Exploring the role of electronic structure on photo-catalytic behavior of carbon-nitride polymorphs

A fully self-consistent density-functional theory (DFT) with improved functionals is used to provide a comprehensive account of structural, electronic, and optical properties of C$_{3}$N$_{4}$ polymorphs. Using our recently developed van Leeuwen-Baerends (vLB) corrected local-density approximation (LDA), we implemented LDA+vLB within full-potential N$^{th}$-order muffin-tin orbital (FP-NMTO) method and show that it improves structural properties and band gaps compared to semi-local functionals (LDA/GGA). We demonstrate that the LDA+vLB predicts band-structure and work-function for well-studied 2D-graphene and bulk-Si in very good agreement with experiments, and more exact hybrid functional (HSE) calculations as implemented in the Quantum-Espresso (QE) package. The structural and electronic-structure (band gap) properties of C$_{3}$N$_{4}$ polymorphs calculated using FP-NMTO-LDA+vLB is compared with more sophisticated hybrid-functional calculations. We also perform detailed investigation of photocatalytic behavior using QE-HSE method of C$_{3}$N$_{4}$ polymorphs through work-function, band (valence and conduction) position with respect to water reduction and oxidation potential. Our results show $\gamma$-C$_{3}$N$_{4}$ as the best candidate for photocatalysis among all the C$_{3}$N$_{4}$~polymorphs but it is dynamically unstable at `zero' pressure. We show that $\gamma$-C$_{3}$N$_{4}$ can be stabilized under hydrostatic-pressure, which improves its photocatalytic behavior relative to water reduction and oxidation potentials.