A second issue in the NBO analysis of e - (aq) relates to the diffuse nature of the excess electron's orbital and its occupation of a solvent cavity. Using an exclusively atom-centered basis augmented with diffuse functions (6-311++G**), we found significant mixing in of Rydberg-like character in the σ * OH NBOs of the water molecules closest to the electron (see Supplementary Ma-terial Fig. ), resulting in artificially high σ * OH occupations of >0.3 e. We found this issue was circumvented by adding a ghost atom with lithium's 6-311++G** basis functions (chosen as the 2nd-row element with the smallest diffuse exponent) at the centroid position of the SOMO. We then assigned the excess electron to an NBO formed largely from the lithium ghost atom's outer valence and diffuse set, with smaller contributions from Rydberg natural atomic orbitals of the water atoms. We identify this ghost atom NBO as an s-like cavity orbital, Cav s . Representative σ * OH and Cav s NBOs are shown in Fig. . Convergence of NBO properties with basis set and QM region size is explored in Section S-II, where we show that our chosen 6-311++G** basis provides comparable results to aug-cc-pVQZ, but at significantly lower computational cost, allowing the full QM region of 32 water molecules to be included.