Pi-stacking

The benzene dimer is the prototypical system for the study of pi stacking, and is experimentally bound by 8–12 kJ/mol (2–3 kcal/mol) in the gas phase with a separation of 4.96 Å between the centers of mass for the T-shaped dimer. The small binding energy makes the benzene dimer difficult to study experimentally, and the dimer itself is only stable at low temperatures and is prone to cluster.{{cite journal | vauthors = Sinnokrot MO, Valeev EF, Sherrill CD | title = Estimates of the ab initio limit for pi-pi interactions: the benzene dimer | journal = Journal of the American Chemical Society | volume = 124 | issue = 36 | pages = 10887–10893 | date = September 2002 | pmid = 12207544 | doi = 10.1021/ja025896h }}

Other evidence against pi stacking comes from X-ray crystallography. Perpendicular and offset parallel configurations can be observed in the crystal structures of many simple aromatic compounds. Similar offset parallel or perpendicular geometries were observed in a survey of high-resolution x-ray protein crystal structures in the Protein Data Bank.{{cite journal | vauthors = Huber RG, Margreiter MA, Fuchs JE, von Grafenstein S, Tautermann CS, Liedl KR, Fox T | title = Heteroaromatic π-stacking energy landscapes | journal = Journal of Chemical Information and Modeling | volume = 54 | issue = 5 | pages = 1371–1379 | date = May 2014 | pmid = 24773380 | pmc = 4037317 | doi = 10.1021/ci500183u | doi-access = free }} Analysis of the aromatic amino acids phenylalanine, tyrosine, histidine, and tryptophan indicates that dimers of these side chains have many possible stabilizing interactions at distances larger than the average van der Waals radii.

The preferred geometries of the benzene dimer have been modeled at a high level of theory with MP2-R12/A computations and very large counterpoise-corrected aug-cc-PVTZ basis sets. The two most stable conformations are the parallel displaced and T-shaped, which are essentially isoenergetic. In contrast, the sandwich configuration maximizes overlap of the pi system, which destabilizes the interaction. The sandwich configuration represents an energetic saddle point, which is consistent with the relative rarity of this configuration in x-ray crystal data.{{citation needed|date=March 2023}}

File:Quadrapole moments.png

The relative binding energies of these three geometric configurations of the benzene dimer can be explained by a balance of quadrupole/quadrupole and London dispersion forces. While benzene does not have a dipole moment, it has a strong quadrupole moment.{{Cite journal | journal = Chem. Phys. Lett. | year = 1981 | volume = 78 | issue = 3 | pages = 421–423 | doi = 10.1016/0009-2614(81)85228-1 | title = The electric quadrupole moments of benzene and hexafluorobenzene| bibcode = 1981CPL....78..421B | vauthors = Battaglia MR, Buckingham AD, Williams JH }} The local C–H dipole means that there is positive charge on the atoms in the ring and a correspondingly negative charge representing an electron cloud above and below the ring. The quadrupole moment is reversed for hexafluorobenzene due to the electronegativity of fluorine. The benzene dimer in the sandwich configuration is stabilized by London dispersion forces but destabilized by repulsive quadrupole/quadrupole interactions. By offsetting one of the benzene rings, the parallel displaced configuration reduces these repulsive interactions and is stabilized. The large polarizability of aromatic rings lead to dispersive interactions as major contribution to stacking effects. These play a major role for interactions of nucleobases e.g. in DNA.{{cite journal | vauthors = Riley KE, Hobza P | title = On the importance and origin of aromatic interactions in chemistry and biodisciplines | journal = Accounts of Chemical Research | volume = 46 | issue = 4 | pages = 927–936 | date = April 2013 | pmid = 22872015 | doi = 10.1021/ar300083h }} The T-shaped configuration enjoys favorable quadrupole/quadrupole interactions, as the positive quadrupole of one benzene ring interacts with the negative quadrupole of the other. The benzene rings are furthest apart in this configuration, so the favorable quadrupole/quadrupole interactions evidently compensate for diminished dispersion forces.

The ability to fine-tune pi stacking interactions would be useful in numerous synthetic efforts. One example would be to increase the binding affinity of a small-molecule inhibitor to an enzyme pocket containing aromatic residues. The effects of heteroatoms and substituents on pi stacking interactions is difficult to model and a matter of debate.

An early model for the role of substituents in pi stacking interactions was proposed by Hunter and Sanders.{{cite journal | journal = J. Am. Chem. Soc. | year = 1990 | volume = 112 | issue = 14 | pages = 5525–5534 | doi = 10.1021/ja00170a016 | title = The nature of π–π Interactions | vauthors = Hunter CA, Sanders JK | bibcode = 1990JAChS.112.5525H }} They used a simple mathematical model based on sigma and pi atomic charges, relative orientations, and van der Waals interactions to qualitatively determine that electrostatics are dominant in substituent effects. According to their model, electron-withdrawing groups reduce the negative quadrupole of the aromatic ring and thereby favor parallel displaced and sandwich conformations. Contrastingly, electron donating groups increase the negative quadrupole, which may increase the interaction strength in a T-shaped configuration with the proper geometry. Based on this model, the authors proposed a set of rules governing pi stacking interactions which prevailed until more sophisticated computations were applied.{{citation needed|date=March 2023}}

Experimental evidence for the Hunter–Sanders model was provided by Siegel et al. using a series of substituted syn- and {{chem name|anti-1,8-di-o-tolylnaphthalenes}}.{{cite journal | journal = J. Am. Chem. Soc. | year = 1993 | volume = 115 | issue = 12 | pages = 5330–5331 | doi = 10.1021/ja00065a069 | title = Dominance of polar/.pi. Over charge-transfer effects in stacked phenyl interactions | vauthors = Cozzi F, Cinquini M, Annuziata R, Siegel JS | bibcode = 1993JAChS.115.5330C }} In these compounds the aryl groups "face-off" in a stacked geometry due to steric crowding, and the barrier to epimerization was measured by nuclear magnetic resonance spectroscopy. The authors reported that aryl rings with electron-withdrawing substituents had higher barriers to rotation. The interpretation of this result was that these groups reduced the electron density of the aromatic rings, allowing more favorable sandwich pi stacking interactions and thus a higher barrier. In other words, the electron-withdrawing groups resulted in "less unfavorable" electrostatic interactions in the ground state.{{citation needed|date=March 2023}}

File:Double Mutant Cycle.png

Hunter et al. applied a more sophisticated chemical double mutant cycle with a hydrogen-bonded "zipper" to the issue of substituent effects in pi stacking interactions.{{cite journal | vauthors = Cockroft SL, Hunter CA, Lawson KR, Perkins J, Urch CJ | title = Electrostatic control of aromatic stacking interactions | journal = Journal of the American Chemical Society | volume = 127 | issue = 24 | pages = 8594–8595 | date = June 2005 | pmid = 15954755 | doi = 10.1021/ja050880n | bibcode = 2005JAChS.127.8594C }} This technique has been used to study a multitude of noncovalent interactions. The single mutation, in this case changing a substituent on an aromatic ring, results in secondary effects such as a change in hydrogen bond strength. The double mutation quantifies these secondary interactions, such that even a weak interaction of interest can be dissected from the array. Their results indicate that more electron-withdrawing substituents have less repulsive pi stacking interactions. Correspondingly, this trend was exactly inverted for interactions with pentafluorophenylbenzene, which has a quadrupole moment equal in magnitude but opposite in sign as that of benzene. The findings provide direct evidence for the Hunter–Sanders model. However, the stacking interactions measured using the double mutant method were surprisingly small, and the authors note that the values may not be transferable to other systems.

In a follow-up study, Hunter et al. verified to a first approximation that the interaction energies of the interacting aromatic rings in a double mutant cycle are dominated by electrostatic effects.{{cite journal | vauthors = Cockroft SL, Perkins J, Zonta C, Adams H, Spey SE, Low CM, Vinter JG, Lawson KR, Urch CJ, Hunter CA | display-authors = 6 | title = Substituent effects on aromatic stacking interactions | journal = Organic & Biomolecular Chemistry | volume = 5 | issue = 7 | pages = 1062–1080 | date = April 2007 | pmid = 17377660 | doi = 10.1039/b617576g | s2cid = 37409177 }} However, the authors note that direct interactions with the ring substituents, discussed below, also make important contributions. Indeed, the interplay of these two factors may result in the complicated substituent- and geometry-dependent behavior of pi stacking interactions.

The Hunter–Sanders model has been criticized by numerous research groups offering contradictory experimental and computational evidence of pi stacking interactions that are not governed primarily by electrostatic effects.{{cite journal |last1=Martinez |first1=Chelsea R. |last2=Iverson |first2=Brent L. |title=Rethinking the term "pi-stacking" |journal=Chemical Science |date=2012 |volume=3 |issue=7 |pages=2191 |doi=10.1039/C2SC20045G|hdl=2152/41033 |hdl-access=free }}

The clearest experimental evidence against electrostatic substituent effects was reported by Rashkin and Waters.{{cite journal | vauthors = Rashkin MJ, Waters ML | title = Unexpected substituent effects in offset pi-pi stacked interactions in water | journal = Journal of the American Chemical Society | volume = 124 | issue = 9 | pages = 1860–1861 | date = March 2002 | pmid = 11866592 | doi = 10.1021/ja016508z }} They used meta- and para-substituted N-benzyl-2-(2-fluorophenyl)-pyridinium bromides, which stack in a parallel displaced conformation, as a model system for pi stacking interactions. In their system, a methylene linker prohibits favorable T-shaped interactions. As in previous models, the relative strength of pi stacking interactions was measured by NMR as the rate of rotation about the biaryl bond, as pi stacking interactions are disrupted in the transition state. Para-substituted rings had small rotational barriers which increased with increasingly electron-withdrawing groups, consistent with prior findings. However, meta-substituted rings had much larger barriers of rotation despite having nearly identical electron densities in the aromatic ring. The authors explain this discrepancy as direct interaction of the edge of hydrogen atoms of one ring with the electronegative substituents on the other ring. This claim is supported by chemical shift data of the proton in question.{{citation needed|date=March 2023}}

Much of the detailed analyses of the relative contributions of factors in pi stacking have been borne out by computation. Sherill and Sinnokrot reported a surprising finding using high-level theory that all substituted benzene dimers have more favorable binding interactions than a benzene dimer in the sandwich configuration.{{cite journal | journal = J. Phys. Chem. A | year = 2003 | volume = 107 | issue = 41 | pages = 8377–8379 | doi = 10.1021/jp030880e | title = Unexpected Substituent Effects in Face-to-Face π-Stacking Interactions | vauthors = Sinnokrot MO, Sherrill CD | bibcode = 2003JPCA..107.8377S }} Later computational work from the Sherill group revealed that the substituent effects for the sandwich configuration are additive, which points to a strong influence of dispersion forces and direct interactions between substituents.{{cite journal | vauthors = Ringer AL, Sinnokrot MO, Lively RP, Sherrill CD | title = The effect of multiple substituents on sandwich and T-shaped pi-pi interactions | journal = Chemistry: A European Journal | volume = 12 | issue = 14 | pages = 3821–3828 | date = May 2006 | pmid = 16514687 | doi = 10.1002/chem.200501316 }} It was noted that interactions between substituted benzenes in the T-shaped configuration were more complex. Finally, Sherill and Sinnokrot argue in their review article that any semblance of a trend based on electron donating or withdrawing substituents can be explained by exchange-repulsion and dispersion terms.{{cite journal | vauthors = Sinnokrot MO, Sherrill CD | title = High-accuracy quantum mechanical studies of pi-pi interactions in benzene dimers | journal = The Journal of Physical Chemistry A | volume = 110 | issue = 37 | pages = 10656–10668 | date = September 2006 | pmid = 16970354 | doi = 10.1021/jp0610416 | bibcode = 2006JPCA..11010656S }}

File:Houk and Wheeler's direct interaction model.png

Houk and Wheeler also provide compelling computational evidence for the importance of direct interaction in pi stacking.{{cite journal | vauthors = Wheeler SE, Houk KN | title = Substituent effects in the benzene dimer are due to direct interactions of the substituents with the unsubstituted benzene | journal = Journal of the American Chemical Society | volume = 130 | issue = 33 | pages = 10854–10855 | date = August 2008 | pmid = 18652453 | pmc = 2655233 | doi = 10.1021/ja802849j | bibcode = 2008JAChS.13010854W }} In their analysis of substituted benzene dimers in a sandwich conformation, they were able to recapitulate their findings using an exceedingly simple model where the substituted benzene, Ph–X, was replaced by H–X. Remarkably, this crude model resulted in the same trend in relative interaction energies, and correlated strongly with the values calculated for Ph–X. This finding suggests that substituent effects in the benzene dimer are due to direct interaction of the substituent with the aromatic ring, and that the pi system of the substituted benzene is not involved. This latter point is expanded upon below.

In summary, it would seem that the relative contributions of electrostatics, dispersion, and direct interactions to the substituent effects seen in pi stacking interactions are highly dependent on geometry and experimental design. The lack of consensus on the matter may simply reflect the complexity of the issue.

The conventional understanding of pi stacking involves quadrupole interactions between delocalized electrons in p-orbitals. In other words, aromaticity should be required for this interaction to occur. However, several groups have provided contrary evidence, calling into question whether pi stacking is a unique phenomenon or whether it extends to other neutral, closed-shell molecules.

In an experiment not dissimilar from others mentioned above, Paliwal and coauthors constructed a molecular torsion balance from an aryl ester with two conformational states.{{cite journal | journal = J. Am. Chem. Soc. | year = 1994 | volume = 116 | issue = 10 | pages = 4497–4498 | doi = 10.1021/ja00089a057 | title = Molecular Torsion Balance for Weak Molecular Recognition Forces. Effects of "Tilted-T" Edge-to-Face Aromatic Interactions on Conformational Selection and Solid-State Structure | vauthors = Paliwal S, Geib S, Wilcox CS | bibcode = 1994JAChS.116.4497P }} The folded state had a well-defined pi stacking interaction with a T-shaped geometry, whereas the unfolded state had no aryl–aryl interactions. The NMR chemical shifts of the two conformations were distinct and could be used to determine the ratio of the two states, which was interpreted as a measure of intramolecular forces. The authors report that a preference for the folded state is not unique to aryl esters. For example, the cyclohexyl ester favored the folded state more so than the phenyl ester, and the tert-butyl ester favored the folded state by a preference greater than that shown by any aryl ester. This suggests that aromaticity is not a strict requirement for favorable interaction with an aromatic ring.

Other evidence for non-aromatic pi stacking interactions results include critical studies in theoretical chemistry, explaining the underlying mechanisms of empirical observations. Grimme reported that the interaction energies of smaller dimers consisting of one or two rings are very similar for both aromatic and saturated compounds.{{cite journal | vauthors = Grimme S | title = Do special noncovalent pi-pi stacking interactions really exist? | journal = Angewandte Chemie | volume = 47 | issue = 18 | pages = 3430–3434 | year = 2008 | pmid = 18350534 | doi = 10.1002/anie.200705157 | doi-access = free }} This finding is of particular relevance to biology, and suggests that the contribution of pi systems to phenomena such as stacked nucleobases may be overestimated. However, it was shown that an increased stabilizing interaction is seen for large aromatic dimers. As previously noted, this interaction energy is highly dependent on geometry. Indeed, large aromatic dimers are only stabilized relative to their saturated counterparts in a sandwich geometry, while their energies are similar in a T-shaped interaction.

File:Homodesmotic dissection of 2-methylnaphthalene and benzene..png

A more direct approach to modeling the role of aromaticity was taken by Bloom and Wheeler.{{cite journal | journal = Angew. Chem. | year = 2011 | volume = 123 | pages = 7993–7995 | doi = 10.1002/ange.201102982 | title = Taking the Aromaticity out of Aromatic Interactions | vauthors = Bloom JW, Wheeler SE | issue = 34| bibcode = 2011AngCh.123.7993B }} The authors compared the interactions between benzene and either 2-methylnaphthalene or its non-aromatic isomer, 2-methylene-2,3-dihydronaphthalene. The latter compound provides a means of conserving the number of p-electrons while, however, removing the effects of delocalization. Surprisingly, the interaction energies with benzene are higher for the non-aromatic compound, suggesting that pi-bond localization is favorable in pi stacking interactions. The authors also considered a homodesmotic dissection of benzene into ethylene and 1,3-butadiene and compared these interactions in a sandwich with benzene. Their calculation indicates that the interaction energy between benzene and homodesmotic benzene is higher than that of a benzene dimer in both sandwich and parallel displaced conformations, again highlighting the favorability of localized pi-bond interactions. These results strongly suggest that aromaticity is not required for pi stacking interactions in this model.

Even in light of this evidence, Grimme concludes that pi stacking does indeed exist. However, he cautions that smaller rings, particularly those in T-shaped conformations, do not behave significantly differently from their saturated counterparts, and that the term should be specified for larger rings in stacked conformations which do seem to exhibit a cooperative pi electron effect.

Buckycatcher JACS 2007 V129 p3843.jpg|A fullerene bound in a buckycatcher through aromatic stacking interactions.{{cite journal | vauthors = Sygula A, Fronczek FR, Sygula R, Rabideau PW, Olmstead MM | title = A double concave hydrocarbon buckycatcher | journal = Journal of the American Chemical Society | volume = 129 | issue = 13 | pages = 3842–3843 | date = April 2007 | pmid = 17348661 | doi = 10.1021/ja070616p | bibcode = 2007JAChS.129.3842S | s2cid = 25154754 }}

File:24 fig. 2.png|The Stoddart synthesis of [2] catenane...

File:QUATERNARY LIGAND BINDING TO AROMATIC RESIDUES IN THE ACTIVE-SITE GORGE OF ACETYLCHOLINESTERASE.png|Tacrine bound to acetylcholinesterase (PDB 1ACJ). A pi stacking interaction between tacrine (blue) and Trp84 (red) is proposed

Polar-pi.svg|Polar π interaction between water molecule and benzene

Areneperfluoroarene.svg|Arene perfluoroarene stacking

SegStackEdgeOnHMTFCQ.jpg|Edge-on view of portion of crystal structure of hexamethyleneTTF/TCNQ charge transfer salt, highlighting the segregated stacking.{{cite journal|author1=D. Chasseau|author2=G. Comberton|author3=J. Gaultier|author4=C. Hauw|journal=Acta Crystallographica Section B|title=Réexamen de la structure du complexe hexaméthylène-tétrathiafulvalène-tétracyanoquinodiméthane|year=1978| volume=34|issue=2|page=689|doi=10.1107/S0567740878003830|doi-access=|bibcode=1978AcCrB..34..689C }}]]

File:Graphite-layers-side-3D-balls.png

Graphite consists of stacked sheets of covalently bonded carbon.{{cite book |last1=Delhaes |first1=Pierre |chapter=Polymorphism of carbon |editor-last1=Delhaes |editor-first1=Pierre |title=Graphite and precursors |date=2000 |publisher=Gordon & Breach |isbn=9789056992286|pages=1–24}}{{cite book |last1=Pierson |first1=Hugh O. |title=Handbook of carbon, graphite, diamond, and fullerenes : properties, processing, and applications |date=2012 |publisher=Noyes Publications |isbn=9780815517399 |pages=40–41}} The individual layers are called graphene. In each layer, each carbon atom is bonded to three other atoms forming a continuous layer of sp² bonded carbon hexagons, like a honeycomb lattice with a bond length of 0.142 nm, and the distance between planes is 0.335 nm.{{cite book |title= Graphite and Precursors |author= Delhaes, P. |publisher= CRC Press |year= 2001 |url= https://books.google.com/books?id=7p2pgNOWPbEC&pg=PA146 |isbn= 978-90-5699-228-6}}

Cation-π interactions are important for the acetylcholine (Ach) neurotransmitter.{{cite journal|last1=Dougherty|first1=D. A.|title=Cation-pi Interactions in Chemistry and Biology: A New View of Benzene, Phe, Tyr, and Trp|journal=Science|volume=271|issue=5246|pages=163–8|year=1996|pmid=8539615|doi=10.1126/science.271.5246.163|bibcode = 1996Sci...271..163D |s2cid=9436105}}{{cite journal|last1=Kumpf|first1=R.|last2=Dougherty|first2=D.|title=A mechanism for ion selectivity in potassium channels: computational studies of cation-pi interactions|journal=Science|volume=261|issue=5129|pages=1708–10|year=1993|pmid=8378771|doi=10.1126/science.8378771|bibcode = 1993Sci...261.1708K }} The structure of acetylcholine esterase includes 14 highly conserved aromatic residues. The trimethyl ammonium group of Ach binds to the aromatic residue of tryptophan (Trp). The indole site provides a much more intense region of negative electrostatic potential than benzene and phenol residue of Phe and Tyr.

Pi–pi and cation–pi interactions are important in rational drug design.{{cite journal | vauthors = Babine RE, Bender SL | title = Molecular Recognition of Proteinminus signLigand Complexes: Applications to Drug Design | journal = Chemical Reviews | volume = 97 | issue = 5 | pages = 1359–1472 | date = August 1997 | pmid = 11851455 | doi = 10.1021/cr960370z }} One example is the FDA-approved acetylcholinesterase (AChE) inhibitor tacrine which is used in the treatment of Alzheimer's disease. Tacrine is proposed to have a pi stacking interaction with the indolic ring of Trp84, and this interaction has been exploited in the rational design of novel AChE inhibitors.{{cite journal | vauthors = da Silva CH, Campo VL, Carvalho I, Taft CA | title = Molecular modeling, docking and ADMET studies applied to the design of a novel hybrid for treatment of Alzheimer's disease | journal = Journal of Molecular Graphics & Modelling | volume = 25 | issue = 2 | pages = 169–175 | date = October 2006 | pmid = 16413803 | doi = 10.1016/j.jmgm.2005.12.002 }}

File:24 fig. 1.png

\pi - \pi , CH-\pi and \pi -cation interactions are widely observed motifs in supramolecular assembly and recognition.

\pi-\pi concerns the direct interactions between two {{pi}}-systems; and cation-\pi interaction arises from the electrostatic interaction of a cation with the face of the {{pi}}-system. Unlike these two interactions, the CH-\pi interaction arises mainly from charge transfer between the C–H orbital and the {{pi}}-system.

π systems contribute to supramolecular assembly. Some catenanes feature π–π interactions. The major challenge for the synthesis of catenane is to interlock molecules in a controlled fashion. Stoddart and co-workers developed a series of systems utilizing the strong π–π interactions between electron-rich benzene derivatives and electron-poor pyridinium rings.{{cite journal | vauthors = Ashton PR, Goodnow TT, Kaifer AE, Reddington MV, Slawin AM, Spencer N, Stoddart JF, Vicent C, Williams DJ |display-authors=6 |title=A [2] Catenane Made to Order |journal=J. Angew. Chem. Int. Ed. |year=1989 |volume=28 |issue=10 |pages=1396–1399 |doi=10.1002/anie.198913961 }} [2]Catanene was synthesized by reacting bis(pyridinium) (A), bisparaphenylene-34-crown-10 (B), and 1, 4-bis(bromomethyl)benzene (C) (Fig. 2). The π–π interaction between A and B directed the formation of an interlocked template intermediate that was further cyclized by substitution reaction with compound C to generate the [2]catenane product.

{{Anchor|TTF-TCNQ}}

A combination of tetracyanoquinodimethane (TCNQ) and tetrathiafulvalene (TTF) forms a strong charge-transfer complex referred to as TTF-TCNQ.{{cite journal |author1=P. W. Anderson |author2=P. A. Lee |author3=M. Saitoh | journal = Solid State Communications | volume = 13 | year = 1973 | pages = 595–598 | doi = 10.1016/S0038-1098(73)80020-1 | title = Remarks on giant conductivity in TTF-TCNQ |issue=5 | bibcode=1973SSCom..13..595A}} The solid shows almost metallic electrical conductance. In a TTF-TCNQ crystal, TTF and TCNQ molecules are arranged independently in separate parallel-aligned stacks, and an electron transfer occurs from donor (TTF) to acceptor (TCNQ) stacks.{{cite journal |doi=10.1021/acs.jchemed.5b00340|title=Opposites Attract: Organic Charge Transfer Salts |year=2015 |last1=Van De Wouw |first1=Heidi L. |last2=Chamorro |first2=Juan |last3=Quintero |first3=Michael |last4=Klausen |first4=Rebekka S. |journal=Journal of Chemical Education |volume=92 |issue=12 |pages=2134–2139 |bibcode=2015JChEd..92.2134V }}

• Noncovalent interaction
• Dispersion (chemistry)
• Cation–pi interaction
• Intercalation (biochemistry)
• Intercalation (chemistry)

{{reflist}}

• {{cite journal | vauthors = Luo R, Gilson HS, Potter MJ, Gilson MK | title = The physical basis of nucleic acid base stacking in water | journal = Biophysical Journal | volume = 80 | issue = 1 | pages = 140–148 | date = January 2001 | pmid = 11159389 | pmc = 1301220 | doi = 10.1016/S0006-3495(01)76001-8 | bibcode = 2001BpJ....80..140L }}
• [http://www.scs.illinois.edu/denmark/wp-content/uploads/gp/2011/gm-2011-1_18.pdf Larry Wolf (2011): π-π (π-Stacking) interactions: origin and modulation]

{{Chemical bonds}}

Category:Organic chemistry

Category:Chemical bonding

Category:Supramolecular chemistry