3.4.3. Hydrated Electron. The aqueous or hydrated electron, e -(aq), 158-162 has a characteristic absorption spectrum peaked at 1.72 eV, 163 which has long been used as a test for theoretical models. This includes different exchange-correlation functionals in TD-DFT calculations. Here, absorption spectra are computed using seven well-spaced snapshots from a DFTbased QM/MM simulation of e -(aq), which is sufficient to converge the envelope of the spectrum. 132 TD-B(α)LYP(TDA)/6-31++G* calculations were performed on these QM/MM snapshots, then the vertical transition energies were weighted by oscillator strength and broadened using a Gaussian function whose standard deviation is 0.2 eV.