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(N⁴) 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 nonperturbative 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 the results against the 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 those based on the DSRG-MRPT3 and MR-LDSRG(2) levels of theory reliably capture the full dissociation behavior and reproduce the experimental vibrational structure.