The electronic structures of [111]-cryptand, H+[111]-cryptate, H[111]-cryptate, H-2(2+)[111]-cryptate, and H2[111]-cryptate {c111, H(+)c111, Hc111, H(2)(2+)c111, and H(2)c111} have been determined previously using a self-consistent-field method (HF) featuring a split-valence basis (6-31G) augmented with diffuse functions (L). In this report we focus on the unusual electronic structure of the Rydberg-like states of H[111]-cryptate and H-2[(111)]-cryptate. These correspond to the C-3 minimum of the singly complexed cryptate and a C-3h minimum (labeled in-in) of the twice protonated cryptate. Density difference plots are used to illustrate that the ground electronic state of Hc111 and the low-lying excited state of H(2)c111 (in-in) are highly diffuse in character. Further, the trace of the polarizability tenser of ground-state Hc111 is 3 times larger than that of a geometrically larger, higher-energy isomer with an encapsulated, intact H atom. The Fermi contact term at the internal hydrogen of the low-energy, C-3 isomer of H[111]-cryptate (0.0005 au) is dramatically reduced compared to free hydrogen (0.30 au).