Research Projects

Accurate computation of electronic excited states is vital for understanding a wide range of fundamental phenomena in molecular systems, especially those involving strong correlation and high-energy excitations. This proposal aims to develop and apply high-precision multi-reference quantum chemistry methods for the computation of such eigenstates, extending their applicability to strongly correlated systems, conical intersections, and vibrational spectra beyond the low-energy exterior part of spectra. In electronic structure theory, single-reference methods such as coupled-cluster (CC) techniques work well for ground and low-lying excited states of weakly correlated systems. However, they fall short when dealing with near-degeneracies and strong correlation effects. The Fock Space Multi-Reference Coupled-Cluster (FSMRCC) method, particularly its Intermediate Hamiltonian (IH-FSMRCC) variant, offers a powerful alternative. IH-FSMRCC enables the accurate description of multiple low-lying and core-excited states while avoiding the intruder state problem, and it maintains numerical stability even with large model spaces. For high-energy vibrational eigenstates and anharmonic vibrational spectra, traditional methods that compute the full spectrum are computationally prohibitive. Instead, interior eigenstate targeting algorithms, such as the Harmonic Davidson method and filter diagonalization, offer a more scalable alternative. Combining such techniques with tensor network state (TNS) approaches, such as the Tree Tensor Network State (TTNS) representation, holds promise for efficiently capturing the entanglement in high-dimensional vibrational wavefunctions. This proposal aims to integrate state-of-the-art techniques, IH-FSMRCC for electronic structure, and TNS-enhanced targeted eigensolvers into a unified computational platform. Applications will target strongly correlated systems such as polyaromatic hydrocarbons, excited states relevant to singlet fission (SF) materials. These systems require the accurate treatment of correlation and excitation effects, particularly in regions where the density of states is high and the convergence of eigenstates is challenging.