First-principles redox energy estimates under the condition of satisfying the general form of Koopmans’ theorem: An atomistic study of aqueous iron

Abstract

In this work, we explore the relative accuracy to which a hybrid functional, in the context of density functional theory, may predict redox properties under the constraint of satisfying the general form of Koopmans’ theorem. Taking aqueous iron as our model system within the framework of first-principles molecular dynamics, direct comparison between computed single-particle energies and experimental ionization data is assessed by both (1) tuning the degree of hybrid exchange, to satisfy the general form of Koopmans’ theorem, and (2) ensuring the application of finite-size corrections. These finite-size corrections are benchmarked through classical molecular dynamics calculations, extended to large atomic ensembles, for which good convergence is obtained in the large supercell limit. Our first-principles findings indicate that while precise quantitative agreement with experimental ionization data cannot always be attained for solvated systems, when satisfying the general form of Koopmans’ theorem via hybrid functionals, theoretically robust estimates of single-particle redox energies are most often arrived at by employing a total energy difference approach. That is, when seeking to employ a value of exact exchange that does not satisfy the general form of Koopmans’ theorem, but some other physical metric, the single-particle energy estimate that would most closely align with the general form of Koopmans’ theorem is obtained from a total energy difference approach. In this respect, these findings provide important guidance for the more general comparison of redox energies computed via hybrid functionals with experimental data.