Search Results for "stacking"

Benzene dimer once again

Once more into the benzene dimer (see these previous posts: “Benzene dimer again“, “Benzene dimer“, “π-π stacking (part 2)“, “π-π stacking“)! Sherrill has published a detailed and impressive benchmark study of the benzene dimer in its three most important configurations: the D6h stacked arrangement (1), the T-shaped arrangement (2) and the parallel displaced arrangement (3). 1

First, they performed a careful extrapolation study to obtain accurate binding energies based on CCSD(T) with large basis sets. Then they compared the potential energy curves of the three configurations of benzene dimer obtained with this accurate method with those obtained with less computationally expensive methods. These alternates include RI-MP2, SCS-MP2 and a variety of different density functional. Their results are summarized in Table 1. The upshot is that the SCS-MP2 results are very similar to the much more expensive CCDS(T) values. And while the errors are a bit larger with the DFT methods, their performance is really quite good, especially given their dramatically lower costs. (Note that the “-D” indicates inclusion of Grimme’s dispersion correction term.) Particularly worth mentioning is the very fine performance of the MO6-2X functional.

Table 1. Binding energies (kcal mol-1) of the three benzene dimers with different computational methods.


























(1) Sherrill, C. D.; Takatani, T.; Hohenstein, E. G., "An Assessment of Theoretical Methods for Nonbonded Interactions: Comparison to Complete Basis Set Limit Coupled-Cluster Potential Energy Curves for the Benzene Dimer, the Methane Dimer, Benzene-Methane, and Benzene-H2S" J. Phys. Chem. A 2009, ASAP, DOI: 10.1021/jp9034375

Aromaticity Steven Bachrach 12 Oct 2009 No Comments

Benzene dimer

Hobza1 has published a very high-level computational study of the benzene dimer as a benchmark for this model of π-π stacking – a topic I have touched upon a number of times in this blog (post 1, post 2) . There are four local energy minima, shown in Figure 1. The most stable dimer is the tilted T-structure (TT), a structure often overlooked. Its complexation energy, computed at CCSD(T)/CBS, is 2.78 kcal mol-1. Only slightly higher in energy is the parallel displaced structure (PD), with a stabilization energy of 2.70 kcal mol-1. The T structure (T) is essentially isoenergetic with the PD one. The perfectly stacked structure (S) is much less stable, with a dimerization energy of 1.64 kcal mol-1. The DTF-D method, using the BLYP functional with dispersion parameters optimized for the benzene dimer provide energies within 0.2 kcal mol-1 of the computationally much more expensive benchmark values. As a word of caution though: use of more general dispersion parameters gives energies far worse and predicts the wrong energy order of the dimers.





Figure 1. Structures of the benzene dimer with stabilization energy (kcal mol-1) computed at CCSD(T)/CBS (bold), DFT-D/BLYP with optimized parameters (italics), and DFT-D/BLYP with general parameters (plain).1


(1) Pitonak, M.; Neogrady, P.; Rexac, J.; Jurecka, P.; Urban, M.; Hobza, P., "Benzene Dimer: High-Level Wave Function and Density Functional Theory Calculations," J. Chem. Theory Comput., 2008, 4, 1829-1834, DOI: 10.1021/ct800229h.

Aromaticity Steven Bachrach 23 Jan 2009 3 Comments

DFT performance with nucleic acid base pairs

Here is another benchmark of the performance of DFT in handling difficult situations, in this case the interaction between nucleic acid base pairs. Sherrill1 has examined the 124 nucleic acid base pairs from the JSCH-2005 database2 compiled by Hobza and coworkers. This database includes 36 hydrogen bonded complexes, and example of which is shown in Figure 1a, and 54 stacked complex, one example of which is shown in Figure 1b.



Figure 1. Optimized geometries (RI-MP2/cc-pVTZ) of two representative structures of base pairs: (a) hydrogen bonded pair and (c) stacked pair.

The energies of these base pairs computed with four different functionals: PBE, PBE-D (where Grimme’s empirical dispersion correction3), and the recently developed MO5-2X4 and MO6-2X5 methods which attempt to treat mid-range electron correlation. The aug-cc-pVDZ basis set was used. These DFT energies are compared with the CCSD(T) energies of Hobza. The mean unsigned error (MUE) for the 28 hydrogen bonded complexes and the 54 stacked complexes are listed in Table 1.

Table 1. Mean unsigned error (kcal mol-1) of the four DFT
methods (relative to CCSD(T)) for the hydrogen bonded and stacked base pairs.



MUE (stacked)













A few interesting trends are readily apparent. First, PBE (representing standard GGA DFT methods) poorly describes the energy of the hydrogen bonded complexes, but utterly fails to treat the stacking interaction. Inclusion of the dispersion correction (PBE-D) results in excellent energies for the HB cases and quite reasonable results for the stacked pairs. Both of Truhlar’s functionals dramatically outperform PBE, though MO5-2X is probably still not appropriate for the stacked case. MO6-2X however seems to be a very reasonable functional for dealing with base pair interactions, indicating that mid-range correlation correction is sufficient to describe these complexes, and that the long-range correlation correction included in the dispersion correction, while giving improved results, is not essential.


(1) Hohenstein, E. G.; Chill, S. T.; Sherrill, C. D., "Assessment of the Performance of the M05-2X and M06-2X Exchange-Correlation Functionals for Noncovalent Interactions in Biomolecules," J. Chem. Theory Comput., 2008, 4, 1996-2000, DOI: 10.1021/ct800308k

(2) Jurecka, P.; Sponer, J.; Cerny, J.; P., H., "Benchmark database of accurate (MP2 and CCSD(T) complete basis set limit) interaction energies of small model complexes, DNA base pairs, and amino acid pairs," Phys. Chem. Chem. Phys., 2006, 8, 1985-1993, DOI: 10.1039/b600027d.

(3) Grimme, S., "Semiempirical GGA-type density functional constructed with a long-range dispersion correction," J. Comput. Chem., 2006, 27, 1787-1799, DOI: 10.1002/jcc.20495

(4) Zhao, Y.; Schultz, N. E.; Truhlar, D. G., "Design of Density Functionals by Combining the Method of Constraint Satisfaction with Parametrization for Thermochemistry, Thermochemical Kinetics, and Noncovalent Interactions," J. Chem. Theory Comput., 2006, 2, 364-382, DOI: 10.1021/ct0502763.

(5) Zhao, Y.; Truhlar, D. G., "The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals," Theor. Chem. Acc., 2008, 120, 215-241, DOI: 10.1007/s00214-007-0310-x.

DFT &nucleic acids Steven Bachrach 12 Jan 2009 2 Comments


What is the topology of a molecule made of fused benzene rings? Hopf and co-workers have examined the case where the benzene rings are fused in an ortho arrangement to complete a circle, the so-called [n]circulenes 1n.1 They computed the series of [3]- to [20]circulene at B3LYP/6-31G(d).


The most common examples of this class are corannulene 15 and coronene 16. Hopf finds that the small circulenes, [3]- through [6]circulene, are bowls, consistent with many previous studies.

15, corannulene

16, coronene

The larger circulenes fall into two distinct topological categories. [7]circulene through [16]circulene are saddles, as shown in Figure 1a. When the compounds are even larger, namely [17]- through [20]circulene, they adopt a helical topology, as seen in Figure 1b. Unfortunately, Hopf does not supply the optimized geometries; there is no supporting material at all. So I have reoptimized [12]circulene at B3LYP/6-31G(d) and [18]circulene at AM1. It is a real shame that authors do not routinely deposit their structures, that referees do not call out the authors on this, and that editors of journals do not demand full geometrical descriptions of all reported computed structures.



112: [12]circulene

118: [18]circulene

Figure 1. Optimized structures of (a) [12]circulene (B3LYP/6-31G(d)) and (b) [20]circulene (AM1).
Note the hydrogens have been omitted for clarity.

Hopf does not provide a comparison of structures and their energies. For example, what is the energy difference between the bowl and saddle topologies of [7]circulene or the energy difference between the saddle and helical topologies of [17]circulene?

The change in topology of the circulenes is fascinating. One wonders if this change is strictly a function of a stringing fused hexagons in a circle and minimizing the surface. Or is their some π-π stacking that leads to the saddle and helical topologies? Further details would be interesting – as would be examining other types of ciculenes as hinted by the authors at the end of the paper regarding isomeric kekulenes 2.

Scheme 1 – examples of kekulenes 2


(1) Christoph, H.; Grunenberg, J.; Hopf, H.; Dix, I.; Jones, P. G.; Scholtissek, M.; Maier, G., "MP2 and DFT Calculations on Circulenes and an Attempt to Prepare the Second Lowest Benzolog, [4]Circulene," Chem. Eur. J. 2008, 14, 5604-5616, DOI: 10.1002/chem.200701837


15: InChI=1/C20H10/c1-2-12-5-6-14-9-10-15-8-7-13-4-3-11(1)16-17(12)19(14)20(15)18(13)16/h1-10H

16: InChI=1/C24H12/c1-2-14-5-6-16-9-11-18-12-10-17-8-7-15-4-3-13(1)19-20(14)22(16)24(18)23(17)21(15)19/h1-12H



Aromaticity Steven Bachrach 01 Jul 2008 3 Comments

More on the Cope Rearrangement

A Stable Bis-allyl Intermediate on the Cope PES

As discussed in Chapter 3.2, the prototypical Cope rearrangement (the degenerate rearrangement of 1,5-hexadiene 1) is understood to proceed through a single concerted transition state. The concerted transition state 2 is described by three resonance structures (Scheme 1), and this allows for understanding the chameleonic nature of the substituted Cope rearrangement. For example, radical stabilizing groups at the 2 and 5 positions would favor the cyclohexyl-diyl structure.

Scheme 1

Schreiner computed the reaction path at BD(T)/cc-pVDZ//BLYP/6-31G* for 64 different variations of the Cope rearrangement.1 A representative sampling from these is presented in Figure 1. The Cope rearrangements are found to fall into one of three categories. The first, called type 1, are concerted rearrangements. Type 2 rearrangements have two competing pathways: either through a concerted transition state or a diradical intermediate. The last group, type 3, comprises nonconcerted reactions with a cyclohexyl-diyl intermediate. Schreiner generalizes the results to the following rule: a nonconcerted reaction takes place when biradical intermediates are stabilized either by allyl or aromatic resonance.

Figure 1. Examples of the three type of Cope rearrangements. Relative energies, in kcal mol-1, were computed at BD(T)/cc-pVDZ//BLYP/6-31G*.1

Interestingly, Schreiner’s study identified reactions where the diyl is a stable intermediate, but he identified no case where the other extreme – two allyl radicals – appeared as a stable intermediate. Kertesz, in 2006, discovered just such an example with the Cope rearrangement of 3.2 Using B3LYP and BPW91 computations with two different basis sets, he identified the stable diradical 5. This structure, shown in Figure 2, clearly has very long distances – 2.836 Å – separating the ends of the two “allylic” components. A true transition state 4 connects the reactant 3 with the intermediate 5 (see Figure 2). The activation energy is 6.3 kcal mol-1 and the intermediate 5 lies 3.3 kcal mol-1 above 3.

3 4 5
xyz file xyz file xyz file
Figure 2. B3LYP/6-31G(d) optimized structures of 3-5. Distances (Å) shown are between C1-C6 and C3-C4 of the hexadiene component of the Cope rearrangement.2

Why does a stable bis-allyl analogue exist on the Cope reaction surface of 3? In the prototype Diels-Alder reaction of 1,5-hexadiene, the possible bis-allyl intermediate (i.e., two isolated allyl radicals) is about 26 kcal mol-1 higher in energy than the Cope transition state. Only with significant radical stabilization might one expect a bis-allyl intermediate to occur. One can consider 5 as composed of two bridged phenalenyl radicals (6). Phenalenyl radical is stable due to electron delocalization; its ESR spectrum has been observed, but it has not been isolated, instead dimerizing to give 7.3 In addition to the stabilization afforded by the extensive delocalization of the radical within the phenalenyl system, two phenalenyl systems can also interact through overlap of their π-systems, creating what has been termed π-dimerization.4-6 MRMP2 computations suggest that the π-dimerization energy of 6 is 11 kcal mol-1.7 While the geometry of 5 is not ideal for π-dimerization, its structure clearly indicates some stacking of the two phenalenyl fragments. Both the enhanced electron delocalization about the large phenalenyl system along with π-dimerization provides sufficient stabilization that the bis-allyl intermediate exits on the Cope rearrangement pathway. This now completes all of the options for how the Cope rearrangement may occur: either directly through a concerted transition state, or multi-step process with a 1,6-diyl intermediate or a bis-allyl intermediate.

Cope Rearrangement of 3-Vinylmethylenecyclobutane

3-Vinylmethylenecyclobutane 8 can undergo a myriad of thermal rearrangements involving [1,3]- and [3,3]-shifts.8 The Cope rearrangement of 8 to 9 has a barrier of 35.7 kcal mol-1.9 This large barrier is consistent with cleavage of a C-C bond leading to a diradical intermediate.

Houk has recently confirmed the diradical nature of this rearrangement.10 The geometries of all reactants intermediates, products and transition states were optimized at UB3LYP/6-31+G(d) and single-point energies were evaluated at CASPT2(6,6)/6-31G(d). Two diradical intermediates, 10 and 11, lie 30.0 and 32.0 kcal mol-1, respectively, above 8. These intermediates are separated by a small barrier, 1.5 kcal mol-1 from 10, and a barrier of 2.0 kcal mol-1 interconverts mirror versions of 10. All of these paths are sketched in Scheme 3 and the geometries of the critical points are displayed in Figure 3.

Scheme 3


xyz file

cmpd TS 8-10

xyz file

cmpd TS 8-11

xyz file

cmpd 10

xyz file

cmpd TS 10-11

xyz file

cmpd 11

xyz file

cmpd TS 11-9x

xyz file

cmpd TS 11-9n

xyz file

cmpd 9

xyz file

Figure 3. Optimized Structures of the critical points in Scheme 3.10

Only the reaction going forward from 11 can lead to product 9. There are two such routes, involving an exo or endo approach. They are of similar energy, and also very close in energy to that of the diradical intermediates. Houk concludes that the diradical intermediates “have substantial conformational freedom and very low barriers for forming stereo- and regioisomeric forms of the ring-enlarged product”, in agreement with the experimentally observed lack of any region- or stereoselectivity in the thermal reactions of 8. The computed barrier, 34.9 kcal mol-1 for TS8-10, is in good accord with the experimental barrier of 35.7 kcal mol-1.

A study by Jung11 the year before actually inspired Houk’s work. Jung discovered that appropriately substituted vinylmethylcyclohexenes will undergo very selective Cope rearrangements; for example, thermolysis of 8a produces 9a in greater than 90% yield. This result is quite contrary to that normally observed for vinylmethylcyclohexene thermoylsis: many products with virtually complete scrambling of all stereochemical information.

Examination of the rearrangement of 8a is computationally prohibitive, so Houk looked at the effect of individual substituents. The role of the trialkylsiloxy group was evaluated through the rearrangement of 8b, leading to diradicals 10b and 11b (Scheme 4). The transition state leading to 11b is 1.5 kcal mol-1 below that leading to 10b. This is opposite the relative ordering of the transition states in the parent reaction, indicating that siloxy substitution would favor the path that leads to direct Cope rearrangement, which must pass through 11. The preference for the opposite TS with the siloxy group results from its torquoselectivity (See Chapter 3.5) Since 11b is more stable than 10b, this would also help preserve the stereochemistry during the rearrangement.

Scheme 4

The effects of the terminal substituents were also evaluated. As shown in Scheme 5, the Cope rearrangement of 8b is predicted to proceed with distinct stereoselectivity. The ring opening step preferentially produces diradical intermediate 12 over 13. The ring forming step is also stereoselective: 12 cyclizes to 14 in a 3:1 ratio, while the ring closure of 13 predominantly gives 15. Overall, the rearrangement of 8b is predicted to give a product ratio 14:15 of 2:1. This is in accord with the Jung’s experimental observation.

Scheme 5


(1) Navarro-Vazquez, A.; Prall, M.; Schreiner, P. R., “Cope Reaction Families: To Be or Not to Be a Biradical,” Org. Lett. 2004, 6, 2981-2984, DOI: 10.1021/ol0488340

(2) Huang, J.; Kertesz, M., “Stepwise Cope Rearrangement of Cyclo-biphenalenyl via an Unusual Multicenter Covalent π-Bonded Intermediate,” J. Am. Chem. Soc. 2006, 128, 7277-7286, DOI: 10.1021/ja060427r

(3) Zheng, S.; Lan, J.; Khan, S. I.; Rubin, Y., “Synthesis, Characterization, and Coordination Chemistry of the 2-Azaphenalenyl Radical,” J. Am. Chem. Soc. 2003, 125, 5786-5791, DOI: 10.1021/ja029236o

(4) Goto, K.; Kubo, T.; Yamamoto, K.; Nakasuji, K.; Sato, K.; Shiomi, D.; Takui, T.; Kubota, M.; Kobayashi, T.; Yakusi, K.; Ouyang, J., “A Stable Neutral Hydrocarbon Radical: Synthesis, Crystal Structure, and Physical Properties of 2,5,8-Tri-tert-butyl-phenalenyl,” J. Am. Chem. Soc. 1999, 121, 1619-1620, DOI: 10.1021/ja9836242

(5) Suzuki, S.; Morita, Y.; Fukui, K.; Sato, K.; Shiomi, D.; Takui, T.; Nakasuji, K., “Aromaticity on the Pancake-Bonded Dimer of Neutral Phenalenyl Radical as Studied by MS and NMR Spectroscopies and NICS Analysis,” J. Am. Chem. Soc. 2006, 128, 2530-2531, DOI: 10.1021/ja058387z

(6) Takano, Y.; Taniguchi, T.; Isobe, H.; Kubo, T.; Morita, Y.; Yamamoto, K.; Nakasuji, K.; Takui, T.; Yamaguchi, K., “Hybrid Density Functional Theory Studies on the Magnetic Interactions and the Weak Covalent Bonding for the Phenalenyl Radical Dimeric Pair,” J. Am. Chem. Soc. 2002, 124, 11122-11130, DOI: 10.1021/ja0177197

(7) Small, D.; Zaitsev, V.; Jung, Y.; Rosokha, S. V.; Head-Gordon, M.; Kochi, J. K., “Intermolecular π-to-π Bonding between Stacked Aromatic Dyads. Experimental and Theoretical Binding Energies and Near-IR Optical Transitions for Phenalenyl Radical/Radical versus Radical/Cation Dimerizations,” J. Am. Chem. Soc. 2004, 126, 13850-13858, DOI: 10.1021/ja046770i

(8) Kozhushkov, S. I.; Kuznetsova, T. S.; Zefirov, N. S., “Mechanism of Thermal Isomerization of 3-Vinylmethylenecyclobutane into 4-Methylenecyclohexane,” Dokl. Akad. Nauk SSSR, 1988, 299, 1395-1399,

(9) Dolbier, W. R.; Mancini, G. J., “Non-concerted Thermal Reorganizations 3,3-Divinylmethylenecyclobutane,” Tetrahedron Lett. 1975, 16, 2141-2144, DOI: 10.1016/S0040-4039(00)72661-X.

(10) Zhao, Y. L.; Suhrada, C. P.; Jung, M. E.; Houk, K. N., “Theoretical Investigation of the Stereoselective Stepwise Cope Rearrangement of a 3-Vinylmethylenecyclobutane,” J. Am. Chem. Soc. 2006, 128, 11106-11113, DOI: 10.1021/ja060913e

(11) Jung, M. E.; Nishimura, N.; Novack, A. R., “Versatile Diastereoselectivity in Formal [3,3]-Sigmatropic Shifts of Substituted 1-Alkenyl-3-alkylidenecyclobutanols and Their Silyl Ethers,” J. Am. Chem. Soc. 2005, 127, 11206-11207, DOI: 10.1021/ja051663p


3: InChI=1/C34H26/c1-19-21-11-12-22-16-24-8-6-10-26-18-28-14-13-27-17-25-9-5-7-23(15-21)29(25)31(19)33(27,3)34(28,4)32(20(22)2)30(24)26/h5-18H,1-4H3/b12-11-/t33-,34+

5: InChI=1/C34H26/c1-19-23-11-12-25-17-29-9-6-10-30-18-26(22(4)32(21(25)3)34(29)30)14-13-24-16-28-8-5-7-27(15-23)33(28)31(19)20(24)2/h5-18H,1-4H3/b12-11-,14-13-

6: InChI=1/C13H9/c1-4-10-6-2-8-12-9-3-7-11(5-1)13(10)12/h1-9H

7: InChI=1/C26H18/c1-5-17-9-3-11-23-21(15-13-19(7-1)25(17)23)22-16-14-20-8-2-6-18-10-4-12-24(22)26(18)20/h1-16,21-22H

8: InChI=1/C7H10/c1-3-7-4-6(2)5-7/h3,7H,1-2,4-5H2

9: InChI=1/C7H10/c1-7-5-3-2-4-6-7/h2-3H,1,4-6H2

Cope Rearrangement &DFT &Houk Steven Bachrach 09 Jul 2007 No Comments

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