An efficient and exact reformulation of fourth-order algebraic diagrammatic construction schemes

We present an exact reformulation of the fourth-order algebraic diagrammatic construction (ADC) schemes for electronically excited, electron-detached, and electron-attached states: EE-ADC(4) and non-Dyson IP/EA-ADC(4). By exploiting the diagonal structure of the highest-excitation-class block of the ADC matrix, these configurations are treated implicitly, reducing the full ADC(4) eigenvalue problem to the lower-excitation classes. This yields a nonlinear effective Hamiltonian with substantially reduced dimensionality and memory requirements. Benchmarks against conventional implementations demonstrate faster convergence and a reduced memory footprint for a given target state. Applications to benzene in a triple-zeta basis, including the computation of the lowest vertical excitation energy, ionization potential, and electron affinity, illustrate the extended applicability of the ADC(4) methods.