Archive for the 'Authors' Category

Testing for method performance using rotational constants

The importance of dispersion in determining molecular structure, even the structure of a single medium-sized molecule, is now well recognized. This means that quantum methods that do not account for dispersion might give very poor structures.

Grimme1 takes an interesting new twist towards assessing the geometries produced by computational methods by evaluating the structures based on their rotational constants B0 obtained from microwave experiments. He uses nine different molecules in his test set, shown in Scheme 1. This yields 25 different rotational constants (only one rotational constant is available from the experiment on triethylamine). He evaluates a number of different computational methods, particularly DFT with and without a dispersion correction (either the D3 or the non-local correction). The fully optimized geometry of each compound with each method is located to then the rotational constants are computed. Since this provides Be values, he has computed the vibrational correction to each rotational constant for each molecule, in order to get “experimental” Be values for comparisons.

Scheme 1.

Grimme first examines the basis set effect for vitamin C and aspirin using B3LYP-D3. He concludes that def2-TZVP or lager basis sets are necessary for reliable structures. However, the errors in the rotational constant obtained at B3LYP-D3/6-31G* is at most 1.7%, and even with CBS the error can be as large as 1.1%, so to my eye even this very small basis set may be completely adequate for many purposes.

In terms of the different functionals (using the DZVP basis set), the best results are obtained with the double hybrid B2PLYP-D3 functional where the mean relative deviation is only 0.3%; omitting the dispersion correction only increases the mean error to 0.6%. Common functionals lacking the dispersion correction have mean errors of about 2-3%, but with the correction, the error is appreciably diminished. In fact B3LYP-D3 has a mean error of 0.9% and B3LYP-NL has an error of only 0.6%. In general, the performance follows the Jacob’s Ladder hierarchy.


(1) Grimme, S.; Steinmetz, M. "Effects of London dispersion correction in density functional theory on the structures of organic molecules in the gas phase," Phys. Chem. Chem. Phys. 2013, 15, 16031-16042, DOI: 10.1039/C3CP52293H.

Grimme Steven Bachrach 11 Feb 2014 No Comments

The Click Reaction in Nature?

The click reaction has become a major workhorse of synthetic chemists since its proposal in 2001.1 Despite its efficiencies, no clear-cut example of its use in nature has been reported until 2012, where Yu and co-workers speculated that it might be utilized in the biosynthesis of lycojaponicumin A and B.2 Krenske, Patel, and Houk have examined the possibility of an enzyme activated click process in forming this natural product.3

First they examined the gas-phase intramolecular [3+2] reaction that takes 1 into 2.

They identified (at M06-2X/def2-TZVPP/M06-2X/6-31+G(d,p)) four different low-energy conformations of 1, of which three have the proper orientation for the cyclization to occur. The lowest energy conformer, the TS, and the product 2 are shown in Figure 1. The free energy activation barrier in the gas phase is 19.8 kcal mol-1. Inclusion of water as an implicit solvent (through a TS starting from a different initial conformation) increases the barrier to 20.0 kcal mol-1. Inclusion of four explicit water molecules, hydrogen bonded to the nitrone and enone, predicts a barrier of 20.5 kcal mol-1. These values predict a slow reaction, but not totally impossible. In fact, Tantillo in a closely related work reported a theoretical study of the possibility of a [3+2] cyclization in the natural synthesis of flueggine A and virosaine, and found barriers of comparable size as here. Tantillo concludes that enzymatic activation is not essential.4




Table 1. M06-2X/6-31+G(d,p) optimized geometries of 1, TS12, and 2.

To model a potential enzyme, the Houk group created a theozyme whereby two water molecules act as hydrogen bond donors to the enone and the use of implicit solvent (diethyl ether) to mimic the interior of an enzyme. This theozyme model predicts a barrier of 15.3 kcal mol-1, or a 2000 fold acceleration of the click reaction. The search for such an enzyme might prove quite intriguing.


(1) Kolb, H. C.; Finn, M. G.; Sharpless, K. B. "Click Chemistry: Diverse Chemical Function from a Few Good Reactions," Angew. Chem. Int. Ed. 2001, 40, 2004-2021, DOI: 10.1002/1521-3773(20010601)40:11<2004::AID-ANIE2004>3.0.CO;2-5.

(2) Wang, X.-J.; Zhang, G.-J.; Zhuang, P.-Y.; Zhang, Y.; Yu, S.-S.; Bao, X.-Q.; Zhang, D.; Yuan, Y.-H.; Chen, N.-H.; Ma, S.-g.; Qu, J.; Li, Y. "Lycojaponicumins A–C, Three Alkaloids with an Unprecedented Skeleton from Lycopodium japonicum," Org. Lett. 2012, 14, 2614-2617, DOI: 10.1021/ol3009478.

(3) Krenske, E. H.; Patel, A.; Houk, K. N. "Does Nature Click? Theoretical Prediction of an Enzyme-Catalyzed Transannular 1,3-Dipolar Cycloaddition in the Biosynthesis of Lycojaponicumins A and B," J. Am. Chem. Soc. 2013, 135, 17638-17642, DOI: 10.1021/ja409928z.

(4) Painter, P. P.; Pemberton, R. P.; Wong, B. M.; Ho, K. C.; Tantillo, D. J. "The Viability of Nitrone–Alkene (3 + 2) Cycloadditions in Alkaloid Biosynthesis," J. Org. Chem. 2014, 79, 432–435, DOI: 10.1021/jo402487d.


1: InChI=1S/C16H21NO3/c1-11-8-12-10-14(18)13-4-2-6-17(20)7-3-5-16(12,13)15(19)9-11/h4,7,11-12H,2-3,5-6,8-10H2,1H3/b13-4-,17-7+

2: InChI=1S/C16H21NO3/c1-9-6-10-8-13(19)16-11(17-5-3-14(16)20-17)2-4-15(10,16)12(18)7-9/h9-11,14H,2-8H2,1H3/t9?,10-,11?,14?,15+,16-/m0/s1

cycloadditions &Houk Steven Bachrach 04 Feb 2014 No Comments

Another example of tunneling control

The notion of tunneling control has been a topic of interest within this blog a number of times. As developed by Schreiner and Allen,1,2 tunneling control is a third means for predicting (or directing) the outcome of a reaction, alongside the more traditionally recognized kinetic and thermodynamic control. Tunneling control occurs when tunneling through a higher barrier is preferred over tunneling through a lower barrier.

Kozuch and Borden propose another example of tunneling control, this time in the rearrangement of the noradamantyl carbene 1.3 This carbene can undergo a 1,2-carbon shift, driven by strain relief to form the alkene 2. The alternative as a 1,2-hydrogen shift that produces the alkene 3.

These two reaction pathways were explored using B3LYP/6-31G(d,p) computations coupled with canonical variational theory and small curvature tunneling corrections. Structures of the reactant 1 and the two transition states leading to the two products 2 and 3 are shown in Figure 1. The activation barrier at 300 K is 5.4 kcal mol-1 leading to 2 and 8.6 kcal mol-1 leading to 3. Tunneling is expected to be much more important for the hydrogen shift than for the carbon shift, but even including tunneling, the rate to form 2 is much faster than the rate to form 3 at 300 K.


TS 1→2


TS 1→3


Figure 1. B3LYP/6 optimized structures of 1-3 and the transition states leading to 2 and 3.

The situation is reversed however at cryogenic temperatures (< 20 K). Tunneling is now the only route for the reactions to occur, and the rate for formation of 3 is dramatically greater than the rate of formation of 2, which is inhibited by the movement of the much heavier carbon atom. Perdeuteration of the methyl group of 1, which drastically slows the rate of tunneling in the path to 3, nonetheless still favors this pathway (forming d3-3) over formation of d3-2. Thus, at low temperatures the formation of 3 is the preferred product, a manifestation of tunneling control.

Kozuch and Borden end their paper with a hope that an experimentalist will examine this interesting case. I concur!


(1) Schreiner, P. R.; Reisenauer, H. P.; Ley, D.; Gerbig, D.; Wu, C.-H.; Allen, W. D. "Methylhydroxycarbene: Tunneling Control of a Chemical Reaction," Science 2011, 332, 1300-1303, DOI: 10.1126/science.1203761.

(2) Ley, D.; Gerbig, D.; Schreiner, P. R. "Tunnelling control of chemical reactions – the organic chemist’s perspective," Org. Biomol. Chem. 2012, 10, 3781-3790, DOI: 10.1039/C2OB07170C.

(3) Kozuch, S.; Zhang, X.; Hrovat, D. A.; Borden, W. T. "Calculations on Tunneling in the Reactions of Noradamantyl Carbenes," J. Am. Chem. Soc. 2013, 135, 17274-17277, DOI: 10.1021/ja409176u.


1: InChI=1S/C11H16/c1-2-11-6-8-3-9(7-11)5-10(11)4-8/h8-10H,3-7H2,1H3

2: InChI=1S/C11H16/c1-7-10-3-8-2-9(5-10)6-11(7)4-8/h8-10H,2-6H2,1H3

3: InChI=1S/C11H16/c1-2-11-6-8-3-9(7-11)5-10(11)4-8/h2,8-10H,1,3-7H2

Borden &Tunneling Steven Bachrach 27 Jan 2014 No Comments

Is the cyclopropenyl anion antiaromatic?

The concept of antiaromaticity is an outgrowth of the well-entrenched notion or aromaticity. While 4n+2 π-electron systems are aromatic, 4n π-electron systems should be antiaromatic. That should mean that antiaromatic systems are unstable. The cyclopropenyl anion 1a has 4 π-electrons and should be antiaromatic. Kass has provided computational results that strongly indicate it is not antiaromatic!1

Let’s first look at the 3-cyclopropenyl cation 1c. Kass has computed (at both G3 and W1) the hydride affinity of 1c-4c. The hydride affinities of the latter three compounds plotted against the C=C-C+ angle is linear. The hydride affinity of 1c however falls way below the line, indicative of 1c being very stable – it is aromatic having just 2 π-electrons.

A similar plot of the deprotonation enthalpies leading to 1a-4d vs. C=C-C- angle is linear including all four compounds. If 1a where antiaromatic, one would anticipate that the deprotonation energy to form 1a would be much greater than expected simply from the effect of the smaller angle. Kass suggests that this indicates that 1a is not antiaromatic, but just a regular run-of-the-mill (very) reactive anion.

A hint at what’s going on is provided by the geometry of the lowest energy structure of 1a, shown in Figure 1. The molecule is non-planar, having Cs symmetry. A truly antiaromatic structure should be planar, really of D3h symmetry. The distortion from this symmetry reduces the antiaromatic character, in the same way that cyclobutadiene is not a perfect square and that cyclooctatraene is tub-shaped and not planar. So perhaps it is more fair to say that 1a has a distorted structure to avoid antiaromaticity, and that the idealized D3h structure, does not exist because of its antiaromatic character.

Figure 1. G3 optimized geometry of 1a.


(1) Kass, S. R. "Cyclopropenyl Anion: An Energetically Nonaromatic Ion," J. Org. Chem. 2013, 78, 7370-7372, DOI: 10.1021/jo401350m.


1a: InChI=1S/C3H3/c1-2-3-1/h1-3H/q-1

1c: InChI=1S/C3H3/c1-2-3-1/h1-3H/q+1

Aromaticity &Kass Steven Bachrach 20 Jan 2014 2 Comments

Tunneling in t-butylhydroxycarbene

Sorry I missed this paper from much earlier this year – it’s from a journal that’s not on my normal reading list. Anyways, here is another fantastic work from the Schreiner lab demonstrating the concept of tunneling control (see this post).1 They prepare the t-butylhydroxycarbene 1 at low temperature to look for evidence of formation of possible products arising from a [1,2]-hydrogen shift (2), a [1,2]-methyl shift (3) or a [1,3]-CH insertion (4).

Schreiner performed CCSD(T)/cc-pVDZ optimizations of these compounds along with the transition states for the three migrations. The optimized geometries and relative energies are shown in Figure 1. The thermodynamic product is the aldehyde 2 while the kinetic product is the cyclopropane 4, with a barrier of 23.8 kcal mol-1 some 3.5 kcal mol-1 lower than the barrier leading to 2.








Figure 1. CCSD(T)/cc-pVDZ optimized structures of 1-4 and the transition states for the three reaction. Relative energies in kcal mol-1.

At low temperature (11 K), 1 is found to slowly convert into 2 with a half-life of 1.7 h. No other product is observed. Rates for the three reactions were also computed using the Wentzel-Kramers-Brillouin (WKB) method (which Schreiner and Allen have used in all of their previous studies). The predicted rate for the conversion of 1 into 2, which takes place at 11 K solely through a tunneling process, is 0.4h, in quite reasonable agreement with experiment. The predicted rates for the other two potential reactions at 11 K are 1031 and 1040 years.

This is clearly an example of tunneling control. The reaction occurs not across the lowest barrier, but through the narrowest barrier.


(1) Ley, D.; Gerbig, D.; Schreiner, P. R. "Tunneling control of chemical reactions: C-H insertion versus H-tunneling in tert-butylhydroxycarbene," Chem. Sci. 2013, 4, 677-684, DOI: 10.1039/C2SC21555A.


1: InChI=1S/C5H10O/c1-5(2,3)4-6/h6H,1-3H3

2: InChI=1S/C5H10O/c1-5(2,3)4-6/h4H,1-3H3

3: InChI=1S/C5H10O/c1-4(2)5(3)6/h6H,1-3H3

4: InChI=1S/C5H10O/c1-5(2)3-4(5)6/h4,6H,3H2,1-2H3

Schreiner &Tunneling Steven Bachrach 11 Nov 2013 No Comments

Acene dimers – open or closed?

The role of dispersion in large systems is increasingly recognized as critical towards understanding molecular geometry. An interesting example is this study of acene dimers by Grimme.1 The heptacene and nonacene dimers (1 and 2) were investigated with an eye towards the separation between the “butterfly wings” – is there a “stacked” conformation where the wings are close together, along with the “open” conformer?



The LPNO-CEPA/CBS potential energy surface of 1 shows only a single local energy minima, corresponding to the open conformer. B3LYP-D3 and B3LYP-NL, two different variations of dealing with dispersion (see this post), do a reasonable job at mimicking the LPNO-CEPA results, while MP2 indicates the stacked conformer is lower in energy than the open conformer.

B3LYP-D3 predicts both conformers for the nonacene dimer 2, and the optimized structures are shown in Figure 2. The stacked conformer is slightly lower in energy than the open one, with a barrier of about 3.5 kcal mol-1. However in benzene solution, the open conformer is expected to dominate due to favorable solvation with both the interior and exterior sides of the wings.



Figure 1. B3LYP-D3/ef2-TZVP optimized structures of the open and stacked conformations of 2.


(1) Ehrlich, S.; Bettinger, H. F.; Grimme, S. "Dispersion-Driven Conformational Isomerism in σ-Bonded Dimers of Larger Acenes," Angew. Chem. Int. Ed. 2013, 41, 10892–10895, DOI: 10.1002/anie.201304674.


1: InChI=1S/C60H36/c1-2-10-34-18-42-26-50-49(25-41(42)17-33(34)9-1)57-51-27-43-19-35-11-3-4-12-36(35)20-44(43)28-52(51)58(50)60-55-31-47-23-39-15-7-5-13-37(39)21-45(47)29-53(55)59(57)54-30-46-22-38-14-6-8-16-40(38)24-48(46)32-56(54)60/h1-32,57-60H

2: InChI=1S/C76H44/c1-2-10-42-18-50-26-58-34-66-65(33-57(58)25-49(50)17-41(42)9-1)73-67-35-59-27-51-19-43-11-3-4-12-44(43)20-52(51)28-60(59)36-68(67)74(66)76-71-39-63-31-55-23-47-15-7-5-13-45(47)21-53(55)29-61(63)37-69(71)75(73)70-38-62-30-54-22-46-14-6-8-16-48(46)24-56(54)32-64(62)40-72(70)76/h1-40,73-76H

Aromaticity &Grimme Steven Bachrach 28 Oct 2013 1 Comment

Unusual carbene ground states

The singlet and triplet carbene is the topic of Chapter 4, especially sections 1 and 2. The ground state of methylene is the triplet, with one electron in the σ-orbital and one electron in the π-orbital, with the spins aligned. The lowest singlet state places the pair of electrons in the σ-orbital, and this state is about 9 kcal mol-1 higher in energy than the triplet. The next lowest singlet state has one electron in each of the σ- and π-orbitals, with the spins aligned. The singlet state with both electrons in the π-orbital is the highest of these four states, some 60 kcal mol-1 above the ground state triplet.

Hoffmann and Borden now pose the question “Can the doubly occupied π carbene (1A10π2) be the ground state with appropriate substitution?” The answer they find is yes!1

The trick is to find a combination of substituents that will raise the energy of the σ-orbital and lower the energy of the π-orbital. The latter effect can be enhanced if the π-orbital can be a part of an aromatic (6e-) ring.

Two of the best possibilities for identifying a ground state 1A10π2 carbene are 1 and 2. The CASSCF/6-31G(d) optimized geometries of these two are shown in Figure 1. In 1, the nitrogen lone pairs act to destabilize the σ-orbital, while the aldehyde group acts as a withdrawing group to stabilize the π-orbital. The result is that the 1A10π6 state of 1 is predicted to be about 8 kcal mol-1 more stable than the triplet state, as per CASPT2 and CCSD(T) computations.



An ever greater effect is predicted for 2. Here the nitrogen lone pairs adjacent to the carbene act to destabilize the σ-orbital. The empty π-orbital on B lowers the energy of the carbene π-orbital by making it part of the 6-electron aromatic ring. The 1A10π6 state of 2 is predicted to be about 25 kcal mol-1 more stable than its triplet state!



Figure 1. CASSCF/6-31G(d) optimized geometries of the 1A10π6 states of 1 and 2.


(1) Chen, B.; Rogachev, A. Y.; Hrovat, D. A.; Hoffmann, R.; Borden, W. T. "How to
Make the σ0π2 Singlet the Ground State of Carbenes," J. Am. Chem. Soc. 2013, 135, 13954-13964, DOI: 10.1021/ja407116e.


1: InChI=1S/C5H2N2O2/c8-1-4-5(2-9)7-3-6-4/h1-2H

2: InChI=1S/C3H3BN2/c1-4-2-6-3-5-1/h1-2,4H

Borden &carbenes Steven Bachrach 14 Oct 2013 4 Comments

The x-ray structure of norbornyl cation

A long sought-after data point critical to the non-classical cation story has finally been obtained. The elusive x-ray crystal structure of a norbornyl cation was finally solved.1 The [C7H11]+[Al2Br7]- salt was crystallized in CH2Br2 at low temperature (40 K). This low temperature was needed to prohibit rotation of the norbornyl cation within the crystal (the cation is near spherical and so subject to relatively easy rotation within the crystal matrix) and hydride scrambling among the three carbons (C1, C2, and C6) involved in the non-classical cation structure.

The authors report a number of different structures, all very similar, depending on slight differences in the crystals used. However, the important features are consistent with all of the structures. The cation is definitely of the non-classical type (see Figure 1) with the basal C1-C2 bond length of 1.39 Å similar that in benzene and long non-classical C1-C6 and C2-C6 distances of 1.80 Å. These distances match very well with the MP2(FC)/def2-QZVPP optimized distances of 1.393 and 1.825 Å, respectively.

Figure 1. X-ray structure of norbornyl cation.


(1) Scholz, F.; Himmel, D.; Heinemann, F. W.; Schleyer, P. v. R.; Meyer, K.; Krossing, I. "Crystal Structure Determination of the Nonclassical 2-Norbornyl Cation," Science 2013, 341, 62-64, DOI: 10.1126/science.1238849.

non-classical &norbornyl cation &Schleyer Steven Bachrach 16 Sep 2013 No Comments

Nonamethylcyclopentyl cation

The nine methyl groups of nonamethylcyclopentyl cation 1 all interconvert with a barrier of 7 kcal mol-1. However, at low temperature only partial scrambling occurs: there are two sets of methyl groups, one containing five groups and the other containing four methyl groups. The barrier for this scrambling is only 2.5 kcal mol-1. While this behavior was found more than 20 years ago, Tantillo and Schleyer1 only now have offered a complete explanation.


The ground state structure of 1 is shown in Figure 1 and has C1 symmetry. The two pseudo-axial methyl groups adjacent to the cationic center show evidence of hyperconjugation: long C-C bonds and Me-C-C+ angles of 100°.

The transition state TS1¸also in Figure 1, is of Cs symmetry. This transition state leads to interchange of the pseudo-axial methyls, and interchange of the pseudo-equatorial methyls, but no exchange between the members of these two groups. The M06-2x/6-31+G(d,p) and mPW1PW91/6-31+G(d,p) estimate of this barrier is 1.5 and 2.5 kcal mol-1, respectively. This agrees well with the experiment.




Figure 1. B3LYP/6-3+G(d,p) optimized geometries.

A second transition state TS2 was found and it corresponds with a twisting motion that interconverts an axial methyl with an equatorial methyl. This TS has Cs symmetry (shown in Figure 1) and the eclipsing interaction give rise to a larger barrier: 7.3 (M06-2x/6-31+G(d,p)) and 6.7 kcal mol-1 (mPW1PW91/6-31+G(d,p)). So twisting through TS2 and scrambling through TS1 allows for complete exchange of all 9 methyl groups.

An interesting point also made by these authors is that these three structures represent the continuum of cationic structure: a classical (localized) cation in TS2, a bridged structure in TS1 and hyperconjugated cation in 1.


(1) Tantillo, D. J.; Schleyer, P. v. R. “Nonamethylcyclopentyl Cation Rearrangement Mysteries Solved,” Org. Lett. 2013, 15, 1725-1727, DOI: 10.1021/ol4005189.


1: InChI=1S/C14H27/c1-10-11(2,3)13(6,7)14(8,9)12(10,4)5/h1-9H3/q+1

non-classical &Schleyer Steven Bachrach 23 Jul 2013 4 Comments

Triplet state aromaticity

One of the most widely recognized principles within organic chemistry is Hückel’s rule: an aromatic compound possesses 4n+2 π-electrons while an antiaromatic compound possesses 4n π-electrons. Much less well known is Baird’s rule:1 the first excited triplet state will be aromatic if it has 4n π-electrons and antiaromatic if it has 4n+2 π-electrons.2

Schleyer used a number of standard methods for assessing aromatic character of a series of excited state triplets, including NICS values and geometric parameters.3 However, Schleyer has long been a proponent of an energetic assessment of aromaticity and it is only now in this recent paper4 that he and co-workers examine the stabilization energy of excited triplet states. The isomerization
stabilization energy (ISE)5 compares an aromatic (or antiaromatic) compound against a non-aromatic reference, one that typically is made by appending an exo-methylene group to the ring. So, to assess the ISE of the T1 state of benzene, Reaction 1 is used. (Note that the inherent assumption here is that the stabilization energy of benzene is essentially identical to that of toluene.) At B3LYP/6-311++G(d,p) the energy of Reaction 1 is +13.5 kcal mol-1. This reaction should be corrected for non-conservation of s-cis and s-trans conformers by adding on the energy of Reaction 2, which is +3.4 kcal mol-1. So, the ISE of triplet benzene is +16.9 kcal mol-1, indicating that it is antiaromatic. In contrast, the ISE for triplet cyclooctatetraene is -15.6 kcal mol-1, and when corrected its ISE value is -24.7 kcal mol-1, indicating aromatic character. These are completely consistent with Baird’s rule. Schleyer also presents an excellent correlation between the computed ISE values for the triplet state of 9 monocyclic polyenes and their NICS(1)zz values.

Reaction 1

Reaction 2

I want to thank Henrik Ottosson for bringing this paper to my attention and for his excellent seminar on the subject of Baird’s rule on his recent visit to Trinity University.


(1) Baird, N. C. "Quantum organic photochemistry. II. Resonance and aromaticity in
the lowest 3ππ* state of cyclic hydrocarbons," J. Am. Chem. Soc. 1972, 94, 4941-4948, DOI: 10.1021/ja00769a025.

(2) Ottosson, H. "Organic photochemistry: Exciting excited-state aromaticity," Nat Chem 2012, 4, 969-971, DOI: 10.1038/nchem.1518.

(3) Gogonea, V.; Schleyer, P. v. R.; Schreiner, P. R. "Consequences of Triplet Aromaticity in 4nπ-Electron Annulenes: Calculation of Magnetic Shieldings for Open-Shell Species," Angew. Chem. Int. Ed. 1998, 37, 1945-1948, DOI: 10.1002/(SICI)1521-3773(19980803)37:13/14<1945::AID-ANIE1945>3.0.CO;2-E.

(4) Zhu, J.; An, K.; Schleyer, P. v. R. "Evaluation of Triplet Aromaticity by the
Isomerization Stabilization Energy," Org. Lett. 2013, 15, 2442-2445, DOI: 10.1021/ol400908z.

(5) Schleyer, P. v. R.; Puhlhofer, F. "Recommendations for the Evaluation of Aromatic Stabilization Energies," Org. Lett. 2002, 4, 2873-2876, DOI: 10.1021/ol0261332.

Aromaticity &Schleyer Steven Bachrach 16 Jul 2013 No Comments

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