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This paper theoretically models the emission expected from shells (generalized to include tori or clumps) expanding away from the hot central stars of PNe. We examine the effects of shocks, FUV (6eV<hν<13.6eV), and soft X rays (50eV≲hν≲1KeV) on the predominantly neutral gas and follow the time dependent chemistry for H₂, solving for the chemical and temperature structure and the emergent spectrum of the evolving shell. We consider a large interval of values for the mass of the central star (from 0.6 to 0.836M_☉) and for the shell properties, using its density and filling factor as free parameters. The calculations give the time dependent physical and chemical properties of the shell (temperature, fractional abundances of HII, HI, H₂ and electrons), as well as the intensities of a number of lines of molecular hydrogen (H₂ v=1-0S(1); v=2-1S(1); and v=0-0S(0), S(1), S(2), S(3), and S(4)) Brγ and the metal lines CII 158µm, OI 63µm, SiII 35µm, OI 6300Å, FeII 1.26µm, which can be compared to the observations and used to determine the physical parameters of the ejection process. We focus on the shell evolution after the star has achieved T_*>30,000K. If the column density in the shell is sufficiently high, a three-layered shell is produced with an inner HII region, a central HI region, and an outer H₂ region. In this case, we can identify three phases in the evolution of the neutral shell. i) The early evolution (T_*∼30,000K) is dominated by FUV photons, as the FUV photon luminosity Φ_FUV of the central star peaks. The shell has a large column of warm H₂ and is very bright in all lines. The vibrationally excited H₂ lines at 2µm are dominated by thermal emission from collisionally excited levels; the heating is predominantly by grain photoelectric heating and FUV pumping of H₂. ii) At somewhat later times, as Φ_FUV and gas density decline, the molecular gas becomes cooler and the line intensity decreases rapidly. This is the only phase in which the emission of the v=1-0 H₂ lines can be dominated by fluorescence, and this fluorescent phase is present only in PNe with low-mass central stars. iii) At even later times, the star heats to T_*>100,000K and soft X-rays heat and partially ionize the neutral gas well above the values determined by the FUV stellar radiation. The duration (and presence) of these phases depends on the evolution with time of the stellar radiation field (i.e., on the mass of the central star), which is the main parameter that controls the PN evolution. For example, we find that a standard M_*=0.6M_☉ central star produces phase (i) from roughly 1000 to 5000yrs, phase (ii) from 5000 to 7000yrs, and phase (iii) from 7000yrs onward. PNe with high mass central stars reach high effective temperatures very quickly, and spend most of their life in the X-ray dominated phase. A M_*=0.836M_☉ case reaches phase (iii) in roughly 1000yrs. The decrease with time of the H₂ line intensity (both in the near and mid-infrared) is less rapid than in PNe with low-mass central stars. Time-dependent H₂ chemistry enhances even further the intensity of these lines. As a result, we find that models with high-mass central stars are the only cases which radiatively produce strong hydrogen molecular line intensities in old (large) PNe. For standard values of the parameters the emission in the vibrationally excited H₂ lines produced in the shock between the expanding shell and the precursor red giant wind is generally small compared to the PDR emission. However, for large red giant wind mass loss rates, {dot}(M)_RG>10^–5M_☉/yr, the shock emission can be significant. Therefore, strong H₂ 2µm emission may also arise from shocks in old PNe.