Archive for the 'Authors' Category

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 No Comments

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

Dispersion in organic chemistry – a review and another example

The role of dispersion in organic chemistry has been slowly recognized as being quite critical in a variety of systems. I have blogged on this subject many times, discussing new methods for properly treating dispersion within quantum computations along with a variety of molecular systems where dispersion plays a critical role. Schreiner1 has recently published a very nice review of molecular systems where dispersion is a key component towards understanding structure and/or properties.

In a similar vein, Wegner and coworkers have examined the Z to E transition of azobenzene systems (1a-g2a-g) using both experiment and computation.2 They excited the azobenzenes to the Z conformation and then monitored the rate for conversion to the E conformation. In addition they optimized the geometries of the two conformers and the transition state for their interconversion at both B3LYP/6-311G(d,p) and B3LYP-D3/6-311G(d,p). The optimized structure of the t-butyl-substituted system is shown in Figure 1.


a: R=H; b: R=tBu; c: R=Me; d: R=iPr; e: R=Cyclohexyl; f: R=Adamantyl; g: R=Ph

1b

1b-TS-2b

2b

Figure 1. B3LYP-D3/6-311G(d,p) optimized geometries of 1a, 2a, and the TS connecting them.

The experiment finds that the largest activation barriers are for the adamantly 1f and t-butyl 1b azobenzenes, while the lowest barriers are for the parent 1a and methylated 1c azobenzenes.

The trends in these barriers are not reproduced at B3LYP but are reproduced at B3LYP-D3. This suggests that dispersion is playing a role. In the Z conformations, the two phenyl groups are close together, and if appropriately substituted with bulky substituents, contrary to what might be traditionally thought, the steric bulk does not destabilize the Z form but actually serves to increase the dispersion stabilization between these groups. This leads to a higher barrier for conversion from the Z conformer to the E conformer with increasing steric bulk.

References

(1) Wagner, J. P.; Schreiner, P. R. "London Dispersion in Molecular Chemistry—Reconsidering Steric Effects," Angew. Chem. Int. Ed. 2015, 54, 12274-12296, DOI: 10.1002/anie.201503476.

(2) Schweighauser, L.; Strauss, M. A.; Bellotto, S.; Wegner, H. A. "Attraction or Repulsion? London Dispersion Forces Control Azobenzene Switches," Angew. Chem. Int. Ed. 2015, 54, 13436-13439, DOI: 10.1002/anie.201506126.

InChIs

1b: InChI=1S/C28H42N2/c1-25(2,3)19-13-20(26(4,5)6)16-23(15-19)29-30-24-17-21(27(7,8)9)14-22(18-24)28(10,11)12/h13-18H,1-12H3/b30-29-
InChIKey=SOCNVTNVHBWFKC-FLWNBWAVSA-N

2b: InChI=1S/C28H42N2/c1-25(2,3)19-13-20(26(4,5)6)16-23(15-19)29-30-24-17-21(27(7,8)9)14-22(18-24)28(10,11)12/h13-18H,1-12H3/b30-29+
InChIKey=SOCNVTNVHBWFKC-QVIHXGFCSA-N

DFT &Schreiner Steven Bachrach 04 Jan 2016 No Comments

Dynamics in the reaction of tetrazine with cyclopropene

Houk and Doubleday report yet another example of dynamic effects in reactions that appear to be simple, ordinary organic reactions.1 Here they look at the Diels-Alder reaction of tetrazine 1 with cyclopropene 2. The reaction proceeds by first crossing the Diels-Alder transition state 3 to form the intermediate 4. This intermediate can then lose the anti or syn N2, through 5a or 5s, to form the product 6. The structures and relative energies, computed at M06-2X/6-31G(d), of these species are shown in Figure 1.

3
17.4

4
-33.2

5a
-28.9

5s
-20.0

6
-86.2

Figure 1. M06-2X/6-31G(d) optimized geometries and energies (relative to 1 + 2) of the critical points along the reaction of tetrazine with cyclopropene.

The large difference in the activation barriers between crossing 5a and 5s (nearly 9 kcal mol-1) suggests, by transition state theory, a preference of more than a million for loss of the anti N2 over the syn N2. However, quasiclassical trajectory studies, using B3LYP/6-31G(d), finds a different situation. The anti pathway is preferred, but only by a 4:1 ratio! This dynamic effect arises from a coupling of the v3 mode which involves a rocking of the cyclopropane ring that brings a proton near the syn N2 functionality, promoting its ejection. In addition, the trajectory studies find short residence times within the intermediate neighborhood for the trajectories that lead to the anti product and longer residence times for the trajectories that lead to the syn product. All together, a very nice example of dynamic effects playing a significant role in a seemingly straightforward organic reaction.

References

(1) Törk, L.; Jiménez-Osés, G.; Doubleday, C.; Liu, F.; Houk, K. N. "Molecular Dynamics of the Diels–Alder Reactions of Tetrazines with Alkenes and N2 Extrusions from Adducts," J. Am. Chem. Soc. 2015, 137, 4749-4758, DOI: 10.1021/jacs.5b00014.

InChIs

1: InChI=1S/C2H2N4/c1-3-5-2-6-4-1/h1-2H
InChIKey=HTJMXYRLEDBSLT-UHFFFAOYSA-N

2: InChI=1S/C3H4/c1-2-3-1/h1-2H,3H2
InChIKey=OOXWYYGXTJLWHA-UHFFFAOYSA-N

4: InChI=1S/C5H6N4/c1-2-3(1)5-8-6-4(2)7-9-5/h2-5H,1H2
InChIKey=JGSMBFYJCNPYDM-UHFFFAOYSA-N

6: InChI=1S/C5H6N2/c1-4-2-6-7-3-5(1)4/h2-5H,1H2
InChIKey=RYJFHKGQZKUXEH-UHFFFAOYSA-N

Diels-Alder &Dynamics &Houk Steven Bachrach 09 Nov 2015 No Comments

Diels-Alder of yne-diyne species

Cramer, Hoye, Kuwata and coworkers have examined the intramolecular cyclization of an alkyne with a diyne.1 Their model system is 1, which can cyclize through a concerted transition state TSC togive the benzyne product 2, or it can proceed through a stepwise pathway, first going through TS1 to form the intermediate INT¸ before traversing through a second transition state TS2 and on to product 2. Using both computations and experiments, they examined a series of compounds with
differing substituents at the ends of the two yne moieties.

The experiments show almost the exact same rate of reaction regardless of the terminal substituents. This includes the parent case where the terminal substituents are hydrogens and also the case where the terminal substituents (which end up on adjacent centers on the benzyne ring) are bulky TMS groups. And though there is no real rate effect due to changes in solvent or the presence of light or triplet oxygen, which suggest a concerted reaction, these substituent effects argue for a step wise reaction.

SMD(o-dichlorobenzene)/B3LYP-D3BJ/6-311+G-(d,p)//M06-2X/6-311+G(d,p)
computations help explain these observations. Shown in Figure 1 are the optimized geometries and relative energies of the critical points on the reaction surface for the conversion of 1 into 2, and these results are similar with the other substituents as well.

1
(0.0)

2
(-56.9)

TSC
(31.5)

 

TS1
(25.5)

INT
(18.8)

TS2
(18.1)

 

Figure 1. SMD(o-dichlorobenzene)/B3LYP-D3BJ/6-311+G-(d,p)//M06-2X/6-311+G(d,p) optimized geometries and relative energies (kcal mol-1).

The first thing to note is that the concerted TSC is higher in energy than the stepwise TS1. The wavefunction for TSC unstable towards moving from a restricted to unrestricted formalism. Reoptimization of some of these concerted TSs actually led to the stepwise TS.

The next item of note is that TS2 for this case is actually lower in energy than the intermediate (this is a true TS on the energy surface, but when zero-point energy and other thermal corrections are included, it becomes lower in energy than INT). For some of the cases the second TS lies above the intermediate, but typically by a small amount.

Therefore, the mechanism of this reaction is stepwise, but the second step might have such a small barrier (or even no barrier) that one might consider this to be concerted, though highly asymmetric and really bearing little resemblance to more traditional concerted pericyclic reactions.

The authors obliquely hinted at some potential interesting dynamics. I suspect that molecular dynamics calculations will show no effect of that second TS, and one might observe some interesting dynamics, which could be seen in kinetic isotope experiments.

References

(1)  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 ASAP, DOI: 10.1021/acs.joc.5b01356.

InChIs

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

2: InChI=1S/C8H4O2/c9-8-7-4-2-1-3-6(7)5-10-8/h2,4H,5H2
InChIKey=MYFORDRJCVOBTH-UHFFFAOYSA-N

Cramer &Diels-Alder &diradicals Steven Bachrach 05 Oct 2015 2 Comments

Triprotonated rosarin: singlet or triplet?

What is the spin state of the ground state of an aromatic species? Can this be spin state be manipulated by charge? These questions are addressed by Borden, Kim, Sessler and coworkers1 for the hexaphyrin 1. B3LYP/6-31G(d) optimization of 1 shows it to be a ground state singlet. This structure is shown in Figure 1.


1


13+

Protonation of the three pyrrole nitrogens creates 13+, which has interesting frontier orbitals. The HOMO of 13+, of a1” symmetry, has nodes running through all six nitrogens. The next higher energy orbital, of a2” symmetry, has a small π-contribution on each nitrogen. Protonation will therefore have no effect on the energy of the a1” orbital, but the charge will stabilize the a2” orbital. This will lower the energy gap between the two orbitals, suggesting that a ground state triplet might be possible. The lowest singlet and triplet states of 13+ are also shown in Figure 1.

1

Singlet 13+

Triplet 13+

Figure 1. (U)B3LYP/6-31G(d) optimized structures of 1 and singlet and triplet 13+.

This spin state change upon protonation was experimentally verified by synthesis of two analogues of 1, shown below. The triprotonated versions of both are observed to have triplet character in their EPR spectrum.

References

(1) Fukuzumi, S.; Ohkubo, K.; Ishida, M.; Preihs, C.; Chen, B.; Borden, W. T.; Kim, D.; Sessler, J. L. "Formation of Ground State Triplet Diradicals from Annulated Rosarin Derivatives by Triprotonation," J. Am. Chem. Soc. 2015, 137, 9780-9783, DOI: 10.1021/jacs.5b05309.

InChIs

1: InChI=1S/C45H24N6/c1-2-8-29-28(7-1)34-16-22-13-24-18-36-30-9-3-4-10-31(30)38-20-26(50-43(38)42(36)48-24)15-27-21-39-33-12-6-5-11-32(33)37-19-25(49-44(37)45(39)51-27)14-23-17-35(29)41(47-23)40(34)46-22/h1-21,46,49-50H/b22-13-,23-14-,24-13-,25-14-,26-15-,27-15-
InChIKey=UMEHBSBBAUKCTH-UIJINECUSA-N

Aromaticity &Borden Steven Bachrach 22 Sep 2015 No Comments

Review of planar hypercoordinate atoms

Yang, Ganz, Chen, Wang, and Schleyer have published a very interesting and comprehensive review of planar hypercoordinate compounds, with a particular emphasis on planar tetracoordinate carbon compounds.1 A good deal of this review covers computational results.

There are two major motifs for constructing planar tetracoordinate carbon compounds. The first involves some structural constraints that hold (or force) the carbon into planarity. A fascinating example is 1 computed by Rasmussen and Radom in 1999.2 This molecule taxed their computational resources, and as was probably quite typical for that time, there is no supplementary materials. But since this compound has high symmetry (D2h) I reoptimized its structure at ω-B97X-D/6-311+G(d) and computed its frequencies in just a few hours. This structure is shown in Figure 1. However, it should be noted that at this computational level, 1 possesses a single imaginary frequency corresponding to breaking the planarity of the central carbon atom. Rasmussen and Radom computed the structure of 1 at MP2/6-31G(d) with numerical frequencies all being positive. They also note that the B3LYP/6-311+G(3df,2p) structure also has a single imaginary frequency.

A second approach toward planar tetracoordinate carbon compounds is electronic: having π-acceptor ligands to stabilize the p-lone pair on carbon and σ-donating ligands to help supply sufficient electrons to cover the four bonds. Perhaps the premier simple example of this is the dication 2¸ whose ω-B97X-D/6-311+G(d,p) structure is also shown in Figure 1.

The review covers heteroatom planar hypercoordinate species as well. It also provides brief coverage of some synthesized examples.

1

2

Figure 1. Optimized structures of 1 and 2.

References

(1) Yang, L.-M.; Ganz, E.; Chen, Z.; Wang, Z.-X.; Schleyer, P. v. R. "Four Decades of the Chemistry of Planar Hypercoordinate Compounds," Angew. Chem. Int. Ed. 2015, 54, 9468-9501, DOI: 10.1002/anie.201410407.

(2) Rasmussen, D. R.; Radom, L. "Planar-Tetracoordinate Carbon in a Neutral Saturated Hydrocarbon: Theoretical Design and Characterization," Angew. Chem. Int. Ed. 1999, 38, 2875-2878, DOI: 10.1002/(SICI)1521-3773(19991004)38:19<2875::AID-ANIE2875>3.0.CO;2-D.

InChIs

1: InChI=1S/C23H24/c1-7-11-3-15-9-2-10-17-5-13-8(1)14-6-18(10)22-16(9)4-12(7)20(14,22)23(22)19(11,13)21(15,17)23/h7-18H,1-6H2
InChIKey=LMDPKFRIIOUORN-UHFFFAOYSA-N

2: InChI=1S/C5H4/c1-2-5(1)3-4-5/h1-4H/q+2
InChIKey=UGGTXIMRHSZRSQ-UHFFFAOYSA-N

Schleyer Steven Bachrach 26 Aug 2015 6 Comments

m-Benzyne

I want to update my discussion of m-benzyne, which I present in my book in Chapter 5.5.3. The interesting question concerning m-benzyne concerns its structure: is it a single ring structure 1a or a bicyclic structure 1b? Single configuration methods including closed-shell DFT methods predict the bicylic structure, but multi-configuration methods and unrestricted DFT predict it to be 1a. Experiments support the single ring structure 1a.

The key measurement distinguishing these two structure type is the C1-C3 distance. Table 1 updates Table 5.11 from my book with the computed value of this distance using some new methods. In particular, the state-specific multireference coupled cluster Mk-MRCCSD method1 with the cc-pCVTZ basis set indicates a distance of 2.014 Å.2 The density cumulant functional theory3 ODC-124 with the cc-pCVTZ basis set also predicts the single ring structure with a distance of 2.101 Å.5

Table 1. C1-C3 distance (Å) with different computational methods using the cc-pCVTZ basis set

method

r(C1-C3)

CCSD5

1.556

CCSD(T)5

2.043

OCD-125

2.101

Mk-MRCCSD2

2.014

References

(1) Evangelista, F. A.; Allen, W. D.; Schaefer III, H. F. "Coupling term derivation and general implementation of state-specific multireference coupled cluster theories," J. Chem. Phys 2007, 127, 024102-024117, DOI: 10.1063/1.2743014.

(2) Jagau, T.-C.; Prochnow, E.; Evangelista, F. A.; Gauss, J. "Analytic gradients for Mukherjee’s multireference coupled-cluster method using two-configurational self-consistent-field orbitals," J. Chem. Phys. 2010, 132, 144110, DOI: 10.1063/1.3370847.

(3) Kutzelnigg, W. "Density-cumulant functional theory," J. Chem. Phys. 2006, 125, 171101, DOI: 10.1063/1.2387955.

(4) Sokolov, A. Y.; Schaefer, H. F. "Orbital-optimized density cumulant functional theory," J. Chem. Phys. 2013, 139, 204110, DOI: 10.1063/1.4833138.

(5) Mullinax, J. W.; Sokolov, A. Y.; Schaefer, H. F. "Can Density Cumulant Functional Theory Describe Static Correlation Effects?," J. Chem. Theor. Comput. 2015, 11, 2487-2495, DOI: 10.1021/acs.jctc.5b00346.

InChIs

1a: InChI=1S/C6H4/c1-2-4-6-5-3-1/h1-3,6H

benzynes &Schaefer Steven Bachrach 18 Aug 2015 No Comments

Domino Tunneling

A 2013 study of oxalic acid 1 failed to uncover any tunneling between its conformations,1 despite observation of tunneling in other carboxylic acids (see this post). This was rationalized by computations which suggested rather high rearrangement barriers. Schreiner, Csaszar, and Allen have now re-examined oxalic acid using both experiments and computations and find what they call domino tunneling.2

First, they determined the structures of the three conformations of 1 along with the two transition states interconnecting them using the focal point method. These geometries and relative energies are shown in Figure 1. The barrier for the two rearrangement steps are smaller than previous computations suggest, which suggests that tunneling may be possible.

1tTt
(0.0)

TS1
(9.7)

1cTt
(-1.4)

TS2
(9.0)

1cTc
(-4.0)

Figure 1. Geometries of the conformers of 1 and the TS for rearrangement and relative energies (kcal mol-1)

Placing oxalic acid in a neon matrix at 3 K and then exposing it to IR radiation populates the excited 1tTt conformation. This state then decays to both 1cTt and 1cTc, which can only happen through a tunneling process at this very cold temperature. Kinetic analysis indicates that there are two different rates for decay from both 1tTt and 1cTc, with the two rates associated with different types of sites within the matrix.

The intrinsic reaction paths for the two rearrangements: 1tTt1cTt and → 1cTc were obtained at MP2/aug-cc-pVTZ. Numerical integration and the WKB method yield similar half-lives: about 42 h for the first reaction and 23 h for the second reaction. These match up very well with the experimental half-lives from the fast matrix sites of 43 ± 4 h and 30 ± 20 h, respectively. Thus, the two steps take place sequentially via tunneling, like dominos falling over.

References

(1) Olbert-Majkut, A.; Ahokas, J.; Pettersson, M.; Lundell, J. "Visible Light-Driven Chemistry of Oxalic Acid in Solid Argon, Probed by Raman Spectroscopy," J. Phys. Chem. A 2013, 117, 1492-1502, DOI: 10.1021/jp311749z.

(2) Schreiner, P. R.; Wagner, J. P.; Reisenauer, H. P.; Gerbig, D.; Ley, D.; Sarka, J.; Császár, A. G.; Vaughn, A.; Allen, W. D. "Domino Tunneling," J. Am. Chem. Soc. 2015, 137, 7828-7834, DOI: 10.1021/jacs.5b03322.

InChIs

1: InChI=1S/C2H2O4/c3-1(4)2(5)6/h(H,3,4)(H,5,6)
InChIKey=MUBZPKHOEPUJKR-UHFFFAOYSA-N

focal point &Schreiner &Tunneling Steven Bachrach 11 Aug 2015 1 Comment

Inverted Carbon Atoms

Inverted carbon atoms, where the bonds from a single carbon atom are made to four other atoms which all on one side of a plane, remain a subject of fascination for organic chemists. We simply like to put carbon into unusual environments! Bremer, Fokin, and Schreiner have examined a selection of molecules possessing inverted carbon atoms and highlights some problems both with experiments and computations.1

The prototype of the inverted carbon is propellane 1. The ­Cinv-Cinv bond distance is 1.594 Å as determined in a gas-phase electron diffraction experiment.2 A selection of bond distance computed with various methods is shown in Figure 1. Note that CASPT2/6-31G(d), CCSD(t)/cc-pVTZ and MP2 does a very fine job in predicting the structure. However, a selection of DFT methods predict a distance that is too short, and these methods include functionals that include dispersion corrections or have been designed to account for medium-range electron correlation.

CASPT2/6-31G(d)

CCSD(T)/cc-pVTZ

MP2/cc-pVTZ

MP2/cc-pVQZ

B3LYP/6-311+G(d,p)

B3LYP-D3BJ/6-311+G(d,p)

M06-2x/6-311+G(d,p)

1.596

1.595

1.596

1.590

1.575

1.575

1.550

Figure 1. Optimized Structure of 1 at MP2/cc-pVTZ, along with Cinv-Cinv distances (Å) computed with different methods.

Propellanes without an inverted carbon, like 2, are properly described by these DFT methods; the C-C distance predicted by the DFT methods is close to that predicted by the post-HF methods.

The propellane 3 has been referred to many times for its seemingly very long Cinv-Cinv bond: an x-ray study from 1973 indicates it is 1.643 Å.3 However, this distance is computed at MP2/cc-pVTZ to be considerably shorter: 1.571 Å (Figure 2). Bremer, Fokin, and Schreiner resynthesized 3 and conducted a new x-ray study, and find that the Cinv-Cinv distance is 1.5838 Å, in reasonable agreement with the computation. This is yet another example of where computation has pointed towards experimental errors in chemical structure.

Figure 2. MP2/cc-pVTZ optimized structure of 3.

However, DFT methods fail to properly predict the Cinv-Cinv distance in 3. The functionals B3LYP, B3LYP-D3BJ and M06-2x (with the cc-pVTZ basis set) predict a distance of 1.560, 1.555, and 1.545 Å, respectively. Bremer, Folkin and Schreiner did not consider the ωB97X-D functional, so I optimized the structure of 3 at ωB97X-D/cc-pVTZ and the distance is 1.546 Å.

Inverted carbon atoms appear to be a significant challenge for DFT methods.

References

(1) Bremer, M.; Untenecker, H.; Gunchenko, P. A.; Fokin, A. A.; Schreiner, P. R. "Inverted Carbon Geometries: Challenges to Experiment and Theory," J. Org. Chem. 2015, 80, 6520–6524, DOI: 10.1021/acs.joc.5b00845.

(2) Hedberg, L.; Hedberg, K. "The molecular structure of gaseous [1.1.1]propellane: an electron-diffraction investigation," J. Am. Chem. Soc. 1985, 107, 7257-7260, DOI: 10.1021/ja00311a004.

(3) Gibbons, C. S.; Trotter, J. "Crystal Structure of 1-Cyanotetracyclo[3.3.1.13,7.03,7]decane," Can. J. Chem. 1973, 51, 87-91, DOI: 10.1139/v73-012.

InChIs

1: InChI=1S/C5H6/c1-4-2-5(1,4)3-4/h1-3H2
InChIKey=ZTXSPLGEGCABFL-UHFFFAOYSA-N

3: InChI=1S/C11H13N/c12-7-9-1-8-2-10(4-9)6-11(10,3-8)5-9/h8H,1-6H2
InChIKey=KTXBGPGYWQAZAS-UHFFFAOYSA-N

Schreiner Steven Bachrach 06 Jul 2015 8 Comments

Next Page »