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

One of the ubiquitous examples of the Hückel rule is cyclooctatetraene dianion (COT^2-). This annulene has, presumably, 10 π electrons and therefore should be aromatic, satisfying the 4n+2 rule. Therefore, the molecule should be planar, right? Well, an article by Dominikowska and Palusiak call into question these assumptions.¹

COT^2-

First off, with either B3LYP or MP2 and a variety of basis sets, optimization of COT^2- starting from the tub-shape of COT itself led to the planar or nearly planar structure most of the time. The exceptions include B3LYP/6-311++G(d,p) and MP2/aug-cc-pVDZ. More interesting is that a number of the MP2 planar structures have one or more imaginary frequency; for example, MP2/6-311G has four imaginary frequencies.

I reoptimized a number of these structures assuming D_8h symmetry, and looked for the number of imaginary frequencies. B3LYP/6-311G(d,p) had no imaginary frequencies, but B3LYP/6-31++G(d,p) and B3LYP/6-311++G(d,p) had 2 and 4 imaginary frequencies, respectively. Many of the MP2 optimizations had imaginary frequencies, with MP2/6-311G(d,p) having 3 imaginary frequencies. The optimized structures of COT^2- at ωB97X-D/6-311G(d,p) had no imaginary frequencies but with the 6-311++G(d,p) basis set, it had two imaginary frequencies. Interestingly, Truhlar’s M06-2x functional with both 6-311G(d,p) and 6-311++G(d,p) gives no imaginary.

This is reminiscent of the situation with benzene and other arenes, where certain combinations of method and basis set gave multiple imaginary frequencies.² The ultimate culprit was identified as intramolecular basis set superposition error. Dominikowska and Palusiak discount this explanation here for two reasons. First, multiple imaginary frequencies are seen with the Dunning correlation consistent basis sets – MP2/aug-cc-pVDZ has 7 imaginary frequencies (though my computation at D_8h gives only one imaginary frequency), something not observed for benzene. Secondly, they noticed that in the non-planar COT^2- optimized structure there are bond paths connecting the hydrogens to non-nuclear attractors situated way outside the molecule. They suggest that the COT^2- might really be a Rydberg state, with the extra electrons located outside the molecule. This implies that the π system has only 8 electrons, giving the tub shape. They note that COT^2- has a very short lifetime and suggest that it is not an aromatic compound, a larger annulene congener of benzene, at all.

It would be interesting to see what would happen with COT^2- correcting for intramolecular basis set superposition error via the method of Asturiol, Duran and Salvador,³ which I described in this post. This correction led to planar benzene having no imaginary frequencies. This type of computation would help assess just what is going on here – is COT^2- afflicted with basis set problems or is it a very unusual, non-aromatic system?

References

(1) Dominikowska, J.; Palusiak, M., "Cyclooctatetraene dianion—an artifact?," J. Comput. Chem., 2011, 32, 1441-1448, DOI: 10.1002/jcc.21730

(2) Moran, D.; Simmonett, A. C.; Leach, F. E.; Allen, W. D.; Schleyer, P. v. R.; Schaefer, H. F., III, "Popular Theoretical Methods Predict Benzene and Arenes To Be Nonplanar," J. Am. Chem. Soc., 2006, 128, 9342-9343, DOI: 10.1021/ja0630285

(3)  Asturiol, D.; Duran, M.; Salvador, P., "Intramolecular basis set superposition error effects on the planarity of benzene and other aromatic molecules: A solution to the problem," J. Chem. Phys., 2008, 128, 144108, DOI: 10.1063/1.2902974

While many pericyclic reactions proceed in a concerted fashion, the stepwise pathway is a distinct possibility. Fernandez, Sierra and Torres report on an interesting [8+2] cycloaddition that
is decidedly stepwise, confirmed through trapping of the intermediate zwitterion.¹

The reaction of 1 with 2 was examined at M06-2x/6-311+G(d) (optimized geometries of the critical points are shown in Figure 1). The first transition state (TS1) has nitrogen acting as a nucleophile, attacking the carbonyl carbon of ketene to give 3. The barrier is 11.6 kcal mol^-1, and 3 lies 0.7 kcal mol^-1 above reactants. While 3 might be described with a tropyllium cation resonance structure, the ring is in fact non-planar and both the NICS(0) and NICS(1)_zz values are positive. The ring is therefore antiaromatic, consistent with the endoergonicity of this step. Closure of the zwitterion through TS2 leads to the formal [8+2] product, with the barrier for this second step slightly lower than the barrier for the first step. Overall, the reaction is quite exothermic.

Scheme 1 (relative energies in kcal mol^-1)

TS1	3
TS2	4

Figure 1. MO6-2x/6-311+G(d) optimized Structures of 3, 4, and the transition states leading to them (TS1 and TS2).

Experiments were performed with a variety of acyl chloride precursors to ketenes (Scheme 2), and along with the [8+2] product, a second product (5) incorporating 2 equivalents of ketene is found; in fact, if the R group is benzyloxy or t-butyl, 5 is the only observed product. This second product comes about via trapping of the intermediate 3. Mixing phenylketene with 4a (where the R group is phenyl) gives no reaction, thus precluding the intermediacy of 4 on the path to 5. MO6-2x computations of the trapping of 3 with phenylketenes indicates a barrier (TS3, see Figure 2) of 9.6 kcal mol^-1, very close to the barrier height of the second TS for ring closure of the [8+2] pathway, supporting the competition between trapping of the intermediate and progress on to the [8+2] product.

Scheme 2.

TS3

Figure 2. MO6-2x/6-311+G(d) optimized Structures of TS3.

References

(1) Lage, M. L.; Fernandez, I.; Sierra, M. A.; Torres, M. R., "Trapping Intermediates in an [8 + 2] Cycloaddition Reaction with the Help of DFT Calculations," Org. Lett., 2011, ASAP, DOI: 10.1021/ol200910z

InChIs

1: InChI=1/C8H6O/c9-7-6-8-4-2-1-3-5-8/h1-6H
InChIKey=RZGZTQYTDRQOEY-UHFFFAOYAC

2: InChI=1/C7H7N/c8-7-5-3-1-2-4-6-7/h1-6,8H
InChIKey=NHNIVEADUHCPRP-UHFFFAOYAI

3: InChI=1/C15H13NO/c17-15(12-13-8-4-3-5-9-13)16-14-10-6-1-2-7-11-14/h1-12,17H/b15-12-/f/h17h,16H
InChIKey=AFLGFPOCUCTUAS-UJUNEOEYDT

4: InChI=1/C15H13NO/c17-15-14(11-7-3-1-4-8-11)12-9-5-2-6-10-13(12)16-15/h1-10,12,14H,(H,16,17)/t12-,14+/m1/s1/f/h16H
InChIKey=BBJCGQGFRRQHHS-KEKMKNANDW