The combined supersonic jet expansion and Fourier transform microwave spectroscopy provides an excellent opportunity for the synergistic workings of experiments and computations. This is nicely demonstrated in the study of 1-methyl-4-piperidone.¹

The careful microwave study allows for the full structural characterization of the equatorial form 1e along with obtaining a good deal of information concerning the axial form 1a. To help evaluate the experimental data, the authors have optimized the structure of the two isomers at MP2, B3LYP and M06-2x using the 6-311++G(d,p) basis set.

The rotational parameters computed with the three methods are in very fine agreement with the experimental values. Of particular note is that the three computations predict a different sign for the nuclear quadrupole coupling tensor elements χ_aa and χ_bb, and this is observed in the experiment as well. It is perhaps the critical identifier of the axial isomer. The computed and experimental geometries of 1e are in fine agreement, with the largest deviation of a few degrees in the dihedral angle of the carbonyl to the ring. The experiment suggests an energy difference of 11.9 kJ mol^-1, which is corroborated by MP2, B3LYP and M06-2x computations. In fact, these first two methods predict an enthalpy difference within a kJ of the experimental value.

References

(1) Evangelisti, L.; Lesarri, A.; Jahn, M. K.; Cocinero, E. J.; Caminati, W.; Grabow, J.-U., "N-Methyl Inversion and Structure of Six-Membered Heterocyclic Rings: Rotational Spectrum of 1-Methyl-4-piperidone," J. Phys. Chem. A, 2011,
115, 9545–9551, DOI: 10.1021/jp112425w

InChIs

1: InChI=1/C6H11NO/c1-7-4-2-6(8)3-5-7/h2-5H2,1H3
InChIKey=HUUPVABNAQUEJW-UHFFFAOYAT

Check out this an incredibly cool host guest complex: the [10]-cycloparaphenylene ([10]CPP) hoop encapsulating C₆₀!¹

(Be sure to click on this image to bring up the 3-D interactive structure – as with all structures in my blog!)

¹H and ¹³C NMR and fluorescence quenching spectrometry clearly indicate that this complex is formed when [10]CPP is mixed with C₆₀ in toluene. In fact, when C₆₀ is mixed with a mixture of nanohoops ranging from 8 to 12 phenyl ring, only the [10]CPP hoop complexes with the fullerene. The experimental binding energy is between 38 and 59 kJ mol^-1.

M06-2x/6-31G* computations give the structure shown above. The computed binding energy is 173 kJ mol^-1, but the computations do not include solvent. So this overestimation might be somewhat due to the difference in gas phase vs. solution complexation.

(Check out this post for other interesting nanohoops.)

References

(1) Iwamoto, T.; Watanabe, Y.; Sadahiro, T.; Haino, T.; Yamago, S., "Size-Selective Encapsulation of C₆₀ by [10]Cycloparaphenylene: Formation of the Shortest Fullerene-Peapod," Angew. Chem. Int. Ed., 2011, 50, 8342-8344, DOI: 10.1002/anie.201102302

The click reaction, the copper-assisted cycloaddition of an azide with an alkyne, has been extended to biological systems by use of a strained alkyne (cyclooctyne) thereby eliminating the need of the toxic copper agent.¹ Fox has extended this analogy with the reaction of strained trans-cyclooctene 1 with tetrazine 2.²

The interesting new twist here is to add more strain to trans-cyclooctene to perhaps make the cycloaddition even faster. Bach³ had pointed out that the half chair conformation of 1 is almost 6 kcal mol^-1 higher in energy than the ground state (Figure 1). Fox suggests that fusing a cyclopropyl ring to the eight-member ring would create a ring in the half chair 3. Since 3 would be even more strained than 1, it should undergo a faster cycloaddition reaction.

1	1 (half chair)
3

Figure 1. M06L/6-311+G(d,p) optimized structures of 1 and 3.

Though Fox did not estimate the strain of 3, I have computed the structure of 1 constrained to the geometry of 3, with the two hydrogens that replace the bonds to the cyclopropyl carbon allowed to optimize. This restricted geometry is in fact 6.1 kcal mol^-1 (M06L/6-311+G(d,p)) higher in energy than 1 – so the fusion of the 3-member ring does net the strain increase expected by Bach.

Fox reports estimates of the free energy of activation (at M06L/6-311+G(d,p)) for the reaction of 1or 3 with 2. The barrier for the raction with trans-cyclooctene 1 is 8.92 kcal mol^-1, while the barrier for the reaction with 3 is 6.95 kcal mol^-1. A methylenehydroxyl derivative of 3 was synthesized and it does react 180 times faster than the reaction with 1. Furthermore, the differences in the experimental free energies of activation is 3.0 kcal mol^-1, in excellent agreement with the computed difference.

References

(1) Agard, N. J.; Prescher, J. A.; Bertozzi, C. R., "A Strain-Promoted [3 + 2] Azide-Alkyne Cycloaddition for Covalent Modification of Biomolecules in Living Systems," J. Am. Chem. Soc., 2004, 126, 15046-15047, DOI: 10.1021/ja044996f

(2) Taylor, M. T.; Blackman, M. L.; Dmitrenko, O.; Fox, J. M., "Design and Synthesis of Highly Reactive Dienophiles for the Tetrazine-trans-Cyclooctene Ligation," J. Am. Chem. Soc., 2011, 133, 9646-9649, DOI: 10.1021/ja201844c

(3) Bach, R. D., "Ring Strain Energy in the Cyclooctyl System. The Effect of Strain Energy on [3 + 2] Cycloaddition Reactions with Azides," J. Am. Chem. Soc., 2009, 131, 5233-5243, DOI: 10.1021/ja8094137

InChIs

1: InChI=1/C8H14/c1-2-4-6-8-7-5-3-1/h1-2HInChIKey

2: InChI=1/C12H8N6/c1-3-7-13-9(5-1)11-15-17-12(18-16-11)10-6-2-4-8-14-10/h1-8H
InChIKey=JFBIRMIEJBPDTQ-UHFFFAOYAE

3: InChI=1/C9H14/c1-2-4-6-9-7-8(9)5-3-1/h1-2,8-9H,3-7H2/b2-1+/t8-,9+
InChIKey=YWIJRSGCJZLJNV-YLSDFIPEBO

As we have noted in many previous posts, Schreiner has observed tunneling in hydroxycarbenes that is either very rapid (1a-c) or not at all (1d-f).^1-4 In a recent paper his group investigates whether cyclopropylhydroxycarbene 2 might have an intermediate lifetime due to the π-donating effect of the three-member ring.⁵

Schreiner makes this carbene in his usual manner: flash pyrolysis of the cyclopropylglyoxylic acid. Let’s now consider three possible rearrangements of carbene 2. The hydrogen can migrate (Scheme 1, path a) to give cyclopropylcarboxyaldehyde 3 similar to what was observed with the related hydroxycarbenes. Carbon can migrate (Scheme 1, path b), opening up the three-member ring to give the cyclobutenol 4. This ring could open to the diene 5 and tautomerize to the ketone 6. Lastly, a hydrogen migration from carbon (Scheme 1, path c) would lead to 7. The relative energies of these species computed at CCSD(T)//cc-pVTZ//M06-2x//6-311++G(d,p) are shown in Scheme 1.

Scheme 1. Relative energies in kcal mol^-1.

The computed barriers for the initial step of each pathway is +30.4 kcal mol^-1 for path a, +21.9 kcal mol^-1 for path b and +35.8 kcal mol^-1 for path c. Thus, one might expect to see only the reaction along path b at low temperature and mostly along b at high temperature with some small percent along path a. So what actually occurs?

After capturing the flash pyrolysis product in an Ar matrix, besides the unreacted cyclopropylglyoxylic acid, 6, 3, and 2 are observed in an approximate 8:5:1 ratio. 2 is identified on the basis of the nice agreement between the experimental and computed IR frequencies. Irradiation of 2 in the matrix leads to clean conversion to 4, also identified by comparison of the observed and computed IR frequencies. This is all consistent with the computed activation barriers. In the pyrolysis, at high T, 6 is the major product and 3 is the minor product. At very low T (11 K), irradiation of 2 produces 4 (crossing only the lowest barrier) and not continuing further along the rearrangement path to 6.

What is perhaps most exciting is that 2 disappears slowly in the dark at both 11 K and 20 K, converting at the same rate to 3. The half life is 17.7 h, much longer than for the alkyl and aryl substituted hydroxycarbenes 1a-c. This confirms the stabilization effect of the cyclopropyl group, as does its large singlet-triplet gap. The computed tunneling half-life using the WKB approach is 16.6 h, in excellent agreement with experiment. And as expected for a tunneling phenomenon, the dueterated analog has a much longer half-life, computed to be 10⁵ years. Experimentally, 2-d persists with no conversion to 3-d observed.

As with methylhydroxycarbene, we see here an example of tunneling control vs kinetic control. At high T, the reaction crosses the lowest barrier (shown in Figure 1a), proceeding to 4 and subsequent rearrangement products. At low T, the reaction crosses a higher barrier (shown in Figure 1b), but this path involves tunneling of the very light hydrogen atom only, producing 3.

TS 2 → 3

TS 2 → 4

Figure 1. M06-2X/6-311++G(d,p) optimized geometry of the transition states connecting 2 to (a) 3 and (b) 4.

References

(1) Schreiner, P. R.; Reisenauer, H. P.; Pickard Iv, F. C.; Simmonett, A. C.; Allen, W. D.; Matyus, E.; Csaszar, A. G., "Capture of hydroxymethylene and its fast disappearance through tunnelling," Nature, 2008, 453, 906-909, DOI: 10.1038/nature07010.

(2) Schreiner, P. R.; Reisenauer, H. P., "Spectroscopic Identification of Dihydroxycarbene," Angew. Chem. Int. Ed., 2008, 47, 7071-7074, DOI: 10.1002/anie.200802105

(3) Gerbig, D.; Reisenauer, H. P.; Wu, C.-H.; Ley, D.; Allen, W. D.; Schreiner, P. R., "Phenylhydroxycarbene," J. Am. Chem. Soc., 2010, 132, 7273-7275, DOI: 10.1021/ja9107885

(4) Schreiner, P. R.; Reisenauer, H. P.; Ley, D.; Gerbig, D.; Wu, C.-H.; Allen, W. D., "Methylhydroxycarbene: Tunneling Control of a Chemical Reaction," Science, 2011, 332, 1300-1303, DOI: 10.1126/science.1203761.

(5) Ley, D.; Gerbig, D.; Wagner, J. P.; Reisenauer, H. P.; Schreiner, P. R., "Cyclopropylhydroxycarbene," J. Am. Chem. Soc., 2011, 133, 13614-13621, DOI: 10.1021/ja204507j

Matt Seibert pointed out to me a paper of his related to a previous blog post that also deals with the allene-yne thermal [2+2] cyclization. (My apologies to Matt and Dean for overlooking this paper!) Tantillo and Brummond looked at the system with various saturated tethers between these functional groups.¹ For example, UB3LYP/6-31+G(d,p) study of the cyclization of 1 indicates two possible paths, where the 5-member ring is formed first, or where the 7 member ring is formed first. The relative energies of the TSs and intermediates are shown in Figure 1. (Note that there are actually two intermediates on the first pathway, differing in the orientation terminal methyne hydrogen.) The closure to the smaller ring first is favored due to the allylic stabilization of the radical intermediate on this pathway.

Figure 1. Relative energies of TSs and critical point in the cyclization of 1.

Next, they examined the regioselectivity for the inner or outer double bond of the allene in 2. For the reaction with the outer double bond, the 6 member ring is formed first. For the reaction with the inner double bond, the 7-member ring is formed first, and this pathway has a higher barrier than the other. The preference for the reaction with the terminal double bond is consistent with experiments.

Figure 2. Relative energies of TSs and critical point in the cyclization of 2.

With potential diradical intermediates, they decided to append a cyclopropyl ring to as a trap. So, for example, the reaction of 3 can lead to the [2+2] product or to a diradical that might be trapped and identified. The computed energies along these two paths are shown in Figure 3. The activation barrier for the closure to the 2+2 product and for ring opening of the cyclopropyl group are nearly identical, so one might expect to observe both processes. Analogues of 3 were prepared and heated; some evidence of the ring opening of the cyclopropyl group was observed.

Figure 3. Relative energies of TSs and critical point in the cyclization of 3.

References

(1) Siebert, M. R.; Osbourn, J. M.; Brummond, K. M.; Tantillo, D. J., "Differentiating Mechanistic Possibilities for the Thermal, Intramolecular [2 + 2] Cycloaddition of Allene-Ynes," J. Am. Chem. Soc., 2010, 132, 11952-11966, DOI: 10.1021/ja102848z

InChIs

1: InChI=1/C7H8/c1-3-5-7-6-4-2/h1,6H,2,5,7H2
InChIKey=IFOUEVYNVOTODB-UHFFFAOYAI

1P: InChI=1/C7H8/c1-2-6-4-5-7(6)3-1/h2,5H,1,3-4H2
InChIKey=UCCCTNVCSUBFQC-UHFFFAOYAW

2: InChI=1/C8H10/c1-3-5-7-8-6-4-2/h1,6H,2,5,7-8H2
InChIKey=SXDPESVCUVUSMY-UHFFFAOYAU

2Pa: InChI=1/C8H10/c1-2-4-8-6-5-7(8)3-1/h3,6H,1-2,4-5H2
InChIKey=TYATUGPSJUHEJF-UHFFFAOYAU

2Pb: InChI=1/C8H10/c1-6-5-7-3-2-4-8(6)7/h5,8H,1-4H2
InChIKey=MKCUOZNLKWXQFA-UHFFFAOYAC

3: InChI=1/C11H14/c1-2-3-4-5-6-7-8-11-9-10-11/h3,11H,1,4-6,9-10H2
InChIKey=XLOBKJCWEUMVHP-UHFFFAOYAK

3P: InChI=1/C11H14/c1-2-4-10-9(3-1)7-11(10)8-5-6-8/h3,8H,1-2,4-7H2
InChIKey=NLALHZZTFZLGMN-UHFFFAOYAM

Here is a nice example of an interesting synthesis, mechanistic explication using computation (with a bit of an unanswered question), and corroboration of the stereochemistry of the product using computed NMR shifts. Gil and Mischne¹ reacted dimedone 1 with dienal 2 under Knoevenagel conditions to give, presumably, 3. But 3 is not recovered, rather the tricycle 4 is observed.

There are four stereoisomers that can be made (4a-d). Computed ¹³C chemical shifts at OPBE/pcS-1 (this is a basis set suggested for computing chemical shifts²) for these four isomers were then compared with the experimental values. The smallest root mean squared error is found for 4d. Better still, is that these authors utilized the DP4 method of Goodman³ (see this post), which finds that 4d agrees with the experiment with 100% probability!

Lastly, the mechanism for the conversion of 3 to 4 was examined at M06/6-31+G**. The optimized geometries of the starting material, transition state, and product are shown in Figure 1. The free energy barrier is a modest 14.5 kcal mol^-1. The TS indicates a conrotatory 4πe^– electrocyclization. The formation of the C-O bond lags far behind in the TS. They could not identify a second transition state. It would probably be worth examining whether the product of this 4πe^– electrocyclization could be located, perhaps with an IRC starting from the transition state. Does this TS really connect 3 to 4?

3	TS
4

Figure 1. M06/6-31+G** optimized geometries of 3 and 4 and the transition state connecting them.

References

(1) Riveira, M. J.; Gayathri, C.; Navarro-Vazquez, A.; Tsarevsky, N. V.; Gil, R. R.; Mischne, M. P., "Unprecedented stereoselective synthesis of cyclopenta[b]benzofuran derivatives and their characterisation assisted by aligned media NMR and ¹³C chemical shift ab initio predictions," Org. Biomol. Chem., 2011, 9, 3170-3175, DOI: 10.1039/C1OB05109A

(2) 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

(3) Smith, S. G.; Goodman, J. M., "Assigning Stereochemistry to Single Diastereoisomers by GIAO NMR Calculation: The DP4 Probability," J. Am. Chem. Soc., 2010, 132, 12946-12959, DOI: 10.1021/ja105035r

InChIs

1: InChI=1/C8H12O2/c1-8(2)4-6(9)3-7(10)5-8/h3-5H2,1-2H3
InChIKey=BADXJIPKFRBFOT-UHFFFAOYAX

2: InChI=1/C12H12O/c1-11(10-13)6-5-9-12-7-3-2-4-8-12/h2-10H,1H3/b9-5+,11-6+
InChIKey=VFBDYWDOVMUDEB-MPEOSAONBY

3: InChI=1/C20H22O2/c1-15(8-7-11-16-9-5-4-6-10-16)12-17-18(21)13-20(2,3)14-19(17)22/h4-12H,13-14H2,1-3H3/b11-7+,15-8+
InChIKey=IBEGRISKTNRVOU-YQQAFNMCBC

4d: InChI=1/C20H22O2/c1-19(2)11-15(21)17-16(12-19)22-20(3)10-9-14(18(17)20)13-7-5-4-6-8-13/h4-10,14,18H,11-12H2,1-3H3/t14-,18+,20+/m1/s1
InChIKey=VEGSTZFBNRXEAX-WNYOCNMUBZ

Continuing their studies of ene-yne cyclizations, the Schmittel group examined the apparent [2+2] cyclization of the allene-yne 1.¹ They proposed that it first closed the diradical 2 and then in a second step the four-member ring is formed, giving 3.

Evidence supporting the intermediate diradical is that heating 1a in the presence of 1,4-cyclohexadiene gives 11% of the trapped species 4a. Interestingly, heating 1b gives 26% of 3b, while the reaction of 1c gives 72% of the ring closed product 3c.

Schmittel suggests the intermediate diradical 2b is planar, while 2c is not, and the radical centers are nicely position in the latter compound for quick closure to product.

UBLYP/6-31G(d) computations support the mechanism. The transition state taking 1b to 2b (TS1, shown in Figure 1) lies 20.2 kcal mol^-1 above reactant. The intermediate diradical 2b is 7.9 kcal mol^-1 above reactant 1b. The second transition state (TS2) for closing the four-member ring lies 27.8 kcal mol^-1 above reactant, making it the rate determining step. The overall reaction is exothermic by -12.4 kcal mol^-1. The transition state for a single step reaction, taking 1b directly into 3b (TS3) is very high, 49.0 kcal mol^-1 above 1b, and is therefore non-competitive with the stepwise pathway. These computations suggest a reversible formation of the intermediate, followed by a rate limiting step to making the four-member ring, completely consistent with the experiments.

2b
TS1	TS2
TS3

Figure 2. UBLYP/6-31G(d) optimized structures of 2b, TS1, TS2, and TS3.

References

1) Cinar, M. E.; Vavilala, C.; Fan, J.; Schmittel, M., "The thermal C²-C⁶/[2 + 2] cyclisation of enyne-allenes: Reversible diradical formation," Org. Biomol. Chem. 2011, 9, 3776-3779, DOI: 10.1039/C0OB01275K

InChIs

1b: InChI=1/C21H20/c1-21(2,3)17-9-14-19-12-7-8-13-20(19)16-15-18-10-5-4-6-11-18/h4-8,10-14,17H,1-3H3/t9-/m0/s1
InChIKey=HRQIWBDQUVQGEK-VIFPVBQEBW>

3b: InChI=1/C21H20/c1-21(2,3)20-17-13-15-11-7-8-12-16(15)19(17)18(20)14-9-5-4-6-10-14/h4-13,20H,1-3H3
InChIKey=GKHJKEWSMNKHEN-UHFFFAOYAW

I am very much contemplating a second edition of my book Computational Organic Chemistry, which is the basis of this blog. I have been in touch with Wiley and they are enthusiastic about a second edition.

Here is a list of some of the things I am contemplating as new topics for the second edition

1. Discussion of the failures of many of the standard functionals (like B3LYP) to treat simple organics
2. Predicting NMR, IR and ORD spectra
3. Möbius compounds, especially aromatics
4. π-π-stacking
5. tunneling in carbenes (Schreiner and Allen’s great work)
6. acidity of amino acids and remote protons
7. bifurcating potential energy surfaces and the resultant need for dynamic considerations
8. even more examples of dynamics – especially the roundabout S_N2

So, I would like to ask my readers for suggestions of other ideas for new topics to add to the book. These can be extensions of the topics already covered, or brand new areas!

Additionally, I am planning on interviewing a few more people for the book, similar in spirit to the 6 interviews in the first addition. Again, I welcome any suggestions for computational chemists to interview!

Laane has utilized high level computations to examine the high resolution IR and raman spectra of cyclopentane and some deuterated isomers.¹ What is particularly of interest here is the excellent agreement between the experiment and computations. The barrier for planarity is estimated from experiment to be 1808 cm^-1 and CCSD/cc-pVTZ predicts a value of 1887 cm^-1 – excellent agreement. The B3LYP/cc-pVTZ computed frequencies for the C₂ and C_i conformations were scaled by 0.985 for frequencies less than 1450 cm^-1, 0.975 for frequencies between 1450 and 200 cm^-1 and by 0.961 for frequencies above 2000 cm^-1. These frequencies are very similar to one another. In comparison of these averaged frequencies with the experimental frequencies the root mean squared error is only 8.8 cm^-1! As stressed by these authors, computational is important partner with experiment in characterizing spectra.

References

(1) Ocola, E. J.; Bauman, L. E.; Laane, J., "Vibrational Spectra and Structure of Cyclopentane and its Isotopomers," J. Phys. Chem. A, 2011, 115, 6531–6542, DOI: 10.1021/jp2032934.

InChIs

Cyclopentane: InChI=1/C5H10/c1-2-4-5-3-1/h1-5H2 InChIKey=RGSFGYAAUTVSQA-UHFFFAOYAL

What is required in order to compute very accurate NMR chemical shifts? Harding, Gauss and Schleyer take on the interesting spectrum of 1-adamantyl cation to try to discern the important factors in computing its ¹³C and ¹H chemical shifts.¹

1

To start, the chemical shifts of 1-adamtyl cation were computed at B3LYP/def2-QZVPP and
MP2/qz2p//MP2/cc-pVTZ. The root means square error (compared to experiment) for the carbon chemical shifts is large: 12.76 for B3LYP and 6.69 for MP2. The proton shifts are predicted much more accurately with an RMS error of 0.27 and 0.19 ppm, respectively.

The authors speculate that the underlying cause of the poor prediction is the geometry of the molecule. The structure of 1 was optimized at HF/cc-pVTZ, MP2/cc-pVTZ and CCSD(T)/pVTZ and then the chemical shifts were computed using MP2/tzp with each optimized geometry. The RMS error of the ¹²C chemical shifts are HF/cc-pVTZ: 9.55, MP2/cc-pVTZ: 5.62, and CCSD(T)/pVTZ: 5.06. Similar relationship is seen in the proton chemical shifts. Thus, a better geometry does seem to matter. The CCSD(T)/pVTZ optimized structure of 1 is shown in Figure 1.

1

Figure 1. CCSD(T)/pVTZ optimized structure of 1.

Unfortunately, the computed chemical shifts at CCSD(T)/qz2p//CCSD(T)/cc-pVTZ are still in error; the RMS is 4.78ppm for the carbon shifts and 0.26ppm for the proton shifts. Including a correction for the zero-point vibrational effects and adjusting to a temperature of 193 K to match the experiment does reduce the error; now the RMS for the carbon shifts is 3.85 ppm, with the maximum error of 6 ppm for C3. The RMS for the proton chemical shifts is 0.21ppm.

The remaining error they attribute to basis set incompleteness in the NMR computation, a low level treatment of the zero-point vibrational effects (which were computed at HF/tz2p), neglect of the solvent, and use of a reference in the experiment that was not dissolved in the same media as the adamantyl cation.

So, to answer our opening question – it appears that a very good geometry and treatment of vibrational effects is critical to accurate NMR shift computation of this intriguing molecule. Let the
computational chemist beware!

References

(1) Harding, M. E.; Gauss, J.; Schleyer, P. v. R., "Why Benchmark-Quality Computations Are Needed To Reproduce 1-Adamantyl Cation NMR Chemical Shifts Accurately," J. Phys. Chem. A, 2011, 115, 2340-2344, DOI: 10.1021/jp1103356

InChI

1: InChI=1/C10H15/c1-7-2-9-4-8(1)5-10(3-7)6-9/h7-9H,1-6H2/q+1
InChIKey=HNHINQSSKCACRU-UHFFFAOYAC