Silicon clusters are prototype building blocks of nanoscale silicon materials, linking molecular chemistry with bulk semiconductor properties that underpin optoelectronics and quantum technologies. Herein, we revisit medium-sized silicon clusters through a workflow that combines machine-learned interatomic potentials (MLIPs), genetic-algorithm searches, electronic-structure geometry optimisations, and DLPNO-CCSD(T) benchmarking. The MLIPs were trained on TPSSh/def2-TZVP and r^2 SCAN-D3/def2-TZVP energies and forces, enabling rapid screening of candidate structures and broad exploration of the configurational landscape. Candidates within 15 kcal/mol of the lowest-energy structure identified by the genetic algorithm were reoptimised at the PBE0/def2-TZVP level, and we computed single-point energies with DLPNO-CCSD(T) in combination with the cc-pVDZ and cc-pVTZ basis sets. This workflow identifies new lowest-energy structures to date for Si18, Si20, Si30, and Si32. Across these clusters, the cc-pVDZ to cc-pVTZ shift in the relative energy difference between the new and previously reported minima ranges from 0.1 to 5.4 kcal/mol. For example, the corresponding gaps for Si20 are 14.7 and 11.5 kcal/mol with cc-pVDZ and cc-pVTZ, respectively, without changing the energetic ordering of the isomers. In contrast, putative new minima identified by DFT for Si17, Si22, Si23, and Si29 were not confirmed by correlated calculations, which placed these candidate structures up to 20 kcal/mol above the corresponding literature minima. This recurring discrepancy reveals a functional sensitivity in which compact cage-like motifs are overstabilised relative to more extended 𝒞_s and 𝒞_2v structures. We also report IR fingerprints for the identified low-energy structures to aid experimental assignment. Overall, these results show how MLIP-accelerated exploration, combined with selective high-level validation, enables efficient discovery and reliable assignment of low-energy structures in silicon clusters.
An orbital-resolved decomposition of the QTAIM delocalization index is introduced to partition interatomic electron sharing into internal, frontier, and cross contributions. The internal term isolates delocalization within the core and valence frameworks, while the frontier component quantifies the contribution of the highest occupied (HOMO) or singly occupied (SOMO) molecular orbitals, depending on the electronic state. The cross term quantifies coupling between frontier and internal orbitals arising from orbital mixing. The formalism is extended to open-shell systems within unrestricted density functional theory, providing a spin-resolved description of electron sharing and spin polarization effects between atomic basins. Frontier orbital degeneracy is further analyzed in relation to molecular symmetry and electronic structure. Applications to representative closed- and open-shell molecules demonstrate how orbital structure, symmetry breaking, and spin polarization govern these components. This algebraic partitioning transforms the delocalization index from a global scalar descriptor into a chemically resolved representation of interatomic electron sharing.
While the structures and energetics of arsine (AsH3) clusters have been characterized in the gas phase, their behavior under condensed-phase conditions, relevant to semiconductor deposition and atmospheric chemistry, remains unexplored. In this work, we present the first systematic investigation of solvent effects on the structures, relative stabilities, binding energies, and hydrogen bond networks of arsine clusters from dimer to hexamer using density functional theory at the PBEPBE/6–31 + + G(d,p) level with the Integral Equation Formalism Polarizable Continuum Model (IEF-PCM). The potential energy surfaces of all cluster sizes are thoroughly explored using the ABCluster program based on the artificial bee colony algorithm. Our results reveal several key findings: (1) The implicit solvent environment stabilizes numerous isomers that are unstable in the gas phase, demonstrating that the solvent expands the accessible configurational space of arsine clusters. (2) The relative energy gaps between isomers are systematically reduced in the solvent phase, compressing the energy landscape and increasing the structural diversity of thermally accessible configurations. (3) The binding energies in the solvent phase are consistently smaller than those in the gas phase, indicating that the dielectric continuum weakens intermolecular As-H⋯As hydrogen bonds. (4) The hydrogen bond network analysis reveals that BD, BBD, and BBDD-type molecular interactions enhance cluster stability, while B or D-type interactions reduce it. These results provide the first comprehensive picture of how implicit solvation modifies the potential energy surface of arsine clusters, with implications for understanding arsine aggregation in condensed-phase environments. These findings were further characterized by atoms in molecules topological analysis and the molecular tailoring approach, and contextualized by MP2/CBS calculations.
The effective fragment orbitals (EFOs) are uniquely, basis set-independent orbitals of any chemically defined atom or molecular fragment, obtained without the requirement of an external reference state, Lewis structure assumption, or population threshold. The EFOs are capable of rationalising bond polarisation, charge transfer, and back-donation at the bond level, and form an effective minimal basis for any atom or fragment regardless of the basis-set employed in the underlying calculation. Building on this foundation, the effective oxidation state (EOS) method assigns formal oxidation states directly from wave function analysis. This review presents the theoretical foundations of the EFOs and surveys a selected variety of chemical applications organised in four themes: formal oxidation state evaluation in ambiguous inorganic and organometallic systems, metal-ligand bonding characterisation in non-innocent and reactive complexes, quantification of donor-acceptor interactions, and prediction of macroscopic chemical properties including spin-crossover transition temperatures and Hammett substituent constants.
By integrating the contribution of chain conformation into the free-energy functional of chain molecules, we present a density functional theory approach to describe phase equilibria and interfacial tensions of n-alkanes. In the theoretical approach, the force field parameters of n-alkanes are taken directly from the TraPPE united-atom model, and the number of chain segments is strictly equal to monomer number; thus, the presented results are strict predictions. During an equilibrium calculation, the transforms of chemical potential and pressure versus density are carried out by taking the effect of volume size into account, and the two singular points of phase transition are obtained. The phase coexistence curves and vaporization enthalpies of a series of n-alkanes (from ethane to n-decane, as well as n-dodecane) are computed. Besides, surface tensions are calculated based on the equilibrium density profiles of vapor–liquid interfaces. These predictions are examined by the corresponding experimental data, and the errors are acceptable in industrial applications.
Inverted singlet–triplet (INVEST) materials, characterized by a negative singlet–triplet energy gap (ΔEST), hold great promise for next-generation Organic Light Emitting Diode (OLED) applications. However, their accurate computational description remains challenging, as conventional low-cost methods often fail to capture the subtle electron correlation effects governing the gap inversion. In this work, we present a systematic fine-tuning of the spin-component scaling (SCS) parameters for the second-order coupled cluster (CC2) and Algebraic Diagrammatic Construction (ADC(2)) methods, targeting the accurate prediction of ΔEST in INVEST systems. Using a set of eight triangular-shaped INVEST compounds, we screened opposite- and same-spin SCS parameters against Theoretical Best Estimate (TBE) reference values from Jacquemin and collaborators.[1] The optimal parameters (cos = 1.0, css = 1.4/1.6 for SCS-CC2/ADC(2)) differ markedly from the conventional ones, demonstrating that reparameterization is essential for a balanced description of the ΔEST in this class of molecules. The spin-component decomposition of the correlation energy allowed deriving a general expression to estimate TBE gaps directly from CCS excitation energies, offering a computationally inexpensive diagnostic tool. Beyond parameter optimization, SCS tuning proved to be a valuable instrument to reveal how electron correlation couples to topology-related features such as electron density redistribution. We also outlined a strategy for extending the SCS tuning to extended INVEST systems. Taken together, these results establish SCS-CC2 and SCS-ADC(2) as cost-effective and physically transparent alternatives to higher-level methods for the study of INVEST photophysics.
Global structure optimization in computational chemistry is often limited not by leaving the current local minimum, which can be achieved by sufficiently large random moves, but by proposing productive moves that exploit local funnel structure without losing diversity. Minima hopping addresses this problem through short molecular-dynamics escape trajectories, local relaxation, and history-dependent feedback, but its efficiency depends strongly on the initial escape direction. We benchmark a curvature-assisted variant in which inverse-Hessian information accumulated by Broyden–Fletcher–Goldfarb–Shanno (BFGS) and limited-memory BFGS (L-BFGS) relaxation is recycled as an escape model. This requires no explicit second derivatives and no additional force evaluations before proposing low-curvature directions. Lennard–Jones (LJ) clusters with 60–74 particles provide controlled landscapes for comparing random and softened random directions, single Hessian modes, multi-mode Hessian combinations, and mixed Hessian-random directions. Dense BFGS curvature information identifies physically meaningful escape subspaces and can reduce repeated local exploration. Single deterministic modes, however, oversample local funnels, and L-BFGS curvature information is not reliable enough for direct mode selection. Combining several BFGS modes improves robustness, but softened random directions with L-BFGS remain the lowest-cost baseline. Curvature reuse is therefore most useful when it provides an inexpensive soft-mode subspace while preserving stochastic diversity, especially when conventional softening or trial-move optimization is expensive.
Charge transport in single-molecule junctions depends strongly on molecular length, backbone conjugation, and molecule–electrode coupling. In this work, density functional theory (DFT) combined with quantum transport calculations is used to investigate length-dependent conductance in oligo (phenylene ethynylene) (OPE) molecular wires terminated with amine (–NH2), thiol (–SH), and direct carbon (–C) contacts. For all anchoring groups, conductance decreases exponentially with increasing molecular length. The extracted attenuation factors show a clear dependence on anchoring groups: thiol- and carbon-terminated junctions exhibit similar decay constants (β ≈ 0.23–0.24 Å⁻1), whereas amine-terminated junctions display a smaller value (β ≈ 0.14 Å⁻1). The theoretical trends are consistent with previously reported STM, MCBJ, and CP-AFM measurements for OPE junctions. Finally, a theoretical scaling relation is derived that quantitatively connects conductance decay in alkane and OPE molecular wires. The proposed relation reproduces both theoretical calculations and experimental datasets with high accuracy (R2 ≈ 0.89–0.93) and provides a theoretical framework for understanding conductance scaling across structurally distinct molecular wires.
Curcumin has attracted considerable interest as a natural medicine due to its diverse pharmacological activities. However, its high molecular flexibility presents a significant challenge for computational characterization. In this study, the conformational space of curcumin was systematically explored using an integrated computational workflow consisting of GFN2-xTB conformational sampling, CENSO-assisted conformer selection and refinement, K-means clustering, and subsequent final geometry optimization. Four different conformational search workflows were evaluated. Based on Boltzmann population analysis and computational efficiency, a workflow comprising conformational sampling, pre-screening, screening, clustering, and APFD/6–311 + + G(d,p) optimization was selected for subsequent investigations. Using this workflow, the effects of solvent polarity on the conformational stability and electronic properties of curcumin were investigated in the gas phase, hexane, ethanol, dimethyl sulfoxide, and water. The results show that solvent environments significantly stabilize both keto and enol conformers relative to the gas phase, with stabilization generally increasing with solvent polarity. Solvent-dependent structural variations were observed, particularly in the orientation of the methoxy groups in the enol form and the bending of the diketone moiety in the keto form. Furthermore, the HOMO–LUMO energy gap decreases in solution relative to the gas phase, with the enol form consistently exhibiting smaller energy gaps than the keto form. Overall, this study provides molecular-level insights into the solvent-dependent conformational and electronic properties of curcumin and demonstrates the effectiveness of an integrated conformational search strategy for highly flexible molecules.
The inclusion of benzoic acid (BA) in β-CD in distinct water-solvent systems poses a challenge for theoretical methodologies. The experimental data indicate a decrease in stabilization with increasing organic solvent content relative to water. In this work, the multi-equilibrium (QC/ME) and quantum computational/molecular dynamics (QC/MD) approaches, both using the GFN2-xTB semiempirical quantum computational method, were applied to investigate the formation of BA@β-CD inclusion complex in water, ethanol, and DMSO, as well as across solvent mixtures. According to the QC/ME data from the investigation of 1512 supramolecular systems, a preferred inclusion mode is one in which the –COOH group of the benzoic acid points toward the tail portion of the CD cavity (Form A). The QC/MD analysis identified this spatial arrangement as the most stable; however, a configuration in which the carboxyl group is oriented toward the wider rim of β-CD (Form B) is also predicted, consistent with experimental findings. MD simulations of β-CD inclusion complexes in explicit solvent indicate that these species are stable only in pure water. In contrast, in pure organic solvents and in solvent mixtures, even at low organic solvent fractions consistent with experimental conditions, the complexes exhibit very low stability and are primarily governed by competition between the guest molecule and solvent molecules for occupancy of the β-CD cavity.
Conventional analyses of indirect nuclear spin–spin coupling (SSC or J-coupling) in molecular systems typically focus on propagation through the framework of formal covalent bonds. However, in systems featuring functional groups in close proximity but separated by multiple covalent bonds, measurable through-space (TS) coupling can occur. Different mechanisms of TS coupling are commonly distinguished by the types of orbitals dominating them (e.g. lone-pair orbitals) or the type of non-covalent interaction keeping the coupling moieties in close proximity (e.g. hydrogen bonds). This article investigates the significance of the propagation of coupling specifically through π -orbitals. Using a novel approach for the evaluation of direct and indirect contributions of π -orbitals to SSC in the framework of non-hybrid density functional theory (DFT), we analyse the role of π -orbitals in TS coupling across small molecular gaps between two π -orbital containing moieties. Therein, we make special use of Komorovský’s version of the spin-spin coupling constant density to confirm the TS character, and of Malkina’s approach to the "indirect" π -orbital contribution to SSC via the transfer of spin polarisation ( π -TSP effect) to evaluate the π -character of the investigated SSCs. Our results demonstrate that measurable C–C TS SSC between π -carbons can occur. However, π -orbitals, beyond their structural role in enabling close proximity between the coupling moieties via π – π stacking interactions and CH ⋯π hydrogen bonds, appear to play only a minor role in the TS transfer of SSC between those moieties.
This theoretical study investigates the photophysical properties and excited-state dynamics of the monocarbonyl curcumin derivative (1E,4E)-1,5-bis(4-dimethylaminophenyl)penta-1,4-dien-3-one (CCM) in aprotic solvents. Using DFT/TD-DFT with the CAM-B3LYP functional and PCM solvation modeling, we analyze the solvent-dependent absorption spectra, $$\pi \rightarrow \pi ^*$$ π → π ∗ transition, and the large Stokes shifts observed experimentally. The $$S_0 \rightarrow S_1$$ S 0 → S 1 transition demonstrates a mixed contribution from locally excited (LE) and intramolecular charge transfer (CT) characters, showing minimal sensitivity to solvent polarity. The CT component accounts for 68–69% of the electronic reorganization, with charge transfer from the N,N-dimethylaniline (donor) units to the divinyl ketone (acceptor) core, as indicated by natural transition orbitals (NTOs) and Hirshfeld population analysis. XMS-CASPT2 multiconfigurational calculations corroborate the TD-DFT picture, revealing a bright $$^1(\pi \pi ^*)$$ 1 ( π π ∗ ) state containing a mixture of LE and CT character. Gas-phase excited-state optimizations show that the lowest excited state is an $$^1(n\pi ^*)$$ 1 ( n π ∗ ) dark state with negligible oscillator strength, while the bright $$^1(\pi \pi ^*)$$ 1 ( π π ∗ ) state lies slightly above it; consequently, fluorescence originates from the relaxed $$^1(\pi \pi ^*)$$ 1 ( π π ∗ ) minimum. Large Stokes shift (3607 to 5773 cm $$^{-1}$$ - 1 ) has been linearly correlated with solvent polarity by Lippert-Mataga plot (R = 0.985), driven by dipole moment changes ( $$\Delta \mu \sim 3.1-3.6$$ Δ μ ∼ 3.1 - 3.6 Debye) upon excitation. Calculations reproduce experimental absorption and emission trends, that is, the redshift in polar solvents, and validate CAM-B3LYP for curcumin derivatives. This work elucidates the mixed ICT-LE character in various solvents and provides design insights for fluorophores in sensing and optoelectronics.
Linear carbon clusters Cn represent one-dimensional, highly reactive assemblies of carbon atoms that serve as fundamental structural units for a wide range of carbon nanomaterials, including graphene and carbon nanotubes. Owing to their unique structural and electronic properties, the investigation of their vibrational characteristics—particularly the fundamental vibrational frequencies—plays a crucial role in understanding their stability, bonding, and chemical reactivity. These vibrational properties are commonly explored through experimental techniques such as Raman and infrared (IR) spectroscopy, as well as through theoretical frameworks. In the present study, the Lie Algebraic Model (LAM) is employed to investigate the stretching and bending vibrational modes of linear carbon clusters C3, C4, C5, C6, C7, and C8. Within this algebraic framework, a model Hamiltonian is constructed that explicitly incorporates the pseudo-Cnv dynamical symmetry associated with these molecular systems. The formulation utilizes a compact set of algebraic parameters capable of effectively describing the C–C stretching and bending dynamics. Furthermore, the invariant Majorana and Casimir operators are systematically derived to characterize the vibrational structure of the clusters. The results obtained from the algebraic treatment exhibit a high degree of consistency with available experimental observations and other theoretical calculations, demonstrating the reliability and effectiveness of the Lie algebraic approach in describing the vibrational behaviour of linear carbon clusters.
Density functional theory calculations have been performed to investigate the influence of confinement on the stability and structure of linear and cyclic EY2 isomers (E = C, Si, Ge; Y = O, S) within C-6(0), C-7(0), and C-8(0) fullerenes. For oxide systems, the energy gap between the linear and cyclic forms of CO2 and SiO2 reduces inside C60, although the linear isomer remains energetically more favorable. In the case of GeO2, the relative stability between linear and cyclic forms changes inside C-6(0), with cyclic forms becoming more stable, which are less stable in the free state. For sulfide systems, CS2 retains its linear geometry within C-7(0) and C-8(0) and remains energetically more stable than the cyclic form. In contrast, the linear forms of SiS2 and GeS2 transform to bent structures inside C-7(0) and C-8(0), with the cyclic isomers becoming energetically more favorable, which are less stable in the free state. Frequency analysis confirms that cyclic isomers correspond to true minima, whereas all linear analogues (except CO2) exhibit imaginary bending modes inside C60, indicating instability. Additionally, the influence of the guest molecules on the electronic properties of the fullerene cages, including the HOMO-LUMO gap, vertical ionization potential (VIP), vertical electron affinity (VEA), and charge transfer between guest species and host cages, is discussed.
Fe-doped graphyne (Fe–GY), defined here as an H1-like hollow-site Fe-doped γ-graphyne single-atom model, is a promising 2D carbon platform for chemiresistive gas sensing because transition-metal dopants can introduce chemically active sites while the conjugated carbon network provides an efficient charge-transport channel. Herein, density functional theory calculations were performed to elucidate the adsorption behavior and electronic-response mechanism of Fe–GY toward three representative volatile organic compounds (VOCs), namely formaldehyde (HCHO), acetone (CH3COCH3), and benzene. The computed adsorption energies indicate strong binding for oxygenated VOCs (HCHO: − 1.349 eV; acetone: − 0.948 eV) and moderate binding for benzene (− 0.528 eV). Examination of atmospheric species shows that O2 binds appreciably to the Fe site (− 0.881 eV), while H2O also shows moderate interaction (− 0.377 eV), indicating that these species may compete for active sites under ambient conditions rather than being negligible interferents. Charge analysis reveals pronounced interfacial charge redistribution for HCHO and acetone, whereas benzene shows nearly negligible net charge transfer, consistent with distinct interaction natures. HLE17 electronic-structure calculations further demonstrate that adsorption induces substantial band-edge modulation: the nearly gapless Fe–GY substrate (0.007 eV) develops opened gaps upon VOC adsorption (0.192, 0.362, and 0.392 eV for HCHO, acetone, and benzene, respectively). Additional orbital analyses indicate that the benzene-induced gap opening arises from functional-sensitive adsorbate–substrate frontier-level alignment rather than strong charge-transfer-driven orbital hybridization. Together with PDOS, OPDOS/COOP, charge-density-difference, IGMH, magnetic-moment, and AIMD analyses, these results provide a more cautious mechanistic picture linking adsorption energetics, spin-dependent electronic perturbation, and sensing-relevant electronic response, highlighting Fe–GY as a viable candidate platform for VOC adsorption while emphasizing the need to consider O2 competition under realistic atmospheres.
In this work, we propose a detailed analysis of the effect of pressure on a prototype Diels–Alder reaction, namely the one occurring between diphenylfulvene and maleimide, recently experimentally explored under ball-milling conditions. Our results are in good agreement with the experimental findings in predicting the endo-product as the major isomer under kinetic control. An analysis of the non-covalent interactions (NCI) allowed to clarify the origin of this selectivity, which is attributed to a loss of symmetry in the transition state leading to the exo-product, caused by steric repulsion between the maleimide carbonyl group and one of the phenyl rings of the diphenylfulvene, not totally compensated by a weak hydrogen-bond interaction between these two groups. Activation strain model (ASM) analysis shows that the selectivity originates from the balance between distortion and interaction energies. Interestingly, our calculations predict that an inversion in selectivity towards the exo-product can be envisaged at high pressures. Under compression, interaction stabilization increases more rapidly for the exo-pathway but is accompanied by a larger distortion penalty; the selectivity inversion occurs when interaction stabilization outweighs the additional distortion energy. The NCI and ASM analyses are thus complementary, providing, respectively, structural and energetic interpretations of the pressure-dependent selectivity. This finding opens new perspectives on the effect of mechanical constraints on reactivity and suggests a possible route towards an exo-selective Diels–Alder reaction.
In this study, the impact of spatial confinement on the linear and nonlinear electrical properties of the helium hydride ion ( HeH^+ ) is investigated using highly accurate ab initio CISD method with an extensive daug-cc-pV6Z basis set. The confinement environment is modeled by a cylindrical harmonic oscillator (HO) potential, and the variation of the dipole moment and (hyper)polarizabilities on the internuclear distance is analyzed along the entire dissociation coordinate. Our findings demonstrate that the spatial restriction leads to a systematic reduction in all investigated electrical properties, a phenomenon primarily attributed to the widening of the HOMO–LUMO energy gap and electronic density compression.
In this study, molecular dynamics (MD) simulation is employed to investigate the influence of resins on the behavior of asphaltenes at the oil–water interface, with simulations conducted to capture the dynamic interfacial behavior over a sufficient timescale. It is found that different asphaltene molecules exhibit distinct distribution patterns at the interface, which is closely related to their hydrophilicity. Specifically, asphaltene 1 has a solvation free energy of − 10.36 kJ/mol, with its hydrophilic groups accounting for 38.7
Arsine (AsH3) clusters—heavy Group 15 hydride systems of critical importance in semiconductor manufacturing and atmospheric arsenic chemistry—lack rigorous high-accuracy ab initio quantification of their binding energetics, hindering the development of reliable computational methods for larger arsenic-containing systems. Here we present a systematic investigation of the structures and binding energies of arsine clusters ranging from dimers to hexamers, employing a validated composite scheme to establish benchmark energies at the CCSD(T)/CBS (coupled-cluster singles, doubles, and perturbative triples extrapolated to the complete basis set) limit. We further evaluate the performance of ten density functional theory functionals spanning hybrid, dispersion-corrected, and long-range corrected categories against our benchmark dataset. Our results reveal that dispersion interactions contribute nearly 40
Density functional theory calculations have been performed to investigate the influence of confinement on the stability and structure of linear and cyclic EY₂ isomers (E = C, Si, Ge; Y = O, S) within C₆₀, C₇₀, and C₈₀ fullerenes. For oxide systems, the energy gap between the linear and cyclic forms of CO₂ and SiO₂ reduces inside C60, although the linear isomer remains energetically more favorable. In the case of GeO₂, the relative stability between linear and cyclic forms changes inside C₆₀, with cyclic forms becoming more stable, which are less stable in the free state. For sulfide systems, CS₂ retains its linear geometry within C₇₀ and C₈₀ and remains energetically more stable than the cyclic form. In contrast, the linear forms of SiS₂ and GeS₂ transform to bent structures inside C₇₀ and C₈₀, with the cyclic isomers becoming energetically more favorable, which are less stable in the free state. Frequency analysis confirms that cyclic isomers correspond to true minima, whereas all linear analogues (except CO₂) exhibit imaginary bending modes inside C60, indicating instability. Additionally, the influence of the guest molecules on the electronic properties of the fullerene cages, including the HOMO–LUMO gap, vertical ionization potential (VIP), vertical electron affinity (VEA), and charge transfer between guest species and host cages, is discussed.
