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

Abstract

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.

Unraveling the Band Gap Trend in the Narrowest Graphene Nanoribbons from the Spin-Adapted Excited-Spectra Reduced Density Matrix Method

“…We treat the excited-state energies from a version of the ES-RDM method, 26 known as the Hermitian operator method, in which the Hermitian combination of single excitations is employed to construct an effective Hamiltonian and an overlap matrix from only the knowledge of the ground-state 2-RDM. [26][27][28][29][30][31]33,34 The ES-RDM method uses regularization of the effective Hamiltonian to remove ill-conditioning in the eigenvalue equation. 26 Although the ES-RDM method generates excited-state energies from the 2-RDM from any correlated ground-state method, we employ 2-RDMs from the variational 2-RDM (v2-RDM) method.…”

Quantum equation of motion for computing molecular excitation energies on a noisy quantum processor

“…n ]] |0 may not be Hermitian, the double commutator of the right-hand side is Hermitian. Note that this expression differs from the one derived for QSE [26] in two points: (i) due to the commutator form, the operators in the numerator and denominator are Hermitian allowing for a systematic reduction of the number of terms to evaluate thanks to the use of the Pauli commutation relations [36], and (ii) the solution of the EOM equations leads directly to the excitation energies rather than the absolute energies, making the approach size intensive (contrary to QSE, which is not size intensive). The EOM approach aims at finding approximate solutions to Eq.…”

Quantum Machine-Learning for Eigenstate Filtration in Two-Dimensional Materials

“…Deflation has been the cornerstone of many classical algorithms in the past for obtaining excited states 63,64 and even a quantum algorithm as well with UCC-VQE. 65 But the formal reduction of our penalty procedure in Eq.S1 based on Theorem 2.1 to deflation offers a slightly different perspective.…”