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-Schrodinger and Brillouin-Wigner perturbative scheme (see arXiv:2408.16505), designed to efficiently access the low-energy spectrum of molecular systems. The method proceeds by combining successive effective Hamiltonian diagonalizations inspired by second-order Rayleigh-Schrodinger perturbation theory, with a Brillouin-Wigner correction applied to individually optimized states using an updated partitioning of the Hamiltonian. At each step, a zeroth-order state is identified and progressively decoupled from the remaining higher-lying states, thereby enabling a well-conditioned Brillouin-Wigner 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 spectroscopic accuracy. The robustness of the method is demonstrated on the LiH and H4 molecules, where accurate excitation energies are obtained for the lowest singlet states using compact model spaces, confirming its potential for realistic applications.