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At the dawn of the Universe, the ions of the light elements produced in the Big Bang nucleosynthesis recombined with each other. In our present study, we have tried to mimic the conditions in the early Universe to show how the recombination process would have led to the formation of the first ever formed diatomic species of the Universe: HeH+, as well as the subsequent processes that would have led to the formation of the simplest triatomic species: H3+. We have also studied some special cases: higher positive charge with fewer number of hydrogen atoms in a dense atmosphere, and the formation of unusual and interesting linear, dicationic He chains beginning from light elements He and H in a positively charged atmosphere. For all the simulations, the ab initio nanoreactor (AINR) dynamics method has been employed.