Another prediction made by quantum chemistry has now been confirmed. In 2010, Zhang, Hrovat, and Borden predicted that the degenerate rearrangement of semibullvalene 1 occurs with heavy atom tunneling.¹ For example, the computed rate of the rearrangement including tunneling correction is 1.43 x 10^-3 s^-1 at 40 K, and this rate does not change with decreasing temperature. The predicted half-life of 485 s is 10¹⁰ shorter than that predicted by transition state theory.

Now a group led by Sander has examined the rearrangement of deuterated 2.² The room temperature equilibrium mixture of d⁴–2 and d²–2 was deposited at 3 K. IR observation showed a decrease in signal intensities associated with d⁴–2 and concomitant growth of signals associated with d²–2. The barrier for this interconversion is about 5 kcal mol^-1, too large to be crossed at this temperature. Instead, the interconversion is happening by tunneling through the barrier (with a rate about 10^-4 s^-1), forming the more stable isomer d²–2 preferentially. This is exactly as predicted by theory!

References

1. Zhang, X.; Hrovat, D. A.; Borden, W. T., "Calculations Predict That Carbon Tunneling Allows the Degenerate Cope Rearrangement of Semibullvalene to Occur Rapidly at Cryogenic Temperatures." Org. Letters 2010, 12, 2798-2801, DOI: 10.1021/ol100879t.

2. Schleif, T.; Mieres-Perez, J.; Henkel, S.; Ertelt, M.; Borden, W. T.; Sander, W., "The Cope Rearrangement of 1,5-Dimethylsemibullvalene-2(4)-d1: Experimental Evidence for Heavy-Atom Tunneling." Angew. Chem. Int. Ed. 2017, 56, 10746-10749, DOI: 10.1002/anie.201704787.

InChIs

1: InChI=1S/C8H8/c1-3-6-7-4-2-5(1)8(6)7/h1-8H
InChIKey=VEAPRCKNPMGWCP-UHFFFAOYSA-N

d⁴–2: InChI=1S/C10H12/c1-9-5-3-7-8(4-6-9)10(7,9)2/h3-8H,1-2H3/i5D
InChIKey=WUJOLJNLXLACNA-UICOGKGYSA-N

d²–2: InChI=1S/C10H12/c1-9-5-3-7-8(4-6-9)10(7,9)2/h3-8H,1-2H3/i7D
InChIKey=WUJOLJNLXLACNA-WHRKIXHSSA-N

Bickelhaupt and Houk present a nice review of their separately developed, but conceptually identical model for assessing reactivity.¹ Houk termed this the “distortion/interaction” model,² while Bickelhaupt named it “activation strain”.³ The concept is that the activation barrier can be dissected in a distortion or stain energy associated with bringing the reactants into the geometry of the transition state, and the interaction energy is the stabilization energy afforded by the molecular orbital interactions of the reactant components with each other in the transition state.

The review discusses a broad range of applications, including S_N2 and E₂ reactions, pericyclic reactions (including Diels-Alder reactions of enones and the dehdydro Diels-Alder reaction that I have discussed in this blog), a click reaction, a few examples involving catalysis, and the regioselectivity of indolyne (see this post). They also discuss the role of solvent and the relationship of this model to Marcus Theory.

I also want to mention in passing a somewhat related article by Jorgensen and co-authors published in the same issue of Angewandte Chemie as the above review.⁴ This article discusses the paucity of 10 electron cycloaddition reactions, especially in comparison to the large number of very important cycloaddition reactions involving 6 electrons, such as the Diels-Alder reaction, the Cope rearrangement, and the Claisen rearrangement. While the article does not focus on computational methods, computations have been widely used to discuss 10-electron cycloadditions. The real tie between this paper and the review discussed above is Ken Houk, whose graduate career started with an attempt to perform a [6+4] cycloaddition, and he has revisited the topic multiple times throughout his career.

References

1. Bickelhaupt, F. M.; Houk, K. N., "Analyzing Reaction Rates with the Distortion/Interaction-Activation Strain Model." Angew. Chem. Int. Ed. 2017, 56, 10070-10086, DOI: 10.1002/anie.201701486.

2. Ess, D. H.; Houk, K. N., "Distortion/Interaction Energy Control of 1,3-Dipolar Cycloaddition Reactivity." J. Am. Chem. Soc. 2007, 129, 10646-10647, DOI: 10.1021/ja0734086

3. Bickelhaupt, F. M., "Understanding reactivity with Kohn-Sham molecular orbital theory: E2-S_N2 mechanistic spectrum and other concepts." J. Comput. Chem. 1999, 20, 114-128

4. Palazzo, T. A.; Mose, R.; Jørgensen, K. A., "Cycloaddition Reactions: Why Is It So
Challenging To Move from Six to Ten Electrons?" Angew. Chem. Int. Ed. 2017, 56, 10033-10038, DOI: 10.1002/anie.201701085.

In this post I cover two papers discussing application of computed NMR chemical shifts to structure identification and (yet) another review of computational techniques towards NMR structure prediction.

Grimblat, Kaufman, and Sarotti¹ take up the structure of rubriflordilactone B 1, which was isolated from Schisandra rubriflora. The compound was then synthesized and its x-ray structure reported, however its NMR did not match with the natural extract. It was suggested that there were actually two compounds in the extract, the minor one was less soluble and is the crystallized 1, and a second compound responsible for the NMR signal.

The authors looked at all stereoisomers of this molecule keeping the three left-most rings intact. The low energy rotamers of these 32 stereoisomers were then optimized at B3LYP/6-31G* and the chemical shifts computed at PCM(pyridine)/mPW1PW91/6-31+G**. To benchmark the method, DP4+ was used to identify which stereoisomer best matches with the observed NMR of authentic 1; the top fit (92.6% probability) was the correct structure.

The 32 stereoisomers were then tested against the experimental NMR of the natural extract. DP4+ with just the proton shifts suggested structure 2 (99.8% probability); however, the ¹³C chemical shifts predicted a different structure. Re-examination of the reported chemical shifts identifies some mis-assigned signals, which led to a higher C-DP4+ prediction. When all 128 stereoisomers were tested, structure 2 had the highest DP4+ prediction (99.5%), but the C-DP4+ prediction remained problematic (10.8%). Analyzing the geometries of all reasonable alternative for agreement with the NOESY spectrum confirmed 2. These results underscore the importance of using all data sources.

Reddy and Kutateladze point out the importance of using coupling constants along with chemical shifts in structure identification.² They examined cordycepol A 3, obtained from Cordyceps ophioglossoides. They noted that the computed chemical shifts and coupling constants of originally proposed structure 3a differed dramatically from the experimental values.

They first proposed that the compound has structure 3b. The computed coupling constants using their relativistic force field.³ The experimental coupling constants for the proton H1 are 13.4 and 7.1 Hz. The computed values for 3a are 8.9 and 1.6 Hz, and this structure is clearly incorrect. The coupling constants are improved with 3b, but the ¹³C chemical shifts are in poor agreement with experiment. So, they proposed structure 3c, the epimer at both C1 and C11 of the original structure.

They optimized four conformations of 3c at B3LYP/6-31G(d) and obtained Boltzmann-weighted chemical shifts at mPW1PW91/6-311+G(d,p). The RMS deviation of the computed ¹³C chemical shifts relative to the experiment is only 1.54 ppm, and more importantly, the computed coupling constants of 13.54 and 6.90 Hz are in excellent agreement with the experiment values.

Lastly, Grimblat and Sarotti present a review of a number of methods for using computed NMR chemical shifts towards structure prediction.⁴ These methods include CP3, DP4, DP4+ (all of which I have posted on in the past) and an artificial neural network approach of their own design. They discuss a number of interesting cases where each of these methods has been crucial in identifying the correct chemical structure.

References

1. Grimblat, N.; Kaufman, T. S.; Sarotti, A. M., "Computational Chemistry Driven Solution to Rubriflordilactone B." Org. Letters 2016, 18, 6420-6423, DOI: 10.1021/acs.orglett.6b03318.

2. Reddy, D. S.; Kutateladze, A. G., "Structure Revision of an Acorane Sesquiterpene Cordycepol A." Org. Letters 2016, 18, 4860-4863, DOI: 10.1021/acs.orglett.6b02341.

3. (a) Kutateladze, A. G.; Mukhina, O. A., "Minimalist Relativistic Force Field: Prediction of Proton–Proton Coupling Constants in 1H NMR Spectra Is Perfected with NBO Hybridization Parameters." J. Org. Chem. 2015, 80, 5218-5225, DOI: 10.1021/acs.joc.5b00619; (b) Kutateladze, A. G.; Mukhina, O. A., "Relativistic Force Field: Parametrization of 13C–1H Nuclear Spin–Spin Coupling Constants." J. Org. Chem. 2015, 80, 10838-10848, DOI: 10.1021/acs.joc.5b02001.

4. Grimblat, N.; Sarotti, A. M., "Computational Chemistry to the Rescue: Modern Toolboxes for the Assignment of Complex Molecules by GIAO NMR Calculations." Chem. Eur. J. 2016, 22, 12246-12261, DOI: h10.1002/chem.201601150.

InChIs

1: InChI=1S/C28H30O6/c1-13-9-20(32-26(13)30)25-14(2)24-17-6-5-15-12-28-21(8-7-16(15)18(17)10-19(24)31-25)27(3,4)33-22(28)11-23(29)34-28/h5-9,14,19-22,24-25H,10-12H2,1-4H3/t14-,19+,20-,21-,22+,24-,25-,28+/m0/s1
InChIKey=JGSLSHOXBXVVTQ-NEUKEVNNSA-N

2: InChI=1S/C28H30O6/c1-13-9-20(32-26(13)30)25-14(2)24-17-6-5-15-12-28-21(8-7-16(15)18(17)10-19(24)31-25)27(3,4)33-22(28)11-23(29)34-28/h5-9,14,19-22,24-25H,10-12H2,1-4H3/t14-,19-,20-,21-,22+,24+,25-,28+/m0/s1
InChIKey=JGSLSHOXBXVVTQ-WQIRXNRDSA-N

3c: InChI=1S/C16H28O2/c1-6-11(2)9-14-16(5)12(3)7-8-13(16)15(4,17)10-18-14/h9,12-14,17H,6-8,10H2,1-5H3/b11-9-/t12-,13-,14-,15-,16+/m0/s1
InChIKey=WPQIVUHVYBQTBG-AWEVENECSA-N

Cyclobutadiene has long fascinated organic chemists. It is the 4e analogue of the 6e benzene molecule, yet it could hardly be more different. Despite nearly a century of effort, cyclobutadiene analogues were only first prepared in the 1970s, reflecting its strong antiaromatic character.

Per-trimethylsilylcyclobutadiene 1 offers opportunities to probe the properties of the cyclobutadiene ring as the bulky substituents diminish dimerization and polymerization of the reactive π-bonds. Kostenko and coworkers have now reported on the triplet state of 1.¹ They observe three EPR signals of 1 at temperatures above 350 K, and these signals increase in area with increasing temperature. This is strong evidence for the existence of triplet 1 in equilibrium with the lower energy singlet. Using the variable temperature EPR spectra, the singlet triplet gap is 13.9 ± 0.8 kcal mol^-1.

The structures of singlet and triplet 1 were optimized at B3LYP-D3/6-311+G(d,p) and shown in Figure 1. The singlet is the expected rectangle, with distinctly different C-C distance around the ring. The triplet is a square, with equivalent C-C distances. Since both the singlet and triplet states are likely to have multireference character, the energies of both states were obtained at RI-MRDDCI2-CASSCF(4,4)/def2-SVP//B3LYPD3/6-311+G(d,p) and give a singlet-triplet gap of 11.8 kcal mol^-1, in quite reasonable agreement with experiment.

singlet

triplet

Figure 1. Optimized geometries of singlet and triplet 1.

References

1. Kostenko, A.; Tumanskii, B.; Kobayashi, Y.; Nakamoto, M.; Sekiguchi, A.; Apeloig, Y., "Spectroscopic Observation of the Triplet Diradical State of a Cyclobutadiene." Angew. Chem. Int. Ed. 2017, 56, 10183-10187, DOI: 10.1002/anie.201705228.

InChIs

1: InChI=1S/C16H36Si4/c1-17(2,3)13-14(18(4,5)6)16(20(10,11)12)15(13)19(7,8)9/h1-12H3
InChIkey=AYOHYRSQVCLGKR-UHFFFAOYSA-N

I recently blogged about a paper arguing that modern density functional development has strayed from the path of improving density description, in favor of improved energetics. The Medvedev paper¹ was met with a number of criticisms. A potential “out” from the conclusions of the work was that perhaps molecular densities do not fare so poorly with more modern functionals, following the argument that better energies might reflect better densities in bonding regions.

The Hammes-Schiffer group have now examined 14 diatomic molecules with the goal of testing just this hypothesis.² They subjected both homonuclear diatomics, like N₂, Cl₂, and Li₂, and heteronuclear diatomics, like HF, LiF, and SC, to 90 different density functionals using the very large aug-cc-pCVQZ basis set. Using the CCSD density as a reference, they examined the differences in the densities predicted by the various functional both along the internuclear axis and perpendicular to it.

The 20 functionals that do the best job in mimicking the CCSD density are all hybrid GGA functionals, along with the sole double hybrid functional included in the study (B2PLYP). These functionals date from 1993 to 2012. The 20 functionals that do the poorest job include functionals from all rung-types, and date from 1980-2012. A very slight upward trend can be observed in the density error increasing with development year, while the error in the dissociation energy clearly is decreasing over time.

They note that six functionals of the Minnesota-type, those that are highly parameterized and of recent vintage, perform very poorly at predicting atomic densities, but do well with the diatomic densities.

Hammes-Schiffer concludes that their diatomic results support the general trend noted by Medvedev’s atomic results, that density description is lagging in more recently developed functionals. I’d add that this trend is not as dramatic for the diatomics as for atoms.

They pose what is really the key question: “Is the purpose to approximate the exact functional or simply to provide chemists with a useful tool for exploring chemical systems?” Since, as they note, the modern highly parameterized functionals have worked so well for predicting energies and geometries, “the observation that many modern functionals produce incorrect densities could be of no great consequence for many studies”. Nonetheless, “the ultimate goal is still to obtain both accurate densities and accurate energies”.

References

1) Medvedev, M. G.; Bushmarinov, I. S.; Sun, J.; Perdew, J. P.; Lyssenko, K. A., "Density functional theory is straying from the path toward the exact functional." Science 2017, 355, 49-52, DOI: 10.1126/science.aah5975.

2) Brorsen, K. R.; Yang, Y.; Pak, M. V.; Hammes-Schiffer, S., "Is the Accuracy of Density Functional Theory for Atomization Energies and Densities in Bonding Regions Correlated?" J. Phys. Chem. Lett. 2017, 8, 2076-2081, DOI: 10.1021/acs.jpclett.7b00774.

Bispericyclic transition states arise when two pericyclic reactions merge to a common transition state. This leads to a potential energy surface with a bifurcation such that reactions that traverse this type of transition state will head towards two different products. The classic example is the dimerization of cyclopentadiene, involving two [4+2] Diels-Alder reactions. Unusual PESs are discussed in my book and in past blog posts.

Houk and coworkers have now identified a bispericyclic transition state involving two [6+4] cycloadditions.¹ Reaching back to work Houk pursued as a graduate student with Woodward for inspiration, these authors examined the reaction of tropone 1 with dimethylfulvene 2. Each moiety can act as the diene or triene component of a [6+4] allowed cycloaddition:

The product with fulvene 2 as the 6 π-e component and tropone as the 4 π-e component [6_F+4_T] is 3, while reversing their participation in the [6_T+4_F] cycloaddition leads to 4. A variety of [4+2] reactions are also possible. All of these reactions were investigated at PCM/M06-2X/6-311+G(d,p)//B3LYP-D3/6-31G(d). The reaction leading to 3 is exothermic by 3.0 kcal mol^-1, while the reaction to 4 endothermic by 1.3 kcal mol^-1.

Interestingly, there is only one transition state that leads to both 3 and 4, the first known bispericyclic transition state for two conjoined [6+4] cycloadditions. The barrier is 27.9 kcal mol^-1. The structures of the two products and the transition state leading to them are shown in Figure 1. 3 and 4 can interconvert through a Cope transition state, also shown in Figure 1, with a barrier of 26.3 kcal mol^-1 (for 4 → 3).

3	4
TS [6+4]	TS Cope

Figure 1. B3LYP-D3/6-31G(d) optimized geometries.

Given that a single transition leads to two products, the product distribution is dependent on the molecular dynamics. A molecular dynamics simulation at B3LYP-D3/6-31G(d) with 117 trajectories indicates that 4 is formed 91% while 3 is formed only 9%. Once again, we are faced with the reality of much more complex reaction mechanisms/processes than simple models would suggest.

References

1) Yu, P.; Chen, T. Q.; Yang, Z.; He, C. Q.; Patel, A.; Lam, Y.-h.; Liu, C.-Y.; Houk, K. N., "Mechanisms and Origins of Periselectivity of the Ambimodal [6 + 4] Cycloadditions of Tropone to Dimethylfulvene." J. Am. Chem. Soc. 2017, 139 (24), 8251-8258, DOI: 10.1021/jacs.7b02966.

InChIs

1: InChI=1S/C7H6O/c8-7-5-3-1-2-4-6-7/h1-6H
InChIKey=QVWDCTQRORVHHT-UHFFFAOYSA-N

2: InChI=1S/C8H10/c1-7(2)8-5-3-4-6-8/h3-6H,1-2H3
InChIKey=WXACXMWYHXOSIX-UHFFFAOYSA-N

3:InChI=1S/C15H16O/c1-15(2)10-6-8-12(14(16)9-7-10)11-4-3-5-13(11)15/h3-12H,1-2H3
InChIKey=SEKRUGIZAIQCDA-UHFFFAOYSA-N

4: InChI=1S/C15H16O/c1-9(2)14-10-7-8-11(14)13-6-4-3-5-12(10)15(13)16/h3-8,10-13H,1-2H3
InChIKey=AQQAMUGJSGJKLC-UHFFFAOYSA-N

A few nice review/opinion pieces have been piling up in my folder of papers of interest for this Blog. So, this post provides a short summary of a number of review articles that computationally-oriented chemists may find of interest.

Holy Grails in computational chemistry

Houk and Liu present a short list of “Holy Grails” in computationally chemistry.¹ They begin by pointing out a few technical innovations that must occur for the Grails to be found: development of a universal density functional; an accurate, generic force field; improved sampling for MD; and dealing with the combinatorial explosion with regards to conformations and configurations. Their list of Grails includes predicting crystal structures and structure of amorphous materials, catalyst design, reaction design, and device design. These Grails overlap with the challenges I laid out in my similarly-themed article in 2014.²

Post-transition state bifurcations and dynamics

Hare and Tantillo review the current understanding of post-transition state bifurcations (PTSB).³ This type of potential energy surface has been the subject of much of Chapter 8 of my book and many of my blog posts. What is becoming clear is the possibility of a transition state followed by a valley-ridge inflection leads to reaction dynamics where trajectories cross a single transition state but lead to two different products. This new review updates the state-of-the-art from Houk’s review⁴ of 2008 (see this post). Mentioned are a number of studies that I have included in this Blog, along with reactions involving metals, and biochemical systems (many of these examples come from the Tantillo lab). They close with the hope that their review might “inspire future studies aimed at controlling selectivity for reactions with PTSBs” (italics theirs). I might offer that controlling selectivity in these types of dynamical systems is another chemical Grail!

The Hase group has a long review of direct dynamics simulations.⁵ They describe a number of important dynamics studies that provide important new insight to reaction mechanism, such as bimolecular S_N2 reactions (including the roundabout mechanism) and unimolecular dissociation. They write a long section on post-transition state bifurcations, and other dynamic effects that cannot be interpreted using transition state theory or RRKM. This section is a nice complement to the Tantillo review.

Benchmarking quantum chemical methods

Mata and Suhm look at our process of benchmarking computational methods.⁶ They point out the growing use of high-level quantum computations as the reference for benchmarking new methods, often with no mention of any comparison to experiment. In defense of theoreticians, they do note the paucity of useful experimental data that may exist for making suitable comparisons. They detail a long list of better practices that both experimentalists and theoreticians can take to bolster both efforts, leading to stronger computational tools that are more robust at helping to understand and discriminate difficult experimental findings.

References

1) Houk, K. N.; Liu, F., "Holy Grails for Computational Organic Chemistry and Biochemistry." Acc. Chem. Res. 2017, 50 (3), 539-543, DOI: 10.1021/acs.accounts.6b00532.

2) Bachrach, S. M., "Challenges in computational organic chemistry." WIRES: Comput. Mol. Sci. 2014, 4, 482-487, DOI: 10.1002/wcms.1185.

3) Hare, S. R.; Tantillo, D. J., "Post-transition state bifurcations gain momentum – current state of the field." Pure Appl. Chem. 2017, 89, 679-698, DOI: 0.1515/pac-2017-0104.

4) Ess, D. H.; Wheeler, S. E.; Iafe, R. G.; Xu, L.; Çelebi-Ölçüm, N.; Houk, K. N., "Bifurcations on Potential Energy Surfaces of Organic Reactions." Angew. Chem. Int. Ed. 2008, 47, 7592-7601, DOI: 10.1002/anie.200800918

5) Pratihar, S.; Ma, X.; Homayoon, Z.; Barnes, G. L.; Hase, W. L., "Direct Chemical Dynamics Simulations." J. Am. Chem. Soc. 2017, 139, 3570-3590, DOI: 10.1021/jacs.6b12017.

6) Mata, R. A.; Suhm, M. A., "Benchmarking Quantum Chemical Methods: Are We Heading in the Right Direction?" Angew. Chem. Int. Ed. 2017, ASAP, DOI: 10.1002/anie.201611308.

Continuing their application of laser ablation molecular beam Fourier transform microwave (LA-MB-FTMW) spectroscopy and computational chemistry to biochemical molecules (see these previous posts), the Alonso group reports on the structure of the glycine-glycine dipeptide 1.¹ The microwave spectrum shows three different conformers. MP2/6-311++G(d,p) computations, the same method they have previously utilized for predicting geometries, revealed a number of different conformations. By matching the spectroscopic parameters obtained from the spectrum with those of the computed structures, they proposed the three conformations 1a, 1b, and 1c, shown in Figure 1.

1a

1b

1c

Figure 1. ωb97xd/6-31G(d) optimized structures of the three conformers of 1.
Note that the authors did not report their structures in their supporting materials(!) so I have optimized them.

The structures of conformers 1a and 1b are nearly planar. MP2 predicts a non-planar rotomer of 1a, which brings the carboxyl group out of plane, to be the lowest conformation in terms of electronic energy. With the M06-2x functional, this non-planar rotomer is about isoenergetic with 1a. With all computational levels 1a is the lowest in free energy. The barrier for rotation between the non-planar rotomer and 1a is very small, and this explains why it is not observed in the supersonic expansion.

References

1) Cabezas, C.; Varela, M.; Alonso, J. L., "The Structure of the Elusive Simplest Dipeptide Gly-Gly." Angew. Chem. Int. Ed. 2017, 56, 6420-6425, DOI: 10.1002/anie.201702425.

InChIs

1: InChI=1S/C4H8N2O3/c5-1-3(7)6-2-4(8)9/h1-2,5H2,(H,6,7)(H,8,9)
InChIKey=YMAWOPBAYDPSLA-UHFFFAOYSA-N

Here’s another take on automating a procedure for using computer ¹³C chemical shifts to assess chemical structure.¹ (Have a look at these previous posts for some alternative methods and applications.) The approach here is to benchmark a few computational methods against a conformationally flexible drug-like molecule, in this case 1. A variety of conformations were optimized using the different computational methods, and ¹³C chemical shifts evaluated from a Boltzmann-weighted distribution. While the best agreement with the experimental chemical shifts (based on the root-mean-squared deviation) is with ωB97XD/cc-pVDZ, the authors opt for B3LYP/cc-pVDZ for its computational efficiency with only slightly poorer performance. (It should be note that WC04/cc-pVDZ, a functional designed for computing ¹³ chemical shifts,² is almost as good as ωB97XD/cc-pVDZ. Also, not mentioned in the article is the dramatically poorer performance of the pcS-2 basis set, despite the fact that it was parametrized³ for NMR computation!)

They apply the procedure to a number of test cases. For example, the HIV-1 reverse transcriptase inhibitor nevirapine hydrolyzes to a compound whose structure has been difficult to identify. The four proposed structures 2a-d were subjected to the computational method, and the ¹³C chemical shift RMSD for 2d is only 2.3ppm, significantly smaller than for the other 3 structures. Compound 2d was then synthesized and its NMR matches that of the nevirapine hydrolysis product.

References

1) Xin, D.; Sader, C. A.; Chaudhary, O.; Jones, P.-J.; Wagner, K.; Tautermann, C. S.; Yang, Z.; Busacca, C. A.; Saraceno, R. A.; Fandrick, K. R.; Gonnella, N. C.; Horspool, K.; Hansen, G.; Senanayake, C. H., "Development of a 13C NMR Chemical Shift Prediction Procedure Using B3LYP/cc-pVDZ and Empirically Derived Systematic Error Correction Terms: A Computational Small Molecule Structure Elucidation Method." J. Org. Chem. 2017, ASAP, DOI: 10.1021/acs.joc.7b00321.

2) Wiitala, K. W.; Hoye, T. R.; Cramer, C. J., “Hybrid Density Functional Methods Empirically Optimized for the Computation of ¹³C and ¹H Chemical Shifts in Chloroform Solution,” J. Chem. Theory Comput. 2006, 2, 1085-1092, DOI: 10.1021/ct6001016.

3) Jensen, F., “Basis Set Convergence of Nuclear Magnetic Shielding Constants Calculated by Density Functional Methods,” J. Chem. Theory Comput., 2008, 4, 719-727, DOI: 10.1021/ct800013z.

InChIs

1: InChI=1S/C24H26F4N2O4S/c1-4-35(33,34)18-7-8-20-15(10-18)9-17(30-20)13-23(32,24(26,27)28)22(2,3)12-14-5-6-16(25)11-19(14)21(29)31/h5-11,30,32H,4,12-13H2,1-3H3,(H2,29,31)/t23-/m0/s1
InChIKey=ILKZCEOVIFOUBJ-QHCPKHFHSA-N

2d: InChI=1S/C15H16N4O2/c1-9-6-8-17-14(18-10-4-5-10)12(9)19-13-11(15(20)21)3-2-7-16-13/h2-3,6-8,10H,4-5H2,1H3,(H,16,19)(H,17,18)(H,20,21)
InChIKey=ZLFOGBWAZNUXAD-UHFFFAOYSA-N

Following on previous work (see these posts on ladderane and hexaphenylethane), Schreiner, Grimme and co-workers have examined the structure of the all-meta tri(di-t-butylphenyl)methane dimer 1₂.¹ In the study of hexaphenylethane,² Schreiner and Grimme note that t-butyl groups stabilize highly congested structures through dispersion, identifying them as “dispersion energy donors”.³ The idea here is that the dimer of 1 will be stabilized by these many t-butyl groups. In fact, the neutron diffraction study of the crystal structure of 1₂ shows an extremely close approach of the two methane hydrogens of only 1.566 Å, the record holder for the closest approach of two formally non-bonding hydrogen atoms.

To understand the nature of this dimeric structure, they employed a variety of computational techniques. (Shown in Figure 1 is the B3LYPD3^ATM(BJ)/def2-TZVPP optimized geometry of 1₂.) The HSE-3c (a DFT composite method) optimized crystal structure predicts the H^…H distance is 1.555 Å. The computed gas phase structure lengthens the distance to 1.634 Å, indicating a small, but essential, role for packing forces. Energy decomposition analysis of 1₂ at B3LYP-D3^ATM(BJ)/def2-TZVPP indicates a dominant role for dispersion in holding the dimer together. While 1₂ is bound by about 8 kcal mol^-1, the analogue of 1₂ lacking all of the t-butyl groups (the dimer of triphenylmethane 2₂) is unbound by over 8 kcal mol^-1. Topological electron density analysis does show a bond critical point between the two formally unbound hydrogen atoms, and the noncovalent interaction plot shows an attractive region between these two atoms.

Figure 1. ATM(BJ)/def2-TZVPP optimized geometry of 1₂, with most of the hydrogens suppressed for clarity. (Selecting the molecule will launch Jmol with the full structure, including the hydrogens.)

References

1) Rösel, S.; Quanz, H.; Logemann, C.; Becker, J.; Mossou, E.; Cañadillas-Delgado, L.; Caldeweyher, E.; Grimme, S.; Schreiner, P. R., "London Dispersion Enables the Shortest Intermolecular Hydrocarbon H···H Contact." J. Am. Chem. Soc. 2017, 139, 7428–7431, DOI: 10.1021/jacs.7b01879.

2) Grimme, S.; Schreiner, P. R., "Steric Crowding Can Stabilize a Labile Molecule: Solving the Hexaphenylethane Riddle." Angew. Chem. Int. Ed. 2011, 50 (52), 12639-12642, DOI: 10.1002/anie.201103615.

3) Grimme, S.; Huenerbein, R.; Ehrlich, S., "On the Importance of the Dispersion Energy for the Thermodynamic Stability of Molecules." ChemPhysChem 2011, 12 (7), 1258-1261, DOI: 10.1002/cphc.201100127.

InChIs

1: InChI=1S/C43H64/c1-38(2,3)31-19-28(20-32(25-31)39(4,5)6)37(29-21-33(40(7,8)9)26-34(22-29)41(10,11)12)30-23-35(42(13,14)15)27-36(24-30)43(16,17)18/h19-27,37H,1-18H3
InChIKey=VFNQDWKFTWSJAU-UHFFFAOYSA-N