Archive for the 'Schleyer' Category

A pentacoordinate carbon

Trying to get carbon to bond in unnatural ways seems to be a passion for many organic chemists! Schleyer has been interested in unusual carbon structures for decades and he and Schaefer now report a molecule with a pentacoordinate carbon bound to five other carbon atoms. Their proposed target is pentamethylmethane cation C(CH3)5+ 1.1 The optimized geometry of 1, which has C3h symmetry, at MP2/cc-pVTZ is shown in Figure 1. The bonds from the central carbon to the equatorial carbon are a rather long 1.612 Å, but the bonds to the axial carbon are even longer, namely 1.736 Å. Bader analysis shows five bond critical points, each connecting the central carbon to one of the methyl carbons. Wiberg bond index and MO analysis suggests that the central carbon is tetravalent, with a 2-electron-3-center bond involving the central and axial carbons.




Figure 1. MP2/cc-pVTZ optimized geometries of 1 and dissociation transition states.

So while 1 is a local energy minimum, it sits in a very shallow well. One computed dissociation path, which passes through TS1 (Figure 1) on its way to 2-methyl-butyl cation and methane has a barrier of only 1.65 kcal mol-1 (CCSD(T)/CBS + ZPE). A second dissociation pathway goes through TS2 to t-butyl cation and ethane with a barrier of only 1.34 kcal mol-1. Worse still is that the free energy estimates suggest “spontaneous dissociation … through both pathways”.

Undoubtedly, this will not be the last word on trying to torture a poor carbon atom.


(1) McKee, W. C.; Agarwal, J.; Schaefer, H. F.; Schleyer, P. v. R. "Covalent Hypercoordination: Can Carbon Bind Five Methyl Ligands?," Angew. Chem. Int. Ed. 2014, 53, 7875-7878, DOI: 10.1002/anie.201403314.


1: InChI=1S/C6H15/c1-6(2,3,4)5/h1-5H3/q+1

Schaefer &Schleyer Steven Bachrach 25 Aug 2014 No 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

Aromatic TS for a non-pericyclic reaction

The activation energy for the 5-endo-dig reaction of the anion 1 is anomalously low compared to its 4-endo-dig and 6-endo-dig analogues. Furthermore, the TS is quite early, earlier than might be expected based on the Hammond Postulate. Alabugin and Schleyer have examined this reaction and found some interesting results.1

First, NICS(0) values for a series of related intermolecular anionic attack at alkynes show some interesting trends (Table 1). Two of the transition states look like they might be aromatic: the TSs for the 3-exo-dig and the 5-endo-dig reaction have NICS(0) values that are quite negative. However, given the geometry of these TSs, particularly the close proximity of the σ bonds to the ring center, one might be concerned about contamination of these orbitals. So, NICS(0)MOzz computations, which look at the tensor component perpendicular to the ring using just the π-MOs, shows that the 3-exo-dig is likely non-aromatic (NICS(0)MOzz is near zero), the TS for the 4-endo-dig reaction is antiaromatic (NICS(0)MOzz very positive) and the TS for the 5-endo-dig reaction is aromatic (NICS(0)MOzz is very negative. So this last reaction is the first example of an aromatic transition that is not for a pericyclic reaction!

Table 1. NICS(0) and NICS(0)MOzz for the TS of some anionic alkyne cyclizations.










5-endo-dig (1)



These authors argue that the reaction of 1 is an “aborted” sigmatropic shift. A normal pericyclic reaction is a single step with a single (concerted) transition state. An interrupted sigmatropic shift has an intermediate that lies higher in energy than the reactants, such as in the Bergman cyclization of an enediyne. The aborted sigmatropic shift has an intermediate that lies lower in energy than the reactants, such as in the cyclization of 1.


(1) Gilmore, K.; Manoharan, M.; Wu, J. I. C.; Schleyer, P. v. R.; Alabugin, I. V. "Aromatic Transition States in Nonpericyclic Reactions: Anionic 5-Endo Cyclizations Are Aborted Sigmatropic Shifts," J. Am. Chem. Soc. 2012, 134, 10584–10594, DOI: 10.1021/ja303341b

Aromaticity &Schleyer Steven Bachrach 24 Jul 2012 5 Comments

Electrophilic aromatic substitution is really addition-elimination

We have all learned about aromatic substitution as proceeding via the following mechanism

(Worse yet – many of us have taught this for years!) Well, Galabov, Zou, Schaefer and Schleyer pour a whole lot of cold water on this notion in their recent Angewandte article.1 Modeling the reaction of benzene with Br2 and using B3LYP/6-311+G(2d,2p) for both the gas phase and PCM simulating a CCl4 solvent, attempts to locate this standard intermediate led instead to a concerted substitution transition state TS1 (see Figure 1).


Figure 1. PCM/B3LYP/6-311+G(2d,2p) optimized transitin state along the concerted pathway

However, this is not the lowest energy pathway for substitution. Rather and addition-elimination pathway is kinetically preferred. In the first step Br2 adds in either a 1,2 or 1,4 fashion to form an intermediate. The lower energy path is the 1,4 addition, leading to P3. This intermediate then undergoes a syn,anti-isomerization to give P5. The last step is the elimination of HBr from P5 to give the product, bromobenzene. This mechanism is shown in Scheme 2 and the critical points are shown in Figure 3.

Scheme 1







Figure 2. PCM/B3LYP/6-311+G(2d,2p) optimized critical points along the addition-elimination pathway

The barrier for the concerted substitution process through TS1 is 41.8 kcal mol-1 (in CCl4) while the highest barrier for the addition-elimination process is through TS3 of 39.4 kcal mol-1.

Now a bit of saving grace is that in polar solvents, acidic solvents and/or with Lewis acid catalysts, the intermediate of the standard textbook mechanism may be competitive.

Textbook authors – please be aware!


(1) Kong, J.; Galabov, B.; Koleva, G.; Zou, J.-J.; Schaefer, H. F.; Schleyer, P. v. R., "The Inherent Competition between Addition and Substitution Reactions of Br2 with Benzene and Arenes," Angew. Chem. Int. Ed. 2011, 50, 6809-6813, DOI: 10.1002/anie.201101852

electrophilic aromatic substitution &Schaefer &Schleyer Steven Bachrach 27 Sep 2011 3 Comments

1-Adamantyl cation – Predicting its NMR spectra

What is required in order to compute very accurate NMR chemical shifts? Harding, Gauss and Schleyer take on the interesting spectrum of 1-adamantyl cation to try to discern the important factors in computing its 13C and 1H chemical shifts.1


To start, the chemical shifts of 1-adamtyl cation were computed at B3LYP/def2-QZVPP and
MP2/qz2p//MP2/cc-pVTZ. The root means square error (compared to experiment) for the carbon chemical shifts is large: 12.76 for B3LYP and 6.69 for MP2. The proton shifts are predicted much more accurately with an RMS error of 0.27 and 0.19 ppm, respectively.

The authors speculate that the underlying cause of the poor prediction is the geometry of the molecule. The structure of 1 was optimized at HF/cc-pVTZ, MP2/cc-pVTZ and CCSD(T)/pVTZ and then the chemical shifts were computed using MP2/tzp with each optimized geometry. The RMS error of the 12C chemical shifts are HF/cc-pVTZ: 9.55, MP2/cc-pVTZ: 5.62, and CCSD(T)/pVTZ: 5.06. Similar relationship is seen in the proton chemical shifts. Thus, a better geometry does seem to matter. The CCSD(T)/pVTZ optimized structure of 1 is shown in Figure 1.


Figure 1. CCSD(T)/pVTZ optimized structure of 1.

Unfortunately, the computed chemical shifts at CCSD(T)/qz2p//CCSD(T)/cc-pVTZ are still in error; the RMS is 4.78ppm for the carbon shifts and 0.26ppm for the proton shifts. Including a correction for the zero-point vibrational effects and adjusting to a temperature of 193 K to match the experiment does reduce the error; now the RMS for the carbon shifts is 3.85 ppm, with the maximum error of 6 ppm for C3. The RMS for the proton chemical shifts is 0.21ppm.

The remaining error they attribute to basis set incompleteness in the NMR computation, a low level treatment of the zero-point vibrational effects (which were computed at HF/tz2p), neglect of the solvent, and use of a reference in the experiment that was not dissolved in the same media as the adamantyl cation.

So, to answer our opening question – it appears that a very good geometry and treatment of vibrational effects is critical to accurate NMR shift computation of this intriguing molecule. Let the
computational chemist beware!


(1) Harding, M. E.; Gauss, J.; Schleyer, P. v. R., "Why Benchmark-Quality Computations Are Needed To Reproduce 1-Adamantyl Cation NMR Chemical Shifts Accurately," J. Phys. Chem. A, 2011, 115, 2340-2344, DOI: 10.1021/jp1103356


1: InChI=1/C10H15/c1-7-2-9-4-8(1)5-10(3-7)6-9/h7-9H,1-6H2/q+1

adamantane &NMR &Schleyer Steven Bachrach 18 Jul 2011 4 Comments

Aromaticity of azines

How is the aromaticity of benzene affected by nitrogen substitution? Are pyridine and pyrimidine more or less aromatic than benzene? This question has been addressed many times, and Schleyer adds to this discussion with a B3LYP/6-311+G** study of the entire series of azines.1 Analysis of the aromaticity is based on a two metrics: NICS(0)πzz and extra cyclic resonance energy (ECRE). The NICS(0) πzz value is now the ring current measurement advocated by Schleyer as it only includes the π orbitals and uses the tensor component perpendicular to the ring. ECRE is obtained by comparing block-localized energies of the azine to appropriate acyclic references.

Interestingly, both metrics give the same result, namely, that the aromaticity of benzene and all of the azines 1-6 are essentially equally aromatic.


(1) Wang, Y.; Wu, J. I. C.; Li, Q.; Schleyer, P. v. R., "Aromaticity and Relative Stabilities of Azines," Org. Lett., 2010, 12, 4824-4827, DOI: 10.1021/ol102012d


1: InChI=1/C5H5N/c1-2-4-6-5-3-1/h1-5H

2a: InChI=1/C4H4N2/c1-2-4-6-5-3-1/h1-4H

2b: InChI=1/C4H4N2/c1-2-5-4-6-3-1/h1-4H

2c: InChI=1/C4H4N2/c1-2-6-4-3-5-1/h1-4H

3a: InChI=1/C3H3N3/c1-2-4-6-5-3-1/h1-3H

3b: InChI=1/C3H3N3/c1-2-5-6-3-4-1/h1-3H

3c: InChI=1/C3H3N3/c1-4-2-6-3-5-1/h1-3H

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

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

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

5: InChI=1/CHN5/c1-2-4-6-5-3-1/h1H

6: InChI=1/N6/c1-2-4-6-5-3-1

Aromaticity &Schleyer Steven Bachrach 25 Jan 2011 No Comments

NMR shifts of aromatic and antiaromatic compounds using BLW

The chemical shift of the benzene proton is about 7.3ppm, significantly downfield from the range of olefinic protons (5.6-58.ppm). This is rationalized as the standard induced diatropic ring current, found in aromatic species. But what should we make of the chemical shift of the protons in cyclobutadiene at 5.8 ppm? Shouldn’t this be much further upfield?

Schleyer and Mo have applied the block localized wavefunction (BLW) technique to aromatic and antiaromatic chemical shifts.1 In BLW, self-consistent localized orbitals are produced to describe a particular resonance structure. So, for benzene, BLW describes in effect 1,3,5-cyclohexatriene, lacking any resonance energy.  When chemical shifts are computed with the BLW description, the proton chemical shift is 6.6 ppm, and is even more upfield if the geometry is optimized (in D3h symmetry) with the BLW method (δ=6.2ppm). Furthermore the NICS(0)πzz (the tensor component corresponding to the perpendicular direction evaluated in the ring center using just the π orbitals) is -36.3 for benzene and 0.0 for the D3h BLW variant, strongly indicating the role of cyclic delocalization in affecting chemical shifts.

Now for cyclobutadiene, the proton chemical shift of 5.7 ppm becomes 7.4 in the BLW case. NICS(0)πzz for cyclobutadiene is +46.9 and +1.6 in the BLW case. The problem is that typical alkenes are poor references for cyclobutadiene – when resonance is turned off, the chemical shift does move downfield – indicating the expected upfield shift for cyclobutadiene. Schleyer and Mo suggest that 3,4-dimethylenecyclobutene is a more suitable reference; its ring protons have chemical shifts of 7.65ppm.

They also describe computations of benzocyclobutadiene and tricyclobutenabenzene and offer straightforward rationalizations of their aromatic vs. antiaromatic behavior.


(1) Steinmann, S. N.; Jana, D. F.; Wu, J. I.-C.; Schleyer, P. v. R.; Mo, Y.; Corminboeuf, C., "Direct Assessment of Electron Delocalization Using NMR Chemical Shifts," Angew. Chem. Int. Ed., 2009, 48, 9828-9833, DOI: 10.1002/anie.200905390


benzene: InChI=1/C6H6/c1-2-4-6-5-3-1/h1-6H

cyclobutadiene: InChI=1/C4H4/c1-2-4-3-1/h1-4H

3,4-dimethylenecyclobutene: InChI=1/C6H6/c1-5-3-4-6(5)2/h3-4H,1-2H2

Aromaticity &NMR &Schleyer Steven Bachrach 04 May 2010 No Comments

Higher-order Möbius Annulenes

An emerging theme in this blog is Möbius systems, ones that can be aromatic or antiaromatic. Rzepa has led the way here, especially in examining annulenes with a twisted structure. Along with Schleyer and Schaefer, they have now explored a series of Möbius annulenes.1 The particularly novel aspect of this new work is the examination of higher-order Möbius systems. In the commonly held notion of the Möbius strip, the strip contains a single half twist. Rzepa points out that the notion of twist must be considered as two parts, a part due to torsions and a part due to writhe.2 We can think of the Möbius strip as formed by a ladder where the ends are connect such that the left bottom post connects with the top right post and the bottom right post connects with the top left post. Let’s now consider the circle created by joining the midpoints of each rug of the ladder. If this circle lies in a plane, then the torsion is π/N where N is the number of rungs in the ladder. But, the collection of midpoints does not have to lie in a plane, and if these points distort out of plane, that’s writhe and allows for less torsion in the strip.The sum of these two parts is called Lk and it will be an integral multiple of π. So the common Möbius strip has Lk = 1.

An example of a molecular analogue of the common Möbius strip is the annulene C9H9+ (1) – see figure 1. But Möbius strips can have more than one twist. Rzepa, Schleyer, and Schaefer have found examples with Lk = 2, 3, or 4. Examples are C14H14 (2) with one full twist (Lk = 2, two half twists), C16H162- (3) with three half twists, and C20H202+ (4) with four half twists.





Figure 1. Structures of annulenes 1-4.

These annulenes with higher-order twisting, namely 2-4, are aromatic, as determined by a variety of measures. For example, all express negative NICS values, all have positive diagmagnetic exaltations, and all express positive isomerization stabilization energies (which are a measure of aromatic stabilization energy).


(1) Wannere, C. S.; Rzepa, H. S.; Rinderspacher, B. C.; Paul, A.; Allan, C. S. M.; Schaefer Iii, H. F.; Schleyer, P. v. R., "The Geometry and Electronic Topology of Higher-Order Charged M&oml;bius Annulenes" J. Phys. Chem. A 2009, ASAP, DOI: 10.1021/jp902176a

(2) Fowler, P. W.; Rzepa, H. S., "Aromaticity rules for cycles with arbitrary numbers of half-twists," Phys. Chem. Chem. Phys. 2006, 8, 1775-1777, DOI: 10.1039/b601655c.

annulenes &Aromaticity &Schaefer &Schleyer Steven Bachrach 20 Oct 2009 1 Comment

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