Determination of electronic excitation energies within the doubly occupied configuration interaction space by means of the Hermitian operator method

In this work, we formulate the equations of motion corresponding to the Hermitian operator method in the framework of the doubly occupied configuration interaction space. The resulting algorithms turn out to be considerably simpler than the equations provided by that method in more conventional spaces, enabling the determination of excitation energies in N-electron systems under an affordable polynomial computational cost. The implementation of this technique only requires to know the elements of low-order reduced density matrices of an N-electron reference state, which can be obtained from any approximate method. We contrast our procedure against the reduced Bardeen-Cooper-Schrieffer and Richardson-Gaudin-Kitaev integrable models, pointing out the reliability of our proposal.