure 1. This manifests in a dramatic change in the relative stability, with the singlet complex now 0.26 kcal mol^-1 (0.44 with the D3 correction) lower in energy than the triplet.

Singlet-1:methanol

Triplet-1:methanol

Figure 1. (U)B3LYP/6-311++G(d,p) optimized geometries of the compelxes of methanol with singlet or triplet 1.

IR spectroscopy of 1 in an argon matrix doped with a small amount of methanol confirms the presence of the singlet carbene, and detailed description of the difference in the reactivities of the singlet and triplet are provided.

References

(1) Costa, P.; Sander, W. "Hydrogen Bonding Switches the Spin State of Diphenylcarbene from Triplet to Singlet," Angew. Chem. Int. Ed. 2014, 53, 5122-5125, DOI: 10.1002/anie.201400176.

InChIs

1: InChI=1S/C13H10/c1-3-7-12(8-4-1)11-13-9-5-2-6-10-13/h1-10H
InChIKey=XMGMFRIEKMMMSU-UHFFFAOYSA-N