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An accurate treatment of the multiphase interstellar medium (ISM) inhydrodynamic galaxy simulations requires that we follow not only the thermalevolution of the gas, but also the evolution of its chemical state, includingits molecular chemistry, without assuming chemical (including ionisation)equilibrium. We present a reaction network that can be used to solve for thisthermo-chemical evolution. Our model follows the evolution of all ionisationstates of the 11 elements that dominate the cooling rate, along with importantmolecules such as H2 and CO, and the intermediate molecular species that areinvolved in their formation (20 molecules in total). We include chemicalreactions on dust grains, thermal processes involving dust, cosmic rayionisation and heating and photochemical reactions. We focus on conditionstypical for the diffuse ISM, with densities of 10^-2 cm^-3 < nH < 10^4 cm^-3and temperatures of 10^2 K < T < 10^4 K, and we consider a range of radiationfields, including no UV radiation. In this paper we consider only gas that isoptically thin, while paper II considers gas that becomes shielded from theradiation field. We verify the accuracy of our model by comparing chemicalabundances and cooling functions in chemical equilibrium with thephotoionisation code Cloudy. We identify the major coolants in diffuseinterstellar gas to be CII, SiII and FeII, along with OI and H2 at densities nH> 10^2 cm^-3. Finally, we investigate the impact of non-equilibrium chemistryon the cooling functions of isochorically or isobarically cooling gas. We findthat, at T < 10^4 K, recombination lags increase the electron abundance aboveits equilibrium value at a given temperature, which can enhance the coolingrate by up to two orders of magnitude. The cooling gas also shows lower H2abundances than in equilibrium, by up to an order of magnitude.

Non-equilibrium chemistry and cooling in the diffuse interstellar medium - I. Optically thin regime