Archive for the 'Authors' Category

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.






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.


(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.


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

2: InChI=1S/C3H4/c1-2-3-1/h1-2H,3H2

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

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

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.

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.









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.


(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.


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

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

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.



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.


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.


(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.


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-

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.



Figure 1. Optimized structures of 1 and 2.


(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.


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

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

Schleyer Steven Bachrach 26 Aug 2015 6 Comments


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












(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.


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.






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.


(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.


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

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.















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.


(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[,7.03,7]decane," Can. J. Chem. 1973, 51, 87-91, DOI: 10.1139/v73-012.


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

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

Schreiner Steven Bachrach 06 Jul 2015 8 Comments

Dyotropic rearrangement

Houk and Vanderwal have examined the dyotropic rearrangement of an interesting class of polycyclic compounds using experimental and computational techniques.1 The parent reaction takes the bicyclo[2.2.2]octadiene 1 into the bicyclo[3.2.1]octadiene 3. The M06-2X/6-311+G(d,p)/B3LYP/6-31G(d) (with CPCM simulating xylene) geometries and relative energies are shown in Figure 1. The calculations indicate a stepwise mechanism, with an intervening zwitterion intermediate. The second step is rate determining.






Figure 1. B3LYP/6-31G(d) and relative energies (kcal mol-1) at M06-2X/6-311+G(d,p).

Next they computed the activation barrier for the second TS for a series of substituted analogs of 1, with various electron withdrawing group as R1 and electron donating groups as R2, and compared them with the experimental rates.

Further analysis was done by relating the charge distribution in these TSs with the relative rates, and they find a nice linear relationship between the charge and ln(krel). This led to the prediction that a cyano substituent would significantly activate the reaction, which was then confirmed by experiment. Another prediction of a rate enhancement with Lewis acids was also confirmed by experiment.

A last set of computations addressed the question of whether a ketone or lactone would also undergo this dyotropic rearrangement. The lactam turns out to have the lowest activation barrier by far.


(1) Pham, H. V.; Karns, A. S.; Vanderwal, C. D.; Houk, K. N. "Computational and Experimental Investigations of the Formal Dyotropic Rearrangements of Himbert Arene/Allene Cycloadducts," J. Am. Chem. Soc. 2015, 137, 6956-6964, DOI: 10.1021/jacs.5b03718.


1: InChI=1S/C11H11NO/c1-12-10(13)7-9-6-8-2-4-11(9,12)5-3-8/h2-5,7-8H,6H2,1H3

3: InChI=1S/C11H11NO/c1-12-10(13)6-9-3-2-8-4-5-11(9,12)7-8/h2-6,8H,7H2,1H3

Houk Steven Bachrach 29 Jun 2015 1 Comment

Making superacidic phenols

Kass and coworkers looked at a series of substituted phenols to tease out ways to produce stronger acids in non-polar media.1 First they established a linear relationship between the vibrational frequency shifts of the hydroxyl group in going from CCl4 as solvent to CCl4 doped with 1% acetonitrile with the experimental pKa in DMSO. They also showed a strong relationship between this vibrational frequency shift and gas phase acidity (both experimental and computed deprotonation energies).

A key recognition was that a charged substituent (like say ammonium) has a much larger effect on the gas-phase (and non-polar solvent) acidity than on the acidity in a polar solvent, like DMSO. This can be attributed to the lack of a medium able to stable charge build-up in non-polar solvent or in the gas phase. This led them to 1, for which B3LYP/6-31+G(d,p) computations of the analogous dipentyl derivative 2 (see Figure 1) indicated a deprotonation free energy of 261.4 kcal mol-1, nearly 60 kcal mol-1 smaller than any other substituted phenol they previously examined. Subsequent measurement of the OH vibrational frequency shift showed the largest shift, indicating that 1 is extremely acidic in non-polar solvent.

Further computational exploration led to 3 (see Figure 1), for which computations predicted an even smaller deprotonation energy of 231.1 kcal mol-1. Preparation of 4 and experimental observation of its vibrational frequency shift revealed an even larger shift than for 1, making 4 extraordinarily acidic.


Conjugate base of 2


Conjugate base of 3

Figure 1. B3LYP/6-31+G(d,p) optimized geometries of 2 and 3 and their conjugate bases.


(1) Samet, M.; Buhle, J.; Zhou, Y.; Kass, S. R. "Charge-Enhanced Acidity and Catalyst Activation," J. Am. Chem. Soc. 2015, 137, 4678-4680, DOI: 10.1021/jacs.5b01805.


1 (cation only): InChI=1S/C23H41NO/c1-4-6-8-10-12-14-20-24(3,21-15-13-11-9-7-5-2)22-16-18-23(25)19-17-22/h16-19H,4-15,20-21H2,1-3H3/p+1


3: InChI=1S/C6H7NO/c1-7-4-2-3-6(8)5-7/h2-5H,1H3/p+1

4 (cation only): InChI=1S/C13H21NO/c1-2-3-4-5-6-7-10-14-11-8-9-13(15)12-14/h8-9,11-12H,2-7,10H2,1H3/p+1

Acidity &Kass Steven Bachrach 02 Jun 2015 No Comments

Host-guest complexes

Grimme and coworkers have a featured article on computing host-guest complexes in a recent ChemComm.1 They review the techniques his group has pioneered, particularly dispersion corrections for DFT and ways to treat the thermodynamics in moving from electronic energy to free energy. they briefly review some studies done by other groups. They conclude with a new study of eight different host guest complexes, three of which are shown in Figure 1.




Figure 1. TPSS-D3(BJ)/def2-TZVP optimized structures of 1-3.

These eight host-guest complexes are fairly large systems, and the computational method employed means some fairly long computations. Geometries were optimized at TPSS-D3(BJ)/def2-TZVP, then single point energy determined at PW6B95-D3(BJ)/def2-QZVP. Solvent was included using COSMO-RS. The curcurbituril complex 2 includes a counterion (chloride) along with the guest adamantan-1-aminium. Overall agreement of the computed free energy of binding with the experimental values was very good, except for 3 and the related complex having a larger nanohoop around the fullerene. The error is due to problems in treating the solvent effect, which remains an area of real computational need.

An interesting result uncovered is that the binding energy due to dispersion is greater than the non-dispersion energy for all of these complexes, including the examples that are charged or where hydrogen bonding may be playing a role in the bonding. This points to the absolute necessity of including a dispersion correction when treating a host-guest complex with DFT.

As an aside, you’ll note one of the reasons I was interested in this paper: 3 is closely related to the structure that graces the cover of the second edition of my book.


(1) Antony, J.; Sure, R.; Grimme, S. "Using dispersion-corrected density functional theory to understand supramolecular binding thermodynamics," Chem. Commun. 2015, 51, 1764-1774, DOI: 10.1039/C4CC06722C.

Grimme &host-guest Steven Bachrach 12 May 2015 1 Comment

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