  Adsorption of CO$_2$ on a semiconductor surface is a prerequisite for its
photocatalytic reduction. Owing to superior photocorrosion resistance,
nontoxicity and suitable band edge positions, TiO$_2$ is considered to be the
most efficient photocatalyst for facilitating redox reactions. However, due to
the absence of adequate understanding of the mechanism of adsorption, the
CO$_2$ conversion efficiency on TiO$_2$ surfaces has not been maximized. While
anatase TiO$_2$ (101) is the most stable facet, the (001) surface is more
reactive and it has been experimentally shown that the stability can be
reversed and a larger percentage (up to ~ 89%) of the (001) facet can be
synthesized in the presence fluorine ions. Therefore, through density
functional calculations we have investigated the CO$_2$ adsorption on TiO$_2$
(001) surface. We have developed a three-state quantum-mechanical model that
explains the mechanism of chemisorption, leading to the formation of a
tridentate carbonate complex. The electronic structure analysis reveals that
the CO$_2$-TiO$_2$ interaction at the surface is uniaxial and long ranged,
which gives rise to anisotropy in binding energy (BE). It negates the widely
perceived one-to-one correspondence between coverage and BE and infers that the
spatial distribution of CO$_2$ primarily determines the BE. A conceptual
experiment is devised where the CO$_2$ concentration and flow direction can be
controlled to tune the BE within a large window of ~1.5 eV. The experiment also
reveals that a maximum of 50% coverage can be achieved for chemisorption. In
the presence of water, the activated carbonate complex forms a bicarbonate
complex by overcoming a potential barrier of ~0.9 eV.
