  Photocatalytic nitrogen fixation provides a promising route to produce
reactive nitrogen compounds at benign conditions. Titania has been reported as
an active photocatalyst for reduction of dinitrogen to ammonia; however there
is little fundamental understanding of how this process occurs. In this work
the rutile (110) model surface is hypothesized to be the active site, and a
computational model based on the Bayesian error estimation functional
(BEEF-vdW) and computational hydrogen electrode is applied in order to analyze
the expected dinitrogen coverage at the surface as well as the overpotentials
for electrochemical reduction and oxidation. This is the first application of
computational techniques to photocatalytic nitrogen fixation, and the results
indicate that the thermodynamic limiting potential for nitrogen reduction on
rutile (110) is considerably higher than the conduction band edge of rutile
TiO$_2$, even at oxygen vacancies and iron substitutions. This work provides
strong evidence against the most commonly reported experimental hypotheses, and
indicates that rutile (110) is unlikely to be the relevant surface for nitrogen
reduction. However, the limiting potential for nitrogen oxidation on rutile
(110) is significantly lower, indicating that oxidative pathways may be
relevant on rutile (110). These findings suggest that photocatalytic dinitrogen
fixation may occur via a complex balance of oxidative and reductive processes.
