Experimental study of molecules and materials under short, intense femtosecond and even attosecond laser pulses is becoming possible due to the advent of ultrashort pulse technology based on high harmonic generation (HHG). This has enabled the development of soft x-ray and extreme ultraviolet laser pulses with ultrafast time resolution, even in tabletop instruments, which promises to make this technology more widely available in the near future. The strong-field phenomena that can be probed with this new generation of instruments poses challenges to well-developed theoretical models that work in the perturbative (weak-field) regime, as new phenomena arise in strong electric fields. These include above-threshold ionization, nonsequential ionization, multiphoton ionization, delayed photoemission, and HHG. Attosecond experiments are expected to provide fundamental probes of electron correlation and ultrafast charge migration in both molecules and materials. Theoretical description of this emergent physics promises to push the envelope of computational quantum chemistry. In the context of time-dependent density functional theory (TDDFT), strong-field phenomena cannot be described within the linear-response approximation that has become essentially synonymous (in quantum chemistry, at least) with the moniker of TDDFT. In principle, an exact theory can still be formulated even in the strong-field or non-perturbative regime, based on direct solution of the time-dependent Kohn-Sham equation. This approach is often called "real-time" TDDFT, although we prefer the term time-dependent Kohn-Sham (TDKS) theory. In practice, however, there are significant questions as to whether existing * herbert@chemistry.ohio-state.edu exchange-correlation functionals that invoke the adiabatic approximation are up to the task, although improving the description of the derivative discontinuity improves the description of ionization, even within the adiabatic approximation. In the present work, we examine the HHG phenomenon in a simple test case, H 2 molecule, using an atom-centered Gaussian representation of the Kohn-Sham orbitals. Previous TDKS simulations of HHG in H 2 have emphasized the importance of using an exchange-correlation functional with correct asymptotic behavior. In some calculations, this has been achieved in practice by using either time-dependent Hartree-Fock (TDHF) theory or else the closely-related time-dependent configuration interaction singles (TD-CIS) method. Functionals with an explicit selfinteraction correction have also been employed, as this helps with the aforementioned derivative discontinuity. Recently, the use of range-separated, "long-range corrected" (LRC) hybrid functionals has been considered for simulation of HHG in H 2 and other small molecules. As compared to either generalized gradient approximations or even global hybrid functionals, LRC functionals do a much better job of approximating the derivative discontinuity. The simulations presented herein will be based upon the LRC-ωPBE functional, which was also used to simulate HHG in Ref. 33.