  g-C$_3$N$_4$ is a promising material for hydrogen production from water via
photo-catalysis, if we can tune its band gap to desirable levels. Using a
combined experimental and ab initio approach, we uncover an almost perfectly
linear relationship between the band gap and structural aspects of
g-C$_3$N$_4$, which we show to originate in a changing overlap of wave
functions associated with the lattice constants. This changing overlap, in
turn, causes the unoccupied $p_z$ states to experience a significantly larger
energy shift than any other occupied state ($s$, $p_x$, or $p_y$), resulting in
this peculiar relationship. Our results explain and demonstrate the possibility
to tune the band gap by structural means, and thus the frequency at which
g-C$_3$N$_4$ absorbs light.
