The observed large σ * OH occupations of 0.20 e might seem surprising considering the energy levels involved. The hydrated electron state has an energy of -3.7 eV relative to vacuum, while the σ * OH orbitals are several eV above the vacuum level. For the hydrated electron state to have significant σ * OH occupation then suggests a very large Hamiltonian coupling (several eV) of the excess electron to the σ * OH orbitals. However, significant populations of σ * OH orbitals also observed in halide ion water clusters, which have donor orbitals even lower in energy than e - (aq) , suggesting that large Hamiltonian couplings between anions and water σ * OH orbitals are not uncommon. NBO analysis allows for a determination of Hamiltonian couplings by computing matrix elements of the Fock operator in the NBO basis. We averaged the matrix elements over our FlexiBLE QM/MM trajectories. The results are presented in Table which shows matrix elements between the Cav s orbital and the five most populated σ * OH orbitals. For simplicity, matrix elements coupling the σ * OH orbitals with each other are omitted. Since these values are found to be sensitive to the choice of density functional (see Supplementary Material section S-III), we caution against a quantitative physical interpretation of the absolute values of the model Hamiltonian; however, relative trends are preserved across functionals, resulting in σ * OH populations that do not depend sensitively on the functional (see Fig. ). We consider first the diagonal elements of the model Hamiltonian in Table , where we observe that all orbitals are above the vacuum level. This makes physical sense for the σ * OH orbitals, but might at first seem surprising for the cavity orbital. However, this cavity orbital is by construction orthogonal to all water-centered occupied and virtual NBOs and is thus rather confined in the cavity region and interstitial regions between the water molecules, raising its kinetic energy.