In section 4.4 of the book, I discuss in great detail the computational (and some experimental) studies of the benzynes, the formal diradicals created by loss of two hydrogen atoms from benzene. Now comes a very nice experimental study on a molecule that takes the next step: 1,3,5-tridehydrobenzene 1, benzene that lacks three hydrogen atoms. Sander reports the preparation and characterization of trifluoro-1,3,5-tridehydrobenzene 2.¹ The characterization of this novel molecule is made through comparison with computed IR spectra.

2 is prepared by flash vapor pyrolysis of 1,3,5-triiodo-2,4,6-trifluorobenezene
and then trapping the products in a low temperature matrix. Sander identifies five IR peaks of a product he believes is 2. These IR frequencies are listed in Table 1.

Table 1. Experimental and computed^a IR frequencies (cm^-1) and relative intensities of 2.

^aUBLYP/cc-pVTZ. ^bTransition state.

In order to confirm that this IR spectra comes from 2, Sander computed the structure and IR frequencies of both 1 and 2. The ²A₁ structure of 1 had been studied previously², but what had gone unnoticed is that another structure is possible, the ²B₂ state. These two states differ in the separation between C₁ and C₃. When the distance is short, the SOMO is of a₁ symmetry and this orbital has bonding character between these two carbon centers, giving rise to the ²A₁ state (1a). As the distance gets longer between C₁ and C₃, a b₂ orbital, having antibonding character between C₁and C₃, becomes lower in energy than the a₁ orbital, so that the structure is ²B₂ (1b). The UBLYP/cc-pVTZ optimized structures are shown in Figure 1. 1a is 2-3 kcal mol^-1 lower in energy than 1b. Furthermore, 1b has one imaginary frequency and is not a local energy minimum. Sander also optimized the structures of 2a and 2b¸ finding little effect due to the fluorine substitution.

1a

1b

Figure 1. UBLYP/cc-pVTZ optimized structures of 1a (²A₁) and 1b (²B₁).

The computed IR frequencies are listed in Table 1. The computed frequencies (and their relative intensities) of 2a match up strikingly well with those of the experiment. Sander concludes that 2a has in fact been prepared and characterized.

References

(1) Venkataramani, S.; Winkler, M.; Sander, W., "Trifluoro-1,3,5-tridehydrobenzene," Angew. Chem. Int. Ed. 2007, 46, 4888-4893, DOI: 10.1002/anie.200700536

(2) Cristian, A. M. C.; Shao, Y.; Krylov, A. I., "Bonding Patterns in Benzene Triradicals from Structural, Spectroscopic, and Thermochemical Perspectives," J. Phys. Chem. A 2004, 108, 6581-6588, DOI: 10.1021/jp049007j.

InChI:

1: InChI=1/C6H3/c1-2-4-6-5-3-1/h1,4-5H
2: InChI=1/C6F3/c7-4-1-5(8)3-6(9)2-4

Kass has once again uncovered a simple system that challenges our notions of basic chemical concepts. It is a well accepted notion that the most acidic proton of all of the amino acids is the carboxylic acid one. However, acidities are strongly influenced by the solvent, and the absence of solvent in the gas phase can dramatically alter things.

Kass and co-workers examined the gas-phase acidity of cysteine with computational and
experimental techniques.¹ The lowest energy conformer of cysteine is 1a, characterized by having three intramolecular hydrogen bonds (Figure 1). The next lowest conformer, 1b, has only two intramolecular hydrogen bonds and is 1.5 kcal mol^-1 higher in energy at G3B3.

1a xyz	1b xyz

Figure 1. B3LYP/aug-cc-pVDZ optimized structures of cysteine 1.¹

They optimized a number of different configurations of the conjugate base of cysteine: two conformers from the loss of the carboxylate proton (2a and 2b), two conformers from the loss of the thiol proton (2c and 2d), and one conformer from the loss of the thiol proton of the zwitterion (2e). These structures are shown in Figure 2 along with their relative energies. All of these structures possess two intramolecular hydrogen bonds.

2a (3.1) xyz	2b (3.4) xyz
2c (0.0) xyz	2d (5.1) xyz
2e (10.1) xyz

Figure 2. B3LYP/aug-cc-pVDZ optimized structures of the conjugate base of cysteine 2. Relative energies (kcal mol^-1) in parenthesis computed at G3B3.¹

The gas phase acidity of carboxylic acids is greater than thiols; the deprotonation energy of propanoic acid (CH₃CH₂CO₂H) is 347.7 kcal mol^-1 at G3B3 (347.2 expt.²), about 6 kcal mol^-1 less than that of ethanethiol (CH₂CH₂SH: 355.0 at G3B3 and 354.2 expt.²). However, the computations indicate that 2c is the lowest energy structure of deprotonated cysteine, and 2c comes about by loss of the thiol proton! Te lowest energy cysteine conjugate base from loss of the carboxylate proton is 1a, which is 3.1 kcal mol^-1 higher in energy. Apparently, the hydrogen bonding network in 2c is quite favorable, able to make up for the inherent favorability of a carboxylate over a thiolate anion.

The G3B3 computed deprotonation energy of cysteine is 333.3 kcal mol^-1 (for removal of the thiol proton). Kass determined the deprotonation energy of cysteine using a kinetic and a thermodynamic method. The kinetic method gives a value of 332.9 ± 3.3 kcal mol^-1­, while the thermodynamic method gives 334.4 ± 3.3 kcal mol^-1­. These are in fine agreement with the computed value.

This study ably demonstrates the dramatic role that solvent can play in determining molecular properties. Kass titled the article “Are carboxyl groups the most acidic sites in amino acids?” and answers with “no” – in the gas phase the thiol group is more acidic. He ends the article with an indication that the alcohol of tyrosine may be competitive in acidity with its carboxylic group, too.

References

(1) Tian, Z.; Pawlow, A.; Poutsma, J. C.; Kass, S. R., "Are Carboxyl Groups the Most Acidic Sites in Amino Acids? Gas-Phase Acidity, H/D Exchange Experiments, and Computations on Cysteine and Its Conjugate Base," J. Am. Chem. Soc., 2007, 129, 5403-5407, DOI: 10.1021/ja0666194.

(2) NIST, NIST Chemistry WebBook, 2005, http://webbook.nist.gov/.

InChIs

1: InChI=1/C3H7NO2S/c4-2(1-7)3(5)6/h2,7H,1,4H2,(H,5,6)

Here’s one more nice application of computationally-derived NMR chemical shifts towards solving a structure. Fattarusso and co-workers¹ identified a component of wormwood called artarborol. COSY and ROESY experiments allowed for deducing four possible diasereomeric structures of artarborol, 1-4.

They then took two computational approaches towards resolving the structure. First, they performed an MM search for low energy conformers of 1-4. These conformers were then screened for those having a dihedral angle of around 90° for the C-8 and C-9 protons, due to a low couple constant for between these protons. Only conformers of 1 and 3 satisfied this criterion. An intense couple of the H-1 and H-5 protons indicated a transannular arrangement, and only conformers of 1 satisfy this criterion.

The second computational approach was to optimize some of the low energy conformers of 1 and 3 at mPW1PW91/6-31G(d,p) and compute their ¹³C chemical shifts. The five low energy conformers, two of 1 and three of 3, are shown in Figure 1. The resulting chemical shifts were averaged according to a Boltzmann distribution. These computed chemical shifts were then fit against the experimental values. The correlation factor for the computed shifts for 1 (r²=0.9997) was much better than that of 3 (r²=0.9713). The average deviation of the chemical shifts (after being corrected using the fitting procedure from the above correlation) was only 0.8ppm for 1 but 2ppm for 3. They therefore conclude that the structure of artarborol is 1.

1a xyz	1b xyz
3a xyz	3b xyz	3c xyz

Figure 1. mPW1PW91 optimized conformations of possible artarborol diasteromers.¹

References

(1) Fattorusso, C.; Stendardo, E.; Appendino, G.; Fattorusso, E.; Luciano, P.; Romano, A.; Taglialatela-Scafati, O., "Artarborol, a nor-Caryophyllane Sesquiterpene Alcohol from Artemisia arborescens. Stereostructure Assignment through Concurrence of NMR Data and Computational Analysis," Org. Lett., 2007, 9, 2377-2380, DOI: 10.1021/ol070803s.

(2) I thank Professor Ernesto Fattorusso for supplying me with the optimized coordinates of these compounds.

InChI

1: InChI=1/C14H24O2/c1-13(2)8-9-10(13)6-7-14(3)12(16-14)5-4-11(9)15/h9-12,15H,4-8H2,1-3H3/t9-,10-,11-,12-,14+/m0/s1

Just a short update here. In Chapter 5.1.2 we discuss nucleophilic substitution at heteroatoms. Unlike the paradigmatic case for substitution at carbon, which proceeds via the S_N2 mechanism. Nucleophilic substitution at second-row atoms (S, Si, P) appears to follow an addition-elimination pathway. Bickelhaupt¹ now adds a more thorough computational examination of nucleophilic substitution at phosphorus. He looked at a few identity reactions involving tricoordinate P, namely

X^– + PH₂X → PH₂X + X^–

X^– + PF₂X → PF₂X + X^–

X^– + PCl₂X → PCl₂X + X^–

where X is chloride or hydroxide. In all cases the only critical point located on the potential energy surface is for a tetracoordinate intermediate. Shown in Figure 1 are the intermediates for the reaction OH^– + PH₂OH and Cl^– + PCl₃. This result is consistent with the studies of nucleophilic substitution at sulfur and silicon.

(a) xyz file

(b) xyz file

Figure 1. OLYP/TZ2P optimized intermediate for the reaction (a) OH^– + PH₂OH
and (b) Cl^– + PCl₃.

References:

(1) vanBochove, M. A.; Swart, M.; Bickelhaupt, F. M., "Nucleophilic Substitution at Phosphorus (S_N2@P): Disappearance and Reappearance of Reaction Barriers," J. Am. Chem. Soc. 2006, 128, 10738-10744, DOI: 10.1021/ja0606529

I just ran across a nice summary article by Peter Schreiner¹ detailing the recent spate of articles describing problems with many DFT methods, especially the ubiquitous B3LYP functional. This article covers essentially the same ground as my previous post Problems with DFT.

References

(1) Schreiner, P. R., “Relative Energy Computations with Approximate Density Functional Theory – A Caveat!,” Angew. Chem. Int. Ed., 2007, 46, 4217-4219, DOI: 10.1002/anie.200700386.

Another three applications of computed NMR chemical shifts towards structure identification have appeared, dealing with carbohydrates and natural products.

Prediction of NMR Signals of Carbohydrates

The study by Cramer and Hoye¹ investigates identification of diastereomers with NMR, in particular, identification of cis and trans isomers of 2-methyl- (1), 3-methyl- (2), and 4-methylcyclohexanol (3). The study discusses the ability of different DFT methods to predict the chemical shifts of these alcohols in regard to distinguishing their different configurations. An interesting twist is that they have developed a functional specifically suited to predict proton chemical shifts and a second functional specifically for predicting carbon chemical shifts.²

The approach they take was first to optimize the six different conformations for each diastereomer including solvent (chloroform). They chose to optimize the structures at B3LYP/6-311+G(2d,p) with PCM. The six conformers (notice the axial/equatorial relationships, along with the position of the alcohol hydrogen) of 1c are presented in Figure 1. Chemical shifts were then obtained with a number of different methods, weighting them according to a Boltzmann distribution.

0.0 xyz	0.20 xyz	0.73 xyz
1.23 xyz	1.56 xyz	1.85 xyz

Figure 1. PCM/B3LYP/6-311+G(2d,p) optimized structures of the conformers of 1c. Relative energies (kcal mol^-1) are listed for each isomer.

Now a brief digression into how they developed their modified functional.² They define the exchange-correlation functional (see Chapter 1.3.1 of my book – or many other computational chemistry books!) as

      E_xc = P₂E_x(HF) + P₃ΔE_x(B) + P₄E_x(LSDA) + P₅ΔE_c(LYP) + P₆E_c(LSDA)

where the Ps are parameters to be fit and E_x(HF) is the Hartree-Fock exchange energy, ΔE_x(B) is the Becke gradient correction to the local spin-density approximation (LSDA), E_x(LSDA) is the exchange energy, ΔE_c(LYP) is the Lee-Yang-Parr correction to the LSDA correlation energy, and E_c(LSDA) is the LSDA correlation energy. Chemical shifts were computed for proton and carbon, and the parameters P were adjusted (between 0 and 1) to minimize the error in the predicted chemical shifts from the experimental values. A total of 43 different molecules were used for this fitting procedure. The values of the parameters are given for the carbon functional (WC04), the proton functional (WP04) and B3LYP (as a reference) in Table 1. Note that there is substantial difference in the values of the parameter among these three different functionals.

Table 1. Values of the parameters P for the functionals WC04, WP04, and B3LYP.

Now, the computed proton and carbon chemical shifts using 4 different functions (B3LYP, PBE1, MP04, and WC04) for 1-3 were compared with the experiment values. This comparison was made in a number of different ways, but perhaps most compellingly by looking at the correlation coefficient of the computed shifts compared with the experimental shifts. This was done for each diastereomer, i.e. the computed shifts for 2c and 2t were compared with the experimental shifts of both 2c and 2t. If the functional works well, the correlation between the computed and experimental chemical shifts of 2c (and 2t) should be near unity, while the correlation between the computed shifts of 2c and the experimental shifts of 2t should be dramatically smaller than one. This is in fact the case for all three functionals. The results are shown in Table 2 for B3LYP and WP04, with the later performing slightly better. The results for the carbon shifts are less satisfactory; the correlation coefficients are roughly the same for all comparisons with B3LYP and PBE1, and WC04 is only slightly improved.
Nonetheless, the study clearly demonstrates the ability of DFT-computed proton chemical shifts to discriminate between diasteromers.

Table 2. Correlation coefficients between the computed and experimental proton chemical shifts.^a

	2ccomp (1.06) xyz	2tcomp (0.0) xyz
2cexp   2texp	0.9971 0.9985 0.8167 0.8098	0.8334 0.9050 0.9957 0.9843
	3c (0.0) xyz	3t (0.63) xyz
3cexp   3texp	0.9950 0.9899 0.8856 0.9310	0.8763 0.8717 0.9990 0.9979
	4c (0.54) xyz	4t (0.0) xyz
4cexp   4texp	0.9993 0.9975 0.8744 0.8675	0.8335 0.9279 0.9983 0.9938

^aPCM/B3LYP/6-311+G(2d,p)//PCM/ B3LYP/6-31G(d) in regular type and PCM/WP04/6-311+G(2d,p)//PCM/ B3LYP/6-31G(d) in italic type. Relative energy (kcal mol^-1) of the most favorable conformer of each diastereomer is given in parenthesis.

Predicting NMR of Natural Products

Bagno has a long-standing interest in ab initio prediction of NMR. In a recent article, his group takes on the prediction of a number of complex natural products.³ As a benchmark, they first calculated the NMR spectra of strychnine (4) and compare it with its experimental spectrum. The optimized PBE1PBE/6-31G(d,p) geometry of 4 is drawn in Figure 2. The correlation between the computed NMR chemical shifts for both ¹H and ¹³C is quite good, as seen in Table 3. The corrected mean average errors are all very small, but Bagno does point out that four pairs of proton chemical shifts and three pairs of carbon chemical shifts are misordered.

Strychnine 4

Figure 2. PBE1PBE/6-31G(d,p) geometry of strychnine 4.³

Table 3. Correlation coefficient and corrected mean average error
(CMAE) between the computed and experiment chemical shifts of 4.

The study of the sesquiterpene carianlactone (5) demonstrates the importance of including solvent in the NMR computation. The optimized B3LYP/6-31G(d,p) geometry of 5 is shown in Figure 3, and the results of the comparison of the computed and experimental chemical are listed in Table 4. The correlation coefficient is unacceptable when the x-ray structure is used. The agreement improves when the gas phase optimized geometry is employed, but the coefficient is still too far from unity. However, optimization using PCM (with the solvent as pyridine to match experiments) and then computing the NMR chemical shifts in this reaction field provides quite acceptable agreement between the computed and experimental chemical shifts.

Corianlactone 5

Figure 3. B3LYP/6-31G(d,p) geometry of carianlactone 5.³

Table 4. Correlation coefficient and corrected mean average error (CMAE) between
the computed and experiment chemical shifts of 5.

Lastly, Bagno took on the challenging structure of the natural product first identified as boletunone B (6a).⁴ Shortly thereafter, Steglich reinterpreted the spectrum and gave the compound the name isocyclocalopin A (6b).⁵ A key component of the revised structure was based on the δ 0.97 ppm signal that they assigned to a methyl above the enone group, noting that no methyl in 6a should have such a high field shift.

Bagno optimized the structures of 6a and 6b at B3LYP/6-31G(d,p), shown in Figure 4. The NMR spectra for 6a and 6b were computed with PCM (modeling DMSO as the solvent). The correlation coefficients and CMAE are much better for the 6b model than for the 6a model., supporting the reassigned structure. However, the computed chemical shift for the protons of the key methyl group in question are nearly identical in the two proposed structures: 1.08 ppm in 6a and 1.02 ppm in 6b. Nonetheless, the computed chemical shifts and coupling constants of 6b are a better fit with the experiment than those of 6a.

boletunone B 6a	isocyclocalopin A 6b

Figure 4. B3LYP/6-31G(d,p) geometry of the proposed structures of Boletunone B, 6a and 6b.³

Table 5. Correlation coefficient and corrected mean average error (CMAE) between the computed (B3LYP/6-31G(d,p) + PCM) and experiment chemical shifts of 6a and 6b.

In a similar vein, Nicolaou and Frederick has examined the somewhat controversial structure of maitotxin.⁶ For the sake of brevity, I will not draw out the structure of maitotxin; the interested reader should check out its entry in wikipedia. The structure of maitotoxin has been extensively studied, but in 2006, Gallimore and Spencer⁷ questioned the stereochemistry of the J/K ring juncture. A fragment of maitotoxin that has the previously proposed stetreochemistry is 7. Gallimore and Spencer argued for a reversed stereochemistry at this juncture (8), one that would be more consistent with the biochemical synthesis of the maitotoxin. Nicolaou noted that reversing this stereochemistry would lead to other stereochemical changes in order for the structure to be consistent with the NMR spectrum. Their alternative is given as 9.

7

8

9

Nicolaou and Freferick computed ¹³C NMR of the three proposed fragments 7-9 at B3LYP/6-31G*; unfortunately they do not provide the coordinates. They benchmark this method against brevetoxin B, where the average error is 1.24 ppm, but they provide no error analysis – particularly no regression so that corrected chemical shift data might be employed. The best agreement between the computed and experimental chemical shifts is for 7, with average difference of 2.01 ppm. The differences are 2.85 ppm for 8 and 2.42 ppm for 9. These computations support the original structure of maitotoxin. The Curious Wavefunction blog discusses this topic, with an emphasis on the possible biochemical implication.

References

(1) Wiitala, K. W.; Al-Rashid, Z. F.; Dvornikovs, V.; Hoye, T. R.; Cramer, C. J., "Evaluation of Various DFT Protocols for Computing ¹H and ¹³C Chemical Shifts to Distinguish Stereoisomers: Diastereomeric 2-, 3-, and 4-Methylcyclohexanols as a Test Set," J. Phys. Org. Chem. 2007, 20, 345-354, DOI: 10.1002/poc.1151

(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) Bagno, A.; Rastrelli, F.; Saielli, G., "Toward the Complete Prediction of the ¹H and ¹³C NMR Spectra of Complex Organic Molecules by DFT Methods: Application to Natural Substances," Chem. Eur. J. 2006, 12, 5514-5525, DOI: 10.1002/chem.200501583

(4) Kim, W. G.; Kim, J. W.; Ryoo, I. J.; Kim, J. P.; Kim, Y. H.; Yoo, I. D., "Boletunones A and B, Highly Functionalized Novel Sesquiterpenes from Boletus calopus," Org. Lett. 2004, 6, 823-826, DOI: 10.1021/ol049953i

(5) Steglich, W.; Hellwig, V., "Revision of the Structures Assigned to the Fungal Metabolites Boletunones A and B," Org. Lett. 2004, 6, 3175-3177, DOI: 10.1021/ol048724t.

(6) Nicolaou, K. C.; Frederick, M. O., "On the Structure of Maitotoxin," Angew. Chem. Int. Ed., 2007, 46, 5278-5282, DOI: 10.1002/anie.200604656.

(7) Gallimore, A. R.; Spencer, J. B., "Stereochemical Uniformity in Marine Polyether Ladders – Implications for the Biosynthesis and Structure of Maitotoxin," Angew. Chem. Int. Ed. 2006, 45, 4406-4413, DOI: 10.1002/anie.200504284.

InChI

1: InChI=1/C7H14O/c1-6-4-2-3-5-7(6)8/h6-8H,2-5H2,1H3
2: InChI=1/C7H14O/c1-6-3-2-4-7(8)5-6/h6-8H,2-5H2,1H3
3: InChI=1/C7H14O/c1-6-2-4-7(8)5-3-6/h6-8H,2-5H2,1H3
4: InChI=1/C21H22N2O2/c24-18-10-16-19-13-9-17-21(6-7-22(17)11-12(13)5-8-25-16)14-3-1-2-4-15(14)23(18)20(19)21/h1-5,13,16-17,19-20H,6-11H
5: InChI=1/C14H14O6/c1-12-2-6(15)8-13(4-18-13)9-10(19-9)14(8,20-12)7-5(12)3-17-11(7)16/h5,7-10H,2-4H2,1H3/t5-,7-,8?,9+,10+,12+,13?,14-/m1/s1
6a: InChI=1/C15H20O6/c1-7-4-5-14(3)12(17)9-8(2)6-20-15(14,11(7)16)21-10(9)13(18)19/h4,8-10,12,17H,5-6H2,1-3H3,(H,18,19)/t8-,9+,10+,12+,14-,15-/m1/s1
6b: InChI=1/C15H20O6/c1-7-4-5-15(12(17)10(7)16)9-8(2)6-20-14(15,3)21-11(9)13(18)19/h4,8-9,11-12,17H,5-6H2,1-3H3,(H,18,19)/t8?,9-,11?,12+,14-,15-/m1/s1

The search for unusual potential energy surface topologies continues. Unusual surfaces can lead to dynamic effects that result in rates and product distributions dramatically divergent from that predicted by statistical theories. I addressed this topic in Chapter 7 of the book.

Houk has found another interesting example in the Diels-Alder reaction of cyclopentadiene with nitrostyrene 1.¹ The [4+2] adduct is 2, which can undergo a [3,3] Cope-like rearrangement to give 3. Product 3 can also result from a [2+4] Diels-Alder cycloaddition where cyclopentadiene acts as the dienophile.

Like some of the examples in Chapter 7, the potential energy surface, computed at B3LYP/6-31+G*, contains a single transition state (TS1) from reactants. Continuing on the reaction path past the transition state, a valley ridge inflection point (VRI) intervenes, causing the path to bifurcate: one path leads to 2 and the other leads to 3. In other words, a single transition state leads to two different products! TS1 is geometrically closer to 2 than 3, while TS2 lies closer to 3 than 2 (Figure 1). This topology directs most molecules to traverse a path over TS1 and on to 2. What is novel in this paper is that the acid-catalyzed reaction, using SnCl₄, shifts TS1 towards 3 and TS2 towards 2, leading to the opposite product distribution. The uncatalyzed reaction favors formation of 2 while the catalyzed reaction favors 3 over 2. Confirmation of this prediction awaits a molecular dynamics study.

TS1	TS1-Cat
TS2	TS2-Cat

Figure 1. B3LYP/6-31+G(d) optimized structures for TS1 and TS2.¹

References

(1) Celebi-Olcum, N.; Ess, D. H.; Aviyente, V.; Houk, K. N., “Lewis Acid Catalysis Alters the Shapes and Products of Bis-Pericyclic Diels-Alder Transition States,” J. Am. Chem. Soc., 2007, 129, 4528-4529. DOI: 10.1021/ja070686w

InChI

1: InChI=1/C8H7NO2/c10-9(11)7-6-8-4-2-1-3-5-8/h1-7H/b7-6+
2: InChI=1/C13H13NO2/c15-14(16)13-11-7-6-10(8-11)12(13)9-4-2-1-3-5-9/h1-7,10-13H,8H2
3: InChI=1/C13H13NO2/c15-14-9-12(10-5-2-1-3-6-10)11-7-4-8-13(11)16-14/h1-6,8-9,11-13H,7H2

Kinked polycyclic benzoids are more stable that their straight chain analogues. For example, the gaseous heat of formation of phenanthrene 1 is 49.6 kcal mol^-1 while that of anthracene 2 is 55.2 kcal mol^-1.¹ This stability of the kinked over the straight chain is reproduced by computation: 1 is 4.24 kcal mol^-1 lower in energy than 2 at BLYP/TZ2P.href="#phenanref2">² The standard explanation for this has been better resonance in 1 than in 2, leading to 1 being more aromatic than 2.

Bader has recently offered at alternative explanation. Topological electron density analysis³ (also referred to as Atoms-In-Molecules, or AIM) examines the electron density distribution to uncover chemically-relevant information. The bond path traces out the ridge of maximum electron density between two atoms, passing through the bond critical point. Bader has argued that the existence of the bond path is the necessary and sufficient condition for a chemical bond. In the AIM analysis of 1, he noted a bond path connecting the hydrogen atoms on C₄ and C₅.⁴ These are the hydrogen atoms in the bay region, labeled explicitly in the sketch above. Based on this bond path, and the fact that the bay region hydrogen atoms are stabilized due to charge transfer from carbon, Bader argued that H-H bonding in 1 stabilizes this molecule, accounting for its lower heat of formation than 2.

In a 2007 JOC paper, Bickelhaupt directly attacked this contention.² The BLYP/TZ2P geometries of 1 and 2 are shown in Figure 1.

1

2

Figure 1. BLYP/TZ2P optimized geometries of 1 and 2.²

He approached the problem by examining the reaction of two 2-methtriylphenyl moieties combining to form either 1 or 2 (Scheme 1). The binding energy ΔE is then decomposed into two terms, ΔE_prep which is the energy required to deform the triradical fragment 3 from its optimum geometry into the geometry within either 1 or 2, designated as 3(1) or 3(2), and ΔE_int which is the interaction energy of the deformed fragments.

Scheme 1.

The deformation energy of the triradical fragment is nearly identical for 1 and 2. Therefore, the interaction energy to from 1 is more negative (stabilizing) than to form 2. The interaction energy for 1 was also obtained in two other ways. First, 3 was fixed to its geometry in 2 (i.e., 3(2)) with the distance of the two forming C-C bonds also that of 2. The interaction energy defined this way is -0.69 kcal mol^-1, indicating a preference for aligning the fragments in the orientation of phenanthrene. Bickelhaupt further partitions the interaction energy to σ- and π-components, and finds the stabilization of the model interaction energy is dominated by π-interactions, not the σ-interactions one would expect from Bader’s model of H-H stabilization. Allowing the C-C distances between the two 3(2) fragments to adjust to those in 1 further strengthens the interaction energy to -2.49 kcal mol^-1. The geometrical changes allow for the p-bonds to strengthen (by shortening the C₉-C₁₀ distance), and the repulsion between the bay area hydrogen atoms to diminish (by lengthening the C_4a-C_4b distance).

Bickelhaupt argues that the presence of a bond path may simply be due to two atomic basins being forced to bump into each other, whether these contacts be stabilizing or destabilizing. For example, two benzene molecules arranged such that a C-H bond points toward the C-H bond of another (see 4), a bond path will connect the two hydrogen atoms and the AIM energies of these two hydrogen atoms will indicate a net stabilization. He concludes by calling into question the basis for the claim that a bond path is the necessary and sufficient conditions for a chemical bond.

InChI:

1: InChI=1/C14H10/c1-3-7-13-11(5-1)9-10-12-6-2-4-8-14(12)13/h1-10H

2: InChI=1/C14H10/c1-2-6-12-10-14-8-4-3-7-13(14)9-11(12)5-1/h1-10H

References

(1) Cox, J. D.; Pilcher, G. Thermochemistry of Organic and Organometallic Compounds; Academic Press: New York, 1970.

(2) Poater, J.; Visser, R.; Sola, M.; Bickelhaupt, F. M., "Polycyclic Benzenoids: Why Kinked is More Stable than Straight," J. Org.Chem. 2007, 72, 1134-1142, DOI: 10.1021/jo061637p

(3) Bader, R. F. W. Atoms in Molecules: A Quantum Theory; Clarendon Press: Oxford, UK, 1990.

(4) Matta, C. F.; Hernández-Trujillo, J.; Tang, T.-H.; Bader, R. F. W., "Hydrogen-Hydrogen Bonding: A Stabilizing Interaction in Molecules and Crystals," Chem. Eur. J. 2003, 9, 1940-1951, DOI: 10.1002/chem.200204626

In the pursuit of further elucidation of just what the concepts “aromatic” and “antiaromatic” mean, Schleyer and Bunz reported the preparation and characterization of a novel antiaromatic compound that is isolable.¹

Bunz synthesized the redox pair of compounds 1 and 2 that differ in the electron count in the pi-system. The former (1) has 14 π electrons and should be aromatic, while the latter (5) has 16 π electrons and should be antiaromatic. The NMR spectrum of both compounds was measured and compared to the computed signals of the parent compounds 3 and 4. The signals match very nicely. The structures of 1 and 2 were further confirmed by x-ray crystallography. 1 and 2 can be interconverted by redox reactions and 2 is stable in air, only slowly oxidizing to 1.

The NICS(0)_πizz values computed for 3 and 4 are shown in Figure 1. (See ref 2 for a discussion on this NICS method and also Chapter 2 of my book.) These values are quite negative for each ring of 3, consistent with its expected aromatic character. On the other hand, the NICS value for each ring of 4 is more positive than the corresponding ring of 3, with the value in the center of the pyrazine ring being positive. These NICS values indicate that 4 is certainly less aromatic than 3, and perhaps even expresses antiaromatic character.

Figure 1. NICS(0)_πzz values for 3 and 4 computed at PW91/6-311G**.

Interestingly, hydrogenation of 3 to give 4 is -14.0, indicating that while 3 appears to be a normal aromatic compound, 4, if it is antiaromatic, exhibits some energetic stabilization. They identify this stabilization as a result of the interaction between the dihydropyrazine ring and the thidiazole ring, evidenced in the exothermicity of the isodemic reaction:

So while 4 may be antiaromatic, it appears to be energetically reasonably stable. It is important to keep in mind though that 4 is not the most stable tricycle isomer; in fact, 5 is 7 kcal mol^-1 lower in energy than 4.

Schleyer and Bunz conclude that antiaromaticity may “not result in a prohibitive energetic penalty.”

References

(1) Miao, S.; Schleyer, P. v. R.; Wu, J. I.; Hardcastle, K. I.; Bunz, U. H. F., "A Thiadiazole-Fused N,N-Dihydroquinoxaline: Antiaromatic but Isolable," Org. Lett. 2007, 9, 1073-1076, DOI: 10.1021/ol070013i

(2) Fallah-Bagher-Shaidaei, H.; Wannere, C. S.; Corminboeuf, C.; Puchta, R.; Schleyer, P. v. R., "Which NICS Aromaticity Index for Planar π Rings Is Best?," Org. Lett., 2006, 8, 863-866, DOI: 10.1021/ol0529546.

InChI

3: InChI=1/C8H4N4S/c1-2-10-6-4-8-7(11-13-12-8)3-5(6)9-1/h1-4H
4: InChI=1/C8H6N4S/c1-2-10-6-4-8-7(11-13-12-8)3-5(6)9-1/h1-4,9-10H
5: InChI=1/C8H6N4S/c1-2-10-6-4-8-7(11-13-12-8)3-5(6)9-1/h1-2H,3-4H2

Here as an interesting, relatively straightforward example of how modern computational methods can help elucidate a reaction mechanism. Brinker¹ examined the thermolysis of (1S,2R,5R,7S,8R)-4,5-dibromotricyclo[6.2.1.0^2,7]undeca-3,9-diene 1. The observed products were cyclopentadiene (and its dimer), bromobenzene and (1R,2S,6S,7R,10R)-1,10-dibromotricyclo[5.2.2.0^2,6]undeca-3,8-diene
2. They proposed two possible mechanisms to account for these products. In the first mechanism, 1 can convert to 2 via a Cope rearrangement (path a, Scheme 1). The alternative mechanism has 1 undergo a retro-Diels-Alder reaction to produce 1,6-dibromo-1,3-cyclohexadiene 3 and cyclopentadiene 4 (path b, Scheme 1) 3 can then lose HBR to give bromobenzene. But more interesting is the possibility that cyclopentadiene and 3 can undergo a Diels-Alder reaction (path c, Scheme 1), but one with role reversal, i.e. cylopentadiene acts as the dienophile here, rather than the diene component as in the reverse of path b. This second Diels-Alder reaction (path c) produces 2.

Scheme 1

Brinker optimized the structures in Scheme 1, along with the transition states from paths a-c, at B3LYP/6-31G(d). These structures are shown in Figure 1 and their relative energies are listed in Table 1. The Cope rearrangement is favored over the retro-Diels-Alder by 3.6 kcal mol^-1. While the subsequent Diels-Alder step (path c) has a low electronic barrier (21.7 kcal mol^-1), it is enthalpically disfavored and the free energy barrier is high (40.4 kcal mol^-1. Thus, formation of 2 derives mostly from the direct Cope rearrangement of 2. Production of bromobenzene from 2 results from the retro-Diels-Alder (path b) followed by loss of HBr.

Table 1. Electronic and Free Energies (kcal mol^-1­) computed at B3LYP/6-31G(d).¹

1 xyz file	2 xyz files
TS(a) xyz files	TS(b) xyz file
TS(c) xyz file

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

InChI:

1: InChI=1/C11H12Br2/c12-10-4-8-6-1-2-7(3-6)9(8)5-11(10)13/h1-2,4,6-9,11H,3,5H2/t6-,7+,8-,9+,11-/m1/s1

2: InChI=1/C11H12Br2/c12-10-6-7-4-5-11(10,13)9-3-1-2-8(7)9/h1,3-5,7-10H,2,6H2/t7-,8+,9+,10+,11+/m0/s1

References

(1) Su, K. J.; Mieusset, J. L.; Arion, V. B.; Brecker, L.; Brinker, U. H., “Cope Rearrangement versus a Novel Tandem Retro-Diels-Alder-Diels-Alder Reaction with Role reversal,” Org. Lett. 2007, 9, 113-115, DOI: 10.1021/ol0626793