Multi-reference algebraic diagrammatic construction theory for excited states: General formulation and first-order implementation

We present a multi-reference generalization of the algebraic diagrammatic construction (ADC) theory [J. Schirmer, Phys. Rev. A 26, 2395 (1982)] for excited electronic states. The resulting multi-reference ADC (MR-ADC) approach can be efficiently and reliably applied to systems, which exhibit strong electron correlation in the ground or excited electronic states. In contrast to conventional multi-reference perturbation theories, MR-ADC describes electronic transitions involving all orbitals (core, active, and external) and enables efficient computation of spectroscopic properties, such as transition amplitudes and spectral densities. Our derivation of MR-ADC is based on the effective Liouvillian formalism of Mukherjee and Kutzelnigg [Many-Body Methods in Quantum Chemistry (Springer, 1989), pp. 257–274], which we generalize to multi-determinant reference states. We discuss a general formulation of MR-ADC, perform its perturbative analysis, and present an implementation of the first-order MR-ADC approximation, termed MR-ADC(1), as a first step in defining the MR-ADC hierarchy of methods. We show results of MR-ADC(1) for the excitation energies of the Be atom, an avoided crossing in LiF, and doubly excited states in C2 and outline directions for our future developments.