Density functional theory is used to rationalize magnetic parameters of hydrated electron trapped in alkaline glasses as observed using electron paramagnetic resonance (EPR) and electron spin echo envelope modulation (ESEEM) spectroscopies. To this end, model water cluster anions (n = 4-8 and n = 20, 24) that localize the electron internally are examined. It is shown that hyperfine coupling tensors of H/D nuclei in the water molecules are defined mainly by the cavity size and the coordination number of the electron; the water molecules in the second solvation shell play a relatively minor role. An idealized model of the hydrated electron (that is usually attributed to L. Kevan) in which six hydroxyl groups arranged in an octahedral pattern point toward the common center is shown to provide the closest match to the experimental parameters, such as isotropic and anisotropic hyperfine coupling constants for the protons (estimated from ESEEM), the second moment of the EPR spectra, and the radius of gyration. The salient feature is the significant transfer (10-20%) of spin density into the frontal O 2p orbitals of water molecules. Spin bond polarization involving these oxygen orbitals accounts for small, negative hyperfine coupling constants for protons in hydroxyl groups that form the electron-trapping cavity. In Part 2, these results are generalized for more realistic geometries of core anions obtained using a dynamic one-electron mixed quantum/classical molecular dynamics model.