Improved Estimates of Host‐Guest Interaction Energies for Endohedral Fullerenes Containing Rare Gas Atoms, Small Molecules, and Cations

Abstract

Endohedral fullerenes have evinced much interest from the fundamental and applications points of view. However, given the nature of the weak interaction between the guest species and the host cage in these confined systems, the interaction energy values obtained using various theoretical methods, and different basis sets vary over a wide range. For example, the reported interaction energy for the HF@C 60 system ranges from À 2.5 kcal/mol to À 14.9 kcal/mol. In the present manuscript, we report reliable interaction energy values for different endohedral fullerenes (He

Electronic Structure Calculations on Endohedral Complexes of Fullerenes: Reminiscences and Prospects

“…In the case of [Li @C ][PF ], the measured diffraction patterns were consistent with a positional disordering of the cation within a shell with a radius of about 1.5 [Å] at 155 [K] and the presence of two crystallographically equivalent positions of Li located 1.40 ± 0.01 [Å] from the cage center at 22 [K] [ 91 ]. These experimental findings are in agreement with the original HF/DZP prediction of the radial displacement amounting to 1.30 [Å] [ 45 ] and the displacements of 1.40, 1.43, and 1.50 [Å] subsequently computed at, respectively, the M06-2X/6-31G** [ 93 ], MN15/cc-pVTZ [ 86 ], and B3LYP/cc-pVTZ [ 94 ] levels of theory.…”

“…Requiring high levels of theory for accurate reproduction, these effects are not reliably accounted for by the presently available approximate functionals of the KS-DFT formalism. For example, although a surprisingly accurate estimate of 172.3 [cm ] was obtained at the MN15/cc-pVTZ level of theory for the red shift of HF, its H counterpart of 142.3 [cm ] turned out to be far less satisfactory [ 86 ]. Ever worse, the same type of calculation predicted a significant (0.189 [Å]) displacement of the He guest from the center of the C cage that is ruled out by direct experimental evidence [ 87 ].…”

“…However, the published attempts in that direction [ 96 , 99 ] were found under closer scrutiny to produce unsatisfactory results [ 100 ]. The same is true about diverse implementations of the KS-DFT formalism that, depending on the functional employed, yield complexation energies that either grossly underestimate [ 86 , 93 ] or overestimate [ 95 , 101 , 102 , 103 , 104 ] their counterparts obtained with rigorous approaches to the electron correlation problem, putting the reliability of the DFT-based calculations in doubt. Although various variants of the MP2 theory fare better in this respect [ 61 , 77 , 96 , 98 , 99 , 101 , 104 , 105 , 106 ], they do not produce sufficiently convergent results, as illustrated by the case of the LiF guest for which the complexation energy computed at the MP2/cc-pVTZ level of theory (−22.8 [kcal/mol] [ 77 ]) is much closer to its HF/4-31G&DZP counterpart of −14.9 [kcal/mol] [ 43 , 45 ] than to that of −50.6 [kcal/mol] obtained from the extrapolation involving the RI-MP2/def2-TZVPP and RI-MP2/def2-QZVPP energies [ 99 ].…”

“…The comparable differences between the uncorrected MP2/cc-pVTZ and DF-LMP2/cc-pVTZ energies arise from the close similarity of the latter to their BSSE-corrected MP2/cc-pVTZ counterparts. It is tempting to attribute this similarity to the assertion that “local correlation methods by design significantly reduce the influence of BSSE on the resulting interaction energies” [ 77 ], which is, alas, invalidated by the comparison of the published uncorrected and BSSE-corrected DLPNO-CCSD(T)/def2-TZVP complexation energies of Na @C (−22.4 vs. −14.6 [kcal/mol]) and CH @C (−15.3 vs. −11.1 [kcal/mol]) [ 86 ]. Thus, it is clear that further improvements in the accuracy of the predictions concerning stabilities of the endohedral complexes of fullerenes hinge upon (admittedly costly) employment of even larger basis sets (likely in conjunction with extrapolation schemes) and tightening of the density-fitting tolerances.…”

“…Only under such circumstances, the chemical accuracy (i.e., that of ca. 1 [kcal/mol]) can be at least approached, the computed complexation energies being of true benchmark quality (which, despite the claims to the contrary, is not attained by the recent DLPNO-CCSD(T)/def2-TZVP data [ 86 ] that, even in the case of He@C , deviate by as much as 3.6 [kcal/mol] from those obtained at the DLPNO-CCSD(T)/cc-pV(T&Q)Z level of theory [ 100 ]).…”