Pavel V. Avramov

Graphitic carbon nitride (g‐C ₃ N ₄ ) is a two‐dimensional polymeric semiconductor whose properties are strongly constrained by lattice topology. By combining experiments (electron microscopy, diffraction, spectroscopy) with density functional theory calculations, we investigate the structural and electronic changes induced by phosphorus incorporation into triazine‐based g‐C ₃ N ₄ (g‐CN1). Phosphorus preserves global lattice connectivity but triggers lattice relaxation and corrugation, observed experimentally as sharp structural ripples (6.5–13.4 nm) in P@g‐CN1 compared with smooth sheets in pristine g‐CN1. DFT calculations semi‐quantitatively reproduce the corrugation period and amplitude and further reveal that phosphorus incorporation introduces weakly dispersing, localized midgap states near the Fermi level. A comparison between a planar‐constrained model and a fully relaxed structure shows that these midgap states are primarily chemically driven (dominant phosphorus orbital contribution), while lattice corrugation shifts the valence and conduction band edges downward by 1.2 eV and 0.6 eV, respectively and dramatically modulate the peaks shape and intensity. The calculated midgap states act as efficient non‐radiative recombination centers, providing a direct explanation for the experimentally observed photoluminescence quenching. Together, the experimental and theoretical results establish corrugation and midgap electronic states as intrinsic features of heteroatom incorporation into polymeric two‐dimensional materials, with direct implications for their optoelectronic and photocatalytic functionality.

This review provides a comparative analysis of the structure and physical properties of low-dimensional aperiodic crystalline solids, aiming to elucidate the origin and nature of aperiodicity in reduced-dimensional lattices. The breakdown of periodicity in low-dimensional systems arises from several mechanisms, including the suppression of specific force constants, thermodynamic instabilities, and topological constraints associated with imperfect space filling. At the nanoscale, certain cubic crystalline materials can form finite, zero-dimensional multiply twinned particles (MTPs) with decahedral or icosahedral symmetry. These clusters lack translational invariance and experience intrinsic structural strain due to solid-angle mismatch at twin junctions, which limits their characteristic size and renders them finite aperiodic solids. Particular attention is devoted to the electronic and spin properties of pentagonally symmetric MTPs: icosahedral particles exhibit symmetry-protected spin degeneracy consistent with centrosymmetric lattices, whereas non-centrosymmetric decahedral particles may display spin polarization and emergent low-dimensional magnetism. Collectively, these systems illustrate the diverse physical origins, manifestations, and consequences of aperiodicity in low-dimensional crystalline matter.

Graphitic carbon nitride (g-C₃N₄) is a promising metal-free photocatalyst, yet its efficiency remains limited by rapid charge recombination. Heteroatom doping offers an effective means to tailor its electronic structure and enhance photocatalytic performance. In this study, structural and electronic modifications in triazine-based g-C₃N₄ (g-CN1) induced by phosphorus incorporation were systematically investigated through a combination of experimental characterization and density functional theory (DFT) calculations, providing complementary insights into the atomic-scale bonding and electronic properties of pristine and phosphorus-doped g-C₃N₄ (P@g-CN1). Both pristine g-CN1 and P@g-CN1 were synthesized via thermal polycondensation of melamine using H₃PO₄ as the dopant source. Transmission electron microscopy, X-ray diffraction, and photoluminescence spectroscopy reveal that phosphorus doping preserves the fundamental lattice topology while inducing lattice relaxation, surface corrugation, and flake extension—features that are well rationalized by the Topology Conservation Theorem. Phosphorus incorporation markedly suppresses charge recombination and enhances charge separation efficiency in the P@g-CN1 composite. DFT analysis confirms that phosphorus atoms induce downward shifts of the valence and conduction bands and introduce localized midgap states near the Fermi level, thereby enhancing electronic delocalization and facilitating carrier transport. The P@g-CN1 system retains its semiconducting character with pronounced σ–π hybridization between carbon and nitrogen 2p orbitals. The strong agreement between experimental results and theoretical analysis underscores the high degree of complementarity between these approaches. This provides a coherent understanding of the structure–property relationships in phosphorus-doped g-C3N4, thereby guiding the rational design of next-generation, metal-free two-dimensional photocatalysts and photovoltaic materials.

The spectral‐luminescence properties and photochemical conversions of phenol were analyzed for an isolated molecule as well as in water solvents in a continuum implicit model and explicit atomistic surroundings. This involved employing cut‐edge hybrid quantum‐classical methodologies to generate static optical spectra and the excited dissipative crossing potential energy curves. A combination of electronic excitations, gradient calculations, and embedding electrostatic potential fitting charges on quantum‐classical molecular dynamic propagation trajectories provided statistically averaged absorption spectra. The mixed‐reference spin‐flip multiconfigurational linear response method based on reference triplet preprocessed in the time‐dependent density‐functional theory was utilized to determine conical intersections between the lowest excited and ground states, as well as two‐stage transitions from the second excitation to the ground state. Non‐adiabatic quantum‐classical molecular dynamics defined photodissipative trajectories of excited states, their lifetimes, and crossing points through trajectory surface hopping together with the mixed‐reference spin‐flip and embedding electrostatic potential fitting approaches. Dyson orbitals of the extended Koopmans' theorem were applied to reveal the nature of molecular states at conical intersections and key points on photodynamic trajectories. Potential hydroxyl group cleavage predicted with conical intersections searching turns to “swift” OH deprotonation through |π→⟩ transition along photodynamic propagations in contrast with “long” processes leading to benzene ring deformation with stable OH bond.

This Review provides the first comprehensive overview of the structure and properties of exotic sp³-crystalline aperiodic cyclic multiply twinned nano- (10-100 nm) and meso- (up to 1 mm) diamond particles (MTPs) exhibiting pentagonal symmetry. It spans their independent experimental discoveries (1963, 1964, 1972, and 1983) and theoretical structural insights (1993) to recent advancements. The Review focuses on high-symmetry MTPs formed by the fusion of multiple cubic diamond fragments through [111] facets. The sp³ diamond lattice of individual fragments offers a vast range of MTP varieties. These particles are shown to be a special case of aperiodic crystalline solids with limited dimensions and rotational symmetry, leading to a breakdown of translational invariance. Detailed mathematical analysis of the MTPs' lattices highlights the crucial role of central cores in determining the symmetry and effective dimensions of these structures. Both structural and kinetic aspects of the formation mechanisms of pentagonal diamond particles are considered, revealing the main role of embryo seeds (low fullerenes, polyhexacyclo[5.5.1.1^2,6.1^8,12.0^3,11.0^5,9]pentadecane (C₁₅), and polyheptacyclo[5.5.1.1^2,7.1^9,14.0^3,13.0^6,11]octadecane (C₁₈)) in determining the MTPs' symmetry and structure. The effective dimensions of multiply twinned diamonds are shown to be limited by structural stress caused by the mismatch of perfect pentagonal and tetrahedral dihedral angles. The extraordinary mechanical and electronic properties of multiply twinned diamonds are discussed, highlighting that hexagonal interfaces between cubic diamond fragments may determine exceptional ultrahard and quantum characteristics. The MTP X-ray diffraction spectra reveal clear pentagonal patterns with single (diamond decahedrons or dodecahedrons) or ten (diamond icosahedra) central 5-fold axes. A comparative analysis of experimental structural data and simulations at different theoretical levels demonstrates a perfect correspondence of theoretical models with crystalline lattices.