Excited-State Spectra of Strongly Correlated Molecules from a Reduced-Density-Matrix Approach

Excited-state energies are computed in the space of single-electron transitions from the ground state from only a knowledge of the two-electron reduced density matrix (2-RDM). Previous work developed and applied the theory to small molecular systems with accurate results, but applications to both larger and more correlated molecules were hindered by ill-conditioning of the effective eigenvalue problem. Here we improve the excited-spectra 2-RDM theory through a stable Hamiltonian-shifted regularization algorithm that removes the near singularities within the computation. The theory with ground-state 2-RDMs from the variational 2-RDM method is applied to the excited energies of strongly correlated molecules including the optical band gap of hydrogen and acene chains, the singlet-triplet splitting of nickel dithiolates, as well as the low-lying excited states of an optical dye. While single-excitation theories like CISD and TD-DFT underestimate band gaps and excited-state splittings, the 2-RDM theory yields band gap and excited-state splittings that are in good agreement with full configuration interaction and experiment where available.