  Nonequilibrium (time-dependent) cooling rates and ionization state
calculations are presented for low-density gas enriched with heavy elements
(metals) and photoionized by external ultraviolet/X-ray radiation. We consider
a wide range of gas densities and metallicities and also two types of external
radiation field: a power-law and the extragalactic background spectra. We have
found that both cooling efficiencies and ionic composition of enriched
photoionized gas depend significantly on the gas metallicity and density, the
flux amplitude, and the shape of ionizing radiation spectrum. The cooling rates
and ionic composition of gas in nonequilibrium photoionization models differ
strongly (by a factor of several) from those in photoequilibrium due to
overionization of the ionic states in the nonequilibrium case. The difference
is maximal at low values of the ionization parameter and similar in magnitude
to that between the equlibrium and nonequilibrium cooling rates in the
collisionally controlled gas. In general, the nonequilibrium effects are
notable at $T\simlt 10^6$ K. In this temperature range, the mismatch of the
ionic states and their ratios between the photoequilibrium and the
photo-nonequilibrium models reach a factor of several. The net result is that
the time-dependent energy losses due to each chemical element (i.e. the
contributions to the total cooling rate) differ singificantly from the
photoequilibrium ones. We advocate the use of nonequilibrium cooling rates and
ionic states for gas with near-solar (and above) metallicity exposed to an
arbitrary ionizing radiation flux. We provide a parameter space (in terms of
temperature, density, metallicity and ionizing radiation flux), where the
nonequilibrium cooling rates are to be used. (abridged)
