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The transition region in the solar atmosphere bridges the lower temperature, higher density chromosphere at the base with the tenuous, high temperature plasma in the corona. It undergoes a change in temperature from 25000K to about 600000K. Plasma conditions mean that fundamentally different models for line emission are required for the corona and chromosphere. The modelling framework of the corona is remarkably straightforward by comparison, and the tendency for modellers and observers is to use coronal modelling in the transition region as well. However, discrepancies with observations become apparent when using the modelling for lines emitted by low charge ions. To investigate more suitable modelling for ions which form in the transition region, the coronal approximation is extended by successively including atomic processes which become more important further down. Firstly, the effects of higher density are added to the modelling of carbon and oxygen, to account for its effects on electron impact ionisation and dielectronic recombination. New calculations are made for electron impact ionisation from long-lived metastable levels, which become populated at these densities. Other atomic processes not normally included in the coronal approximation are also added to the modelling of carbon and oxygen. These include processes induced by the radiation field, photo-ionisation and -excitation, and collisions involving neutral and ionised hydrogen and helium, principally charge transfer. The same models are built for other elements routinely observed in the atmosphere: these are nitrogen, neon, magnesium, silicon and sulphur. For these models an approximation is used for ionisation rates from metastable levels. All of the models are run in steady state equilibrium, to allow an assessment of how much atomic processes alter the modelling separately from dynamic events taking place in the plasma. To test how the new models compare with observations, the resulting ion balances from the models are used in conjunction with differential emission measure modelling to predict line intensities in the transition region. Observations of the quiet Sun show that the models resolve a number of the discrepancies found when using the coronal approximation for emission from low charge ions.