That said, previous work on small-molecule HHG has emphasized the important role that is played by Rydberg and continuum states, which is unsurprising given the role of tunneling ionization in the HHG process, yet these states are not well described by standard Gaussian basis sets and very diffuse basis functions are required. Even so, a strong laser field will push the electronic wave packet into regions of space where support from the atom-centered basis functions is waning, and this will manifest as spurious reflection of that wave packet by the artificial potential wall created by the lack of basis function support. To circumvent this problem, previous work on strong-field electron dynamics within an atom-centered Gaussian representation has employed a heuristic finite-lifetime model in which unbound states are given complex energies corresponding to finite lifetimes. As an alternative, in the present work we replace the heuristic lifetime model with the machinery of a complex absorbing potential (CAP). Such potentials are often used for the description of metastable electronic states, whose wave functions are not squareintegrable, and also as absorbing boundary conditions in wave packet quantum dynamics calculations. The CAP absorbs the wave packet as it reaches the edge of a finite grid or a finite basis set, thus preventing artificial interference between the outgoing and a reflected wave, the latter of which is an artifact of the finite-basis representation. The connection between CAPs and the heuristic lifetime model have been discussed elsewhere. We will see that the use of a CAP is crucial to obtaining reasonable HHG spectra, as only the very lowest harmonics are well-resolved in its absence. As demonstrated herein, Gaussian-orbital-based TDKS simulations with an appropriate CAP afford high-quality HHG spectra.