At the Spring ACS meeting in New Orleans this past April, Jonathan Goodman told me about his group’s new work on computed NMR spectra. This study has now appeared.¹ The new aspect of this work is taking on compounds with significant conformational flexibility. They first examined the bifuranyl- and pyranopyrans acetals 1-6.

1	2	3
4	5	6

They identified all energetically low-lying conformers through a Monte Carlo MM search, and reoptimized the structures at B3LYP/6-31G**. PCM energies, with the dielectric set to 4.81 to simulate CHCl₃, were obtained using the gas-phase geometries. ¹³C NMR shifts were then computed and weighted based on Boltzmann averaging. Compounds 4-7 require consideration of 4, 5, or 7 conformations, respectively, to account for at least 95% of the population. (The lowest energy conformation for each compound is displayed in Figure 1.) The computed ¹³C NMR chemical shifts were then compared against the experimental values that have been obtained for 5 of these 6 compounds, though it was not known which experimental spectra corresponds with which structure. Based on the correlation coefficients and the mean and maximum values of the differences between the calculated and experimental shifts allows for identification of the structure that corresponds to each of the five spectra.

1	2	3
4	5	6

Figure 1. B3LYP/6-31G** minimum energy conformation of 1-6.¹

They next took on the absolute structure of elatenyne 7. This compound has been isolated and its ¹³C NMR obtained nd interpreted.² The compound can exist in one of 32 different diastereomers. Instead of having to stereospecifically synthesize each diastereomer, obtain its NMR spectra and compare with the natural product, Goodman suggests that one can compute the ¹³C NMR spectra for each isomer, identified the likely candidates, and synthesize just those if verification is necessary. So, they computed the spectra of all 32 isomers following the above prescription. The chemical shifts for the carbons bearing bromine have relatively large errors, though these can by systematically corrected by reducing the computed values by about 20 ppm. Comparison of the computed spectra of each isomer with the experimental spectra gave three possible isomers (7a-c, see Figure 2) with very strong correlation coefficients. Examination of the men value of the difference of the computed chemical shifts with the experimental values (not including the carbon atoms with a bromine attached) suggests one more possibility 7d (see Figure 2).

7
7a	7b
7c	7d

Figure 2. B3LYP/6-31G** minimum energy conformation of 7a-d.¹

References

(1) Smith, S. G.; Paton, R. S.; Burton, J. W.; Goodman, J. M., "Stereostructure Assignment
of Flexible Five-Membered Rings by GIAO 13C NMR Calculations: Prediction of the Stereochemistry of Elatenyne," J. Org. Chem., 2008, DOI: 10.1021/jo8003138.

(2) Sheldrake, H. M.; Jamieson, C.; Burton, J. W., “The Changing Faces of Halogenated Marine Natural Products: Total Synthesis of the Reported Structures of Elatenyne and an Enyne from Laurencia majuscula,” Angew. Chem. Int. Ed., 2006, 45, 7199-7202, DOI: 10.1002/anie.200602211

InChIs

1-3: InChI=1/C10H18O4/c1-11-9-5-3-8-7(13-9)4-6-10(12-2)14-8/h7-10H,3-6H2,1-2H3

4-6: InChI=1/C10H18O4/c1-11-9-5-3-7(13-9)8-4-6-10(12-2)14-8/h7-10H,3-6H2,1-2H3

7: InChI=1/C15H20Br2O2/c1-3-5-6-7-13-11(17)9-15(19-13)14-8-10(16)12(4-2)18-14/h1,5-6,10-15H,4,7-9H2,2H3/b6-5-
InChIKey=SKSTYQSRJPCZSW-WAYWQWQTBQ

The importance of the interactions between neighboring aromatic molecules cannot be overemphasized – π-π-stacking is invoked to explain the structure of DNA, the hydrophobic effect, molecular recognition, etc. Nonetheless, the nature of this interaction is not clear. In fact the commonly held notion of π-π orbital overlap is not seen in computations.

Grimme¹ has now carefully examined the nature of aromatic stacking by comparison with aliphatic analogues. He has examined dimers formed of benzene 1, naphthalene 2, anthracene 3, and teracene 4 and compared these with the dimers of their saturated analogues (cyclohexane 1s, decalin 2s, tetradecahydroanthracene 3s, and octadecahydrotetracene 4s. The aromatic dimmers were optimized in the T-shaped and stacked arrangements, and these are shown for 3 along with the dimer of 3s in Figure 1. These structures are optimized at B97-D/TZV(2d,2p) – a functional designed for van der Waals compounds. Energies were then computed at B2LYP-D/QZV3P, double-hybrid functional that works very well for large systems.

Figure 1. Optimized structures of 3s, 3t, and 3a.

The energies for formation of the complexes are listed in Table 1. The first interesting result here is that the benzene and naphthalene dimmers (whether stacked or T-shaped) are bound by about the same amount as their saturated analogues. Grimme thus warns that “caution is required to not overestimate the effect of the π system”.

Table 1. Complexation energy (kcal mol^-1)

	1	2	3	4
T-shape (t)	2.82	5.46	8.25	11.12
Stacked saturated (s)	3.09	5.92	8.88	11.83
Stacked aromatics (a)	2.62	6.81	11.46	16.33

The two larger aromatics here do show a significantly enhanced complexation energy than their saturated analogues, and Grimme refers to this extra stabilization as the π-π stacking effect (PSE). Energy decomposition analysis suggests that electrostatic interactions actually favor the complexation of the saturated analogues over the aromatics. However, Pauli exchange repulsion essentially cancels the electrostatic attraction for all the systems, and it is dispersion that accounts for the dimerization energy. Dispersion increases with size of the molecule, and “classical” dispersion forces (the R^-6 relationship) accounts for more than half of the dispersion energy in the saturated dimmers, while it is the non-classical, or orbital-based, dispersion that dominates in the stacked aromatic dimmers. Grimme attributes this to “special nonlocal electron correlations between the π electrons in the two fragments at small interplane distances”.

References

(1) Grimme, S., "Do Special Noncovalent π-π Stacking Interactions Really Exist?," Angew. Chem. Int. Ed., 2008, 47, 3430-3434, DOI: 10.1002/anie.200705157.

InChIs

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

1s: InChI=1/C6H12/c1-2-4-6-5-3-1/h1-6H2

2: InChI=1/C10H8/c1-2-6-10-8-4-3-7-9(10)5-1/h1-8H

2s: InChI=1/C10H18/c1-2-6-10-8-4-3-7-9(10)5-1/h9-10H,1-8H2

3: InChI=1/C14H10/c1-2-6-12-10-14-8-4-3-7-13(14)9-11(12)5-1/h1-10H

3s: InChI=1/C14H24/c1-2-6-12-10-14-8-4-3-7-13(14)9-11(12)5-1/h11-14H,1-10H2

4: 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

4s: InChI=1/C18H30/c1-2-6-14-10-18-12-16-8-4-3-7-15(16)11-17(18)9-13(14)5-1/h13-18H,1-12H2

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

	Rel E	Frequencies (scaled)
H+(acetylene)Ar non-classical	0.0	3139, 2123
H+(acetylene)Ar classical	7.8	3084, 2954, 2878, 1673
H+(acetylene) non-classical	0.0	3219, 2250
H+(acetylene) classical	7.1	3162, 29947, 2874
Experiment		3364, 3212, 3146, 2217

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