ZUSCHRIFTEN 2600  WILEY-VCH Verlag GmbH, D-69451 Weinheim, 2001 0044-8249/01/11313-2600 $ 17.50+.50/0 Angew. Chem. 2001, 113, Nr. 13 DFT Calculation of Intermolecular Nuclear Spin ± Spin Coupling in van der Waals Dimers** Alessandro Bagno,* Giacomo Saielli, and Gianfranco Scorrano Nuclear magnetic resonance is probably the most powerful technique for the determination of molecular structure and conformation in solution; a wide array of experimental methods is available, which exploit scalar (spin ± spin) or dipolar (nuclear Overhauser effect) coupling. Spin ± spin couplings are normally thought of as probes of connectivities through covalent bonds only. Lately, however, it has been demonstrated that spin ± spin coupling can also be transmitted through various types of hydrogen bonds (HBs). [1±6] Most notably, the sensitivity of NMR experiments has made it possible to detect through-HB coupling constants as low as 0.14 Hz. [3] These findings have stimulated much theoretical work aimed at understanding the factors affecting such coupling constants. [1, 7±11] An obvious extension is that spin ± spin coupling might be detectable even in the case of dispersion-bound van der Waals complexes. In fact, Salsbury and Harris calculated a very small (< 10 3 Hz) coupling for Xe ´ ´ ´ Xe and Xe ´ ´ ´ H. [12] Apart from fundamental implications, exploitation of such couplings might become important in at least two areas, namely the use of optically pumped Xe as a spin probe [12] and structural investigations of host ± guest complexes, which often owe their stability to favorable dispersive interactions. [13] Hence, we have carried out a computational investigation of intermo- lecular spin ± spin couplings in methane ± benzene and ben- zene ± benzene dimers as models. The stabilization energy for the two dimers has been calculated using Gaussian 98 [14] at the MP2/cc-pVTZ level, [15±17] corrected for the basis-set superposition error. [18] The geometry of the individual monomers was kept fixed. Spin ± spin coupling constants were calculated with deMon- NMR, [19] which allows the calculation of the three major contributions to the nuclear spin ± spin coupling: the Fermi contact (FC), the paramagnetic spin-orbit (PSO), and the diamagnetic spin-orbit (DSO) contributions. The spin ± dipole term is often negligible, especially for simple hydrocarbons [20] and when the nuclei are separated by relatively large distances. [19e] The local Vosko-Wilk-Nusair (VWN) exchange correlation functional [21] was used with the IGLO-III basis set. [22] A preliminary set of calculations on the methane ± methane dimer (not reported here) showed that VWN gives essentially the same results as the gradient-corrected Perdew functional (PWP), which is preferred for couplings involving covalent bonds. [19e] Moreover, the VWN functional requires a much more coarse integration grid than the PWP while maintaining the same accuracy, [19] thus reducing the computational time by a factor of five. For these reasons, we have used the VWN functional for the calculations presented here. The perturba- tion (l  0.001) [19e] was placed on the lighter (hydrogen) atom of a methane or benzene molecule, as shown in Figure 1; this yields the couplings with all the essentially equivalent hydro- gen and carbon atoms of the other molecule. The same computational scheme was adopted [7] for through-HB cou- plings in peptide models, in which a very good accuracy was obtained. Further validation is provided by the values of direct couplings ( 1 J C,H ) in the methane, ethylene, and benzene molecules at the PWP/IGLO-III level, which are less than 4% smaller than experimental values. All results are compiled in Table 1. C H I II H R C-i R i-i Figure 1. Schematic representation of the two dimers. As an example of an alkyl ± aromatic interaction, we have considered the methane ± benzene dimer in the configuration I (Figure 1). The geometry of both monomers has been optimized at the MP2/cc-pVTZ level. The interaction energy is reported in Figure 2 as a function of the intermolecular separation R C-i between the carbon atom of the methane and the center of symmetry of the benzene molecule. The MP2 interaction energy has a minimum at R C-i  3.685  with a stabilization energy of 1.40 kcal mol 1 . The J H,H coupling is essentially zero over the distances investigated. On the contrary, a weak but detectable coupling exists between the hydrogen of the methane and the carbon atoms of the benzene molecule, about 0.3 Hz at R C-i  3.3 . For J H,H we have a large compensation between the PSO and DSO terms (Table 1), as previously noted in covalent species, [23] whereas for J C,H the compensation is incomplete. An arrangement of atoms similar to I has been found, for example, in the inclusion complex of tert-butylcalix[4]arene [*] Dr. A. Bagno, Dr. G. Saielli, Prof. G. Scorrano Centro CNR Meccanismi Reazioni Organiche Dipartimento di Chimica Organica Universita Á degli Studi di Padova Via Marzolo 1, 35131, Padova (Italy) Fax: ( 39) 0498275239 E-mail : alex@chor.unipd.it [**] The authors wish to thank V. G. Malkin and O. L. Malkina for providing the deMon-NMR program and for helpful discussions. Table 1. Main contributions to the intermolecular spin ± spin couplings at some selected distances. R [] J HH [Hz] J C,H [Hz] FC PSO DSO FC PSO DSO CH 4 ±C 6 H 6 (I) 4.485 0.00  0.21 0.21 0.02  0.19 0.26 3.685 0.00  0.13 0.12 0.11  0.30 0.41 3.285 0.01  0.02 0.00 0.19  0.42 0.53 C 6 H 6 ±C 6 H 6 (II) 5.100 0.00  0.33 0.32 0.08  0.36 0.46 4.900 0.00  0.30 0.28 0.11  0.42 0.52 4.400 0.04  0.16 0.13 0.07  0.64 0.73