BWs-ADC: The algebraic diagrammatic construction for the polarization propagator using a size-consistent Brillouin–Wigner partitioning up to third order in perturbation theory

We present the algebraic diagrammatic construction for the polarization propagator (PP-ADC) formulated with a two-parameter, size-consistent Brillouin-Wigner partitioning (BWs) up to third order in perturbation theory (BWs-ADC). The resulting method is size-consistent, size-extensive, and regular and extends the applicability of ADC to systems with degenerate electronic ground states. We demonstrate that the secular matrices of BWs-ADC(2) and BWs-ADC(3) are structurally equivalent to their Møller-Plesset (MP-ADC) counterparts and determine optimal regularization parameters by analyzing the dissociation of H2 in a minimal basis. These parameters are subsequently refined using a benchmark set of 122 single excitations comprising both valence and Rydberg states. BWs-ADC(2) favors strong regularization in the occupied space, whereas virtual-space regularization is found to significantly increase excitation energy errors. In contrast, BWs-ADC(3) generally benefits from slight de-regularization. Both methods achieve a mean absolute error (MAE) of 0.15 eV, representing a substantial improvement over the corresponding MP-ADC approaches; for BWs-ADC(3), this error is dominated by a small number of outliers, whereas BWs-ADC(2) exhibits more uniform accuracy. A second benchmark demonstrates that parameter-optimized BWs-ADC methods also yield significantly improved oscillator strengths and excited-state dipole moments. Overall, BWs-ADC provides improved accuracy for single-reference systems while simultaneously extending the applicability of ADC to few-reference regimes, including bond dissociation processes, diradical species, and selected transition metal complexes.