Stefan Grimme

Quantum chemistry has firmly established itself as a reliable method for investigating present-day problems in biological and materials chemistry. Understanding inclusion complexes represents one of the cutting edges of simulation sciences. In this tutorial review, we focus on the role and composition of non-covalent interactions, which are essential when studying inclusion complexes. A selected set of recently developed pragmatic methods used to study inclusion complexes are then surveyed including e.g. dispersion corrected DFT, double-hybrid functionals and spin-component scaled MP2. Finally, three case studies are outlined: (a) endohedral fullerene complexes, (b) buckyball catcher and (c) resorcinarene capsule. These case studies were carefully chosen to help illustrate how one may accurately investigate inclusion complexes, at a modest computational cost, using state-of-the-art quantum chemical methods (67 references).

The time-dependent density functional theory (TD-DFT) double-hybrid methods TD-B2-PLYP and TD-B2GP-PLYP are applied to five linear and 12 nonlinear polycyclic aromatic hydrocarbons. The absolute errors compared to experiment for the two lowest-lying ¹L_a and ¹L_b excited states are evaluated and it is also tested whether the energetic order of those states and their energy difference is reproduced correctly. The results are compared to published CC2, global hybrid, and long-range corrected hybrid TD-DFT results. The two double-hybrids outmatch the other methods in terms of absolute and relative accuracy without an empirical adjustment of parameters. Although of different electronic character, both types of states are described on an equal footing by the double-hybrids. Particularly, the B2GP-PLYP functional yields very good results, which is in accordance with previous benchmarks.

Reaction of the N,N′-diisobutyl-substituted benzannulated N-heterocyclic plumbylene (NHPb) 1 with [Pd(PPh₃)₄] and [Pt(PPh₃)₄] gave the complexes [M(NHPb)(PPh₃)₃] (M = Pd [2], Pt [3]). X-ray diffraction studies of both complexes showed an angle of ∼125° between the plumbylene plane and the transition-metal–Pb axis, indicating coordination of the transition metal to the empty π orbital of the plumbylene Pb atom. The experimentally determined metric parameters of complexes [2] and [3] are discussed on the basis of DFT calculations.

Potential energy curves for five complexes with weak to medium strong hydrogen bonds have been computed with dispersion corrected DFT methods. The electronic density based vdW-DF2 and VV10 van der Waals density functionals have been tested, as well as an atom pair-wise correction method (DFT-D3). The short-range exchange–correlation components BLYP and rPW86-PBE together with the extended aug-cc-pVQZ basis sets have been employed. Reference data have been computed at the estimated CCSD(T)/CBS(aQ-a5) level of theory. The investigated systems are CH₄·NH₃, Cl₃CH·NH₃, NH₃·NH₃, CH₃F·C₂H₂ and CH₃F·H₂O with binding energies ranging from −0.7 kcal mol⁻¹ to −5.5 kcal mol⁻¹. We find that all dispersion corrected methods perform reasonably well for these hydrogen bonds, but also observe distinct differences. The BLYP-D3 method provides the best results for three out of five systems. For the fluorinated complexes, the VV10 method gives remarkably good results. The vdW-DF2 method yields good interaction energies similar to the other methods (mean average deviation of 0.2–0.3 kcal mol⁻¹), but fails to provide accurate equilibrium separations. Based on these results and previous experience with the computation of non-covalent interactions, for large-scale applications we can recommend DFT-D3 based structure optimizations with subsequent checking of interaction energies by single-point VV10 computations. Comparison of the DFT-D3 and VV10 results leads to the conclusion that the short-range exchange–correlation functional and not the dispersion correction mainly determines the achievable accuracy.