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g-C$_3$N$_4$ is a promising material for hydrogen production from water viaphoto-catalysis, if we can tune its band gap to desirable levels. Using acombined experimental and ab initio approach, we uncover an almost perfectlylinear relationship between the band gap and structural aspects ofg-C$_3$N$_4$, which we show to originate in a changing overlap of wavefunctions associated with the lattice constants. This changing overlap, inturn, causes the unoccupied $p_z$ states to experience a significantly largerenergy shift than any other occupied state ($s$, $p_x$, or $p_y$), resulting inthis peculiar relationship. Our results explain and demonstrate the possibilityto tune the band gap by structural means, and thus the frequency at whichg-C$_3$N$_4$ absorbs light.

Structural band-gap tuning in g-C$_3$N$_4$