  High harmonic generation (HHG) takes place in all phases of matter. In
gaseous atomic and molecular media, it has been extensively studied and is very
well-understood. In solids research is ongoing, but a consensus is forming for
the dominant microscopic HHG mechanisms. In liquids on the other hand, no
established theory yet exit and approaches developed for gases and solids are
generally inapplicable, hindering our current understanding. We develop here a
powerful and reliable ab-initio cluster-based approach for describing the
nonlinear interactions between isotropic bulk liquids and intense laser pulses.
The scheme is based on time-dependent density functional theory and utilizes
several approximations that make it feasible yet accurate in realistic systems.
We demonstrate our approach with HHG calculations in water, ammonia, and
methane liquids, and compare the characteristic response of polar and non-polar
liquids. We identify unique features in the HHG spectra of liquid methane that
could be utilized for ultrafast spectroscopy of its chemical and physical
properties: (i) a structural minima at 15-17eV, and (ii) a well-like shape in
the perturbative region that is reminiscent of a shape resonance. Our results
pave the way to accessible calculations of HHG in liquids and illustrate the
unique nonlinear nature of liquid systems.
