The π–π stacking interaction between arenes and polyfluoroarenes is being increasingly use in crystal engineering [1Hori, A. The Importance of Pi-Interactions in Crystal Engineering: Frontiers in Crystal Engineering2012.-13Oosterwijk, M.A.; Saunders, G.C.; Zou, W. Polyfluoroarene-arene π–π stacking in three directions to provide crystal polarity. J. Fluor. Chem., 2016, 188, 80-84.
[http://dx.doi.org/10.1016/j.jfluchem.2016.06.015] ]. A number of studies have indicated its geometric properties, in particular a separation of ca. 3.35 Å between the planes of the virtually parallel arene and polyfluoroarene, and an offset of ca. 1.7 Å [1Hori, A. The Importance of Pi-Interactions in Crystal Engineering: Frontiers in Crystal Engineering2012.-29Williams, J.H.; Cockcroft, J.K.; Fitch, A.N. Structure of the lowest temperature phase of the solid benzene–hexafluorobenzene adduct. Angew. Chem. Int. Ed. Engl., 1992, 31, 1655-1657.
[http://dx.doi.org/10.1002/anie.199216551] ], and strength, which has been calculated as 36 and 47 kJ mol^-1 for that between toluene and hexafluorobenzene [30Gung, B.W.; Amicangelo, J.C. Substituent effects in C₆F₆-C₆H₅X stacking interactions. J. Org. Chem., 2006, 71(25), 9261-9270.
[http://dx.doi.org/10.1021/jo061235h] [PMID: 17137351] ], and that between naphthalene and octafluoronaphthalene [31Bacchi, S.; Benaglia, M.; Cozzi, F.; Demartin, F.; Filippini, G.; Gavezzotti, A. X-ray diffraction and theoretical studies for the quantitative assessment of intermolecular arene-perfluoroarene stacking interactions. Chemistry, 2006, 12(13), 3538-3546.
[http://dx.doi.org/10.1002/chem.200501248] [PMID: 16506260] ] respectively. The majority of crystal structures of arene-polyfluoroarene co-crystals and molecules which display π–π stacking have been determined either at room temperature [14Naae, D.G. Biphenyl-perfluorobiphenyl; 1:1 molecular complex. Acta Crystallogr., 1979, B35, 2765-2768.
[http://dx.doi.org/10.1107/S0567740879010499] -18Adamson, A.J.; Archambeau, Y.; Banks, R.E.; Beagley, B.; Helliwell, M.; Pritchard, R.G.; Tipping, A.E. p-Methyl-N-(pentafluorobenzylidene)aniline (1), 1,2,3,4-tetrafluoro-7-methoxyacridine (2), 1,2,3,4,7-pentafluoroacridine (3) and 3-(p-methylanilino)-1,2,4-trifluoro-7-methylacridine (4): four molecules representing key stages in the one-pot synthesis of 1,2,3,4-tetrafluoroacridines by treating pentafluorobenzaldehyde with para-substituted anilines. Acta Crystallogr., 1994, 50, 967-971., 32Potenza, J.; Mastropaolo, D. Naphthalene-octafluoronaphthalene, 1:1 Solid Compound. Acta Crystallogr., 1975, B31, 2527-2529.
[http://dx.doi.org/10.1107/S0567740875008011] ] or low temperature [19Day, M.W.; Matzger, A.J.; Grubbs, R.H. 1,3,5-tris(2-Phenylethynyl)benzene tris(hexafluorobenzene)., 2001, -23Grzegorczyk, M.; Gdaniec, M. 2,2′,3,3′,4,4′,5,5′,6,6′-Decafluorodiphenylamine and its 1:1 cocrystal with diphenylamine. Acta Crystallogr. 2006, C62, o419-o422. (b) Stoll, I.; Brodbeck, R.; Neumann, B.; Stammler, H.-G.; Mattay, J. Controlling the self assembly of arene functionalised 2-aminopyrimidines by arene-perfluoroarene interaction and by silver(I) complex formation. CrystEngComm, 2009, 11, 306-317.], but rarely both [24Dahl, T. Crystal structure of the trigonal form of the 1:1 complex between hexamethylbenzene and hexafluorobenzene. Acta Chem. Scand., 1972, 26, 1569-1575.
[http://dx.doi.org/10.3891/acta.chem.scand.26-1569] -29Williams, J.H.; Cockcroft, J.K.; Fitch, A.N. Structure of the lowest temperature phase of the solid benzene–hexafluorobenzene adduct. Angew. Chem. Int. Ed. Engl., 1992, 31, 1655-1657.
[http://dx.doi.org/10.1002/anie.199216551] ], and to our knowledge only one variable temperature structural study has been undertaken, that for the crystal structure of 1,2,3,4-tetrafluoronaphthalene (CCDC reference CAXNUL) [33Bagryanskaya, I.Y.; Gatilov, Y.V.; Maksimov, A.M.; Platonov, V.E.; Zibarev, A.V. Supramolecular synthons in crystals of partially fluorinated fused aromatics: 1,2,3,4-Tetrafluoronaphthalene and its aza-analogue 1,3,4-trifluoroisoquinoline. J. Fluor. Chem., 2005, 126, 1281-1287.
[http://dx.doi.org/10.1016/j.jfluchem.2005.06.011] , 34Cozzi, F.; Bacchi, S.; Filippini, G.; Pilati, T.; Gavezzotti, A. Synthesis, X-ray diffraction and computational study of the crystal packing of polycyclic hydrocarbons featuring aromatic and perfluoroaromatic rings condensed in the same molecule: 1,2,3,4-tetrafluoronaphthalene, -anthracene and -phenanthrene. Chemistry, 2007, 13(25), 7177-7184.
[http://dx.doi.org/10.1002/chem.200700267] [PMID: 17568459] ]. However, although theoretical lattice energies were calculated, changes in the π–π stacking geometry and the energy of interaction were not reported.

In order to address this deficiency, we decided to perform a variable temperature structural study on a suitable co-crystal containing infinite columns of π–π stacked alternating arene and polyfluoroarene molecules. For the study, it would be desirable if the columns, and consequently the π–π stacking interaction, occurs along one crystallographic axis, so that any changes in this direction can be related directly to the interaction. For simplicity it would also be desirable if the interactions were symmetric about each molecule, i.e. the midpoint of each molecule lies on a crystallographic centre of inversion. The crystal structure of naphthalene-octafluoronaphthalene, 1, which has been determined at room temperature [32Potenza, J.; Mastropaolo, D. Naphthalene-octafluoronaphthalene, 1:1 Solid Compound. Acta Crystallogr., 1975, B31, 2527-2529.
[http://dx.doi.org/10.1107/S0567740875008011] ] (CCDC reference NPOFNP) satisfies both criteria. Here, we report the results of the study.

The crystal structure of naphthalene-octafluoronaphthalene co-crystal, 1, was determined at 100, 150, 200 and 250 K, all of which are consistent with that previously reported for room temperature [32Potenza, J.; Mastropaolo, D. Naphthalene-octafluoronaphthalene, 1:1 Solid Compound. Acta Crystallogr., 1975, B31, 2527-2529.
[http://dx.doi.org/10.1107/S0567740875008011] ] (CCDC reference NPOFNP). Co-crystal 1 crystallizes in the P2₁/c space group, with columns of alternating parallel naphthalene and octafluoronaphthalene molecules, parallel to the a axis (Fig. 1), with the midpoints of all the molecules lying on centres of inversion. The crystal data are presented in Table 1, selected bond distances and angles in Table 2, and selected intermolecular distances and angles in Table 3. The molecular structure of 1 at 100 K and the atom numbering scheme are shown in Fig. (2).

Fig. (1) The crystal structure of 1 100 K viewed (a) parallel to the a axis and (b) parallel to the planes of the molecules of the columns at the edges of the unit cell. Hydrogen atoms are omitted for clarity. (Red = fluorine, grey = carbon).

Table 1
Crystallographic Data and Refinement Parameters for naphthalene-octafluoronaphthalene, 1.^a

Table 2
Selected bond distances (Å) and angles (°) for naphthalene-octafluoronaphthalene, 1.^a

Table 3
Selected intermolecular distances (Å) and angles (°) for naphthalene-octafluoronaphthalene, 1.^a

Fig. (2) The molecular structure of 1 at 100 K showing the atom numbering scheme. Thermal ellipsoids are at the 50% level. (Red = fluorine, grey = carbon, blue = hydrogen).

The planes defined by the carbon atoms of octafluoronaphthalene and naphthalene subtend angles with the a axis of 66.7 and 69.9° respectively. The molecules of the column at the centre of the unit cell are tilted oppositely to those centred at the vertices. The planes defined by the carbon atoms of octafluoronaphthalene and naphthalene are at 34.1 and 31.5° respectively to those of analogous differently tilted molecules.

As expected, the unit cell contracts as the temperature is lowered with a greater contraction along the a and c axes, 0.110 Å (1.5%) and 0.162 Å (1.3%) respectively, than along the b axis, 0.053 Å (0.6%), on decreasing the temperature from 250 to 100 K. The coefficients of linear expansion, α_L, are 1.0 × 10^-4, 0.4 × 10^-4 and 0.9 × 10^-4 K^-1 along the a, b and c axes respectively. There is a commensurate decrease in β of ca. 0.6° (by ca. 4 × 10^-3 ° K^-1). The values of α_L are similar to those observed for 1,2,3,4-tetrafluoronaphthalene [31Bacchi, S.; Benaglia, M.; Cozzi, F.; Demartin, F.; Filippini, G.; Gavezzotti, A. X-ray diffraction and theoretical studies for the quantitative assessment of intermolecular arene-perfluoroarene stacking interactions. Chemistry, 2006, 12(13), 3538-3546.
[http://dx.doi.org/10.1002/chem.200501248] [PMID: 16506260] ] (1.0 × 10^-4, 0.3 × 10^-4 and 0.7 × 10^-4 K^-1), but the change in β, although of similar magnitude, is of opposite sign.

The bond distances and angles are invariant with temperature within experimental error, but the intermolecular distances increase with temperature (Table 3). The distance between the parallel rings is reduced by ca. 1.2% and the offset by ca. 2% on cooling from 250 to 100 K. The change in the intermolecular distance is smaller than those between other adjacent molecules (Fig. 3) which are ca. 2%. The energies of the interactions were calculated for isolated pairs molecules in the gas phase by the long-range corrected functional ωB97xD [35Chai, J-D.; Head-Gordon, M. Long-range corrected hybrid density functionals with damped atom-atom dispersion corrections. Phys. Chem. Chem. Phys., 2008, 10(44), 6615-6620.
[http://dx.doi.org/10.1039/b810189b] [PMID: 18989472] ] method using the 6-311G++(2d,2p) basis set. The values for the structure at 100 K are -59 kJ mol^-1 for the π–π stacking interaction, -10, -8 and -6 kJ mol^-1 for the C₁₀F₈···C₁₀F₈, C₁₀H₈···C₁₀H₈ and C₁₀F₈···C₁₀H₈ interactions shown in Fig. (3a), and -9 and -7 kJ mol^-1 for the C₁₀F₈···C₁₀F₈ and C₁₀F₈···C₁₀H₈ shown in Fig. (3b). There is little variation in the energies with temperature; a decrease of < 2 kJ mol^-1 on going from 100 to 250 K.

Calculations reveal that the energy of the π–π stacking interaction has a much steeper minimum than the other interactions (Fig. 4), which are presumably van der Waals in nature. The π–π stacking interaction energy increases by ca. 8 kJ mol^-1 as the distance between the two planes is increased or decreased by 0.3 Å, whereas for the other interactions the energies vary by only ca. 2 kJ mol^-1 over 1 Å. Thus, the π–π stacking interaction is expected to show much less variability in geometry than the other intermolecular interactions. Experimental observation is consistent with this expectation.

Fig. (3) Short intermolecular distances between adjacent molecules of different stacks in the crystal structure of 1 at 100 K viewed (a) parallel to the c axis and (b) parallel to the b axis. Thermal ellipsoids are at the 50% level. (Red = fluorine, grey = carbon, blue = hydrogen).

Fig. (4) Variation of interaction energy with distance relative to that found experimentally at 100 K for the π–π stacking interaction along the C(2)∙··C(11) axis (red) and the interactions along the F(4)∙··H(13) (orange), F(4)∙··F(4) (violet), C(14)∙··F(14) (yellow), C(1)∙··H(13) (blue) and C(2)∙··C(4) (green) axes.

Naphthalene-octafluoronaphthalene, 1, was prepared by mixing and melting the two reagents as previously described [36Owens, A.R.; Saunders, G.C.; Thomas, H.P.; Wehr-Candler, T. Solvent-free mechanochemical syntheses and reactions of π–π stacked arene-perfluoroarene co-crystals. J. Fluor. Chem., 2015, 175, 139-144.
[http://dx.doi.org/10.1016/j.jfluchem.2015.04.004] ]. A crystal suitable for single crystal X-ray diffraction was grown from acetone. The same crystal (0.177 × 0.059 × 0.034 mm) was used to determine the structure at the four different temperatures. Diffraction data were collected on an Agilent SuperNova, single source at offset, Atlas diffractometer with graphite-monochromated Cu-K_α radiation. The structures were solved using Olex2 [37Dolomanov, O.V.; Bourhis, L.J.; Gildea, R.J.; Howard, J.A.K.; Puschmann, H. OLEX2: A complete structure solution, refinement and analysis program. J. Appl. Cryst., 2009, 42, 339-341.
[http://dx.doi.org/10.1107/S0021889808042726] ] structure solution programme using Charge Flipping and refined with the olex2.refine [38Bourhis, L.J.; Dolomanov, O.V.; Gildea, R.J.; Howard, J.A.K.; Puschmann, H. The anatomy of a comprehensive constrained, restrained refinement program for the modern computing environment - Olex2 dissected. Acta Crystallogr. A Found. Adv., 2015, 71(Pt 1), 59-75.
[http://dx.doi.org/10.1107/S2053273314022207] [PMID: 25537389] ] refinement package using Gauss-Newton minimization. The non-hydrogen atoms were refined with anisotropic thermal parameters. Hydrogen atom positions were added in idealized positions and a riding model with fixed thermal parameters (Uij = 1.2Ueq for the atom to which they are bonded (1.5 for CH₃)) was used for subsequent refinements. The function minimized was Σ[w(|F_o|² - |F_c|²)] with reflection weights w^-1 = [σ² |Fo|² + (g1P)² + (g2P)] where P = [max |F_o|² + 2|F_c|²]/3. The crystal data are presented in Table 1. CCDC 1947799 - 1947802 contain the supplementary crystallographic data for this paper. These data can be obtained free of charge from The Cambridge Crystallographic Data Centre viawww.ccdc. cam.ac.uk/data_request/cif. DFT calculations using the long-range corrected functional ωB97XD [35Chai, J-D.; Head-Gordon, M. Long-range corrected hybrid density functionals with damped atom-atom dispersion corrections. Phys. Chem. Chem. Phys., 2008, 10(44), 6615-6620.
[http://dx.doi.org/10.1039/b810189b] [PMID: 18989472] ] method with the 6-311G++(2d,2p) basis sets were performed using Gaussian 09 [39Frisch, M.J.; Trucks, G.W.; Schlegel, H.B.; Scuseria, G.E.; Robb, M.A.; Cheeseman, J.R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G.A.; Nakatsuji, H.; Caricato, M.; Li, X.; Hratchian, H.P.; Izmaylov, A.F.; Bloino, J.; Zheng, G.; Sonnenberg, J.L.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Montgomery, J.A., Jr; Peralta, J.E.; Ogliaro, F.; Bearpark, M.; Heyd, J.J.; Brothers, E.; Kudin, K.N.; Staroverov, V.N.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A.; Burant, J.C.; Iyengar, S.S.; Tomasi, J.; Cossi, M.; Rega, N.; Millam, J.M.; Klene, M.; Knox, J.E.; Cross, J.B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R.E.; Yazyev, O.; Austin, A.J.; Cammi, R.; Pomelli, C.; Ochterski, J.W.; Martin, R.L.; Morokuma, K.; Zakrzewski, V.G.; Voth, G.A.; Salvador, P.; Dannenberg, J.J.; Dapprich, S.; Daniels, A.D.; Farkas, Ö.; Foresman, J.B.; Ortiz, J.V.; Cioslowski, J.; Fox, D.J. Gaussian 09, Revision A.2., 2009, ]. The energies of interaction were calculated as the difference between the energy of the species and the sum of those of its components. The C─H bonds of the experimental structures were normalized to 1.083 Å [40Allen, F.H.; Kennard, O.; Watson, D.G.; Brammer, L.; Orpen, A.G.; Taylor, R. International Tables for Crystallography., 1995, Vol. C, 685-706.] before single point energy calculations were performed.

The crystal structure of naphthalene-octafluoronaphthalene, 1, has been determined at a range of temperatures. The molecular structures are invariant with temperature. The π–π stacking between the virtually parallel naphthalene and octafluoronaphthalene molecules, which is the strongest interaction, undergoes less variation than the other intermolecular interactions, which are weaker. Calculations reveal that this is to be expected since the latter possess shallower minima.