Multireference equation-of-motion driven similarity renormalization group for X-ray photoelectron spectra

We formulate and implement the core-valence separated multireference equation-of-motion driven similarity renormalization group method (CVS-IP-EOM-DSRG) for simulating X-ray photoelectron spectra (XPS) of strongly correlated molecular systems. This method is numerically robust and computationally efficient, delivering accurate core-ionization energies with O(N^4) scaling relative to basis set size N in the EOM step. To ensure rigorous core intensivity, we propose a simple modification of the ground-state MR-DSRG formalism. We develop and compare three variants of the theory based on different approximations of the effective Hamiltonian: two derived from low-order perturbative methods (DSRG-MRPT2 and DSRG-MRPT3), and one from a non-perturbative scheme truncated to 1- and 2-body operators [MR-LDSRG(2)]. We benchmark the CVS-IP-EOM-DSRG methods by computing vertical core-ionization energies for a representative molecular test set and comparing results against established single-reference and multireference methods. To demonstrate the applicability of CVS-IP-EOM-DSRG to strongly correlated systems, we compute the potential energy curves and vibrationally resolved XPS of N2 and CO and the XPS of ozone. Comparison with experimental data and other high-level theoretical results shows that all three CVS-IP-EOM-DSRG variants accurately predict vertical ionization energies, but only DSRG-MRPT3 and MR-LDSRG(2) levels of theory reliably capture the full dissociation behavior and reproduce the experimental vibrational structure.