The analysis and interpretation of the H2 line emission from planetary nebulae have been done in the literature assuming that the molecule survives only in regions where the hydrogen is neutral, as in photodissociation, neutral clumps or shocked regions. However, there is strong observational and theoretical evidence that at least part of the H2 emission is produced inside the ionized region of such objects. The aim of the present work is to calculate and analyze the infrared line emission of H2 produced inside the ionized region of planetary nebulae using a one-dimensional photoionization code. The photoionization code Aangaba was improved in order to calculate the statistical population of the H2 energy levels and the intensity of the H2 infrared emission lines in physical conditions typical of planetary nebulae. A grid of models was obtained and the results are analyzed and compared with the observational data. We show that the contribution of the ionized region to the H2 line emission can be important, particularly in the case of nebulae with high temperature central stars. This result explains why H2 emission is more frequently observed in bipolar planetary nebulae (Gatleys rule), since this kind of object typically has hotter stars. Collisional excitation plays an important role on the population of the rovibrational levels of the electronic ground state of H2. Radiative mechanisms are also important, particularly for the upper vibrational levels. Formation pumping can have minor effects on the line intensities produced by de-excitation from very high rotational levels, especially in dense and dusty environments. We included the effect of the H2 on the thermal equilibrium of the gas, concluding that H2 only contributes to the thermal equilibrium in the case of a very high temperature of the central star or a high dust-to-gas ratio, mainly through collisional de-excitation.
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