Decoding Shake-up Satellites in XPS through Large-Scale ab initio Simulations: Spectral Signatures of Ring Fusion in Porphyrins

TL;DR

The paper tackles the interpretation of shake-up satellites in XPS, which encode structural information but are difficult to model. It introduces and applies a fully ab initio $GW+C$ framework to large molecular systems, achieving quantitative agreement with experiment for both main N1s peaks and satellites in porphyrins up to ~170 atoms. The work reveals that ring fusion reshapes satellite features while leaving main peaks largely unchanged, with the mechanism rooted in the spatial localization of valence excitations and governed by monopole selection rules. This approach broadens the utility of XPS by enabling satellites to provide actionable chemical information and demonstrates scalable, first-principles predictions for complex organic molecules.

Abstract

In X-ray photoelectron spectroscopy (XPS), shake-up satellites arise when core ionization is accompanied by simultaneous charge-neutral valence excitations. Although these satellites can contain detailed structural information, they are rarely interpreted due to the lack of accurate and scalable theoretical methods. Here, we develop and apply a many-body perturbation theory framework within the $GW$ plus cumulant ($GW+C$) approach that enables accurate predictions of shake-up satellites in large molecular systems. For unfused, mono-fused, and doubly fused porphyrin derivatives with up to 170 atoms, we achieve excellent agreement with experiment, reproducing both main photoionization signals and satellite features within $0.2-0.3$ eV. We show that ring fusion strongly affects satellite features, whereas the N 1s photoionization signals remain unchanged. Our calculations reveal the mechanism behind these changes, identifying the spatial localization of valence excitations as the driving force. This work not only deepens understanding of the shake-up mechanism in porphyrins but also shows how predictive computations can unlock the chemical information encoded in satellites.

Figures (4)

• Figure 1: Summary of the porphyrin molecules considered in this study. The conjugated macrocycle is highlighted in blue. Systems 1-4 have been realized experimentally (see Refs. oleszak2024fused and martin2020oxidative), while 5 and 6 are experimentally not realizable, but serve as smaller model systems for the computational analysis of compounds 3 and 4.
• Figure 2: Comparison of the experimental XP spectrum (dots) alongside the computed spectral function $A_\mathrm{N1s}^{GW+C}(\omega)$ (solid line) for molecules 1-4 (a-d), with the inset zooming into the region of the pyrrolic satellite around $3.0-3.5$ eV by a factor of 8. All spectra are aligned at the energy of maximum intensity in the N 1s spectrum $\varepsilon_\mathrm{N1s}^\mathrm{Max}$. For $A_\mathrm{N1s}^{GW+C}(\omega)$, the individual spectra of the pyrrolic (pink, violet) and iminic (green, purple) N 1s levels are indicated by the shaded areas. The respective nitrogen atoms are highlighted in the structures, with functional groups abbreviated as Ph=Phenyl and Ar*=3,5-di-tert-butyl-phenyl.
• Figure 3: a) Summary of the four-orbital Gouterman model for valence excitations in Porphyrins. b) Direct comparison of the first-order N 1s satellite spectra (colored lines) of the symmetry-equivalent N1/N2 and N3/N4 states with the optical absorption spectrum (black line). Individual satellite intensities $\gamma^\nu_\mathrm{N1s}$ are shown as stick spectrum. Excitations with large intensities in the satellite spectrum are highlighted by the dotted lines and labeled following the Gouterman model if possible. The maximum of each spectrum is set to the same value to enable comparison. The respective broadened $GW+C$ satellite spectra of 2 (from Figure \ref{['fig:experiment_comparison']}) are shown in gray as reference. c-h) show iso-surfaces of transition densities $n_\nu(\mathbf{r})$ for all excitations highlighted in b). The two possible mirror planes $\sigma_v^{x,y}$, which are perpendicular to the molecular plane, are shown in grey.
• Figure 4: a) Direct comparison of the first-order N 1s satellite spectra (colored lines) of all N 1s states with the optical absorption spectra (black line). Individual satellite intensities $\gamma^\nu_\mathrm{N1s}$ are shown as stick spectrum. The maximum of each spectrum is set to the same value to enable comparison. The respective broadened $GW+C$ satellite spectra of 4 (from Figure \ref{['fig:experiment_comparison']}) are shown in gray as reference. b,c) show iso-surfaces of transition densities $n_\nu(\mathbf{r)}$ for excitations highlighted in a).