  We derive new self-consistent theoretical UV, optical, and IR diagnostics for
the ISM pressure and electron density in the ionized nebulae of star-forming
galaxies. Our UV diagnostics utilize the inter-combination, forbidden and
resonance lines of silicon, carbon, aluminum, neon, and nitrogen. We also
calibrate the optical and IR forbidden lines of oxygen, argon, nitrogen and
sulfur. We show that line ratios used as ISM pressure diagnostics depend on the
gas-phase metallicity with a residual dependence on the ionization parameter of
the gas. In addition, the traditional electron density diagnostic [S II]
{\lambda}6731/[S II] {\lambda}6717 is strongly dependent on the gas-phase
metallicity. We show how different emission-line ratios are produced in
different ionization zones in our theoretical nebulae. The [S II] and [O II]
ratios are produced in different zones, and should not be used interchangeably
to measure the electron density of the gas unless the electron temperature is
known to be constant. We review the temperature and density distributions
observed within H II regions and discuss the implications of these
distributions on measuring the electron density of the gas. Many H II regions
contain radial variations in density. We suggest that the ISM pressure is a
more meaningful quantity to measure in H II regions or galaxies. Specific
combinations of line ratios can cover the full range of ISM pressures (4 <
log(P/k) < 9). As H II regions become resolved at increasingly high redshift
through the next generation telescopes, we anticipate that these diagnostics
will be important for understanding the conditions around the young, hot stars
from the early universe to the present day.
