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

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

The search for a stable molecule containing a hypercoordinated carbon atom may finally be over. Abboud and Yáñez¹ report mass spectra and computations on the unusual cation Si(CH₃)₃CH₃Si(CH₃)₃⁺ (1). Using low pressure FT-ICR, upon ionization of Si(CH₃)₄ (TMS) they observe a small signal with m/z 161.12, which corresponds to the mass of 1⁺. When Si(CH₃)₄ and Si(CD₃)₄ are mixed, introduced into the spectrometer and ionized, the mixed isotopomer of 1⁺ is observed, and scrambling to the CH₃ and CD₃ groups occurs.

The geometry of 1⁺ was optimized at B3LYP/6-311+G(3df,2pd) and QCISD/6-311+G(d,p). The latter structure is shown in Figure 1, though the geometry differs little between the two computations. The enthalpy for the dissociation of 1⁺ into TMS and Si(CH₃)₃⁺ is 23.2 kcal mol^-1 at QCISD. This compares very well with the experimental² value of 22.3 kcal mol^-1.

xyz file

Figure 1. QCISD/6-311+G(d,p) optimized structure of 1⁺.¹

The structure has C_3h symmetry with the central carbon to silicon distance of 2.071 Å, a bit more than a 10% increase over the length of a typical C-Si bond. Topological electron density analysis indicates a bond critical point does connect the central carbon atom with each silicon atom, and the value of the Laplacian of the electron density at this critical point is negative. This analysis strongly suggests that the central carbon atom is pentacoordinate!

Abboud and Yáñez argue that 1⁺ can be considered as a complex of methyl cation and two Si(CH₃)₃ radicals. The empty p orbital of the central methyl carbon can then interact with the radical-bearing orbital on each silicon, forming a three-center two-electron bonding molecular orbital (Scheme 1). The positive charge is delocalized, with the central methyl group having a charge of +0.26 while the charge on each Si(CH₃)₃ groups is +0.37.

Scheme 1.

Though not discussed in this paper, the all carbon analogue, namely C(CH₃)₃CH₃C(CH₃)₃⁺
is not a stable structure when restricted to have C_3h symmetry (see Figure 2). Rather, this geometry corresponds to the transition state for the transfer of a methyl group from one C(CH₃)₃ group to the other.

xyz files

Figure 1. B3LYP/6-311+G(d,p) optimized geometry of C(CH₃)₃CH₃C(CH₃)₃⁺.

References

(1) Daacute;valos, J. Z.; Herrero, R.; Abboud, J.-L. M.; Mó, O.; Yáñez, M., "How Can a Carbon Atom Be Covalently Bound to Five Ligands? The Case of Si₂(CH₃)₇⁺," Angew. Chem. Int. Ed. 2007, 46, 381-385, DOI: 10.1002/anie.200601164

(2) Wojtyniak, A. C. M.; Li, X.; Stone, J. A., "The Formation of CH₃)₇Si₂⁺ in (CH₃)₄Si/CH₄ Mixtures and CH₃−Exchange Reactions between (CH₃)₄Si, (CH₃)₄Ge, and (CH₃)₄Sn Studied by High Pressure Mass Spectrometry," Can. J. Chem. 1987, 65, 2849-2854,

We noted in Chapter 2.1 some serious errors in the prediction of bond dissociation energies using B3LYP. For example, Gilbert examined the C-C bond dissociation energy of some simple branched alkanes.¹ The mean absolute deviation (MAD) for the bond dissociation energy predicted by G3MP2 is 1.7 kcal mol^-1 and 2.8 kcal mol^-1 using MP2. In contrast, the MAD for the B3LYP predicted values is 13.7 kcal mol^-1, with some predictions in error by more than 20 kcal mol^-1. Furthermore, the size of the error increases with the size of the molecule. Consistent with this trend, Curtiss and co-workers noted a systematic underestimation of the heat of formation of linear alkanes of nearly 0.7 kcal mol^-1 per bond using B3LYP.²

Further evidence disparaging the general performance of DFT methods (and B3LYP in particular) was presented in a paper by Grimme and in two back-to-back Organic Letters articles, one by Schreiner and one by Schleyer. Grimme³ noted that the relative Energy of two C₈H₁₈ isomers, octane and 2,2,3,3-tetramethylbutane are incorrectly predicted by DFT methods (Table 1). While MP2 and CSC-MP2 (spin-component-scaled MP2) correctly predict that the more branched isomer is more stable, the DFT methods predict the inverse! Grimme attributes this error to a failure of these DFT methods to adequately describe medium-range electron correlation.

Schreiner⁵ also compared the energies of hydrocarbon isomers. For example, the three lowest energy isomers of C₁₂H₁₂ are 1-3, whose B3LYP/6-31G(d) structures are shown in Figure 1. What is disturbing is that the relative energies of these three isomers depends strongly upon the computational method (Table 2), especially since these three compounds appear to be quite ordinary hydrocarbons. CCSD(T) predicts that 2 is about 15 kcal mol^-1 less stable than 1 and that 3 lies another 10 kcal mol^-1 higher in energy. MP2 exaggerates the separation by a few kcal mol^-1. HF predicts that 1 and 2 are degenerate. The large HF component within B3LYP leads to this DFT method’s poor performance. B3PW91 does reasonably well in reproducing the CCSD(T) results.

1 xyz file

2 xyz file

3 xyz file

Figure 1. Structures of 1-3 at B3LYP/6-31G(d).

Another of Schreiner’s examples is the relative energies of the C₁₀H­₁₀ isomers; Table 3 compares their relative experimental heats of formation with their computed energies. MP2 adequately reproduces the isomeric energy differences. B3LYP fairs quite poorly in this task. The errors seem to be most egregious for compounds with many single bonds. Schreiner recommends that while DFT-optimized geometries are reasonable, their energies are unreliable and some non-DFT method should be utilized instead.

Schleyer’s example of poor DFT performance is in the isodesmic energy of Reaction 1 evaluated for the n-alkanes.⁶ The energy of this reaction becomes more positive with increasing chain length, which Schleyer attributes to stabilizing 1,3-interactions between methyl or methylene groups. (Schleyer ascribes the term “protobranching” to this phenomenon.) The stabilization energy of protobranching using experimental heats of formation increases essentially linearly with the length of the chain, as seen in Figure 2.

n-CH₃(CH₂)_mCH₃ + mCH₄ → (m + 1)C₂H₆         Reaction 1

Schleyer evaluated the protobranching energy using a variety of methods, and these energies are also plotted in Figure 2. As expected, the G3 predictions match the experimental values quite closely. However, all of the DFT methods underestimate the stabilization energy. Most concerning is the poor performance of B3LYP. All three of these papers clearly raise concerns over the continued widespread use of B3LYP as the de facto DFT method. Even the new hybrid meta-GGA functionals fail to adequately predict the protobranching phenomenon, leading Schleyer to conclude: “We hope that Check and Gilbert’s pessimistic admonition that ‘a computational chemist cannot trust a one-type DFT calculation’¹ can be overcome eventually”. These papers provide a clear challenge to developers of new functionals.

Figure 2. Comparison of computed and experimental protobranching stabilization energy (as defined in Reaction 1) vs. m, the number of methylene groups of the n-alkane chain.⁶

Truhlar believes that one of his newly developed functionals answers the call for a reliable method. In a recent article,⁴ Truhlar demonstrates that the M05-2X⁷ functional performs very well in all three of the cases discussed here. In the case of the C₈H₁₈ isomers (Table 1), M05-2X properly predicts that 2,2,3,3-tetramethylbutane is more stable than octane, and estimates their energy difference within the error limit of the experiment. Second, M05-2X predicts the relative energies of the C₁₂H₁₂ isomers 1-3 within a couple of kcal mol^-1 of the CCSD(T) results (see Table 2). Last, in evaluating the isodesmic energy of Reaction 1 for hexane and octane, M05-2X/6-311+G(2df,2p) predicts energies of 11.5 and 17.2 kcal mol^-1 respectively. These are in excellent agreement with the experimental values of 13.1 kcal mol^-1 for butane and 19.8 kcal mol^-1 for octane.

Truhlar has also touted the M05-2X functional’s performance in handling noncovalent interactions.⁸ For example, the mean unsigned error (MUE) in the prediction of the binding energies of six hydrogen-bonded dimers is 0.20 kcal mol^-1. This error is comparable to that from G3 and much better than CCSD(T). With the M05-2X functional already implemented within NWChem and soon to be released within Gaussian and Jaguar, it is likely that M05-2X may supplant B3LYP as the new de facto functional in standard computational chemical practice.

Schleyer has now examined the bond separation energies of 72 simple organic molecules computed using a variety of functionals,⁹ including the workhorse B3LYP and Truhlar’s new M05-2X. Bond separation energies are defined by reactions of each compound, such as three shown below:

The new M05-2X functional performed the best, with a mean absolute deviation (MAD) from the experimental energy of only 2.13 kcal mol^-1. B3LYP performed much worse, with a MAD of 3.96 kcal mol^-1. As noted before, B3LYP energies become worse with increasing size of the molecules, but this problem is not observed for the other functionals examined (including PW91, PBE, and mPW1PW91, among others). So while M05-2X overall appears to solve many of the problems noted with common functionals, it too has some notable failures. In particular, the error is the bond separation energies of 4, 5, and 6 is -8.8, -6.8, and -6.0 kcal mol^-1, respectively.

References

(1) Check, C. E.; Gilbert, T. M., “Progressive Systematic Underestimation of Reaction Energies by the B3LYP Model as the Number of C-C Bonds Increases: Why Organic Chemists Should Use Multiple DFT Models for Calculations Involving Polycarbon Hydrocarbons,” J. Org. Chem. 2005, 70, 9828-9834, DOI: 10.1021/jo051545k.

(2) Redfern, P. C.; Zapol, P.; Curtiss, L. A.; Raghavachari, K., “Assessment of Gaussian-3 and Density Functional Theories for Enthalpies of Formation of C₁-C₁₆ Alkanes,” J. Phys. Chem. A 2000, 104, 5850-5854, DOI: 10.1021/jp994429s.

(3) Grimme, S., “Seemingly Simple Stereoelectronic Effects in Alkane Isomers and the Implications for Kohn-Sham Density Functional Theory,” Angew. Chem. Int. Ed. 2006, 45, 4460-4464, DOI: 10.1002/anie.200600448

(4) Zhao, Y.; Truhlar, D. G., “A Density Functional That Accounts for Medium-Range Correlation Energies in Organic Chemistry,” Org. Lett. 2006, 8, 5753-5755, DOI: 10.1021/ol062318n

(5) Schreiner, P. R.; Fokin, A. A.; Pascal, R. A.; deMeijere, A., “Many Density Functional Theory Approaches Fail To Give Reliable Large Hydrocarbon Isomer Energy Differences,” Org. Lett. 2006, 8, 3635-3638, DOI: 10.1021/ol0610486

(6) Wodrich, M. D.; Corminboeuf, C.; Schleyer, P. v. R., “Systematic Errors in Computed Alkane Energies Using B3LYP and Other Popular DFT Functionals,” Org. Lett. 2006, 8, 3631-3634, DOI: 10.1021/ol061016i

(7) Zhao, Y.; Schultz, N. E.; Truhlar, D. G., “Design of Density Functionals by Combining the Method of Constraint Satisfaction with Parametrization for Thermochemistry, Thermochemical Kinetics, and Noncovalent Interactions,” J. Chem. Theory Comput. 2006, 2, 364-382, DOI: 10.1021/ct0502763.

(8) Zhao, Y.; Truhlar, D. G., “Assessment of Model Chemistries for Noncovalent Interactions,” J. Chem. Theory Comput. 2006, 2, 1009-1018, DOI: 10.1021/ct060044j.

(9) Wodrich, M. D.; Corminboeuf, C.; Schreiner, P. R.; Fokin, A. A.; Schleyer, P. v. R., “How Accurate Are DFT Treatments of Organic Energies?,” Org. Lett., 2007, 9, 1851-1854, DOI: 10.1021/ol070354w.

InChI

1: InChI=1/C11H10/c1-2-5-7-3(1)4(1)8-6(2)10-9(5)11(7,8)10/h1-10H

2: InChI=1/C12H12/c1-2-4-10-6-8-11-7-5-9(3-1)12(10)11/h1-12H

3: InChI=1/C12H12/c1-2-4-8-11(7-3-1)12-9-5-6-10-12/h1-12H

4: InChI=1/C6H6/c1-4-5(2)6(4)3/h1-3H2

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

6: InChI=1/C10H10/c1-2-8-5-6-9-4-3-7(1)10(8)9/h1-10H

Addition of enolboranes to α-substituted aldehydes

In Chapter 5.2, we discussed a number of computation studies of the origins of asymmetry in 1,2-additions. We discussed the importance of the Felkin-Anh model, but that modifications of this model are needed to rationalize the broad range of addition reactions.

One modification was presented by Frenking,¹ who noted that in the addition of LiH to propanal, it was the conformation of the aldehyde that dictated the energy of the possible transition states. The lowest energy transition state is 1a, lying 1.3 kcal mol^-1 below 1b and 1.6 kcal mol^-1 below 1c (computed at MP2/6-31G(d)//HF/6-31G(d)). When the LiH fragment is removed and all other atoms kept frozen in their positions in the three transition states, 1a remains the lowest in energy.

A recent article by Cramer and Evans² examined the addition of enolboranes to aldehydes and also noted the importance of the aldehyde conformation in dictating the stereochemical outcome. The main thrust was, however, that the Cram-Conforth type model for 1,2-addition is more appropriate for some enolborane additions.

This work derives from Evans’ earlier experimental study of the addition of the boron enolate of 2-methyl-3-pentanone to a-alkoxyaldehydes (Scheme 1).³ Evans suggested that there were four transition state models that give a 3,4-anti relationship in the product (Scheme 2). The Felkin-Anh model favors B, since it avoids the syn interaction, and so E enolates will have a greater anti selectivity than Z enolates. On the other hand, the Conforth model favors transition state C, and predicts that Z enolates will have greater anti selectivity. The addition of Z enolates in fact gives large anti selectivity, while addition of E enolates gives poor anti selectivity. These results are consistent with the Cram-Cornforth model.

Scheme 1.

Scheme 2.

Cee, Cramer and Evans² examined the addition of enolborane to a number of a-substituted propanal compounds. They located six transition states (Figure 1) for the reaction of 2-fluoropropanal, three leading to the (R,S) product (2A-C) and three leading to the (S,S) product (2A’-C’). The lowest energy transition states, 2A and 2A’, both have the fluorine atom positioned anti to the carbonyl, consistent with the Cornforth model. This reflects the stability of 2-fluoropropanal. Similar results are found for addition to 2-chloropropanal

2A (0.0) xyz file		2B (2.4) xyz file
2C (2.6) xyz file
2A’ (0.8) xyz file		2B’ (1.4) xyz file
2C’ (3.7) xyz file

Figure 1. Optimized transition states and relative energies (kcal mol^-1) for the reaction of 2-fluoropropanal with enolborane computed at B3LYP/6-31G(d).²

For the reaction of enolborane with 2-methoxypropanal, the lowest energy transition state, 3, also has the methoxy group anti to the carbonyl (see Figure 2). However, the lowest energy transition state for the reaction of 2-methylthiopropanal, 4, has the MeS group perpendicular to the carbonyl, as predicted by the Felkin-Anh model. Similarly, the lowest energy transition states for the addition to 2-dimethylaminopropanal (5) and to 2-dimenthylphosphinopropanal (6) follow the Felkin-Anh model.

The lowest energy conformer of propanal with F, Cl, or OMe as the 2-substituent has the substituent anti to the carbonyl. All three of these aldehydes undergo addition of enolborane through the Cornforth TS. The lowest energy conformer with SMe₂ or PMe₂ has the substituent perpendicular to the carbonyl, which mimics its location in the enolborane transition state. Only 2-dimethylaminopropanal falls outside this pattern; its lowest energy conformer positions the substituent about 150° from the carbonyl, but rotation to a perpendiculat (Felkin-Anh) position requires only 2 kcal mol^-1, half of that need for F, Cl, or methoxy rotation. Cee, Cramer, and Evans draw two conclusions. First, the stereochemistry 1,2-addition of enolborane parallels the conformation of the aldehyde itself, and second, this implies that the Cornforth pathway can be preferred over the Felkin-Anh for those aldehydes where the anti conformation is particularly stable.

3 xyz file		4 xyz file
5 xyz file		6 xyz file

References

(1) Frenking, G.; F., K. K.; Reetz, M. T., “On the Origin of π-Facial Diastereoselectivity in Nucleophilic Additions to Chiral Carbonyl Compounds. 2. Calculated Transition State Structures for the Addition of Nucleophiles to Propionaldehyde 1, Chloroacetyldehyde 2, and 2-Chloropropionaldehyde 3.,” Tetrahedron 1991, 47, 9005-9018, DOI: 10.1016/S0040-4020(01)86505-4.

(2) Cee, V. J.; Cramer, C. J.; Evans, D. A., “Theoretical Investigation of Enolborane Addition to α-Heteroatom-Substituted Aldehydes. Relevance of the Cornforth and Polar Felkin-Anh Models for Asymmetric Induction,” J. Am. Chem. Soc. 2006, 128, 2920-2930, DOI: DOI: 10.1021/ja0555670

(3) Evans, D. A.; Siska, S. J.; Cee, V. J., “Resurrecting the Cornforth Model for Carbonyl Addition: Studies on the Origin of 1,2-Asymmetric Induction in Enolate Additions to Heteroatom-Substituted Aldehydes,” Angew. Chem. Int. Ed. 2003, 42, 1761-1765, DOI: 10.1002/anie.200350979.

Monohydrated Glycolaldehyde (2-hydroxyethanal)

In Chapter 6.3.1 we discussed the conformation energy profile of solvated ethylene glycol and glycerol. The conformational preference is determined by the two competing hydrogen bonding interactions: intramolecular hydrogen bonding versus hydrogen bonding to the water molecules. For both glycerol and ethylene glycol, the lowest energy solvated structures retain the maximal number of internal hydrogen bonds possible.

The conformational space of glycoladehyde 1 exhibits four local minima. ¹ The lowest energy structure possesses an internal hydrogen bond, 1-CC (Figure 1). The other conformers are at least 3 kcal mol^-1 higher in energy. Will this internal hydrogen bond persist when 1 is hydrated?

1-CC (0.0) xyz file	1-TT (3.06) xyz file
1-TG (3.33) xyz file	1-CT (4.84) xyz file

Figure 1. Optimized geometries of the conformers of 1 at MP2/aug-cc-pVTZ. ¹ The letters C, T, and G indicate cis¸ trans, or gauche around the C-C and C-O bonds, in that order. Relative energies in kcal mol^-1.

A recent computational (B3LYP/6-311++G(2df,p)) and experimental study examined the structure of monohydrated glycoladehyde.² Optimization of the monohydrated cluster of 1 indicated that the lowest energy structures all have the glycolaldehyde fragment in the CC conformation (see Figure 2). The lowest energy cluster not in the CC arrangement is 1-TG-w, and it lies 2.86 kcal mol^-1 above the lowest monohydrate, 1-CC-w1.

The lowest energy monohydrate (1-CC-w1) does not maintain the internal hydrogen bond of 1-CC. Rather, the water molecule inserts into this hydrogen bond, such that it donates a hydrogen to the carbonyl oxygen, and accepts the hydrogen from the hydroxyl group. The other conformations provide no opportunity for forming two hydrogen bonds with a water molecule, and so their hydrates are higher in energy. The microwave FT spectrum² of the monohydrate of 1 is interpreted as a dynamic interconversion of the two lowest energy complexes, 1-CC-w1 and 1-CC-w2.

1-CC-w1 (0.0) xyz file	1-CC-w2 (0.51) xyz file
1-CC-w3 (0.96) xyz file	1-CC-w4 (1.39) xyz file
1-TG-w (2.86) xyz file	1-TT-w (3.71) xyz file
1-CT-w (5.98) xyz file

Figure 2. Optimized geometries (B3LYP/6-311++G(2df,p)) of the monohydrated glycolaldehyde structures.² All distances in Å and relative energies (G3MP2B3) in kcal mol^-1.

References

(1) Ratajczyk, T.; Pecul, M.; Sadlej, J.; Helgaker, T., “Potential Energy and Spin-Spin Coupling Constants Surface of Glycolaldehyde,” J. Phys. Chem. A 2004, 108, 2758-2769, DOI: 10.1021/jp0375315

(2) Aviles-Moreno, J. R.; Demaison, J.; Huet, T. R., “Conformational Flexibility in Hydrated Sugars: the Glycolaldehyde-Water Complex,” J. Am. Chem. Soc. 2006, 128, 10467-10473, DOI: 10.1021/ja062312t