Ionization Potentials at Mean-Field Computational Cost: The Extended Koopmans' Framework for pCCD

We introduce a mean-field-like computational model for calculating ionization potentials (IPs) based on the pair Coupled Cluster Doubles (pCCD) wave function. Specifically, our model combines the extended Koopmans' theorem (EKT) with the advantages of a variationally orbital-optimized (oo)-pCCD ansatz. The computational cost of the EKT(pCCD) method is negligible $\left(O\left(N^3\right)\right)$ as the response 1- and 2-particle reduced density matrices used to construct the generalized Fock matrix are readily available after an oo-pCCD calculation. We benchmarked our new computational model for IPs of atoms, small molecules, and a set of organic acceptor molecules against experimental and theoretical reference data. The EKT(pCCD) model significantly improves upon the modified Koopmans' approach [J. Chem. Phys. 162, 184110 (2025)], and the obtained IPs are comparable to those of computationally more expensive IP-EOM-pCCD-based models, approaching CCSD(T) reference values (with a mean error of 0.05 eV). Most importantly, the EKT(pCCD) approach is almost independent of the basis set size, and reliable IPs are already obtained with small basis sets.