Assessment of atomic partial charge schemes for polarisation and charge transfer effects in ionic liquids

In this work, we assess several popular atomic partial charge schemes with the view of accurately quantifying charge distribution, dipole moments and charge transfer in routinely used ionic liquids (ILs). We investigated a series of ion pairs of imidazolium-based ILs such as [C((1-4))mim]X (where X = Cl, BF(4) and NTf(2)) and ionic clusters of [NMe(4)][BF(4)], [C(1)mim][BF(4)] and [C(1)mim]Cl that were composed of two, four and eight ion pairs. Assessed partial charge schemes include restrained electrostatic potentials (RESP) employing ChelpG, Connolly and Geodesic point selection algorithms, as well as density matrix partitioning schemes including Mulliken, Löwdin and Natural Population Analysis (NPA). The quality of charge distribution was analysed using the following criteria: (1) treatment of symmetry identical atoms, (2) invariance of charge in the imidazolium ring with increasing alkyl chain and (3) recalculation to dipole moments as a measure of electronic polarisation. The RESP schemes such as Connolly and Geodesic clearly outperform the ChelpG scheme as well as the density matrix-based schemes for these three criteria. Calculated partial charges reveal that dipole moments were best represented by the RESP schemes and confirmed the presence of charge transfer in ILs to a various degree. The degree of charge transfer was dependent on anions as well as cluster size. In the ion pairs, the chloride anion showed the largest charge transfer, followed by the NTf(2) and BF(4) anions. In ionic clusters the charge transfer was shown to gradually converge from two to eight ion pairs in the case of the [NMe(4)][BF(4)] and [C(1)mim][BF(4)] ILs to a value, close to that for corresponding ion pairs. In contrast, charge transfer in the [C(1)mim]Cl clusters converges to a lower value, showing an unusually strong inter-ionic bond with the chloride anion. NPA charges were found to perform poorly, with near-unity charges being retained on the anions and cations in ion pairs and ionic clusters. Mulliken and Löwdin charges were shown to be highly basis set dependent and unpredictable with marked fluctuations in partial charges and therefore their use for ILs is particularly discouraged. Ability of the partial charge schemes to capture fluctuations in the dipole moment within the ionic clusters was also examined. The Connolly and Geodesic RESP schemes were found to slightly outperform ChelpG. Evidence to suggest that chloride-based ILs might be poor model systems for ILs is also presented.