Archive for the 'Authors' Category

Polytriangulane

Cyclopropyl rings can be joined together in a spiro fashion to form triangulanes. An interesting topology can be made by joining the rings to form a helical pattern, as shown in the [9]triangulane 1 below. Allen, Quanz, and Schreiner1 have examined the notion of an infinite helical molecule formed in this way.


1

First, they describe how one can generate the coordinates of such a beast using a closed analytical expression, which is a really nice demonstration of applied geometry. Next, they compute the geometry of a series of [n]triangulanes at M06-2x/6-31G(d). The geometries of [9]triangulane and their largest example, [42]triangulane 2 are shown in Figure 1.

1

2

Figure 1. M06-2x/6-31G(d) optimized geometries of 1 and 2.

They show that the geometry of 2 exhibits a structure that has two different C-C distances: one between the spiro carbons, and the second between the spiro carbon and the methylene carbon. The distance between the spiro carbons is rather short (1.458 Å), suggesting that the bonding here is between carbons that are nearly sp2-hybridized.

Lastly, they discuss the thermodynamics of polytriangulane. They employ a series of homodesmotic reactions to attempt to determine the enthalpy for adding another cyclopropyl ring to an extended triangulane. Unfortunately, the computed enthalpy is quite dependent on functional used. Similar attempts to define the strain energy is also flawed in this way. However, regardless of the functional the enthalpy for adding a cyclopropane ring appears to reach an asymptote rather quickly. So, using [3]triangulane they estimate that the strain energy per mole of cyclopropane in triangulane is about 42.7 kcal mol-1, or about 14 kcal mol-1 of strain due to the spiroannulation.

References

(1) Allen, W. D.; Quanz, H.; Schreiner, P. R. “Polytriangulane,” J. Chem. Theory Comput. 2016, 12, 4707–4716, DOI: 10.1021/acs.jctc.6b00669.

InChIs

1: InChI=1S/C19H22/c1-2-12(1)5-14(12)7-16(14)9-18(16)11-19(18)10-17(19)8-15(17)6-13(15)3-4-13/h1-11H2/t14-,15-,16-,17-,18-,19-/m0/s1
InChIKey=XBTZCZDSKVTALB-DYKIIFRCSA-N

Schreiner Steven Bachrach 27 Sep 2016 1 Comment

Dynamics in a reaction where a [6+4] and [4+2] cycloadditons compete

Enzyme SpnF is implicated in catalyzing the putative [4+2] cycloaddition taking 1 into 3. Houk, Singleton and co-workers have now examined the mechanism of this transformation in aqueous solution but without the enzyme.1 As might be expected, this mechanism is not straightforward.

Reactant 1, transition states, and products 2 and 3 were optimized at SMD(H2O)/M06-2X/def2-TZVPP//B3LYP-D3(BJ)//6-31+G(d,p). Geometries and relative energies are shown in Figure 1. The reaction 12 is a formal [6+4] cycloaddition, and the reaction 13 is a formal [4+2] cycloaddition. Interestingly, only a single transition state could be located TS1. It is a bispericyclic TS (see Chapter 4 of my book), where these two pericyclic reaction sort of merge together. After TS1 is traversed the potential energy surface bifurcates, leading to 2 or 3. This is yet again an example of a single TS leading to two different products. (See the many posts I have written on this topic.) The barrier height is 27.6 kcal mol-1, with 2 lying 13.1 kcal mol-1 above 3. However, the steepest descent pathway from TS1 leads to 2. There is a second transition state TScope that describes a Cope rearrangement between 2 and 3. Using the more traditional TS theory description, 1 undergoes a [6+4] cycloaddition to form 2 which then crosses a lower barrier (TScope) to form the thermodynamically favored 3, which is the product observed in the enzymatically catalyzed reaction.

1 (0.0)

TS1 (27.6)

2 (4.0)

3 (-9.1)

(24.7)

Figure 1. B3LYP-D3(BJ)//6-31+G(d,p) optimized geometries and relative energies in kcal mol-1.

Molecular dynamics computations were performed on this system by tracking trajectories starting in the neighborhood of TS1 on a B3LYP-D2/6-31G(d) PES. The results are that 63% of the trajectories end at 2, 25% end at 3, and 12% recross back to reactant 1, suggesting an initial formation ratio for 2:3 of 2.5:1. The reactions are very slow to cross through the “transition zone”, typically 2-3 times longer than for a usual Diels-Alder reaction (see this post).

Once again, we see an example of dynamic effects dictating a reaction mechanism. The authors pose a tantalizing question: Can an enzyme control the outcome of an ambimodal reaction by altering the energy surface such that the steepest downhill path from the transition state leads to the “desired” product(s)? The answer to this question awaits further study.

References

(1) Patel, A; Chen, Z. Yang, Z; Gutierrez, O.; Liu, H.-W.; Houk, K. N.; Singleton, D. A. “Dynamically
Complex [6+4] and [4+2] Cycloadditions in the Biosynthesis of Spinosyn A,” J. Amer. Chem. Soc. 2016, 138, 3631-3634, DOI: 10.1021/jacs.6b00017.

InChIs

1: InChI=1S/C24H34O5/c1-3-21-15-12-17-23(27)19(2)22(26)16-10-7-9-14-20(25)13-8-5-4-6-11-18-24(28)29-21/h4-11,16,18-21,23,25,27H,3,12-15,17H2,1-2H3/b6-4+,8-5+,9-7+,16-10+,18-11+/t19-,20+,21-,23-/m0/s1
InChIKey=JEKALMRMHDPSQK-ZTRRSECRSA-N

2: InChI=1S/C24H34O5/c1-3-19-8-6-10-22(26)15(2)23(27)20-12-11-17-14-18(25)13-16(17)7-4-5-9-21(20)24(28)29-19/h4-5,7,9,11-12,15-22,25-26H,3,6,8,10,13-14H2,1-2H3/b7-4-,9-5+,12-11+/t15-,16-,17-,18-,19+,20+,21-,22+/m1/s1
InChIKey=AVLPWIGYFVTVTB-PTACFXJJSA-N

3: InChI=1S/C24H34O5/c1-3-19-5-4-6-22(26)15(2)23(27)11-10-20-16(9-12-24(28)29-19)7-8-17-13-18(25)14-21(17)20/h7-12,15-22,25-26H,3-6,13-14H2,1-2H3/b11-10+,12-9+/t15-,16+,17-,18-,19+,20-,21-,22+/m1/s1
InChIKey=BINMOURRBYQUKD-MBPIVLONSA-N

cycloadditions &Diels-Alder &Dynamics &Houk &Singleton Steven Bachrach 30 Aug 2016 No Comments

Dehydro-Diels-Alder Reactions

I have been delinquent in writing about the dehydro-Diels-Alder reactions, but really can’t put it off any further. These sets of reactions really deserve a fuller analysis than I am going to summarize here, but this post will provide a good jumping off point for anyone interested in further investigation.

So the Diels-Alder reaction is among the most famous and most important reactions in organic chemistry. The reaction creates a 6-member ring and sets up to four stereocenters. In the past couple of years many chemists have expressed interest in the variant where the four-carbon component is more highly unsaturated, i.e. enyne or diyne. I will summarize the results of three recent computational papers dealing with the reaction of a diyne with an yne.

The first paper is by Skraba-Joiner, Johnson, and Agarwal.1 They discuss, among a number of interesting pericyclic reactions, the intramolecular Diels-Alder reaction of triyne 1 to give 2. They examined a concerted and stepwise pathway at (U)M05-2X/6-311+G(d,p) and find the concerted to be favored by 6.0 kcal mol-1. CCSD(T) using these geometries increases the difference to 8.2 kcal mol-1. The T1 diagnostic is fairly large for both the concerted and stepwise transition states, so they also performed CCSD(T)/CBS computations, which had much lower T1 values. The concerted TS remained favorable, but by only 2.7 kcal mol-1.

In the same special issue of the Journal of Organic Chemistry, Cramer, Hoye, and Kuwata examined a reaction closely related to what Johnson examined above.2 They looked at the reaction taking 3 into 4 via both experiments and computations. The M06-2x/6-311+G(d,p) geometries for the concerted and first TS along the stepwise path (with R1=R2=H) are shown in Figure 1. Evaluating the energies at SMD(o-dichlorobenzene)/B3LYP-D3BJ/6-311+G-(d,p)//M06-2X/6-311+G(d,p) find in this case (along with all of the other R1/R2 variants they examined) that the stepwise path has a lower barrier than the concerted path. In the case where R1=R2=H, the stepwise path is favored by 6.0 kcal mol-1. Additionally, these stepwise barriers are in reasonable agreement with the experimentally-derived barriers.

Concerted TS

Stepwise TS

Figure 1. M06-2x/6-311+G(d,p) optimized geometries of the concerted and stepwise TSs for the reaction of 3H going to 4H.

It should be pointed out that the wavefunctions for the concerted TSs were all found to be unstable with regard to a restricted to unrestricted relaxation. Given this problem, they also performed a CASPT2 energy evaluation of the concerted and stepwise transition states for the case R1=R2=H. CASPT2 finds the stepwise barrier to be 3.7 kcal mol-1 lower than the concerted barrier.

The last paper comes from the Houk lab, and examines the simplest set of intermolecular dehdro-Diels-Alder reactions.3 I will focus here on the most unsaturated analogue, the reaction of 1,3-butadiyne 5 with ethyne to give benzyne 6.

The concreted and stepwise transition states for this reaction (at (U)M06-2X/6-311+G(d,p)) are shown in Figure 2. The concerted barrier is 36.0 kcal moml-1 while the stepwise barrier is slightly lower: 35.2 kcal mol-1. The distortion energy for the concerted reaction is large (43.2 kcal mol-1) due mostly to angle changes in the diyne. Its interaction energy is -7.2 kcal mol-1, similar to the interaction energy in other similar Diels-Alder reactions. In contrast, the distortion energy for the stepwise pathway is 27.5 kcal mol-1, but the interaction energy is +7.7 kcal mol-1. These values are very similar to the distortion and interaction energy of the related (but less saturated DA reactions).

Concerted TS

Stepwise TS

Figure 2. (U)M06-2X/6-311+G(d,p) optimized concerted and stepwise TS for the reaction of 1,3-diyne with ethyne.

Molecular dynamics trajectories for both the concerted and stepwise paths reveal interesting differences. The concerted trajectories show an oscillatory behaviour of bending the angles at the C2 and C3 carbons prior to the TS, and then near synchronous formation of the new C-C bonds. The trajectories initiated at the stepwise TS show no systematic motion. Once the bond is formed, the biradical exhibits a long lifetime, on the order of picoseconds, much longer than the trajectory runs.

These three studies indicate the nature of the dehydro Diels-Alder reaction is very sensitive to reaction conditions, substituents, solvation, and all other manner of effects and will likely prove an area of interest for some time. It should keep a number of computational chemists busy for some time!

References

(1) Skraba-Joiner, S. L.; Johnson, R. P.; Agarwal, J. "Dehydropericyclic Reactions: Symmetry-Controlled Routes to Strained Reactive Intermediates," J. Org. Chem. 2015, 80, 11779-11787, DOI: 10.1021/acs.joc.5b01488.

(2) Marell, D. J.; Furan, L. R.; Woods, B. P.; Lei, X.; Bendelsmith, A. J.; Cramer, C. J.; Hoye, T. R.; Kuwata, K. T. "Mechanism of the Intramolecular Hexadehydro-Diels–Alder Reaction," J. Org. Chem. 2015, 80, 11744-11754, DOI: 10.1021/acs.joc.5b01356.

(3) Yu, P.; Yang, Z.; Liang, Y.; Hong, X.; Li, Y.; Houk, K. N. "Distortion-Controlled Reactivity and Molecular Dynamics of Dehydro-Diels–Alder Reactions," J. Am. Chem. Soc. 2016, 138, 8247-8252, DOI: 10.1021/jacs.6b04113.

InChIs

1: InChI=1S/C9H8/c1-3-5-7-9-8-6-4-2/h1-2H,5,7,9H2
InChIKey=IYZAZSVBWMMSLQ-UHFFFAOYSA-N

2: InChI=1S/C9H8/c1-2-5-9-7-3-6-8(9)4-1/h1,4H,3,6-7H2
InChIKey=PZJMTUKDGZUDBH-UHFFFAOYSA-N

3H: InChI=1S/C8H4O2/c1-3-5-6-7-10-8(9)4-2/h1-2H,7H2
InChIKey=MGXDIFXPYGGQLF-UHFFFAOYSA-N

4H: InChI=1S/C10H8O4/c1-6(11)14-8-2-3-9-7(4-8)5-13-10(9)12/h2-4H,5H2,1H3
InChIKey=GEFLHLNIKGXWCA-UHFFFAOYSA-N

5: InChI=1S/C4H2/c1-3-4-2/h1-2H
InChIKey=LLCSWKVOHICRDD-UHFFFAOYSA-N

6: InChI=1S/C6H4/c1-2-4-6-5-3-1/h1-4H
InChIKey=KLYCPFXDDDMZNQ-UHFFFAOYSA-N

benzynes &Cramer &Diels-Alder &Houk Steven Bachrach 25 Jul 2016 No Comments

Mechanism of dimethyldioxirane oxidation

Dimethyldioxirane can oxidize alkanes to alcohols. The mechanism for the oxidation has been controversial, ranging from concerted, to radical intermediates to an H-abstraction—O-rebound mechanism. Yang, Yu, and Houk now offer a molecular dynamics examination of the reaction of dimethyldioxirane with isobutane.1

Gas–phase (U)B3LYP/6-311++G(d,p)//(U)B3LYP/6-31G(d) computations give critical points outlined in the reaction below. The structures of the transition states and the intermediate are shown in Figure 1.

TS1
26.6
(25.9)

INT
8.6
(9.3)

TS2
8.6
(-0.8)

Figure 1. (U)B3LYP/6-31G(d) optimized geometries of TS1, INT, and TS2. Relative free energies (kcal mol-1) in the gas (top) and solution (bottom) phases

The PES indicates a rebound mechanism, though in acetone solution phase, there was no transition state located for the second step; it appears to be barrierless. It should be noted that the size of the barrier is very small even in the gas phase. The energy given in Figure 1 is for the gas phase structure computed in solution.

Trajectories for both gas and solution phase were computed. For the gas phase, about 90% of the trajectories lead to separated radicals, but in an acetone about 90% of the trajectories lead directly to the alcohol, with only 10% leading to radicals. Even so, the acetone trajectories divide into two types, a dynamically concerted path where the time gap between the formation of the new C-O and O-H bonds is less than 60 fs, and a dynamically stepwise path where the time gap is greater than 60 fs, though for the trajectories that lead to product the gap is typically still less than 150 fs.

References

(1)  Yang, Z.; Yu, P.; Houk, K. N. "Molecular Dynamics of Dimethyldioxirane C–H Oxidation," J. Am. Chem. Soc. 2016, 138, 4237-4242, DOI: 10.1021/jacs.6b01028.

InChIs

Dimethyldioxirane: InChI=1S/C3H6O2/c1-3(2)4-5-3/h1-2H3
InChIKey=FFHWGQQFANVOHV-UHFFFAOYSA-N

Isobutane: InChI=1S/C4H10/c1-4(2)3/h4H,1-3H3
InChIKey=NNPPMTNAJDCUHE-UHFFFAOYSA-N

Houk Steven Bachrach 06 Jun 2016 No Comments

Benchmarking Platonic solids and related hydrocarbons

Karton, Schreiner, and Martin have benchmarked the heats of formation of some Platonic Solids and related hydrocarbons.1 The molecules examined are tetrahedrane 1, cubane 2, dodecahedrane 3, trisprismane 4, pentaprismane 5, and octahedrane 6.

The optimized structures (B3LYP-D3BJ/def2-TZVPP) of these compounds are shown in Figure 1.

1

2

3

4

5

6

Figure 1. B3LYP-D3BJ/def2-TZVPP optimized geometries of 1-6.

Using the W1-F12 and W2-F12 composite methods, the estimated the heats of formation of these hydrocarbons are listed in Table 1. Experimental values are available only for 2 and 3; the computed values are off by about 2 kcal mol-1, which the authors argue is just outside the error bars of the computations. They suggest that the experiments might need to be revisited.

Table 1. Heats of formation (kcal mol-1) of 1-6.

compound

ΔHf (comp)

ΔHf (expt)

1

128.57

 

2

144.78

142.7 ± 1.2

3

20.18

22.4 ± 1

4

132.84

 

5

119.42

 

6

63.08

 

They conclude with a comparison of strain energies computed using isogyric, isodesmic, and homodesmotic reactions with a variety of computational methods. Somewhat disappointingly, most DFT methods have appreciable errors compared with the W1-F12 results, and the errors vary depend on the chemical reaction employed. However, the double hybrid method DSD-PBEP86-D3BJ consistently reproduces the W1-F12 results.

References

(1)  Karton, A.; Schreiner, P. R.; Martin, J. M. L. "Heats of formation of platonic hydrocarbon cages by means of high-level thermochemical procedures," J. Comput. Chem. 2016, 37, 49-58, DOI: 10.1002/jcc.23963.

InChIs

1: InChI=1S/C4H4/c1-2-3(1)4(1)2/h1-4H
InChIKey=FJGIHZCEZAZPSP-UHFFFAOYSA-N

2: InChI=1S/C8H8/c1-2-5-3(1)7-4(1)6(2)8(5)7/h1-8H
InChIKey=TXWRERCHRDBNLG-UHFFFAOYSA-N

3: InChI=1S/C20H20/c1-2-5-7-3(1)9-10-4(1)8-6(2)12-11(5)17-13(7)15(9)19-16(10)14(8)18(12)20(17)19/h1-20H
InChIKey=OOHPORRAEMMMCX-UHFFFAOYSA-N

4: InChI=1S/C6H6/c1-2-3(1)6-4(1)5(2)6/h1-6H
InChIKey=RCJOMOPNGOSMJU-UHFFFAOYSA-N

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

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

QM Method &Schreiner Steven Bachrach 10 May 2016 No Comments

Diels-Alder reactions of some arenes

Houk has examined the Diels-Alder reaction involving ethene with benzene 1 and all of its aza-substituted isomers having four or fewer nitrogen atoms 2-11.1 The reactions were computed at M06-2X/6-311+G(d,p).

All of the possible Diels-Alder reactions were examined, and they can be classified in terms of whether two new C-C bonds are formed, one new C-C and one new C-N bond are formed, or two new C-N bonds are formed. Representative transition states of these three reaction types are shown in Figure 1, using the reaction of 7 with ethene.

Figure 1. M06-2X/6-311+G(d,p) optimized transition states for the Diels-Alders reactions of 7 with ethene.

A number of interesting trends are revealed. For a given type of reaction (as defined above), as more nitrogens are introduced into the ring, the activation energy decreases. Forming two C-C bonds has a lower barrier than forming a C-C and a C-N, which has a lower barrier than forming two C-N bonds. The activation barriers are linearly related to the aromaticity of the ring defined by either NICS(0) or aromatic stabilization energy, with the barrier decreasing with decreasing aromaticity. The barrier is also linearly related to the exothermicity of the reaction.

The activation barrier is also linearly related to the distortion energy. With increasing nitrogen substitution, the ring becomes less aromatic, and therefore more readily distorted from planarity to adopt the transition state structure.

References

(1) Yang, Y.-F.; Liang, Y.; Liu, F.; Houk, K. N. "Diels–Alder Reactivities of Benzene, Pyridine, and Di-, Tri-, and Tetrazines: The Roles of Geometrical Distortions and Orbital Interactions," J. Am. Chem. Soc. 2016, 138, 1660-1667, DOI: 10.1021/jacs.5b12054.

Aromaticity &Diels-Alder &Houk Steven Bachrach 26 Apr 2016 No Comments

Cyclization reaction of 1,2-cyclohexadiene

1,2-Cyclohexadiene 1 is a very strained and highly reactive species. Houk, Garg and co-workers report on its use as the ene component in a cyclization with a 1,3-dipole, namely nitrones.1 For example, 1 reacts with nitrone 2 to give the cycloadducts 3a and 3b in a ratio of 8.9:1.

To investigate the mechanism of this reaction, they optimized the structures of all compounds at CPCM(acetonitrile)B3LYP/6-31G(d) and single-point energies were obtained using the B3LYP-D3 functional. The structures of some pertinent critical points are shown in Figure 1. They did locate a concerted transition state (TS1) leading to 3a, with a barrier of 14.5 kcal mol-1, but could not find a concerted TS leading to 3b. (Also, the barriers leading to the other regioisomer are much higher than the ones leading to the observed products.) Rather, they identified a stepwise transition state (TS2) with a barrier of nearly the same energy (14.4 kcal mol-1) that leads to the intermediate (INT), which lies 16.5 kcal mol-1 below reactants. They located two transition states from his intermediate, TS3a and TS3b, leading to the two different products. The barrier to 3a is 1.2 kcal mol-1 lower than the barrier leading to 3b, and this corresponds nicely with the observed diastereoselectivity.

1
(0.0)

TS1
(14.5)

TS2
(14.4)

 

INT
(-16.5)

 

TS3a
(-7.4)

TS3b
(-6.2)

Figure 1. CPCM(acetonitrile)B3LYP/6-31G(d) optimized geometries and CPCM(acetonitrile)B3LYP-D3/6-31G(d) free energies.

References

(1) Barber, J. S.; Styduhar, E. D.; Pham, H. V.; McMahon, T. C.; Houk, K. N.; Garg, N. K.
"Nitrone Cycloadditions of 1,2-Cyclohexadiene," J. Am. Chem. Soc. 2016, 138, 2512-2515, DOI: 10.1021/jacs.5b13304.

InChIs

1: InChI=1S/C6H8/c1-2-4-6-5-3-1/h1,5H,2,4,6H2
InChIKey=NMGSDTSOSIPXTN-UHFFFAOYSA-N

2: InChI=1S/C11H15NO/c1-11(2,3)12(13)9-10-7-5-4-6-8-10/h4-9H,1-3H3/b12-9-
InChIKey=IYSYLWYGCWTJSG-XFXZXTDPSA-N

3a: InChI=1S/C17H23NO/c1-17(2,3)18-16(13-9-5-4-6-10-13)14-11-7-8-12-15(14)19-18/h4-6,9-11,15-16H,7-8,12H2,1-3H3/t15-,16-/m0/s1
InChIKey=HQIBSHJEOJPFTI-HOTGVXAUSA-N

3b: InChI=1S/C17H23NO/c1-17(2,3)18-16(13-9-5-4-6-10-13)14-11-7-8-12-15(14)19-18/h4-6,9-11,15-16H,7-8,12H2,1-3H3/t15-,16+/m1/s1
InChIkey=HQIBSHJEOJPFTI-CVEARBPZSA-N

cycloadditions &Houk Steven Bachrach 11 Apr 2016 No Comments

Mechanism of organocatalysis by Cinchona alkaloids

Cinchona alkaloids cat catalyze reactions, such as shown in Reaction 1. Wynberg1 proposed a model to explain the reaction, shown in Scheme 1, based on NMR. Grayson and Houk have now used DFT computations to show that the mechanism actually reverses the arrangements of the substrates.2

Reaction 1

Scheme 1.


Wynberg Model


Grayson and Houk Model

M06-2X/def2-TZVPP−IEFPCM(benzene)//M06-2X/6-31G(d)−IEFPCM(benzene) computations show that the precomplex of catalyst 3 with nucleophile 1 and Michael acceptor 2 is consistent with Wynberg’s model. The alternate precomplex is 5.6 kcal mol-1 higher in energy. These precomplexes are shown in Figure 1.

Wynberg precomplex

Grayson/Houk precomplex

Figure 1. Precomplexes structures

However, the lowest energy transition state takes the Grayson/Houk pathway and leads to the major isomer observed in the reaction. The Grayson/Houk TS that leads to the minor product has a barrier that is 3 kcal mol-1 higher in energy. The lowest energy TS following the Wynberg path leads to the minor product, and is 2.2 kcal mol-1 higher than the Grayson/Houk path. These transition states are shown in Figure 2. The upshot is that complex formation is not necessarily indicative of the transition state structure.

Wynberg TS (major)
Rel ΔG = 5.3

Wynberg TS (minor)
Rel ΔG = 2.2

Grayson/Houk TS (major)
Rel ΔG = 0.0

Grayson/Houk TS (minor)
Rel ΔG = 3.0

Figure 2. TS structures and relative free energies (kcal mol-1).

References

(1) Hiemstra, H.; Wynberg, H. "Addition of aromatic thiols to conjugated cycloalkenones, catalyzed by chiral .beta.-hydroxy amines. A mechanistic study of homogeneous catalytic asymmetric synthesis," J. Am. Chem. Soc. 1981, 103, 417-430, DOI: 10.1021/ja00392a029.

(2) Grayson, M. N.; Houk, K. N. "Cinchona Alkaloid-Catalyzed Asymmetric Conjugate Additions: The Bifunctional Brønsted Acid–Hydrogen Bonding Model," J. Am. Chem. Soc. 2016, 138, 1170-1173, DOI: 10.1021/jacs.5b13275.

InChIs

1: InChI=1S/C10H14S/c1-10(2,3)8-4-6-9(11)7-5-8/h4-7,11H,1-3H3
InChIKey=GNXBFFHXJDZGEK-UHFFFAOYSA-N

2: InChI=1S/C8H12O/c1-8(2)5-3-4-7(9)6-8/h3-4H,5-6H2,1-2H3
InChIKey=CDDGRARTNILYAB-UHFFFAOYSA-N

3: InChI=1S/C18H22N2O/c1-12-11-20-9-7-13(12)10-17(20)18(21)15-6-8-19-16-5-3-2-4-14(15)16/h2-6,8,12-13,17-18,21H,7,9-11H2,1H3/t12?,13?,17?,18-/m1/s1
InChIKey=ZOZLJWFJLBUKKL-NKHWWFDVSA-N

4: InChI=1S/C18H26OS/c1-17(2,3)13-6-8-15(9-7-13)20-16-10-14(19)11-18(4,5)12-16/h6-9,16H,10-12H2,1-5H3/t16-/m0/s1
InChIKey=XUTYYZOSKLYWLW-INIZCTEOSA-N

Houk &Michael addition &stereoinduction Steven Bachrach 03 Mar 2016 No Comments

QM/MM trajectory of an aqueous Diels-Alder reaction

I discuss the aqueous Diels-Alder reaction in Chapter 7.1 of my book. A key case is the reaction of methyl vinyl ketone with cyclopentadiene, Reaction 1. The reaction is accelerated by a factor of 740 in water over the rate in isooctane.1 Jorgensen argues that this acceleration is due to stronger hydrogen bonding to the ketone than in the transition state than in the reactants.2-4

Rxn 1

Doubleday and Houk5 report a procedure for calculating trajectories including explicit water as the solvent and apply it to Reaction 1. Their process is as follows:

  1. Compute the endo TS at M06-2X/6-31G(d) with a continuum solvent.
  2. Equilibrate water for 200ps, defined by the TIP3P model, in a periodic box, with the transition state frozen.
  3. Continue the equilibration as in Step 2, and save the coordinates of the water molecules after every addition 5 ps, for a total of typically 25 steps.
  4. For each of these solvent configurations, perform an ONIOM computation, keeping the waters fixed and finding a new optimum TS. Call these solvent-perturbed transition states (SPTS).
  5. Generate about 10 initial conditions using quasiclassical TS mode sampling for each SPTS.
  6. Now for each the initial conditions for each of these SPTSs, run the trajectories in the forward and backward directions, typically about 10 of them, using ONIOM to compute energies and gradients.
  7. A few SPTS are also selected and water molecules that are either directly hydrogen bonded to the ketone, or one neighbor away are also included in the QM portion of the ONIOM, and trajectories computed for these select sets.

The trajectory computations confirm the role of hydrogen bonding in stabilizing the TS preferentially over the reactants. Additionally, the trajectories show an increasing asynchronous reactions as the number of explicit water molecules are included in the QM part of the calculation. Despite an increasing time gap between the formation of the first and second C-C bonds, the overwhelming majority of the trajectories indicate a concerted reaction.

References

(1) Breslow, R.; Guo, T. "Diels-Alder reactions in nonaqueous polar solvents. Kinetic
effects of chaotropic and antichaotropic agents and of β-cyclodextrin," J. Am. Chem. Soc. 1988, 110, 5613-5617, DOI: 10.1021/ja00225a003.

(2) Blake, J. F.; Lim, D.; Jorgensen, W. L. "Enhanced Hydrogen Bonding of Water to Diels-Alder Transition States. Ab Initio Evidence," J. Org. Chem. 1994, 59, 803-805, DOI: 10.1021/jo00083a021.

(3) Chandrasekhar, J.; Shariffskul, S.; Jorgensen, W. L. "QM/MM Simulations for Diels-Alder
Reactions in Water: Contribution of Enhanced Hydrogen Bonding at the Transition State to the Solvent Effect," J. Phys. Chem. B 2002, 106, 8078-8085, DOI: 10.1021/jp020326p.

(4) Acevedo, O.; Jorgensen, W. L. "Understanding Rate Accelerations for Diels−Alder Reactions in Solution Using Enhanced QM/MM Methodology," J. Chem. Theor. Comput. 2007, 3, 1412-1419, DOI: 10.1021/ct700078b.

(5) Yang, Z.; Doubleday, C.; Houk, K. N. "QM/MM Protocol for Direct Molecular Dynamics of Chemical Reactions in Solution: The Water-Accelerated Diels–Alder Reaction," J. Chem. Theor. Comput. 2015, , 5606-5612, DOI: 10.1021/acs.jctc.5b01029.

Diels-Alder &Houk &Solvation Steven Bachrach 02 Feb 2016 1 Comment

Fractional occupancy density

Assessing when a molecular system might be subject to sizable static (non-dynamic) electron correlation, necessitating a multi-reference quantum mechanical treatment, is perhaps more art than science. In general one suspects that static correlation will be important when the frontier MO energy gap is small, but is there a way to get more guidance?

Grimme reports the use of fractional occupancy density (FOD) as a visualization tool to identify regions within molecules that demonstrate significant static electron correlation.1 The method is based on the use of finite temperature DFT.2,3

The resulting plots of the FOD for a series of test cases follow our notions of static correlation. Molecules, such as alkanes, simple aromatics, and concerted transition states show essentially no fractional orbital density. On the other hand, the FOD plot for ozone shows significant density spread over the entire molecule; the transition state for the cleavage of the terminal C-C bond in octane shows FOD at C1 and C2 but not elsewhere; p-benzyne shows significant FOD at the two radical carbons, while the FOD is much smaller in m-benzyne and is negligible in o-benzyne.

This FOD method looks to be a simple tool for evaluating static correlation and is worth further testing.

References

(1) Grimme, S.; Hansen, A. "A Practicable Real-Space Measure and Visualization of Static Electron-Correlation Effects," Angew. Chem. Int. Ed. 2015, 54, 12308-12313, DOI: 10.1002/anie.201501887.

(2) Mermin, N. D. "Thermal Properties of the Inhomogeneous Electron Gas," Phys. Rev. 1965, 137, A1441-A1443, DOI: 10.1103/PhysRev.137.A1441.

(3) Chai, J.-D. "Density functional theory with fractional orbital occupations," J. Chem. Phys 2012, 136, 154104, DOI: doi: 10.1063/1.3703894.

Grimme Steven Bachrach 20 Jan 2016 2 Comments

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