**3. Theoretical**

Geometric parameters and DOS of the unit cells were calculated by the density functional theory using the Quantum ESPRESSO Software [39] and the nonlocal exchange-correlation functional in the Perdew-Burke-Ernzerhof parameterization [40]. The interactions between ionic cores and electrons were described by the projected augmented wave (PAW) method [41] with the kinetic energy cutoff *E*cut = 40 Ry (320 Ry for the charge-density cutoff) for a plane-wave basis set. The Gaussian spreading for the Brillouin-zone integration was 0.02 Ry; the Marzari-Vanderbilt cold smearing was used [42], and the van der Waals (vdW) corrections were included [43].

**4. Inelastic electron scattering in near-surface layer**

with a matrix element *f(E, σ)*:

to each other due to strongly localized vacant states at *E*<sup>F</sup>

∫

0 *E*

*Woff*(*E*) = *f*(*E*, *σ*) *σVB*(ϕ − *E*)

The shake-off CEE moves *σ*VB to free DOS at the vacuum level. According to the Rutherford

angles *Θ* [48, 49]. The probability *W(E)*off in Eq. (1) therefore includes one-dimensional (1D) free DOS. According to Van Hove singularities, the 1D DOS is equal to 0, infinity, and

respectively, and because of domination of the equal *d*zx, *d*zy, and *d*xy states in total DOS [30]. An agreement between experimental and simulated spectral fragments in **Figure 2** implies regular involvement of the Pt DOS into CEE events, as well as similar matrix elements *f(E, σ)* for different partial densities of states (pDOS) in Eq. (1) and no symmetry ban for CEE transitions.

**Figure 2(b)** demonstrates tracing over the adsorbed hydrogen atoms, which is beyond AES and XPS facilities. It is important to note that none of the satellites in the DAPS spectra was assigned to the interatomic CEE transition (from the VB of the adsorbed species to free state of

*<sup>E</sup>* <sup>−</sup> *EF* <sup>−</sup> <sup>ϕ</sup>*Pt* at the energies below, at, and above the vacuum level, respectively [50], as shown in **Figure 2(a)** (where ϕ*Pt* = 5.6 eV is the work function of Pt(100) [51]). This provides the resonant CEE behavior and multiple tracing over the adsorbed species (including hydrogen atoms and reaction intermediates) around different thresholds [8–11]. The shake-off satellite of adsorbed particle is an intense peak of the 1–2 eV base-width and coverage-proportional intensity, which is located at its ionization potential above the Pt threshold. The DAPS spectra in **Figure 2** particularly exhibit the σ state of the *H*ad atom and 1π, 5σ, and 4σ states of the *CO*ad molecule, which fit published UPS data in **Table 1** [52–55]. Similar accordance between the DAPS and UPS measurements has been found for the adsorbed O, N, NO, and NH species [7]. The Pt shake-off spectrum in **Figure 2(b**, **c)** was constructed on the basis of DFT data as follows. The VB was inverted (because the larger *σ*VB the larger *W*off*(E)* in Eq. (1), and the larger the spectral dip); differentiated, and shifted to the higher energy by ϕ*Pt*. Adsorbed layer makes significant contribution into the DAPS spectrum due to superior surface sensitivity of this technique, whose probing depth 2–3 ML is determined by half the electron mean free path in a solid. The Pt shake-up spectrum in **Figure 2(b)** corresponds to convolution of the occupied and vacant *d* states by Eq. (1). The calculated Pt shake-up and shake-off spectra in **Figure 2** are close

energy relative to *E*<sup>F</sup>

relation *ds*/*d* ~sin<sup>4</sup>

\_\_\_\_\_\_\_\_\_

1/ √

*Wup*(*E*) <sup>=</sup>

DAPS theory directs core and primary electrons to nearest vacant states above *E*<sup>F</sup>

larger is the vacant DOS, the larger is the spectral dip, and the lack of free DOS gives no signal. The DAPS technique discovers all channels of the elastic electron consumption, which are specifically related to CEE phenomena and consisted of shake-up and shake-off VB transitions coupled with the threshold core-level excitation of an atom. These channels are electron transitions from the ground *σ*VB to vacant DOS *σ*Vac and the vacuum level, whose probability *W(E)* is in proportion to the corresponding convolution and *σ*VB, respectively, on the absolute

*f*(*E*, *σ*) *σVB*(−*E*) *σVac*(*E* − *ε*)*d*

(*Θ*/2), the cross-section for the nonrelativistic scattering is efficient for small

Hidden Resources of Coordinated XPS and DFT Studies http://dx.doi.org/10.5772/intechopen.80002

and the 1D DOS at the vacuum level,

[32]. The

151

(1)

The Pt DOS was calculated using the Perdew-Burke-Ernzerhof functional [44] and the PAW with the optimized lattice constant 3.99 Å. The kinetic energy cutoff *E*cut = 40 Ry and a 12 × 12 × 12 grid of Monkhorst-Pack k-points were applied.

HOPG was modeled with a bilayer C24 unit cell of the Bernal and Hexagonal (*hex*) structure (**Figure 1**) and optimized lattice parameters (*a* = 2.46 Å × 3, *b* = 2.46 Å × 2) [45].

Half-fluorinated graphite, pristine and imbedded with the Br<sup>2</sup> molecule, was modeled with a bilayer C24F12 and C24F12Br<sup>2</sup> unit cell, respectively, with the optimized lattice parameters *a* = 2.49 Å × 3, *b* = 2.48 Å × 2 for the *hex* structure and *a* = 2.50 Å × 3, *b* = 2.48 Å × 2 for the Bernal structure. The F was attached to C atoms all outside and half inside and half outside a cell (**Figure 1**) with 40 Bohr space between slabs to prevent the interactions. In latter case, the entry interlayer distance *d*layer in a C24F12Br<sup>2</sup> unit cell was taken larger by 2 Å than optimized *d*layer in a C24F12 unit cell (in order to avoid unrealistic Br<sup>2</sup> F formation or F ↔ Br<sup>2</sup> replacement under relaxation of the system), in line with experimental measurements [46]. All atoms were allowed to move free under an optimization of the unit cells. The Brillouin-zone integration was performed on a 20 × 20 × 1 grid of Monkhorst-Pack k-points [47]. The accuracy was verified by testing the energy convergence. The default numbers of bands were used for free bromine particles.

**Figure 1.** Unit cells C24 with the Bernal and *hex* structure (top panel) and unit cell C24F12 Bernal with arrangement of the F atoms half inside and half outside and all outside a cell. Adapted from [30].
