RE-ADC: The algebraic diagrammatic construction scheme for the polarization propagator using the retaining-the-excitation-degree partitioning

We present the novel suite of RE-ADC schemes for electronically excited states through third-order perturbation theory. These methods extend the family of established algebraic diagrammatic construction (ADC) schemes, but employ a retaining-the-excitation-degree (RE) partitioning of the electronic Hamiltonian, replacing the conventional Møller-Plesset partitioning. We derive the working equations and compare their algebraic structure to that of the standard ADC. We find that this change of partitioning leads to the inclusion of some higher-order terms in the RE-ADC secular matrix, i.e., a subset of terms appearing at (n + 1)th-order in standard ADC is already incorporated at nth-order in RE-ADC. At second-order, the mean absolute error of excitation energies for singly excited states is increased from 0.20 to 0.64 eV compared to standard ADC(2). At third-order, however, RE-ADC(3) surpasses ADC(3), lowering the mean absolute error from 0.23 eV to only 0.13 eV. For doubly excited states, RE-ADC(2) and RE-ADC(3) mirror the performance of standard ADC(3). Notably, RE-ADC(2) provides a better description of transition excited-state properties than ADC(2), while both third-order methods improve upon their second-order variants and exhibit similar performance. These discoveries provide insight into the role of the partitioning of the Hamiltonian for ADCs, providing an additional degree of freedom for the construction of accurate excited-state methods.