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.

References

(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

InChIs

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

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

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

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

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

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

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

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

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

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

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

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

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 D_3h 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 D_3h 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.

References

(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

InChIs

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

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

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

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 L_k and it will be an integral multiple of π. So the common Möbius strip has L_k = 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 L_k = 2, 3, or 4. Examples are C₁₄H₁₄ (2) with one full twist (L_k = 2, two half twists), C₁₆H₁₆^2- (3) with three half twists, and C₂₀H₂₀²⁺ (4) with four half twists.

1	2
3	4

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).

References

(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.

Once again into the breach – how much strain can an aromatic species withstand and remain aromatic? Cyranski, Bodwell and Schleyer employ the [n](2,7)pyrenophanes 1 to explore this question.¹ As the tethering bridge gets shorter, the pyrene framework must pucker, presumably reducing its aromatic character. Systematic shrinking allows one to examine the loss of aromaticity as defined by aromatic stabilization energy (ASE), magnetic susceptibility exaltation (Λ) and NICS, among other measures.

They examined the series of pyrenophanes where the tethering chain has 6 to 12 carbon atoms. I have shown the structures of three of these compounds in Figure 1. The bend angle α is defined as the angle made between the outside ring plane and the horizon. Relative ASE is computed using Reaction 1, which cleverly avoids the complication of exactly (a) what is the ASE of pyrene itself and (b) what is the strain energy in these compounds.

1a	1d
1g

Figure 1. B3LYP/6-311G** optimized geometries of 1a, 1d, and 1g.¹

Reaction 1

The results of the computations for this series of pyrenophanes is given in Table 1. The bending angle smoothly increases with decreasing length of the tether. The ASE decreases in the same manner. The ASE correlates quite well with the bending angle, as does the relative magnetic susceptibility exaltation. The NICS(1) values become less negative with decreasing tether length.

Table 1. Computed values for the pyrenophanes.

All of these trends are consistent with reduced aromaticity with increased out-of-plane distortion of the pyrene framework. What may be surprising is the relatively small loss of aromaticity in this sequence. Even though the bend angle is as large as almost 40°, the loss of ASE is only 16 kcal mol^-1, only about a quarter of the ASE of pyrene itself. Apparently, aromatic systems are fairly robust!

References

(1) Dobrowolski, M. A.; Cyranski, M. K.; Merner, B. L.; Bodwell, G. J.; Wu, J. I.; Schleyer, P. v. R.,
"Interplay of π-Electron Delocalization and Strain in [n](2,7)Pyrenophanes," J. Org. Chem., 2008, 73, 8001-8009, DOI: 10.1021/jo8014159

InChIs

1a: InChI=1/C22H20/c1-2-4-6-16-13-19-9-7-17-11-15(5-3-1)12-18-8-10-20(14-16)22(19)21(17)18/h7-14H,1-6H2
InChIKey=SJCYSWGQWCIONQ-UHFFFAOYAF

1b: InChI=1/C23H22/c1-2-4-6-16-12-18-8-10-20-14-17(7-5-3-1)15-21-11-9-19(13-16)22(18)23(20)21/h8-15H,1-7H2
InChIKey=VHVKAELFYUXZEM-UHFFFAOYAW

1c: InChI=1/C24H24/c1-2-4-6-8-18-15-21-11-9-19-13-17(7-5-3-1)14-20-10-12-22(16-18)24(21)23(19)20/h9-16H,1-8H2
InChIKey=HXPWDTNIUQNKLV-UHFFFAOYAQ

1d: InChI=1/C25H26/c1-2-4-6-8-18-14-20-10-12-22-16-19(9-7-5-3-1)17-23-13-11-21(15-18)24(20)25(22)23/h10-17H,1-9H2
InChIKey=DWYMZJZWMFVOIR-UHFFFAOYAM

1e: InChI=1/C26H28/c1-2-4-6-8-10-20-17-23-13-11-21-15-19(9-7-5-3-1)16-22-12-14-24(18-20)26(23)25(21)22/h11-18H,1-10H2
InChIKey=PZBADGOJPAEUIK-UHFFFAOYAZ

1f: InChI=1/C27H30/c1-2-4-6-8-10-20-16-22-12-14-24-18-21(11-9-7-5-3-1)19-25-15-13-23(17-20)26(22)27(24)25/h12-19H,1-11H2
InChIKey=YVZIXELCLJHDLW-UHFFFAOYAO

1g: InChI=1/C28H32/c1-2-4-6-8-10-12-22-19-25-15-13-23-17-21(11-9-7-5-3-1)18-24-14-16-26(20-22)28(25)27(23)24/h13-20H,1-12H2
InChIKey=QDAMLTATWKFTFB-UHFFFAOYAF

Pyrene: InChI=1/C16H10/c1-3-11-7-9-13-5-2-6-14-10-8-12(4-1)15(11)16(13)14/h1-10H
InChIKey=BBEAQIROQSPTKN-UHFFFAOYAB

4,9-dimethylenepyrene: InChI=1/C18H12/c1-11-9-13-5-4-8-16-12(2)10-14-6-3-7-15(11)17(14)18(13)16/h3-10H,1-2H2
InChIKey=XAAPFSHIUHWWCM-UHFFFAOYAM

Angewandte Chemie has published a rather unusual short article – an appeal by Roald Hoffmann, Paul Schleyer and Fritz Schaefer (the latter two were interviewed in my book!) to use “more realism, please!”¹

These noted computational chemists suggest that we all have been sloppy in the language we use in describing our computations. They first take on the term “stable”, and rightfully point out that this is a very contextual term – stable where? on my desktop? In a 1M aqueous solution? Inside a helium glove box? Inside a mass spectrometer? In an interstellar cloud? Stable for how long? Indefinitely? For a day? For a day in the humid weather of San Antonio? Or a day inside a cold refrigerator? Or how about inside a Ne matrix? Or for the time it takes to run a picosecond laser experiment?

The authors offer up the terms “viable” and “fleeting” as reasonable alternatives and proscribe a protocol for meeting the condition of “viable” – and I must note that this protocol is very demanding, likely beyond the computational abilities of many labs and certainly beyond what can be done for a reasonably large molecule.

They also take on the uncertainty of computed results, pointing out the likely largely overlooked irreproducibility of many DFT results, due to size difference of the computed grids, difference in implementation of the supposedly same functional, etc. They conclude with a discussion of how many significant figures one should employ.

None of this is earth-shattering, and most is really well-known yet often neglected or overlooked. In another interesting publication treat in this issue, four referee reports of the article are reproduced. The first, by Gernot Frenking,² argues exactly this point – that the lack of new information, and the sort of whimsical literary approach make the article unacceptable for publication. The other three referees disagree,^3-5 and note that though the article is not novel, the authors forcefully remind us that better behaviors should be put into practice.

The article is a nice reminder that careful studies should be carefully reported. (And both the authors of the article and the referees note that these same comments apply to our experimental colleagues, too.)

References

(1) Hoffmann, R.; Schleyer, P. v. R.; Schaefer III, H. F., “Predicting Molecules – More Realism, Please!,” Angew. Chem. Int. Ed., 2008, 47, 7164-7167, DOI: 10.1002/anie.200801206.

(2) Frenking, G., “No Important Suggestions,” Angew. Chem. Int. Ed. 2008, 47, 7168-7169, doi: 10.1002/anie.200802500.

(3) Koch, W., “Excellent, Valuable, and Entertaining,” Angew. Chem. Int. Ed., 2008, 47, 7170, DOI: 10.1002/anie.200802996.

(4) Reiher, M., “Important for the Definition of Terminology in Computational Chemistry,” Angew. Chem. Int. Ed., 2008, 48, 7171, DOI: 10.1002/anie.200802506.

(5) Bickelhaupt, F. M., “Attractive and Convincing,” Angew. Chem. Int. Ed., 2008, 47, 7172, DOI: 10.1002/anie.200802330.

Schleyer continues his study of aromaticity with a paper¹ that picks up on the theme presented in one² I have previously blogged on – the relationship between a formally aromatic pyrazine and formally antiaromatic dihydropyrazine. He now examines the diazotetracene 1 and it dihydro analogue 2.¹ In terms of formal electron count, 1 should be aromatic, just like the all carbon analogue tetracene 3, and 2 should be antiaromatic.

Schleyer used the NICS_πzz values obtained in the center of each ring to evaluate the aromatic/antiaromatic character of these three molecules. These calculations were performed using canonical molecular orbitals and repeated using localized molecular orbitals. The results are similar for each method, and the canonical MO values are presented in Table 1. As expected for an aromatic compound, each ring of tetracene 3 has large negative NICS values, indicating that each ring is locally aromatic and the molecule as a whole is aromatic. The same is true for the diazotetracene 1. (In fact the NICS values for 1 and 3 are remarkably similar.) However, for 2, the dihydropyrazine ring has a positive NICS values, indicative of a locally antiaromatic ring. While the three phenyl rings have negative NICS values, these absolute values are smaller than for the rings of 1 or 3, indicating an attenuation of their aromaticity. Nonetheless, the sum of the NICS values of 2 is negative, suggesting that the molecule is globally aromatic, though only marginally so. This is due to the antiaromaticity of the dihydropyrazine ring being delocalized to some extent over the entire molecule. Schleyer, concludes that “large 4n π compounds […] are not appreciably destabilized relative to their 4n+2 π congeners.”

Table 1 NICS_πzz (ppm) for each ring of 1-3 and their sum.¹

References

(1) Miao, S.; Brombosz, S. M.; Schleyer, P. v. R.; Wu, J. I.; Barlow, S.; Marder, S. R.; Hardcastle, K. I.; Bunz, U. H. F., "Are N,N-Dihydrodiazatetracene Derivatives Antiaromatic?," J. Am. Chem. Soc., 2008, 130, 7339-7344, DOI: 10.1021/ja077614p.

(2) Miao, S.; Schleyer, P. v. R.; Wu, J. I.; Hardcastle, K. I.; Bunz, U. H. F., "A Thiadiazole-Fused N,N-Dihydroquinoxaline: Antiaromatic but Isolable," Org. Lett. 2007, 9, 1073-1076, DOI: 10.1021/ol070013i

InChIs

1: InChI=1/C18H12/c1-2-6-14-10-18-12-16-8-4-3-7-15(16)11-17(18)9-13(14)5-1/h1-12H

2: InChI=1/C16H10N2/c1-2-6-12-10-16-15(9-11(12)5-1)17-13-7-3-4-8-14(13)18-16/h1-10H

3: InChI=1/C16H12N2/c1-2-6-12-10-16-15(9-11(12)5-1)17-13-7-3-4-8-14(13)18-16/h1-10,17-18H

Duncan and Schleyer¹ have investigated protonated acetylene and the protonated acetylene dimer. These ions are created in a pulsed supersonic nozzle/pulsed electrical discharge with a weakly bound argon atom as a tag. IR laser photodissociation spectroscopy allows for the detection of peaks down to 2000 cm^-1, a region not previously explored for this cation. The experimental IR spectrum for H⁺(C₂H₂)^.Ar has two main features: at 3146 and 2217 cm^-1. The 3146 cm^-1 corresponds to the previously observed peak² at 3142 cm^-1 and is similar to the absorption in acetylene (3136 cm^-1). MP2/6-311+G(2d,2p) computations were performed on the classical and non-classical structures of H⁺(C₂H₂), with and without a complexed argon atom. These geometries are displayed in Figure 1 and the predicted vibrational frequencies are listed in Table 1.

Figure 1. MP2/6-311+

Table 1. Relative energies (kcal mol^-1) and frequencies of protonated acetylene
and the protonated acetylene-argon cluster.¹

The argon tag only slightly perturbs the spectrum, as expected for a weakly bond atom remote from most of the hydrogen atoms. The predicted spectra of the two non-classical ions are in nice agreement with the experiment – particularly the interesting peak at 2123 cm^-1 that is due to the bridged proton. This spectra, and the confirmation of the bridging, non-classical structure, makes a nice pair with the recently reported bridging, non-classical structure of the ethyl cation,³ which I blogged on previously.

The spectrum of the H⁺(C₄H₄) ion show a doublet at 3129 and 3158 cm^-1 and two small peaks at 1261 and 1365 cm^-1. The computed structure that comes closest to matching this spectrum is for the asymmetrically bridged dimer (See Figure 2), though is much more energetic than its isomers. The authors speculate that the bridged dimer is trapped in an energy-well during the thermal expansion, which prevents the formation of the lower energy isomers.

Figure 2. Schematic drawing and relative energies of the H⁺(C₄H₄) ion.
(Note – unfortunately the authors have supplied insufficient information in the Supporting Materials to completely define the geometries of these molecules!)

References

(1) Douberly, G. E.; Ricks, A. M.; Ticknor, B. W.; McKee, W.
C.; Schleyer, P. v. R.; Duncan, M. A., "Infrared Photodissociation
Spectroscopy of Protonated Acetylene and Its Clusters," J. Phys. Chem. A, 2008, 112, 1897-1906, DOI: 10.1021/jp710808e.

(2) Gabrys, C. M.; Uy, D.; Jagod, M. F.; Oka, T.; Amano, T., "Infrared Spectroscopy of Carboions. 8. Hollow Cathode Spectroscopy of Protonated Acetylene, C2H3+," J. Phys. Chem., 1995, 99, 15611-15623, DOI: 10.1021/j100042a042.

(3) Andrei, H.-S.; Solcà, N.; Dopfer, O., "IR Spectrum of the Ethyl Cation: Evidence
for the Nonclassical Structure," Angew. Chem. Int. Ed., 2008, 47, 395-397, DOI: 10.1002/anie.200704163

What happens when antiaromatic rings stack? One can draw an MO interaction diagram for π-stacked cyclobutadiene dimer (Figure 1) and recognize at once that this cluster should be stabilized. In fact, it is reminiscent of an orbital diagram for an aromatic species!

Figure 1. MO Interaction diagram of stacked butadiene (modified from Ref 1).

Houk had examined just this dimer (1) in 1996 and located a D_4h critical point at CASSCF(8,8)/6-31G* (see Figure 2).² This structure is energetically below two isolated cyclobutadiene molecules; however, it is a second-order saddle point.

1

Figure 1. CASSCF(8,8)/6-31G* optimized structure of 1.

Schleyer has examined a series of superphanes constructed from anti- and aromatic rings linked by methano bridges, 2-7.¹ These structures were optimized at B3LYP/6-311+G** and their magnetic properties computed at GIAO-PW91. The optimized structures of 3 and 4 are shown in Figure 3.

3

4

Figure 3. B3LYP/6-311+G** optimized structures of 3 and 4.¹

The inter-ring separation (D) in these compounds is quite interesting (Table 1). It decreases in the series 2-4, with the distance in the latter compound of only 2.002 Å. The inter-ring distance is much larger in 5, which has two (aromatic) benzene rings. All of the other comounds (except 2) have shorter distances and these all involve antiaromatic rings. These short distances for the antiaromatic superphanes suggests stabilizing interactions between the rings, as indicated by the MO diagram of Figure 1.

Table 1. Inter-ring distance and NICS values for 2-7.¹

^aDistance (Å) between the carbon of one ring and the closest carbon of the second ring.

The NICS values are also interesting. Schleyer computed a variety of different NICS values, and we list here the isotropic NICS value at the cage center (NICS_cage) and the zz-component evaluated 1 Å above the ring on the outside face NICS(1)_zzring). The NICS(1)_zzring is perhaps the best measure of magnetic properties related to aromatic/antiaromatic character. All six compounds have rings that have negative values of NICS(1)_zzring, indicating of aromatic character. In fact, the value for 5 is less negative than for isolated benzene alone. This suggests that the stacked antiaromatic rings become aromatic, while the stacked aromatic rings become less aromatic. For all six compounds, the NICS_cage value is negative indicating diatropicity, associated with aromatic character – again consistent with the MO argument presented in Figure 1. To answer our lead off question, stacked antiaromatic rings are aromatic!

References

(1) Corminboeuf, C.; Schleyer, P. v. R.; Warner, P., "Are Antiaromatic Rings Stacked Face-to-Face Aromatic?," Org. Lett. 2007, 9, 3263-3266, DOI: 10.1021/ol071183y.

(2) Li, Y.; Houk, K. N., "The Dimerization of Cyclobutadiene. An ab Initio CASSCF Theoretical Study," J. Am. Chem. Soc. 1996, 118, 880-885, DOI: 10.1021/ja921663m.

InChIs

2: InChI=1/C9H6/c1-4-6-2-7-5(1)9(7)3-8(4)6/h1-3H2/q-2

3: InChI=1/C12H8/c1-5-7-2-8-6(1)10-3-9(5)11(7)4-12(8)10/h1-4H2

4: InChI=1/C15H10/c1-6-8-2-9-7(1)11-3-10(6)14-5-15(11)13(9)4-12(8)14/h1-5H2/q+2

5: InChI=1/C18H12/c1-7-9-2-10-8(1)12-3-11(7)15-5-16(12)18-6-17(15)13(9)4-14(10)18/h1-6H2

6: InChI=1/C21H14/c1-8-10-2-11-9(1)13-3-12(8)16-5-17(13)21-7-20(16)18-6-19(21)15(11)4-14(10)18/h1-7H2/q-2

7: InChI=1/C24H16/c1-9-11-2-12-10(1)14-3-13(9)17-5-18(14)22-7-21(17)23-8-24(22)20-6-19(23)15(11)4-16(12)20/h1-8H2

In the book I extensively discuss the singlet-triplet gap of methylene and some of the chemistry of phenylcarbene. Schleyer and Schaefer have now reported computations on the singlet-triplet gap of arylcarbenes.¹ The geometries of phenylcarbene 1, diphenylcarbene 2, 1-naphthylcarbene 3, bis(1-naphtyl)carbene 4, and 9-anthrylcarbene 5 were optimized at B3LYP/6-311+G(d,p). These geometries are shown in Figure 1.

1s	1t
2s	2t
3s	3t
4s	4s
4s	4s

Figure 1. B3LYP/6-311+G(d,p) optimized structures of singlet and triplet 1-5.

Since this functional is known to underestimate the singlet-triplet gap of carbenes, they employ an empirical correction based on the difference in this gap for methylene between the computed value (11.89 kcal mol^-1) and the experimental value (9.05 kcal mol^-1). These corrected energy gaps are listed in Table 1.

Table 1. Corrected singlet-triplet energy gaps (kcal mol^-1) at B3LYP/6-311+G(d,p).

Using the following isodesmic reactions, they estimate the stabilization of the singlet or triplet carbene afforded by the aryl substituent:

R-C-H + CH₄ → H-C-H + R-CH₃

R-C-R + CH₄ → R-C-H + R-CH₃

These isodesmic energies are listed in Table 2. For phenylcarbne, the phenyl group stabilizes the singlet more than the triple, reducing the ST gap by 6.3 kcal mol^-1. However, adding a second phenyl group (making 2) stabilizes both the singlet and triplet by about the same amount, leading to little change in the ST gap. The singlet does not get accrue the potential benefit of the second aryl group because sterics prohibit the two rings from being coplanar.

Table 2. Aryl effect for 1-5 based on the isodesmic reaction energies (kcal mol^-1)

References

(1) Woodcock, H. L.; Moran, D.; Brooks, B. R.; Schleyer, P. v. R.; Schaefer, H. F., "Carbene Stabilization by Aryl Substituents. Is Bigger Better?," J. Am. Chem. Soc., 2007, 129, 3763-3770, DOI: 10.1021/ja068899t.

InChIs

1: InChI=1/C7H6/c1-7-5-3-2-4-6-7/h1-6H

2: InChI=1/C13H10/c1-3-7-12(8-4-1)11-13-9-5-2-6-10-13/h1-10H

3: InChI=1/C11H8/c1-9-5-4-7-10-6-2-3-8-11(9)10/h1-8H

4: InChI=1/C21H14/c1-2-8-19-14-16(12-13-17(19)6-1)15-20-10-5-9-18-7-3-4-11-21(18)20/h1-14H

5: InChI=1/C15H10/c1-11-14-8-4-2-6-12(14)10-13-7-3-5-9-15(11)13/h1-10H

Robinson and Schleyer report the synthesis of and computations on the novel structure gallepin 1.¹ This is the gallium analogue of tropyllium, the prototype of a seven-member aromatic ring. Robinson actually prepared the bis-benzannulated analogue 2, which is found to coordinate to TMEDA in the crystal.

Schleyer computed (B3LYP/LANL2DZ) the gallepin portion of 2 in its naked form 3 and associated with trimethylamine 4. The crystal structure of 2 reveals that the 7 member ring is boat-shaped, and this is reproduced in the computed structure of 4. Interestingly, the naked gallepin is planar, suggestive of an aromatic structure. NICS_πZZ computations were performed to gauge the aromaticity of these compounds. The value for the 7-member ring is -9.0 in 4 and -9.9 in 3, indicating aromatic character. These values are less then in the parent gallepin 1, which has a value of -15.3, but this is the normal type of diminishment expected from benzannulation.
But borapin has a NICS_πZZ substantially more negative (-27.7) and so gallepins are less aromatic than borapins. Nonetheless, it is very interesting that aromaticity can be extended in this interesting way – different heteroatom and different ring size.

3	4

References

(1) Quillian, B.; Wang, Y.; Wei, P.; Wannere, C. S.; Schleyer, P. v. R.; Robinson, G. H., "Gallepins. Neutral Gallium Analogues of the Tropylium Ion: Synthesis, Structure, and Aromaticity," J. Am. Chem. Soc., 2007, 129, 13380-13381, DOI: 10.1021/ja075428d.