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.