  X-ray photoelectron spectra provide a wealth of information on the electronic
structure. The extraction of molecular details requires adequate theoretical
methods, which in case of transition metal complexes has to account for effects
due to the multi-configurational and spin-mixed nature of the many-electron
wave function. Here, the Restricted Active Space Self-Consistent Field method
including spin-orbit coupling is used to cope with this challenge and to
calculate valence and core photoelectron spectra. The intensities are estimated
within the frameworks of the Dyson orbital formalism and the sudden
approximation. Thereby, we utilize an efficient computational algorithm that is
based on a biorthonormal basis transformation. The approach is applied to the
valence photoionization of the gas phase water molecule and to the core
ionization spectrum of the $\text{[Fe(H}_2\text{O)}_6\text{]}^{2+}$ complex.
The results show good agreement with the experimental data obtained in this
work, whereas the sudden approximation demonstrates distinct deviations from
experiments.
