BETTERXPS: Guiding Peak Assignment in Photoelectron Spectroscopy

with ab-initio Simulations

Background

Core level X-ray Photoelectron Spectroscopy (XPS) relies on the fact that the energy required to remove a core electron from a particular atom depends on the chemical environment of that atom. As such, a core level XPS spectrum contains information about the chemical environments that are present in a sample. However, the analysis of experimental XPS spectra can be difficult – in particular, is is not always clear, which chemical environments specific features in a recorded spectrum correspond to. This is called the peak-assignment problem in XPS.

The aim of the BETTERXPS project is to tackle the peak assignment problem using theoretical methods. We are concerned with developing accurate first-principles methods for calculating core electron binding energies that can be used to guide the analysis of experimental spectra. In particular, most of the work carried out as part of the BETTERXPS project is concerned with the refinement of the Δ-Self-Consistent-Field (ΔSCF) approach.

In the ΔSCF method, the core electron binding energy is calculated as the total energy difference between the N electron ground state, and the N–1 electron final state with a core hole.

E_B = E_N–1 - E_N (1)

Typically, both of these energies are calculated using density functional theory. In the calculation of the final state, an occupancy constraint is applied to one of the core orbitals: the occupation number of one of the core orbitals is set to zero in one of the spin channels, and the self-consistent field is converged subject to that constraint.

Equation (1) yields core electron binding energies referenced to the vacuum level. This is appropriate for comparing against experimental results from gas phase photoelectron spectroscopy.

Of course, most experimental work is concerned with solid samples, rather than gaseous ones. The ΔSCF method can be used to calculate core electron binding energies in solids and surface species, and very good agreement between theory and experiment has been observed in a number of studies.

However, there are two important aspects that must be handled with care when dealing with solids and surfaces:

(i) Energy referencing – instead of the vacuum level, either the Fermi level or the valence band maximum (VBM) must be used as the point of reference. This also means that Equation (1) needs to be modified accordingly.

(ii) Finite size effects – either cluster models or periodic models can be used for solids and surface species, and convergence of the calculated binding energies with respect to system size must be considered in each case. If periodic models are used, the charge must be somehow neutralized in the calculation of the final state. In many ways, ΔSCF calculations of core electron binding energies are analogous to the problem of modelling charged defects.

The basics of applying the ΔSCF method to periodic solids are discussed in [JPCL 12, 9353 (2021)] and [JCTC 19, 3276 (2023)] . Calculations of surface species have been reported in many articles, although mostly only binding energy shifts, rather than absolute binding energies have been calculated. Some practical considerations regarding the use of periodic vs cluster models can be found in [JPCM 33, 154005 (2021)].

In order to better meet the needs of the experimental XPS community, additional work is required to make ΔSCF calculations more “black box”-like, and to better understand their strengths and limitations when applied to complex chemical systems, such as dry and wet interfaces, large biomolecules, 2D-materials, various types of solids, and so on.