  Understanding the atomic-scale interaction mechanism of CO$_2$ and H$_2$O on
TiO$_2$ surface is crucial to establish a correlation between the catalytic
efficiency with its exposed facet. Here, with the aid of a three-state model,
nudged elastic band simulations, and DFT calculations, we examine the chemical
restructuring of these molecules during the process of adsorption, coadsorption
and conversion on (001) including (1$\times$4)-reconstructed, (010), and (101)
facets of anatase TiO$_2$ and thereby, evaluate the step selective reactivity
order. In addition, the results reveal the unexplored non-trivialities in the
reaction mechanisms. For the most stable (101) facet, we show that the
unfavorable carbonate complex formation becomes favorable by switching the
reaction from endothermic to exothermic in the presence of water. Further, we
find that small binding energy does not necessarily imply physisorption. It can
also give rise to chemisorption, where the loss in energy due to repulsive
Hartree and Madelung interactions is comparable to the energy gained through
the chemical bonding. Such a scenario is demonstrated for the CO$_2$ adsorption
on (010) and (101) facets. Though (001) remains the most reactive surface, if
it undergoes reconstruction, which happens at ultra-high vacuum and high
temperature, the number of active sites is reduced by three-fourths.
