Aims. Excitation of far-infrared and submillimetric molecular lines may originate from nonreactive collisions, chemical formation, or far infrared, near-infrared, and optical fluorescences. As a template, we investigate the impact of each of these processes on the excitation of the methylidyne cation CH+ and on the intensities of its rotational transitions recently detected in emission in dense photodissociation regions (PDRs) and in planetary nebulae. Methods. We have developed a nonlocal thermodynamic equilibrium (non-LTE) excitation model that includes the entire energy structure of CH+, i.e. taking into account the pumping of its vibrational and bound and unbound electronic states by near-infrared and optical photons. The model includes the theoretical cross-sections of nonreactive collisions with H, H2, He, and e-, and a Boltzmann distribution is used to describe the probability of populating the excited levels of CH+ during its chemical formation by hydrogenation of C+. To confirm our results we also performed an extensive analytical study, which we use to predict the main excitation process of several diatomic molecules, namely HF, HCl, SiO, CS, and CO. Results. At densities nH = 10^4 cm-3, the excitation of the rotational levels of CH+ is dominated by the radiative pumping of its electronic, vibrational, and rotational states if the intensities of the radiation field at sim 0.4, sim 4, and sim 300 mum are stronger than 10^5, 10^8, and 10^4 times those of the local interstellar radiation field (ISRF). Below these values, the chemical pumping is the dominant source of excitation of the J > 1 levels, even at high kinetic temperatures (sim 1000 K). The far-infrared emission lines of CH+ observed in the Orion Bar and the NGC 7027 PDRs are consistent with the predictions of our excitation model assuming an incident far-ultraviolet (FUV) radiation field of sim 3 times 10^4 (in Draines unit) and densities of sim 5 times 10^4 and sim 2 times 10^5 cm-3. In the case of NGC 7027, the estimate of the density is 10 to 100 times lower than those deduced by traditional excitation codes. Applying our model to other X1Sigma+ ground state diatomic molecules, we find that HF, and SiO and HCl are the species the most sensitive to the radiative pumping of their vibrational and bound electronic states. In both cases, the minimal near-infrared and optical/UV radiation field intensities required to modify their rotational level populations are sim 10^3 times those of the local ISRF at densities nH = 10^4 cm-3. All these results point towards interstellar and circumstellar media with densities lower than previously established and cast doubts on the clumpiness of well-studied molecular clouds.
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