The benzene dimer (BD) is an archetypal model of π∙∙∙π and C-H∙∙∙π noncovalent interactions as they occur in its cofacial and perpendicular arrangements, respectively. The enthalpic stabilization of the related BD structures has been debated for a long time and is revisited here. The revisit is based on results of computations that apply the coupled-cluster theory with singles, doubles and perturbative triples [CCSD(T)] together with large basis sets and extrapolate results to the complete basis set (CBS) limit in order to accurately characterize the three most important stationary points of the intermolecular interaction energy (ΔE) surface of the BD, which correspond to the tilted T-shaped (TT), fully symmetric T-shaped (FT) and slipped-parallel (SP) structures. In the optimal geometries obtained by searching extensive sets of the CCSD(T)/CBS ΔE data of the TT, FT and SP arrangements, the resulting ΔE values were -11.84, -11.34 and -11.21 kJ/mol, respectively. The intrinsic strength of the intermolecular bonding in these configurations was evaluated by analyzing the distance dependence of the CCSD(T)/CBS ΔE data over wide ranges of intermonomer separations. In this way, regions of the relative distances that favor BD structures with either π∙∙∙π or C-H∙∙∙π interactions were found and discussed in a broader context.

Institute of Macromolecular Chemistry Czech Academy of Sciences Heyrovsky Square 2 162 00 Prague Czech Republic

Zobrazit více v PubMed

Karshikoff A. Non-Covalent Interactions in Proteins. 2nd ed. World Scientific; Singapore: 2021. DOI

Cerveri A., Scarica G., Sparascio S., Hoch M., Chiminelli M., Tegoni M., Protti S., Maestri G. Boosting Energy-Transfer Processes via Dispersion Interactions. Chem. Eur. J. 2023;29:e202304010. doi: 10.1002/chem.202304010. PubMed DOI

Guo M., Jayakumar S., Luo M., Kong X., Li C., Li H., Chen J. The promotion effect of π-π interactions in Pd NPs catalysed selective hydrogenation. Nat. Commun. 2022;13:1770. doi: 10.1038/s41467-022-29299-0. PubMed DOI PMC

Zhang Y.F., Zhang Y.N., Ding R., Zhang K., Guo H.Y., Lin Y.Y. Self-Assembled Nanocarrier Delivery Systems for Bioactive Compounds. Small. 2024;20:2310838. doi: 10.1002/smll.202310838. PubMed DOI

Savastano M., de la Torre M.D.L., Pagliai M., Poggi G., Ridi F., Bazzicalupi C., Melguizo M., Bianchi A. Crystal engineering of high explosives through lone pair-π interactions: Insights for improving thermal safety. iScience. 2023;26:107330. doi: 10.1016/j.isci.2023.107330. PubMed DOI PMC

Pan X., Montes E., Rojas W.Y., Lawson B., Vázquez H., Kamentska M. Cooperative Self-Assembly of Dimer Junctions Driven by π Stacking Leads to Conductance Enhancement. Nano Lett. 2023;23:6937–6943. doi: 10.1021/acs.nanolett.3c01540. PubMed DOI

Tuttle M.R., Davis S.T., Zhang S. Synergistic Effect of Hydrogen Bonding and π–π Stacking Enables Long Cycle Life in Organic Electrode Materials. ACS Energy Lett. 2021;6:643–649. doi: 10.1021/acsenergylett.0c02604. DOI

Carter-Fenk K., Liu M.L., Pujal L., Loipersberger M., Tsanai M., Vernon R.M., Forman-Kay J.D., Head-Gordon M., Heidar-Zadeh F., Head-Gordon T. The Energetic Origins of Pi-Pi Contacts in Proteins. J. Am. Chem. Soc. 2023;145:24836–24851. doi: 10.1021/jacs.3c09198. PubMed DOI PMC

Samaroo S., Hengesbach C., Bruggeman C., Carducci N.G.G., Mtemeri L., Staples R.J., Guarr T., Hickey D.P. C–H···π interactions disrupt electrostatic interactions between non-aqueous electrolytes to increase solubility. Nat. Chem. 2023;15:1365–1373. doi: 10.1038/s41557-023-01291-1. PubMed DOI

Herman K.M., Aprà E., Xantheas S.S. A critical comparison of CH···π versus π···π interactions in the benzene dimer: Obtaining benchmarks at the CCSD(T) level and assessing the accuracy of lower scaling methods. Phys. Chem. Chem. Phys. 2023;25:4824–4838. doi: 10.1039/D2CP04335A. PubMed DOI

Tummanapelli A.K., Vasudevan S. Communication: Benzene dimer—The free energy landscape. J. Chem. Phys. 2013;139:201102. doi: 10.1063/1.4834855. PubMed DOI

Van der Avoird A., Podeszwa R., Ensing B., Szalewicz K. Comment on “Communication: Benzene dimer—The free energy landscape” [J. Chem. Phys. 139, 201102 (2013)] J. Chem. Phys. 2014;140:227101. doi: 10.1063/1.4882015. PubMed DOI

Tummanapelli A.K., Vasudevan S. Response to “Comment on ‘Communication: Benzene dimer—The free energy landscape’” [J. Chem. Phys. 140, 227101 (2014)] J. Chem. Phys. 2014;140:227102. doi: 10.1063/1.4882016. PubMed DOI

Law K.S., Schauer M., Bernstein E.R. Dimers of aromatic molecules: (Benzene)2, (toluene)2, and benzene–toluene. J. Chem. Phys. 1984;81:4871–4882. doi: 10.1063/1.447514. DOI

Arunan E., Gutowsky H.S. The rotational spectrum, structure and dynamics of a benzene dimer. J. Chem. Phys. 1993;98:4294–4296. doi: 10.1063/1.465035. DOI

Erlekam U., Frankowski M., Meijer G., von Helden G. An experimental value for the B1u C–H stretch mode in benzene. J. Chem. Phys. 2006;124:171101. doi: 10.1063/1.2198828. PubMed DOI

Lee E.C., Kim D., Jurečka P., Tarakeshwar P., Hobza P., Kim K.S. Understanding of Assembly Phenomena by Aromatic−Aromatic Interactions:  Benzene Dimer and the Substituted Systems. J. Phys. Chem. A. 2007;111:3446–3457. doi: 10.1021/jp068635t. PubMed DOI

Van der Avoird A., Podeszwa R., Szalewicz K., Leforestier C., van Harrevelt R., Bunker P.R., Schnell M., von Helden G., Meijer G. Vibration–rotation-tunneling states of the benzene dimer: An ab initio study. Phys. Chem. Chem. Phys. 2010;12:8219–8240. doi: 10.1039/c002653k. PubMed DOI

Schnell M., Erlekam U., Bunker P.R., von Helden G., Grabow J.-U., Meijer G., van der Avoird A. Structure of the Benzene Dimer—Governed by Dynamics. Angew. Chem. Int. Ed. 2013;52:5180–5183. doi: 10.1002/anie.201300653. PubMed DOI

Fatima M., Steber A.L., Poblotzki A., Pérez C., Zinn S., Schnell M. Rotational Signatures of Dispersive Stacking in the Formation of Aromatic Dimers. Angew. Chem. Int. Ed. 2019;58:3108–3113. doi: 10.1002/anie.201812556. PubMed DOI

Grover J.R., Walters E.A., Hui E.T. Dissociation Energies of the Benzene Dimer and Dimer Cation. J. Phys. Chem. 1987;91:3233–3237. doi: 10.1021/j100296a026. DOI

Krause H., Ernstberger B., Neusser H.J. Binding energies of small benzene clusters. Chem. Phys. Lett. 1991;184:411–417. doi: 10.1016/0009-2614(91)80010-U. DOI

Calvin J.A., Peng C., Rishi V., Kumar A., Valeev E.F. Many-Body Quantum Chemistry on Massively Parallel Computers. Chem. Rev. 2021;121:1203–1231. doi: 10.1021/acs.chemrev.0c00006. PubMed DOI

Patkowski K. Recent developments in symmetry-adapted perturbation theory. Wiley Interdiscip. Rev. Comput. Mol. Sci. 2020;10:e1452. doi: 10.1002/wcms.1452. DOI

Shahbaz M., Szalewicz K. Evaluation of methods for obtaining dispersion energies used in density functional calculations of intermolecular interactions. Theor. Chem. Acc. 2019;138:25. doi: 10.1007/s00214-019-2414-5. DOI

Carter-Fenk C., Lao K.U., Herbert J.M. Predicting and Understanding Non-Covalent Interactions Using Novel Forms of Symmetry-Adapted Perturbation Theory. Acc. Chem. Res. 2021;54:3679–3690. doi: 10.1021/acs.accounts.1c00387. PubMed DOI

Morales-Silva M.A., Jordan K.D., Shulenburger L., Wagner L.K. Frontiers of stochastic electronic structure calculations. J. Chem. Phys. 2021;154:170401. doi: 10.1063/5.0053674. PubMed DOI

Al-Hamdani Y.S., Nagy P.R., Zen A., Barton D., Kállay M., Bradenburg J.G., Tkatchenko A. Interactions between large molecules pose a puzzle for reference quantum mechanical methods. Nat. Commun. 2021;12:3927. doi: 10.1038/s41467-021-24119-3. PubMed DOI PMC

Grimme S., Goerigk L., Fink R.F. Spin-component-scaled electron correlation methods. Wiley Interdiscip. Rev. Comput. Mol. Sci. 2012;2:886–906. doi: 10.1002/wcms.1110. DOI

Miliordos E., Aprà E., Xantheas S.S. Benchmark Theoretical Study of the π–π Binding Energy in the Benzene Dimer. J. Phys. Chem. A. 2014;118:7568–7578. doi: 10.1021/jp5024235. PubMed DOI

Carter-Fenk K., Herbert J.M. Electrostatics does not dictate the slip-stacked arrangement of aromatic π–π interactions. Chem. Sci. 2020;11:6758–6765. doi: 10.1039/D0SC02667K. PubMed DOI PMC

Czernek J., Brus J., Czerneková V., Kobera L. Quantifying the Intrinsic Strength of C–H⋯O Intermolecular Interactions. Molecules. 2023;28:4478. doi: 10.3390/molecules28114478. PubMed DOI PMC

Sauceda H.E., Vassilev-Galindo V., Chmiela S., Müller K.-R., Tkatchenko A. Dynamical strengthening of covalent and non-covalent molecular interactions by nuclear quantum effects at finite temperature. Nat. Commun. 2021;12:442. doi: 10.1038/s41467-020-20212-1. PubMed DOI PMC

Igarashi M., Nozawa T., Matsumoto T., Yagihashi F., Kikuchi T., Sato K. Parallel-stacked aromatic molecules in hydrogen-bonded inorganic frameworks. Nat. Commun. 2021;12:7025. doi: 10.1038/s41467-021-27324-2. PubMed DOI PMC

Di S., Wu Q., Shi C., Zhu S. Hydroxy-Containing Covalent Organic Framework Combined with Nickel Ferrite as a Platform for the Recognition and Capture of Bisphenols. ACS Appl. Mater. Interfaces. 2023;15:1827–1842. doi: 10.1021/acsami.2c17728. PubMed DOI

Lao Z., Tang Y., Dong X., Tan Y., Li X., Liu X., Li L., Guo C., Wei G. Elucidating the reversible and irreversible self-assembly mechanisms of low-complexity aromatic-rich kinked peptides and steric zipper peptides. Nanoscale. 2024;16:4025–4038. doi: 10.1039/D3NR05130G. PubMed DOI

Dunning T.H., Jr. Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen. J. Chem. Phys. 1989;90:1007–1023. doi: 10.1063/1.456153. DOI

Kendall R.A., Dunning T.H., Jr., Harrison R.J. Electron affinities of the first-row atoms revisited. Systematic basis sets and wave functions. J. Chem. Phys. 1992;96:6796–6806. doi: 10.1063/1.462569. DOI

Boys S.F., Bernardi F. The calculation of small molecular interactions by the differences of separate total energies. Some procedures with reduced errors. Mol. Phys. 1970;19:553–566. doi: 10.1080/00268977000101561. DOI

Czernek J., Brus J., Czerneková V. A Cost Effective Scheme for the Highly Accurate Description of Intermolecular Binding in Large Complexes. Int. J. Mol. Sci. 2022;23:15773. doi: 10.3390/ijms232415773. PubMed DOI PMC

Czernek J., Brus J. On the Intermolecular Interactions in Thiophene-Cored Single-Stacking Junctions. Int. J. Mol. Sci. 2023;24:13349. doi: 10.3390/ijms241713349. PubMed DOI PMC

Czernek J., Brus J. Reliable Dimerization Energies for Modeling of Supramolecular Junctions. Int. J. Mol. Sci. 2024;25:602. doi: 10.3390/ijms25010602. PubMed DOI PMC

Podeszwa R., Bukowski R., Szalewicz K. Potential Energy Surface for the Benzene Dimer and Perturbational Analysis of π−π Interactions. J. Phys. Chem. A. 2006;110:10345–10354. doi: 10.1021/jp064095o. PubMed DOI

Tamagawa K., Iijima T., Kimura M. Molecular structure of benzene. J. Mol. Struct. 1976;30:243–253. doi: 10.1016/0022-2860(76)87003-2. DOI

Müller M., Hansen A., Grimme S. ωB97X-3c: A composite range-separated hybrid DFT method with a molecule-optimized polarized valence double-ζ basis set. J. Chem. Phys. 2023;158:014103. doi: 10.1063/5.0133026. PubMed DOI

Gorges J., Bädorf B., Grimme S., Hansen A. Efficient Computation of the Interaction Energies of Very Large Non-covalently Bound Complexes. Synlett. 2023;34:1135–1146. doi: 10.1055/s-0042-1753141. DOI

Řezáč J., Riley K.E., Hobza P. S66: A Well-balanced Database of Benchmark Interaction Energies Relevant to Biomolecular Structures. J. Chem. Theory Comput. 2011;7:2427–2438. doi: 10.1021/ct2002946. PubMed DOI PMC

Sargent C.T., Kasera R., Glick Z.L., Sherrill C.D., Cheney D.L. A quantitative assessment of deformation energy in intermolecular interactions: How important is it? J. Chem. Phys. 2023;158:244106. doi: 10.1063/5.0155895. PubMed DOI

Scheiner S. Strengthening of Noncovalent Bonds Caused by Internal Deformations. J. Phys. Chem. A. 2024;128:2357–2365. doi: 10.1021/acs.jpca.4c00541. PubMed DOI

Stone A.J. The Theory of Intermolecular Forces. 1st ed. Clarendon Press; Oxford, UK: 2002. pp. 79–102.

Carter-Fenk K., Herbert J.M. Reinterpreting π-stacking. Phys. Chem. Chem. Phys. 2020;22:24870–24886. doi: 10.1039/D0CP05039C. PubMed DOI

Cabaleiro-Lago E.M., Rodríguez-Otero J., Vázquez S.A. Electrostatic penetration effects stand at the heart of aromatic π interactions. Phys. Chem. Chem. Phys. 2022;24:8979–8991. doi: 10.1039/D2CP00714B. PubMed DOI

Vernon R.M., Chong P.A., Tsang B., Kim T.H., Bah A., Farber P., Lin H., Forman-Kay J.D. Pi-Pi contacts are an overlooked protein feature relevant to phase separation. eLife. 2018;7:e31476. doi: 10.7554/eLife.31486. PubMed DOI PMC

Halkier A., Helgaker T., Jørgensen P., Klopper W., Koch H., Olsen J., Wilson A.K. Basis-set convergence in correlated calculations on Ne, N2, and H2O. Chem. Phys. Lett. 1998;286:243–252. doi: 10.1016/S0009-2614(98)00111-0. DOI

Balasubramani S.G., Chen G.P., Coriani S., Diedenhofen M., Frank M.S., Franzke Y.J., Furche F., Grotjahn R., Harding M.E., Hättig C., et al. TURBOMOLE: Modular program suite for ab initio quantum-chemical and condensed-matter simulations. J. Chem. Phys. 2020;152:184107. doi: 10.1063/5.0004635. PubMed DOI PMC

Weigend F., Häser M. RI-MP2: First derivatives and global consistency. Theor. Chem. Acc. 1997;97:331–340. doi: 10.1007/s002140050269. DOI

Weigend F., Häser M., Patzelt H., Ahlrichs R. RI-MP2: Optimized auxiliary basis sets and demonstration of efficiency. Chem. Phys. Lett. 1998;294:143–152. doi: 10.1016/S0009-2614(98)00862-8. DOI

Werner H.J., Knowles P.J., Manby F.R., Black J.A., Doll K., Hesselmann A., Kats D., Kohn A., Korona T., Kreplin D.A., et al. The Molpro quantum chemistry package. J. Chem. Phys. 2020;152:144107. doi: 10.1063/5.0005081. PubMed DOI

Heßelmann A., Jansen G. Density-functional theory-symmetry-adapted intermolecular perturbation theory with density fitting: A new efficient method to study intermolecular interaction energies. J. Chem. Phys. 2005;122:014103. doi: 10.1063/1.1824898. PubMed DOI

Czernek J., Brus J., Czerneková V. A computational inspection of the dissociation energy of mid-sized organic dimers. J. Chem. Phys. 2022;156:204303. doi: 10.1063/5.0093557. PubMed DOI

Heßelmann A., Jansen G. First-order intermolecular interaction energies from Kohn–Sham orbitals. Chem. Phys. Lett. 2002;357:464–470. doi: 10.1016/S0009-2614(02)00538-9. DOI

Heßelmann A., Jansen G. Intermolecular dispersion energies from time-dependent density functional theory. Chem. Phys. Lett. 2003;367:778–784. doi: 10.1016/S0009-2614(02)01796-7. DOI

Heßelmann A., Jansen G. Intermolecular induction and exchange-induction energies from coupled-perturbed Kohn–Sham density functional theory. Chem. Phys. Lett. 2002;362:319–325. doi: 10.1016/S0009-2614(02)01097-7. DOI

Moszynski R., Heijmen T.G.A., Jeziorski B. Symmetry-adapted perturbation theory for the calculation of Hartree–Fock interaction energies. Mol. Phys. 1996;88:741–758. doi: 10.1080/00268979650026262. DOI

Adamo C., Barone V. Toward reliable density functional methods without adjustable parameters: The PBE0 model. J. Chem. Phys. 1999;110:6158–6170. doi: 10.1063/1.478522. DOI

Grimme S., Antony J., Ehrlich S., Krieg H. A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. J. Chem. Phys. 2010;132:154104. doi: 10.1063/1.3382344. PubMed DOI

Weigend F., Ahlrichs R. Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: Design and assessment of accuracy. Phys. Chem. Chem. Phys. 2005;7:3297–3305. doi: 10.1039/b508541a. PubMed DOI

Frish M.J., Trucks J.W., Schlegel H.B., Scuseria G.E., Robb M.A., Cheeseman J.R., Scalmani G., Barone V., Petersson G.A., Nakatsuji H., et al. Gaussian 16; Revision C.01. Gaussian, Inc.; Wallingford, CT, USA: 2019.

Neese F. Software update: The ORCA program system—Version 5.0. Wiley Interdiscip. Rev. Comput. Mol. Sci. 2022;12:e1606. doi: 10.1002/wcms.1606. DOI

ORCA4wB97X-3c A Fortran Script for Setting Up a ωB97X-3c Calculation with ORCA 5.0.3 or Higher. [(accessed on 28 June 2024)]. Available online: https://github.com/grimme-lab/ORCA4wB97X-3c.

Bende A., Farcaş A.-A. Intermolecular-Type Conical Intersections in Benzene Dimer. Int. J. Mol. Sci. 2023;24:2906. doi: 10.3390/ijms24032906. PubMed DOI PMC

Pham H.Q., Ouyang R.S., Lv D.S. Scalable Quantum Monte Carlo with Direct-Product Trial Wave Functions. J. Chem. Theory Comput. 2024;20:3524–3534. doi: 10.1021/acs.jctc.3c00769. PubMed DOI

Vinod V., Kleinekathöfer U., Zaspel P. Optimized multifidelity machine learning for quantum chemistry. Mach. Learn. Sci. Technol. 2024;5:015054. doi: 10.1088/2632-2153/ad2cef. DOI

On the Potential Energy Surface of the Pyrene Dimer