and E i is the energy of state i. For our DFT simulations, we take the band gap to be the SOMO-SOMO+1 gap. For the MQC simulations, the band gap is the excitation energy between the lowest two eigenvalues of the one-electron Hamiltonian using the Turi-Borgis electronwater pseudopotential, 4 as described in paper I. Representative orbital plots of the SOMO and SOMO+1 are shown in Fig. (a) and (b) respectively, and are consistent with the s-like and p-like states of the particle-in-a-spherical-box model of e - (aq) originally put forward from MQC simulations, 1 and later confirmed by numerous many-electron calculations. The density of states of the SOMO and SOMO+1 are shown in Fig. ). The average BH&HLYP SOMO energy of -2.6 eV is compatible with the experimental binding energy of 3.7 eV, given the limitations of Koopman's theorem. A slightly lower average SOMO energy of -3 eV was observed in HF QM/MM simulations; however, we caution against a direct comparison of absolute SOMO energies between different studies, due to differences in solvation structures, QM region sizes, basis sets, MM models, and treatments of long-range interactions. From Fig. , the SOMO to SOMO+1 gap is seen to be ∼3 eV. This overestimates the experimental absorption peak of 1.7 eV, likely as a result of the 50% fraction of exact exchange in the BH&HLYP functional. Timedependent density functional theory would provide a better description of electronic excitation energies of e - (aq) , 67 however at significant additional computational expense. For the purposes of revealing the influence of the excess electron on water's vibrational frequencies, our interest is in the dynamic fluctuations of the band gap, rather than the absolute magnitude of the gap, supporting our use of the orbital energy gap.