The algebraic diagrammatic construction (ADC) scheme for polarization propagator is a family of many-body Green’s function methods for excited states.

The ADC expressions can be alternatively derived via the intermediate state representation (ISR). In ISR, the \(n\)th order Møller-Plesset (MP) ground state is used as a reference and a correlated excited-state basis set is generated by applying excitation operators to the reference. ADC can be thought of as a MP(n) perturbation theory for excited states.

The high-lying core-excited states can be accessed by adopting the core-valence separation (CVS) scheme in which the coupling matrix elements between the core and valence orbitals are set to zero.

ADC provides size-consistent, Hermitian, compact and accurate methods for calculating core-excited states and simulating X-ray spectra.