We present the theory and implementation of a relativistic third-order algebraic diagrammatic construction [ADC(3)] method based on a four-component (4c) Dirac–Coulomb Hamiltonian for the calculation of ionization potentials (IPs), electron affinities (EAs), and excitation energies (EEs). Benchmarking calculations for IP, EA, and EE were performed on both atomic and molecular systems to assess the accuracy of the newly developed four-component relativistic ADC(3) method. The results show good agreement with the available experimental data. The Hermitian nature of the 4c-ADC(3) Hamiltonian, combined with the perturbative truncation of the wave function, offers significant computational advantages over the standard equation-of-motion coupled-cluster approach, particularly for property calculations. The method’s suitability for property calculations is further demonstrated by computing oscillator strengths and excited-state dipole moments for heavy elements.
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