Understanding and quantifying electronic structure complexity remains a central challenge in quantum chemistry. In this work, we introduce a spectral framework based on the distribution of second-order Møller–Plesset (MP2) excitation denominators, providing a statistical characterization of the excitation-energy landscape underlying perturbative correlation treatments. We define a set of descriptors that capture complementary features of the denominator spectrum, including its energetic span, the accumulation of low-energy excitations, and its statistical organization through entropy. These quantities enable a resolved characterization of the excitation manifold beyond single-parameter descriptions. Applying this framework to the S22 benchmark set (57 molecules), we identify systematic relationships between the proposed spectral descriptors across chemically diverse systems. In particular, the behavior of the I_ND^MAX diagnostic is found to correlate with distinct regions of the spectral descriptor space, suggesting a connection between occupation-based diagnostics and the organization of excitation energies. The results indicate that systems with compressed denominator spectra tend to exhibit higher spectral entropies and larger I_ND^MAX values, whereas broader spectra are generally associated with lower entropy and smaller diagnostic values. The present work introduces a complementary perspective for analyzing electronic structure complexity through the statistical properties of the MP2 denominator spectrum and provides a framework for exploring relationships between excitation-energy distributions and established electronic structure diagnostics.
Cannabidiol (CBD) is a highly lipophilic bioactive compound whose poor aqueous solubility limits its formulation and bioavailability. Cyclodextrins provide a promising strategy for improving CBD solubilization through host–guest inclusion complexation; however, the molecular factors governing the relative stability of CBD complexes with different cyclodextrin hosts remain incompletely understood. In this study, a multilevel computational investigation was performed to characterize the energetic, structural, and electronic features of CBD inclusion complexes with α-, β-, γ-, and hydroxypropyl-β-cyclodextrin (HP-β-CD). Extensive conformational sampling using the GFN2-xTB method was combined with a comparative assessment of three dispersion-corrected DFT approaches, BLYP-D4, B97-3c, and r2SCAN-3c, together with implicit solvation calculations. The lowest energy complexes were further characterized through Gibbs free energy calculations, frontier molecular orbital analysis, the Independent Gradient Model based on Hirshfeld partition (IGMH), Pair Interaction Energy Decomposition Analysis (PIEDA), and Natural Bond Orbital (NBO) analysis. At the r2SCAN-3c/SMD level, the calculated Gibbs free energies of complexation were − 23.34, − 51.63, − 37.50, and − 73.30 kJ mol−1 for α-CD, β-CD, γ-CD, and HP-β-CD, respectively, yielding the stability order HP-β-CD > β-CD > γ-CD > α-CD, in qualitative agreement with the available experimental trends. Structural and interaction analyses indicate that complex stability results from a balance between host–guest geometric complementarity, van der Waals contacts, electrostatic interactions, polarization/charge-transfer contributions, hydrogen bonding, and solvent effects. Frontier molecular orbitals remain predominantly localized on CBD, indicating limited host–guest orbital mixing, whereas IGMH, PIEDA, and NBO analyses reveal complementary features of the noncovalent interactions responsible for complex stabilization. Within the computational models considered, HP-β-CD exhibits the most favorable thermodynamic complexation, although this result refers to the specific hydroxypropyl substitution pattern investigated. These findings provide molecular-level insight into CBD–cyclodextrin recognition and clarify how cavity size and cyclodextrin functionalization influence host–guest complexation.
Aromaticity is one of the most influential and widely employed concepts in chemistry, encompassing characteristic features of cyclic electron delocalization and its structural, energetic, and magnetic manifestations. Over the years, numerous descriptors have been developed to characterize these complementary, and sometimes overlapping, aspects of aromaticity. Each criterion provides distinct information, but its interpretation depends on the physical property being examined. In this minireview, we present a concise overview of the most commonly used aromaticity indices, emphasizing their theoretical foundations, interpretation, applicability, and limitations. Particular attention is devoted to electronic descriptors based on electron delocalization, including bond-order-based indices, multicenter indices, and the electron density of delocalized bonds, together with their spin-resolved formulations relevant to open-shell systems and excited-state aromaticity. Magnetic criteria are discussed through magnetically induced current densities, ring-current strengths, and nucleus-independent chemical shifts. Geometric descriptors, as well as energetic measures including resonance and aromatic stabilization energies, are also briefly summarized. The examples presented illustrate that no single index provides a universally applicable description of aromaticity. Reliable assessments therefore require complementary descriptors and a critical understanding of what each measure represents and how methodological choices may affect its interpretation. This minireview aims to serve as an accessible guide to aromaticity indices across a broad range of molecular systems, from classical organic compounds to heteroaromatics, organometallic species, and expanded conjugated macrocycles.
Poly(ADP-ribose) polymerase 1 (PARP1) is an important drug target for various diseases, with several drugs approved for clinical use. However, the development of next-generation PARP1 inhibitors is necessary due to the adverse effects, toxicity, and drug resistance associated with current inhibitors. Therefore, we developed eight machine learning (ML) models using a newly developed molecular representation called surface-property spectrum. They were systematically evaluated on both the test set and a manually curated external dataset comprising 100 bioactive PARP1 inhibitors and 100 decoy compounds. It was found that, without an external dataset, model choice can be biased, underscoring the importance of large and high-quality data for ML models. We also observed that the multi-layer perceptron model generalizes to unseen data, demonstrating its ability to predict novel PARP1 inhibitors.
First-principles calculations have been carried out to explore the effects of non-metal atoms (B, C, N, P, S and Se) surface modification on the structural, electronic and optical properties of ZnO monolayer (ZnO-m). We find that (B, P, S, Se)-ZnO-m, CO-ZnO-m and (CZn, NZn, PZn)-ZnO-m all exhibit strong visible-light absorption with pronounced optical absorbance (up to 105 cm−1), while B adsorption as well as BZn, 2CZn and 2NZn doping could extend light absorption into the near-infrared region. In particular, 2CZn– and 2NZn–ZnO-m display high absorption peaks over a wide spectral range. Moreover, P–, CZn– and 2CZn–ZnO-m possess suitable band gaps (1.847, 1.577 and 1.141 eV) for solar-cell applications. Furthermore, our calculations also predict that S–ZnO-m with band gap of 2.601 eV is an ideal visible-light-driven photocatalyst for water splitting with good acid–alkali resistance. The work provides a valuable theoretical guidance for the application of non-metal modified ZnO-m in photoelectric devices and photocatalytic water splitting.
