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