Which ab initio calculation methods describe the charge transfer in ionic liquid vapors? Case study on EMIM-OTF reveals the frontier orbitals and the ionization threshold

Abstract

Time-of-flight mass-spectrometry (TOF-MS) measurements of 1-ethyl-3-methylimidazolium trifluoromethanesulfonate ([EMIM][OTF]) vapors have been conducted in order to gain insight into the VUV (vacuum ultraviolet) absorption thresholds. The experimental data were interpreted with hybrid density-functional theory (DFT), time-dependent DFT (TD-DFT), and several flavours of many-body perturbation theory (MBPT): second-order MBPT, Hedin's GW and Bethe–Salpeter equation (BSE) calculations. To our knowledge, this is the first comprehensive comparison of DFT functionals for an ionic liquid (IL) vapor. More than 60 exchange–correlation approximations, including many range-separated hybrids (RSHs) and optimally tuned variants, were assessed. The theoretical methods predicted a wide range of energies; only the experimental TOF-MS data allowed the truly predictive approaches to be identified. The experimental spectra reveal charge transfer (CT) states at an optical gap of 6.75 eV and a maximum ion yield signal at 8.3 eV. Combining the experiment and theory enabled the re-examination of the ion-pair geometry and the reconstruction of the frontier orbitals of [EMIM][OTF]. The HOMO and LUMO energies were found to be −9.05 eV and −2.30 eV, respectively; energies for HOMO−1 and LUMO+1 were also determined. Although a ΔSCF calculation with the non-hybrid M11-L functional gives a reasonable ionization threshold, ≥50% exact Hartree–Fock (HF) exchange is required to correctly describe both the optical gap and the ultraviolet photoemission spectrum (UPS). The RCAM-B3LYP functional and the Bartlett's QTP family of functionals showed good performance in predicting the CT excitations from TD-DFT calculations. No method was able to predict the proposed LUMO energy, though the M08-SO functional was closest overall. Within the limitations of the present work, the global hybrid PBE-2X functional demonstrates the most consistent overall performance. Its range-separated hybrid (RSH) analogue CAM-PBE50* also performed well for the calculation of CT excitations.