# A Buckycatcher in Solution—A Computational Perspective

^{*}

## Abstract

**:**

_{60}H

_{28}) in solution using quantum chemical models. We investigate the conformational equilibria in several media and the effects that molecules of solvent might have in interconversion barriers between the different conformers. These are studied in a hypothetical gas phase, in the dielectric of a solvent, as well as with hybrid solvation. In the latter case, due to a disruption of π-stacking interactions, the transition states are destabilized. We also evaluate the complexation of the buckycatcher with solvent-like molecules. In most cases studied, there should be no adducts formed because the enthalpy driving force cannot overcome entropic penalties.

## 1. Introduction

_{60}and C

_{70}[8,9,10,11,12,13,14,15,16,17]. This curvature is key for binding, since it promotes strong ball–socket π interactions that keep the complex together [8].

^{7})) makes it impracticable to use on systems of the size of C

_{60}, let alone a complex of this fullerene with the corannulene pincer.

## 2. Results

#### 2.1. Systems Studied and Nomenclature

_{60}H

_{28}is described by four main conformations. The most known of these is the structure in which the two corannulene units point inwards to form a convex shape (ii for in–in). Other open conformations may be found by giving the pincers a concave shape (ee for ex–ex) or to round the arms of the pincers in the same direction (ie). The latter conformer may exist furthermore in a tight/closed form (iet).

_{rx}= E

_{AB}– E

_{A}– E

_{B}, and the binding energy E

_{bind}is the negative of E

_{rx}. Consequently, a negative binding energy describes an unstable complex.

#### 2.2. Conformations of the Corannulene Pincer

_{P}in Figure 2) as defined by Zhao and Truhlar [12].

_{P}); however, π-stacking forces in iet are stronger and hold the pincer’s arms closer together. Our R

_{P}values match reasonably well with the literature data [12,13]—in particular, the GFN2-xTB calculations.

#### 2.3. Equilibria between Conformers

#### 2.4. Interconversion between Conformers

#### 2.5. Explicit Interaction with Toluene

_{P}values than does the latter.

_{60}H

_{28}. Comparing with the free case, the presence of toluene induces the pincers to come together for the transition between ie and ii (R

_{P}of 8.09 Å instead of 12.88), which forces the transitory arm to bend slightly inwards. In the case of the transition between ee and ie, the presence of toluene changes the R

_{P}by less than 0.05 Å.

#### 2.6. Binding to Tetrachloroethane

_{P}value for the complex TCA@ii optimized at the PM6-D3H4X level is 7.50 Å, whereas, at PM6-D3H+, it takes the value of 6.85 Å. As PM6-D3H4X and GFN2-xTB are two completely disparate methods and yet they give identical results, we tend to trust these more in detriment to the PM6-D3H+ data.

#### 2.7. Caging of Other Solvents

_{60}H

_{28}, the presence of a single molecule of toluene will promote the closing of the pincer’s arms, forming a van der Waals cage for the solvent. The value of R

_{P}when toluene is inside the pincer is 6.61 Å, which should be compared against the 12.01 Å for the free catcher in vacuum. A similar behavior was observed for all other solvents studied, where, however, R

_{P}varied mainly according to the volume of the caged molecule. We obtained R

_{P}values of 6.68 Å for acetonitrile, 6.84 Å for dichloromethane, 7.21 Å for chloroform, 7.32/9.31 for tetrachloroethane (respectively for TCA and TCB) and 8.01 Å for n-hexane.

_{P}reported above. The key question is then not whether binding is possible but rather how strong the enthalpy is compared to the entropic penalty for forming the adduct.

## 3. Discussion

_{3}@C

_{60}H

_{28}is within 1 kcal/mol of the higher-level ones. Still, the deviations between methods in the binding of acetonitrile and in toluene are too large. Contrary to the case of chloroform, these last two systems are dominated by π dispersion. By construction, DLPNO methods use MP2 for the so-called weak pairs. Weak pairs consist of contributions from doubly excited configurations, where the orbitals involved in the excitation are reasonably distant from one another. Each weak pair carries significantly less correlation energy than any strong pair, which builds the rationale for treating the former at a lower level of theory.

_{60}. If we assume a direct aggregation reaction, then we correct our previous GFN2-xTB results by −1.5 kcal/mol, resulting in the value of −14.4 kcal/mol.

_{60}D PhMe + C

_{60}@catcher), the Gibbs free energy increases to −9.6 kcal/mol. Both values are significantly off from the −4.8 kcal/mol obtained experimentally [11]. From those 2 values, one could propose that more molecules of toluene might be involved in the process. Even if the resulting Gibbs energies match the experimental data, enthalpies and entropies will not. The experimental change in entropy is very close to zero [11], which indicates a 1:1 exchange reaction.

_{60}. The advantage of this system is that it is very similar to the present case studies but also there is experimental data available: corannulene:C

_{60}adducts do not form spontaneously in the gas phase [43].

_{60}aggregate at the DLPNO-CCSD(T) level, all the data herein discussed shows systematically that binding energies calculated with GFN2-xTB are lower than those at the DLPNO-CCSD(T) level. Thus, we expect that using the linear scaling variant of CCSD(T) would make the Gibbs free energies for forming the corannulene:C

_{60}adducts even more negative. Based on this analysis, it seems plausible that the DLPNO-CCSD(T) binding energies significantly contribute to the errors.

## 4. Materials and Methods

^{−8}E

_{h}for energies and 2.5 × 10

^{−5}E

_{h}/a

_{0}for gradients. The Hessian was approximated using the method of Lindh et al. [45]. Transition states were optimized using Baker’s Rational Function Optimization (RFO) [46] with convergence criteria of 10

^{−5}E

_{h}for energies and 5.0 × 10

^{−4}E

_{h}/a

_{0}for gradients. The geometry optimization of transition states used the numerical Hessian instead of Lindh’s.

^{−1}. Absolutely no vibrational frequency was disregarded in any part of this work. This speaks for the unprecedented high accuracy of the structures we are working with.

## 5. Conclusions

## Supplementary Materials

^{−1}mol

^{−1}.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 4.**Thermodynamic functions for the corannulene pincer conformers with respect to species ie. Data generated from the PM6-D3H+ (

**left**) and GFN2-xTB (

**right**) calculations.

**Figure 5.**Energy (in kcal/mol) diagram for the interconversion of the corannulene pincer conformers according to PM6-D3H4X, PM6-D3H+ and GFN2-xTB. Only stationary points along the energy surface were calculated.

**Figure 6.**Structure of the two conformers of tetrachloroethane considered here: (

**left**), conformer A and (

**right**), conformer B.

**Table 1.**R

_{P}distances (in Å) for the several conformers of the corannulene pincer according to the four methods used in this study.

PM6 | PM6-D3H4X | PM6-D3H+ | GFN2-xTB | |
---|---|---|---|---|

ii | 11.08 | 10.49 | 10.44 | 12.01 |

ee | 14.61 | 14.28 | 14.49 | 14.91 |

ie | 12.90 | 12.49 | 12.56 | 13.46 |

iet | --- | 3.93 | 3.72 | 3.61 |

**Table 2.**Energy differences between conformers of the buckycatcher according to several methods. All values in kcal/mol. CCSD and CCSD(T) calculations evaluated on the PM6-D3H4X geometries, whereas the M06-2X calculations were performed on the GFN2-xTB geometries.

PM6 | PM6-D3H4X | PM6-D3H+ | GFN2-xTB | M06-2X | CCSD | CCSD(T) | |
---|---|---|---|---|---|---|---|

ii | −0.1 | −0.2 | −0.2 | 0.4 | −0.1 | −0.2 | −0.2 |

ee | 0.2 | 0.3 | 0.3 | −0.3 | 0.1 | 0.3 | 0.3 |

ie | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |

iet | --- | 0.8 | 2.0 | −4.2 | 7.7 | −4.0 | −6.7 |

**Table 3.**Gibbs free energies for the interconversion between different conformers and the species ie in gas phase (for reference) and in toluene at 300 K. All energies are given in kcal/mol.

$\mathit{ie}\text{}\rightleftharpoons \text{}\mathit{ii}$ | $\mathit{ie}\text{}\rightleftharpoons \text{}\mathit{ee}$ | $\mathit{ie}\text{}\rightleftharpoons \text{}\mathit{iet}$ | |
---|---|---|---|

$\Delta {G}_{gas}^{GFN2-xTB}$ | 1.3 | 0.1 | −2.4 |

$\mathsf{\Delta}{G}_{\mathrm{gas}}^{PM6-D3H4X}$ | 0.0 | 0.7 | 1.6 |

$\mathsf{\Delta}{G}_{\mathrm{gas}}^{PM6-D3H+}$ | −0.1 | 0.7 | 3.0 |

$\mathsf{\Delta}{G}_{\mathrm{CH}2\mathrm{Cl}2}^{GFN2-\mathrm{xTB}/\mathrm{ALPB}}$ | 1.3 | 0.2 | 3.0 |

$\mathsf{\Delta}{G}_{\mathrm{CHCl}3}^{GFN2-\mathrm{xTB}/\mathrm{ALPB}}$ | 1.3 | 0.2 | 4.7 |

$\mathsf{\Delta}{G}_{\mathrm{MeCN}}^{GFN2-\mathrm{xTB}/\mathrm{ALPB}}$ | 1.3 | 0.2 | 6.1 |

$\mathsf{\Delta}{G}_{\mathrm{PhH}}^{GFN2-\mathrm{xTB}/\mathrm{ALPB}}$ | 1.3 | 0.2 | 4.6 |

$\mathsf{\Delta}{G}_{\mathrm{PhOH}}^{GFN2-\mathrm{xTB}/\mathrm{ALPB}}$ | 1.3 | 0.2 | 4.0 |

$\mathsf{\Delta}{G}_{PhMe}^{GFN2-\mathrm{xTB}/ALPB}$ | 1.3 | 0.2 | −2.0 |

$\mathsf{\Delta}{G}_{PhMe}^{PM6-D3H4X/ALPB}$ | 0.0 | 0.7 | 2.0 |

$\mathsf{\Delta}{G}_{PhH}^{PM6-D3H4X/ALPB}$ | 0.0 | 0.7 | 8.6 |

$\mathsf{\Delta}{G}_{PhMe}^{PM6-D3H+/ALPB}$ | −0.1 | 0.7 | 3.4 |

$\mathsf{\Delta}{G}_{PhH}^{PM6-D3H+/ALPB}$ | −0.1 | 0.7 | 9.9 |

$\mathsf{\Delta}{G}_{PhMe}^{GFN2-\mathrm{xTB}/COSMO}$ | 1.3 | 0.0 | 0.0 |

$\mathsf{\Delta}{G}_{PhMe}^{PM6-D3H4X/COSMO}$ | 0.0 | 0.5 | 4.0 |

$\mathsf{\Delta}{G}_{PhMe}^{PM6-D3H+/COSMO}$ | −0.1 | 0.5 | 5.3 |

**Table 4.**Energetics for the main species in the system at the CCSD and CCSD(T) level on the PM6-D3H4X and GFN2-xTB geometries.

PM6-D3H4X Geometries | GFN2-xTB Geometries | |||
---|---|---|---|---|

CCSD | CCSD(T) | CCSD | CCSD(T) | |

TS (ii → ie) | 9.1 | 9.5 | 8.5 | 8.9 |

TS (ie → ee) | 9.5 | 9.9 | 8.9 | 9.3 |

**Table 5.**Binding energies, enthalpies (gas), entropies (gas) and Gibbs free energies (gas and in toluene) for the formation of aggregates between the conformers of C

_{60}H

_{28}corannulene pincers with toluene, in which the latter is caged within the former. Thermodynamic data were calculated at 300 K, all energies are in units of kcal/mol, whereas entropies are in units of cal K

^{−1}mol

^{−1}.

PhMe@ii | PhMe@ie | PhMe@ee | |
---|---|---|---|

$\Delta {E}_{bind}^{GFN2-xTB}$ | 17.5 | 14.8 | 12.2 |

$\mathsf{\Delta}{E}_{\mathrm{bind}}^{PM6-D3H4X}$ | 9.7 | 13.5 | 10.7 |

$\mathsf{\Delta}{E}_{\mathrm{bind}}^{PM6-D3H+}$ | 10.5 | 14.4 | 11.0 |

$\mathsf{\Delta}{S}_{gas}^{GFN2-\mathrm{xTB}}$ | −44.3 | −45.0 | −40.8 |

$\mathsf{\Delta}{S}_{gas}^{PM6-D3H4X}$ | −43.3 | −44.1 | −43.3 |

$\mathsf{\Delta}{S}_{gas}^{PM6-D3H+}$ | −43.9 | −46.8 | −43.6 |

$\mathsf{\Delta}{G}_{\mathrm{gas}}^{GFN2-\mathrm{xTB}}$ | −3.5 | −0.7 | 0.4 |

$\mathsf{\Delta}{G}_{\mathrm{gas}}^{PM6-D3H4X}$ | 3.8 | 0.3 | 3.1 |

$\mathsf{\Delta}{G}_{\mathrm{gas}}^{PM6-D3H+}$ | 3.5 | 0.5 | 2.8 |

$\mathsf{\Delta}{G}_{\mathrm{PhMe}}^{GFN2-\mathrm{xTB}/\mathrm{ALPB}}$ | 3.1 | 4.4 | 2.6 |

$\mathsf{\Delta}{G}_{\mathrm{PhMe}}^{PM6-D3H4X/COSMO}$ | 6.8 | 3.6 | 5.1 |

$\mathsf{\Delta}{G}_{\mathrm{PhMe}}^{PM6-D3H+/COSMO}$ | 6.5 | 3.8 | 4.8 |

**Table 6.**Gibbs free energies (kcal/mol) for the formation of buckycatcher fullerene complexes according to several semi-empirical methods in gas and with several solvation models. Conformer averaged data with the conformational entropy considered. Structures of conformers in Figure 6.

TCA@C_{60}H_{28} | TCB@C_{60}H_{28} | TC@C_{60}H_{28} | |
---|---|---|---|

$\Delta {H}_{gas}^{GFN2-xTB}$ | −18.8 | −17.4 | −18.3 |

$\mathsf{\Delta}{H}_{gas}^{PM6-D3H4X}$ | −20.7 | −18.0 | −20.4 |

$\mathsf{\Delta}{H}_{\mathrm{gas}}^{PM6-D3H+}$ | −25.1 | −24.0 | −24.7 |

$\mathsf{\Delta}{S}_{gas}^{GFN2-\mathrm{xTB}}$ | −48.0 | −47.1 | −45.8 |

$\mathsf{\Delta}{S}_{gas}^{PM6-D3H4X}$ | −49.4 | −49.6 | −48.4 |

$\mathsf{\Delta}{S}_{gas}^{PM6-D3H+}$ | −51.6 | −51.4 | −50.5 |

$\mathsf{\Delta}{G}_{\mathrm{gas}}^{GFN2-\mathrm{xTB}}$ | −4.4 | −3.3 | −4.5 |

$\mathsf{\Delta}{G}_{\mathrm{gas}}^{PM6-D3H4X}$ | −5.8 | −3.1 | −5.9 |

$\mathsf{\Delta}{G}_{\mathrm{gas}}^{PM6-D3H+}$ | −9.6 | −8.6 | −9.6 |

$\mathsf{\Delta}{G}_{\mathrm{CH}2\mathrm{Cl}4}^{GFN2-\mathrm{xTB}/\mathrm{ALPB}}$ | −0.2 | 0.2 | −0.6 |

$\mathsf{\Delta}{G}_{\mathrm{CH}2\mathrm{Cl}4}^{PM6-D3H4X/ALPB}$ | −1.0 | 0.8 | −1.2 |

$\mathsf{\Delta}{G}_{\mathrm{CH}2\mathrm{Cl}4}^{PM6-D3H+/ALPB}$ | −4.6 | −4.4 | −4.9 |

$\mathsf{\Delta}{G}_{\mathrm{CH}2\mathrm{Cl}4}^{GFN2-\mathrm{xTB}/\mathrm{COS}\mathrm{MO}}$ | −0.0 | 0.3 | −0.5 |

$\mathsf{\Delta}{G}_{\mathrm{CH}2\mathrm{Cl}4}^{PM6-D3H4X/COSMO}$ | −1.4 | 0.7 | −1.5 |

$\mathsf{\Delta}{G}_{\mathrm{CH}2\mathrm{Cl}4}^{PM6-D3H+/COSMO}$ | −5.1 | −4.7 | −5.3 |

**Table 7.**Enthalpies (kcal/mol), entropies (cal/[K.mol]) and Gibbs free energies (kcal/mol) for the formation of complexes between the buckycatcher and several solvents at 300 K. Dissociation constants (K

_{d}) calculated in solution.

$\mathbf{\Delta}\mathit{H}$ | $\mathbf{\Delta}\mathit{S}$ | $\mathbf{\Delta}\mathit{G}$ | $\mathbf{\Delta}{\mathit{G}}^{\mathit{A}\mathit{L}\mathit{P}\mathit{B}}\text{}$ | ${\mathbf{K}}_{\mathit{d}}\text{}$ | |
---|---|---|---|---|---|

MeCN | −9.3 | −29.5 | −0.4 | 7.7 | 3.7 × 10^{5} |

CHCl_{3} | −16.2 | −39.3 | −4.4 | 1.4 | 9.9 |

CH_{2}Cl_{2} | −13.0 | −37.0 | −1.9 | 1.0 | 5.5 |

n-C_{6}H_{14} | −12.2 | −41.1 | 0.1 | 5.9 | 2.0 × 10^{4} |

TCA | −21.2 | −46.0 | −7.4 | −2.3 | 2.3 × 10^{−2} |

TCB | −19.8 | −45.4 | −6.2 | −1.8 | 5.4 × 10^{−2} |

C_{2}H_{2}Cl_{4} | −18.3 | −45.8 | −4.5 | −0.6 | 3.8 × 10^{−1} |

**Table 8.**Binding energies in kcal/mol for the complexes between the buckycatcher and acetonitrile and chloroform. Data obtained based on GFN2-xTB geometries.

GFN2-xTB | CCSD | CCSD(T) | |
---|---|---|---|

MeCN | 9.3 | 12.6 | 14.6 |

CHCl_{3} | 16.1 | 17.0 | 19.9 |

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**MDPI and ACS Style**

Menezes, F.; Popowicz, G.M.
A Buckycatcher in Solution—A Computational Perspective. *Molecules* **2023**, *28*, 2841.
https://doi.org/10.3390/molecules28062841

**AMA Style**

Menezes F, Popowicz GM.
A Buckycatcher in Solution—A Computational Perspective. *Molecules*. 2023; 28(6):2841.
https://doi.org/10.3390/molecules28062841

**Chicago/Turabian Style**

Menezes, Filipe, and Grzegorz M. Popowicz.
2023. "A Buckycatcher in Solution—A Computational Perspective" *Molecules* 28, no. 6: 2841.
https://doi.org/10.3390/molecules28062841