We present a combined equation of motion coupled-cluster cumulant Green’s function approach for calculating and understanding intrinsic inelastic losses in core level x-ray absorption spectra (XAS) and x-ray photoemission spectra. The method is based on a factorization of the transition amplitude in the time domain, which leads to a convolution of an effective one-body absorption spectrum and the core-hole spectral function. The spectral function characterizes intrinsic losses in terms of shake-up excitations and satellites using a cumulant representation of the core-hole Green’s function that simplifies the interpretation. The one-body spectrum also includes orthogonality corrections that enhance the XAS at the edge.

X-ray photoemission spectra generally exhibit satellite features beyond the main peak due to many-body excitations. However, the satellites associated with charge-transfer excitations in correlated materials have proved difficult to calculate from first principles and their interpretation has been controversial. Here we show that these satellites can be attributed to local density fluctuations in response to a suddenly created core hole. Our approach is based on a cumulant representation of the core-hole Green's function with a real-time, time-dependent density functional theory calculation of the cumulant. This approach includes effects that cannot be accounted for by cluster methods and yields a direct real-space, real-time interpretation. Illustrative results for ${\mathrm{TiO}}_2$ and NiO are in good agreement with XPS experiment.