A growing area for the application of computational chemistry is in the structural identification of compounds. In the book, I discussed the use of computed IR spectra to identify intermediates in the photolysis of phenyl nitrene and carbine and the benzynes. In previous blogs, I have written posts (here, here and here) about recent use of computed NMR spectra to discern the structure of new natural products. With this post I discus the use of computed optical activity to determine the absolute configuration of molecules.

Rosini and co-workers have examined a number of oxygenated cyclohexene epoxides.to explore the use of TDDFT computed optical activity as a means for determining absolute configuration.¹ In chapter 1.6.3, I discuss the work of the Gaussian team on benchmarking optical rotation and ORD. They find that B3LYP/aug-cc-pVDZ computed optical activities are in quite reasonable agreement with experiment.^2-4 In this work, Rosini explores using a smaller basis set (6-31G(d)), the role of solvent, and also if computed spectra can be used to assess the absolute configuration of new molecules.

They first benchmark the B3LYP/6-31G(d) computed optical activities for a number of related cyclohexene epoxides against B3LYP/aug-cc-pVDZ and experimental values. I will begin by discussing two of their examples: (+)-chaloxone 1 (PubChem)
and (+)-epoxydon 2
(PubChem).

Five conformations of 1 were optimized in the gas phase and then their optical activities for the sodium D line were computed using TDDFT with both the small and larger basis set. These computations were then repeated to model the effect of solvent using PCM; the solution (methanol) B3LYP/6-31G(d) structures are shown in Figure 1.

1a 0.0	1b 2.40	1c 0.87
1d 1.02	1e 3.12

Figure 1. PCM(methanol)/B3LYP/6-31G(d) optimized structures of 1. Relative free energies of each conformer in kcal/mol.¹

The optical rotation at the sodium D line was then computed with TDDFT in both gas and solution phase with the smaller and larger basis set. The values were then averaged base on a Boltzmann weighting using the computed free energies of each conformer. The optical rotation for each conformer and the average values are listed in Table 1. The experimental optical rotation is +271. The authors note that while the gas phase B3LYP/6-31G(d) average value is far off the experimental value, it does predict the correct sign, and since all of the five conformers give rise to a positive rotation, any error in the energies will not affect the sign. The computed gas phase value with the larger basis set is in better agreement with experiment. However, it is still too large, but the solution values are much better. In fact, the PCM/B3LYP/aug-cc-pVDZ value is in excellent agreement with experiment.

Table 1. Computed optical activity of the conformers of 1 in gas and solution phase.

^aBased on a Boltzmann weighting of the population of each conformation.

Five conformers of epoxydon 2 were also located, and the computed solution structures are shown in Figure 2. The computed optical rotations for both the gas and solution phase for these structures (and the Boltzmann weighted averages) are listed in Table 2. The experimental value for the optical rotation of 2 is +93.

2a 0.0	2b 0.32	2c 0.23
2d 0.22	2e 0.66

Figure 2. PCM(methanol)/B3LYP/6-31G(d) optimized structures of 2. Relative free energies of each conformer in kcal/mol.¹

In this case, the small basis set performs very poorly. The gas phase B3LYP/6-31G(d) value
of [α]_D is -16, predicting the wrong sign, let alone the wrong magnitude. Things improve with the larger basis set, which predicts a value of +57. Since conformer 2ais levorotatory and the other four are dextrorotatory, the computed relative energies are key to getting the correct prediction. This is made even more poignant with the solution results, where the PCM/B3LYP/aug-cc-pVDZ prediction is quite acceptable.

Table 2. Computed optical activity of the conformers of 2 in gas and solution phase.

^aBased on a Boltzmann weighting of the population of each conformation.

Threy conclude with two examples of application of computation to assignment of structure. I discuss here the absolute configuration of (-)-sphaeropsidone 3 (PubChem).
Rosini located two conformations of 3, shown in Figure 3. The computed optical rotations are listed in Table 3. The experimental value for 3 is -130. Both conformers are computed to be dextrorotatory with all computational methods. The magnitude of the computed values using the larger basis set is in nice agreement with experiment, but the sign is wrong. Rosini concludes that the absolute configuration of 3 has been misassigned.

3a 0.06

3b 0.0

Figure 3. PCM(methanol)/B3LYP/6-31G(d) optimized structures of 3. Relative free energies of each conformer in kcal/mol.¹

Table 3. Computed optical activity of the conformers of 3 in gas and solution phase.

^aBased on a Boltzmann weighting of the population of each conformation.

References

(1) Mennucci, B.; Claps, M.; Evidente, A.; Rosini, C., "Absolute Configuration of Natural Cyclohexene Oxides by Time Dependent Density Functional Theory Calculation of the Optical Rotation: The Absolute Configuration of (-)-Sphaeropsidone and (-)-Episphaeropsidone Revised," J. Org. Chem. 2007, 72, 6680-6691, DOI: 10.1021/jo070806i

(2) Stephens, P. J.; Devlin, F. J.; Cheeseman, J. R.; Frisch, M. J., "Calculation of Optical Rotation Using Density Functional Theory," J. Phys. Chem. A 2001, 105, 5356-5371, DOI: 10.1021/jp0105138.

(3) Stephens, P. J.; McCann, D. M.; Cheeseman, J. R.; Frisch, M. J., "Determination of
absolute configurations of chiral molecules using ab initio time-dependent Density Functional Theory calculations of optical rotation: How reliable are absolute configurations obtained for molecules with small rotations?," Chirality 2005, 17, S52-S64, DOI: 10.1002/chir.20109.

(4) Stephens, P. J.; McCann, D. M.; Devlin, F. J.; Flood, T. C.; Butkus, E.; Stoncius,
S.; Cheeseman, J. R., "Determination of Molecular Structure Using Vibrational Circular Dichroism Spectroscopy: The Keto-lactone Product of Baeyer-Villiger Oxidation of (+)-(1R,5S)-Bicyclo[3.3.1]nonane-2,7-dione," J. Org. Chem. 2005, 70, 3903-3913, DOI: 10.1021/jo047906y.

InChI

1: InChI=1/C7H8O4/c1-10-4-2-3(8)6-7(11-6)5(4)9/h2-3,6-8H,1H3

2: InChI=1/C7H8O4/c8-2-3-1-4(9)6-7(11-6)5(3)10/h1,4,6-9H,2H2

3: InChI=1/C7H8O4/c1-10-4-2-3(8)6-7(11-6)5(4)9/h2,5-7,9H,1H3

Dynamic and non-statistical behavior is the subject of Chapter 7 in my book. Hase and co-workers have uncovered another interesting case of dynamic behavior.¹ The reaction of interest here is F^– + CH₃OOH. A number of different critical points and reactions exist on this surface. The complex CH₃OOH^…F^– (1) lies 36.5 kcal mol^-1 below separated reactants. 1 can rearrange through TS1 (with a barrier of 24.1 kcal mol^-1) to give F^–…CH₃OOH (2). 2 can then cross a second transition state (TS2) with a barrier of 4.7 kcal mol^-1) to give CH₂(OH)₂^…F^– (3), which lies in a very deep well. The B3LYP/6-311+G(d,p) geometries of these critical points are shown in Figure 1.

1 -36.5	TS1 -12.4	2 -16.2
TS2 -11.5	3 -104.8

Figure 1. B3LYP/6-311+G(d,p) optimized geometries of the critical points on the PES for the reaction of F^– with CH₃OOH.¹ Energies in kcal mol^-1 relative to separated reactants

What drew Hase to this problem were the interesting experimental results of Blanksby, Ellison, Bierbaum and Kato.² The gas phase reaction produced HF + CH₂O + OH^–, not 3 or HF + CH₂(OH)O^–. Hase and coworkers ran a number of trajectories simulating reaction at 300 K, the experimental condition. Reactions were started at three points: (1) F^– separated by 15 Å from CH₃OOH, (2) at TS2 or (3) at a point along the intrinsic reaction coordinate (IRC) of the form HOCH₂O^–…HF.

76 of the 80 trajectories that start from TS2 result in the formation of HF + CH₂O + OH^–. The majority of the trajectories that start with separated reactants produce the complex 1 (97 out of 200), reflecting its low energy and high exit barriers. 55 of these200 trajectories remain as isolated reactants. However, 45 trajectories give HF + CH₂O + OH^–, as do all 5 trajectories that start with HOCH₂O^–…HF. No trajectories give 3, the product expected from following the IRC. The computations are in complete agreement with the experimental results; the unusual decomposition products result from following a non-IRC pathway!

Since motion along the imaginary frequency of TS2 initially is to cleave the O-O bond and the C-H bond, momentum in that direction carries the reaction over to the decomposition product rather than making a tight turn on the PES necessary to make 3. These computations show once again that reactions can follow pathways that lie far from steepest descent or IRC pathways.

References

(1) Lopez, J. G.; Vayner, G.; Lourderaj, U.; Addepalli, S. V.; Kato, S.; deJong, W. A.; Windus, T. L.; Hase, W. L., "A Direct Dynamics Trajectory Study of F^– + CH3OOH Reactive Collisions Reveals a Major Non-IRC Reaction Path," J. Am. Chem. Soc. 2007, 129, 9976-9985, DOI: 10.1021/ja0717360.

(2) Blanksby, S. J.; Ellison, G. B.; Bierbaum, V. M.; Kato, S., "Direct Evidence for Base-Mediated Decomposition of Alkyl Hydroperoxides (ROOH) in the Gas Phase," J. Am. Chem. Soc. 2002, 124, 3196-3197, DOI: 10.1021/ja017658c.

I mentioned “mindless chemistry” in the interview with Fritz Schaefer. This term, the title of the article by Schaefer and Schleyer,¹ refers to locating minimum energy structures through a stochastic search driven solely by a computer algorithm. No chemical rationale or intuition is used; rather, the computer simply tries a slew of different possibilities and mindlessly marches through them.

The approach employed by Schaefer and Schleyer is to use the ‘kick” algorithm of Saunders.² An arbitrary initial geometry is first selected (Saunders even suggests the case where all atoms are located at the same point!) and then a kick is applied to each atom, with random direction and displacement, to create a new geometry. An optimization is then performed with some quantum mechanical method, to produce a new structure. The kick is then applied to this new structure (or to the initial one again) to generate another geometry to start up another optimization. By doing many different “kicks” with different kick size, one can span a large swath of configuration space.

In their first “mindless chemistry” paper, Schafer and Schleyer identified some new structures of BCONS, C₆Be and C₆Be^2-.¹ In their next application,³ they explored the novel molecule periodane, which has the molecular formula LiBeBCNOF, named to reflect its make-up of one atom of every element (save neon) on the first full row of the periodic table. Krüger⁴ located the planar structure 1 (see Figure 1). But Schaefer and Schleyer, employing the “kick” algorithm located 27 structures that are lower in energy than 1, Their lowest energy structure 2 is 122 kcal mol^-1 lower than 1. They advocate for this stochastic search to gain broad understanding of the nature of the potential energy surface and then refining the search using “human logic”.

1

2

Figure 1. Optimized structures of periodane 1 and 2.

(Note – I have only provided a sketch of 2 since the supporting information for the article has not yet been posted on the Wiley web site. I will update this post with the actual structure when it becomes available.)

References

(1) Bera, P. P.; Sattelmeyer, K. W.; Saunders, M.; Schaefer, H. F.; Schleyer, P. v. R., "Mindless Chemistry," J. Phys. Chem. A, 2006, 110, 4287-4290, DOI: 10.1021/jp057107z.

(2) Saunders, M., "Stochastic Search for Isomers on a Quantum Mechanical Surface," J. Comput. Chem.. 2004, 25, 621-626, DOI: 10.1002/jcc.10407

(3) Bera, P. P.; Schleyer, P. v. R.; Schaefer, H. F., III, "Periodane: A Wealth of Structural Possibilities Revealed by the Kick Procedure," Int. J. Quantum Chem. 2007, 107, 2220-2223, DOI: 10.1002/qua.21322

(4) Krüger, T., "Periodane – An Unexpectedly Stable Molecule of Unique Composition," Int. J. Quantum Chem. 2006, 106, 1865-1869, DOI: 10.1002/qua.20948

I discuss the concept of σ-aromaticity in Chapter 2.3.1. The arguments for its existence in cyclopropane include surface delocalization of electron density, MO energies, an energetic stability greater than predicted by traditional assessments of its ring strain energy, and a negative value of its NICS(0) and NICS(1).

Fowler, Baker and Lillington have computed the ring current in cyclopropane, cyclobutane and cyclopentane.¹ The later two are computed for their planar conformations, which are not local minima, but make the graphical comparisons simpler. Unfortunately, I do not have electronic access to the journal article and so cannot link to their images, but the plots of the current density of cyclopropane clearly indicates a large diatropic current circling the outside of the ring. In the interior of the ring is a smaller paratropic current.

For this concept to have applicability, cyclobutane should express σ-antiaromaticity. The ring current map for cyclobutane does show a strong paratropic current in the inside of the ring with a weaker diatropic current on the outside of the ring. The current map of cyclopentane shows an interior paratropic and external diatropic currents of nearly identical magnitude, suggestive of a simple superposition of circulation due to five local bonds. Thus, cyclopropane expresses significant σ-aromaticity, cyclobutane is weakly σ-antiaromatic, and cyclopentane is non-aromatic.

References

(1) Fowler, P. W.; Baker, J.; Mark Lillington, M., "The Ring Current in Cyclopropane," Theor. Chem. Acta 2007, 118, 123-127, DOI: 10.1007/s00214-007-0253-2.

InChI:

cyclopropane: InChI=1/C3H6/c1-2-3-1/h1-3H2

cyclobutane: InChI=1/C4H8/c1-2-4-3-1/h1-4H2

cyclopentane: InChI=1/C5H10/c1-2-4-5-3-1/h1-5H2

Despite the fact that Wes Borden has indicated the he has written his last paper on the Cope rearrangement (see my interview with Wes at the end of Chapter 3), others remain intrigued by this reaction and continue to report on it. In a recent JACS communication, Tantillo¹ examines the palladium-promoted Cope rearrangement.

The ordinary Cope rearrangement displays chameleonic character – switching from concerted to stepwise with a diradical intermediate – based on substituents. The palladium-promoted Cope is suggested to proceed through a stepwise mechanism with a zwitterionic intermediate (Scheme 1).²

Scheme 1.

Tantillo¹ has examined a variety of these rearrangements at the B3LYP/LANL2DZ level. The palladium complex is PdCl₂NCMe. For all cases where R is a substituted phenyl group, the mechanism is stepwise, with the intermediate 1 sitting in a shallow well. The most stable intermediate (based on lying in the deepest well) is with the 4-dimethylaminophenyl group, and the well is 5.1 kcal mol^-1 deep. The structures of the transition state (2-pNMe₂) and the intermediate (1-pNMe₂) are shown in Figure 1.

2-pNMe2

1-pNMe2

Figure 1. B3LYP/LANL2DZ optimized structures of 2-pNMe₂ and 1-pNMe₂.¹

However, the well associated with 1 can be very shallow, as little as 0.4 kcal mol^-1 (R = 4-trifluoroimethylphenyl and 4-nitrophenyl). This suggests that perhaps when properly substituted the intermediate might vanish and the reaction become concerted. This is in fact what happens when R is CF₃, CN, or H. The transition state for the reaction with R = H is shown in Figure 2. So, this metal-assisted Cope rearrangement displays chameleonic behavior, just like the metal-free case, except that the intermediate is zwitterionic with the metal, instead of diradical in the metal-free cases.

2-H

Figure 1. B3LYP/LANL2DZ optimized structure of 2-H.¹

References

(1) Siebert, M. R.; Tantillo, D. J., "Transition-State Complexation in Palladium-Promoted [3,3] Sigmatropic Shifts," J. Am. Chem. Soc. 2007, 129, 8686-8687, DOI: 10.1021/ja072159i.

(2) Overman, L. E.; Renaldo, A. E., "Catalyzed Sigmatropic Rearrangements. 10. Mechanism of the Palladium Dichloride Catalyzed Cope Rearrangement of Acyclic Dienes. A Substituent Effect Study," J. Am. Chem. Soc. 1990, 112, 3945-3949, DOI: 10.1021/ja00166a034.