This work develops stochastic compression and downfolding methodologies for large-scale correlated electronic structure calculations. These approaches enable reduced representations of many-body Hamiltonians and correlated wavefunctions that retain essential electron correlation effects while significantly lowering computational cost. The resulting framework extends high-level electronic structure techniques to chemically relevant systems embedded within complex environments.

Applications are presented across several classes of problems relevant to catalysis and molecular materials. Stochastic downfolding methodologies are developed for the calculation of charged excitations at catalytic and molecular interfaces, enabling accurate treatment of large orbital spaces while preserving active-region correlation effects. Stochastic compression techniques are further applied to total-energy calculations in solvated and reactive systems where conventional correlated approaches become computationally intractable. Finally, nonequilibrium many-body simulations are used to investigate plasmon-assisted charge transfer at driven catalytic interfaces, demonstrating that transient external driving can dynamically modify molecular spectral structure and create additional resonant pathways for hot-carrier injection.

Together, these methods provide scalable strategies for incorporating strong electron correlation and nonequilibrium effects into electronic structure simulations of complex chemical systems, broadening the applicability of many-body approaches in chemistry, catalysis, and materials science.