Combining Effective Hamiltonians and Brillouin-Wigner Approach: A Perturbative Approach to Spectroscopy

The numerical cost of variational methods suggests using perturbative approaches to determine the electronic structure of molecular systems. In this work, a sequential construction of effective Hamiltonians drives the definition of approximate model functions and energies in a multi-state Rayleigh-Schr\"odinger perturbative scheme. A second step takes advantage of an updated partitioning of the Hamiltonian to perform a state-specific Brillouin-Wigner energy correction based on a well-tempered perturbation expansion. The multi-step RSBW method is exemplified on model-Hamiltonians to stress its robustness, efficiency and applicability to spectroscopy determination.