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In quasi-1D π-conjugated polymers such as trans-polyacetylene and polyenes, electron correlation effects determine the "reversed" excited state ordering in which the lowest two-photon 2A g state lies below the lowest one-photon 1B u state. In this work, we present conclusive theoretical evidence of reversed excited state ordering in fairly 2D π-conjugated systems, namely, diamond-shaped graphene quantum dots (DQDs). Our electron correlated calculations show that DQDs begin to exhibit reversed excited ordering with increasing size, in disagreement with independent-particle picture. This signals the onset of strong correlation effects which renders them nonluminescent.Further, we calculate and analyze the two-photon absorption (TPA) spectra as well as photoinduced absorption (PA) spectra of these systems and find excellent agreement with the available experimental results. Our investigations demonstrate that unlike a strictly 1D system like transpolyacetylene, the non-linear and excited state absorptions in DQDs are highly intricate, with several even parity states responsible for strong absorptions. Our results could play an important role in the design of graphene-based non-linear optical devices.

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The electronic and optical properties of graphene quantum dots can be significantly tailored by doping it with heteroatoms, thus extending its potential applications. In this work, we have employed time-dependent density functional theory to systematically explore the effect of introduction of nitrogen atoms in varying concentration at pyridinic and graphitic configuration in armchair and zigzag-edged triangular shaped graphene quantum dots (TQDs) of different sizes. Our results indicate that the electronic band-gap in these N-doped systems can be effectively tuned by varying the configuration as well as concentration of dopants and nature of edge-termination. The variation of electronic band-gap is critically determined by the localized/delocalized nature of molecular orbitals and presence of additional energy levels due to dopant nitrogen atoms. However, the significance of these extra energy levels in modulating the optical properties (appearance of characteristic N-dopant absorption peaks) becomes conspicuous only for specific configuration and concentration of nitrogen atoms. In addition, our studies have attributed the strong dependence of blue/red-shift of absorption spectra and variation in the peak profile to position as well as concentration of dopant atoms and edge-termination pattern. Further, it is observed that the effect of increasing size of TQDs on the strength of most intense absorption peak of pyridinic N-doped TQDs is remarkably different from graphitic N-doped systems. This selective manipulation of optical properties in TQDs due to different N-doping pattern can open up new frontiers for rational design of novel optoelectronic devices.