A state-specific iterative decoupling scheme based on perturbation theory for low-energy electronic states

Abstract In this work, we introduce a selective and scalable extension of the multi-step Rayleigh–Schrödinger (RS) and Brillouin–Wigner (BW) perturbative scheme (see Bindech et al (2024) Electron. Struct. 6 045009), designed to efficiently access the low-energy spectrum of molecular systems. The method proceeds by combining successive effective Hamiltonian diagonalizations inspired by second-order RS perturbation theory, with a BW correction applied to individually optimized states using an updated partitioning of the Hamiltonian. At each step, a candidate zeroth-order state is identified and progressively decoupled from the remaining higher-lying states, thereby enabling a well-conditioned BW expansion for the energy correction. In contrast to previous approaches, the method selectively targets a small number of low-lying states, significantly reducing the numerical overhead while maintaining chemical accuracy. The robustness of the method is demonstrated on the LiH and H 4 molecules, where accurate excitation energies are obtained for the lowest singlet states using compact model spaces, confirming its potential for realistic applications.