Imidazolium-fulleride ionic liquids - a DFT prediction

Ionic liquids (ILs) exhibit tunable physicochemical properties due to the flexibility of being able to select their cation-anion combination from a large pool of ions. The size of the ions controls the properties of the ILs in the range from ionic to molecular, and thus large ions play an important role in regulating the melting temperature and viscosity. Here, we show that the exohedral addition of anionic X^- moieties to C₆₀ (X = H, F, OH, CN, NH₂, and NO₂) is a thermodynamically viable process for creating large X-fulleride anions (C₆₀X)^-. The addition of X^- to C₆₀ is modelled by locating the transition state for the reaction between C₆₀ and 1,3-dimethyl-2X-imidazole (IMX) at the M06L/6-311++G(d,p)//M06L/6-31G(d,p) level. The reaction yields the ion-pair complex IM⁺⋯(C₆₀X)^- for X = H, F, OH, CN, NH₂, and NO₂ and the ordered pair of (activation free energy, reaction free energy) is found to be (14.5, 1.1), (6.1, 3.1), (16.7, 2.3), (14.7, -7.9), (27.9, 0.5) and (11.9, 12.4), respectively. The low barrier of the reactions suggests their feasibility. The reaction is slightly endergonic for X = H, F, OH, and NH₂, while X = CN shows a significant exergonic character. The X-fulleride formation is not observed when X = Cl and Br. The ion-pair interactions (E_ion-pair) observed for IM⁺⋯(C₆₀X)^- range from -64.0 to -73.0 kcal mol^-1, which is substantially lower (∼10%) than the typically reported values for imidazolium-based ionic liquids such as [EMIm]⁺[trz]^-, [EMIm]⁺[dc]^-, [EMIm]⁺[dtrz]^-, and [EMIm]⁺[NH₂tz]^-. The quantum theory of atoms in molecules (QTAIM) analysis showed that the C-X bonding in (C₆₀X)^- is covalent, while that in (IM⁺⋯X^-)⋯C₆₀ (for X = Cl and Br) is non-covalent. Furthermore, molecular electrostatic potential (MESP) analysis showed that the X-fulleride could behave as a large spherical anion due to the delocalization of the excess electron in the system over the entire carbon framework. The large anionic character of the X-fulleride is also revealed by the identification of several close lying local energy minima for the IM⁺⋯(C₆₀X)^- ion-pair. The low E_ion-pair value, the significant contribution of dispersion to the E_ion-pair and the spherical nature of the anion predict low-melting point and highly viscous IL formation from X-fullerides and the imidazolium cation.

Quantum states of the endohedral fullerene Li+@C60 surrounded by anions: energy decomposition analysis of nuclear wave functions

Lithium is the lightest metal element. To date, little is known about its quantized nuclear motion in nanoscale porous structures. Endohedral fullerene Li+@C60 is an ideal porous system for studying such a quantized motion. Recent studies suggest that the anions surrounding the C60 cage exterior and a slight cage distortion can alter the potential field in the cage interior and thus the nuclear wave function of Li+. It has yet to be clarified how the electronic state, particularly the flexible π electron cloud of the C60 cage, is associated with (de)localization of the Li+ wave function. Focusing on the [Li+@C60]PF6- crystal, we constructed a local structure model considering the PF6- coordination and the cage distortion. We developed model functions that fit the post-Hartree-Fock potential energy surface for the Li+ motion and its decomposed components, four interaction energy surfaces. The decomposition clarified the origins of the shell-like adsorbent potential and the potential wells therein. The Fourier grid Hamiltonian method allowed us to obtain low-energy Li+ wave functions. The ground state is nearly two-fold degenerate, and its wave functions are mostly localized underneath two C6 rings, near the disordered sites of Li+ in the X-ray crystal structure. By extending the energy decomposition analysis within the clamped-nuclei approximation to incorporate the delocalization of nuclear wave functions, we demonstrated that the ground state is stabilized by the polarization, dispersion, and electrostatic interactions. Beyond the common picture of Li+ moving in a classical electrostatic field, our approach will deepen the understanding of the flexible Li+ wave function confined in a polarizable porous structure by various intermolecular interactions.

Theoretical characterization of supramolecular complexes formed by fullerenes and dimeric porphyrins

Intramolecular stacking is very strong in dimeric porphyrins. However, in solution they are able to inhibit folding and can trap fullerenes with very high association constants. Diabatic interaction energies can be a useful approach to evaluate the strength of porphyrin/fullerene supramolecular complexes.

A Least-Squares Commutator in the Iterative Subspace Method for Accelerating Self-Consistent Field Convergence

A least-squares commutator in the iterative subspace (LCIIS) approach is explored for accelerating self-consistent field (SCF) calculations. LCIIS is similar to direct inversion of the iterative subspace (DIIS) methods in that the next iterate of the density matrix is obtained as a linear combination of past iterates. However, whereas DIIS methods find the linear combination by minimizing a sum of error vectors, LCIIS minimizes the Frobenius norm of the commutator between the density matrix and the Fock matrix. This minimization leads to a quartic problem that can be solved iteratively through a constrained Newton's method. The relationship between LCIIS and DIIS is discussed. Numerical experiments suggest that LCIIS leads to faster convergence than other SCF convergence accelerating methods in a statistically significant sense, and in a number of cases LCIIS leads to stable SCF solutions that are not found by other methods. The computational cost involved in solving the quartic minimization problem is small compared to the typical cost of SCF iterations and the approach is easily integrated into existing codes. LCIIS can therefore serve as a powerful addition to SCF convergence accelerating methods in computational quantum chemistry packages.

Versatile interactions of boron fullerene B80with gas molecules

Stable all-boron fullerene B₈₀supplements a family of elemental cage molecules.

The tricyanomethanide anion favors low viscosity of the pure ionic liquid and its aqueous mixtures

Low-viscous ionic liquids favor new applications.