Density functional and graph theory computations of vibrational, electronic, and topological properties of porous nanographenes

Abstract We have utilized the density functional theory (DFT) in conjunction with graph‐theoretical techniques to compute the vibrational, electronic and topological properties of porous nanographenes starting with the building blocks of kekulene, septulene, extended kekulenes, and circumkekulene. Furthermore, graph theoretically based spectral polynomials and other topological properties including Kekulé counts, delocalization energies, and resonance energies are computed for such structures and larger tessellations of kekulenes which are precursors to nanographene belts with multiple pores. The success of the DFT methods is demonstrated with the computed vibrational modes and infrared and Raman spectra of several of these structures. The computed spectral polynomials and the spectra reveal the underlying patterns of the energy levels and structural features and hence suggest the possibility of integration of graph theory with quantum chemical techniques for the computations of properties of large porous graphenes including the possibility of the Pariser–Parr–Pople (PPP) method with parameters extracted from machine learning of the DFT computations on a combinatorial library of precursors. Finally, the computations reveal that the porous structures can be tailored for sequestration of various ions including heavy metal ions for environmental remediation.