Binding energy and the photoelectron spectra
Figure 2 shows spectra obtained in the experimental XPS measurements in contrast to those plotted using the BE calculated via the ΔKS method. Note that an experimental measurement produces a spectrum which is then interpreted by researchers so that the BE values obtained by thedeconvolution are manually assigned to individual atoms. On the contrary, calculations give BE values for individual atoms and the spectrum is obtained by convolution of their Gaussian functions with a standard deviation of 0.5 eV.
Furthermore, during experiments, the measured spectrum might shift due to the instability of spectrometer and studied IL as well as due to photoelectron emission. To eliminate the systematic drift, measured BE values are corrected by shifting the spectrum so that the aliphatic C(1s) electron BE value equals to a reference value of 285.0 or 285.3 eV (see Ref 7 and references therein). The choice of the reference is disputable, and it introduces a man-made difference between the shifted experimental and absolute computational values. Also, the reference energy levels in experiment and computation – Fermi and vacuum energy, respectively – do not necessarily match each other. Table 1 shows that the calculated ΔKS BEs for the aliphatic carbon are higher than the reference value of 285 eV by 4–5 eV. Most of that difference is an artefact, while a part is due to the inaccuracy of the method. For example, in the case of ε(1s) method, the difference can be dumped by correcting the result with the Perdew–Zunger self-interaction error correction (see Table 2).45,46 For a fair comparison, below we denote as relative BEs all values shifted so that the aliphatic C(1s) electron BE value equals to the reference value. When both experimental and predicted spectra are shifted in the same way, as in Figure 2, a reasonably good agreement between the experimental data and ΔKS results becomes visible. Bearing in mind that an ion pair is the simplest model of a bulk IL, we leave the explanation of minor deviations to future work on modelling of bulk ILs.
Figure 3 depicts isosurfaces of the charge density difference between the positively charged excited state and the neutral ground state of EMImBF4 – the positive value corresponds to a loss of electron density. Recently Golze et al. hypothesised that the negative charge at an anion could displace to neutralise the core-hole at a cation atom in the excited ion pair.18 As can be seen in Figure 3, there is no notable partial charge transfer between the BF4 anion and the EMIm+ cation; a small redistribution of the electron density happens only in the vicinity of the carbon atom with a full core-hole.
Figure 4 compares experimental and theoretical spectra for EMImBF4, which is one of the most studied ILs by the XPS method. All spectra shown have a very similar shape, yet, as can be anticipated, there is a difference in the sequence of the peaks associated with specific carbon atoms. All BE values are given in Table 1 as well as marked in Figure 4 with rounded numbers corresponding tointer atoms C1, C2, and C3 of the imidazolium ring, chainatoms C4 and C5 connected to the nitrogen atoms, an aliphatic C6 (as defined in Figure 3). The IUPAC atom numbering is also given in Table 1 to simplify the comparison with the literature.
In comparison to the previously reported BE sequences data for EMImBF4, the ΔKS method swaps the order of C2/C3 and C4/C5 peaks (see Table 2 and Figure 4). As stated above, the assignment of peaks to certain atoms is somehow arbitrary. In case of imidazolium-based ILs, the widely accepted order originates from work 47, where no clear reasoning is given. Later, Kruusma et al. and Reinmöller et al. used calculated C(1s) Kohn–Sham orbital energies for reconstructing the experimental spectra.3,16 Accordingly, their results are in agreement with our calculated ε(1s) BEs position in the spectra. However, BEs obtained via Eq. 2 are only approximate, as the negative eigenvalues of orbitals below εHOMO do not precisely correspond to the vertical ionisation potential.48Moreover, the ε(1s) method neglects the electron density relaxation effects in response to the core-hole creation illustrated in Figure 3. It was also previously shown that ΔKS method provides much more accurate predictions than Janak’s or Koompan’s theorem-based calculations.21 Finally, the most recent difference spectroscopy study resolved the order of peaks in favour of the ΔKS method.49 We conclude that the ΔKS method does give more reliable results than the ε(1s) method.
Figure 5 demonstrates a correlation between the relative ΔKS BEs and the relative ε(1s) BEs for forty ion pairs. Despite a good correlation withR 2 = 0.93, the standard deviation of 0.32 eV allows swapping the order of peaks in spectra, as can be seen in case of EMImBF4. When the order of BEs is essential, the ΔKS method or even better, the GW method should be used.21,50,51 Nonetheless, because the ε(1s) method is computationally cheaper and more accessible, it can be used for predicting XPS spectra of larger systems as well as in longer simulations, especially with periodic boundary conditions. GW or ΔKS methods are currently impractical for large systems. The most recent implementation of the GW method for massively parallel execution applies to systems up to 100 atoms.18,52 The ΔKS method requires additional calculations for each BE value, making it substantially more resource-demanding than the ε(1s) method. Therefore, the use of the ε(1s) method is justified for large systems, e.g.complex interface models calculated with DFT (with or without periodic boundary conditions) or simulated with DFT-based molecular dynamics, discussed in Refs 53–57. ε(1s) method might also be useful when the changes in the XPS spectra upon variation of the chemical composition are a focus of a study, for example, in studies of interfacial reactions.58