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

Area of Science:

• Quantum Chemistry
• Computational Physics
• Materials Science

Background:

• Calculating excited-state energies is crucial for understanding molecular properties and reactions.
• Previous two-electron reduced density matrix (2-RDM) methods faced computational challenges with larger, correlated molecules due to ill-conditioning.
• Accurate excited-state calculations are essential for designing new materials and understanding photochemical processes.

Purpose of the Study:

• To develop a more stable and applicable 2-RDM theory for computing excited-state energies.
• To address the ill-conditioning issues in previous excited-spectra 2-RDM methods.
• To accurately calculate excited-state properties of strongly correlated molecules.

Main Methods:

• Implementation of a stable Hamiltonian-shifted regularization algorithm to improve the 2-RDM theory.
• Utilizing ground-state 2-RDMs from the variational 2-RDM method.
• Application to compute excited energies for hydrogen and acene chains, nickel dithiolates, and an optical dye.

Main Results:

• The improved 2-RDM theory successfully removes near singularities in the eigenvalue problem.
• Accurate optical band gaps for hydrogen and acene chains were computed.
• Singlet-triplet splitting for nickel dithiolates and low-lying excited states of an optical dye were accurately determined.

Conclusions:

• The stabilized excited-spectra 2-RDM theory provides accurate excited-state energies and splittings for strongly correlated systems.
• This method overcomes limitations of single-excitation theories like CISD and TD-DFT, which tend to underestimate band gaps and splittings.
• The results show good agreement with high-level computational methods (full configuration interaction) and experimental data where available.