While direct adiabatic-to-diabatic (ATD) transformations for two-state systems have been extensively studied, their extension to three-state systems remains less explored. Building upon the framework of the valence bond wave function-based automatic diabatization (VBADA) approach, this study investigates the application of various O(3) group unitary transformations for the construction of three-state diabatic representations. These include Householder and composite Givens transformations, Euler angles, Tait-Bryan angles, quaternions, and the Rodrigues' rotation formula. Using the dissociation of lithium hydride and the hydrogen abstraction reaction H + HCl → Cl + H2 as test cases, we evaluate the performance of these different unitary matrices in the diabatization process. Our results reveal a clear performance hierarchy among the O(3) parametrizations. While transformations such as Householder reflections and composite Givens rotations show numerical instability in intermediate geometric regions, and Euler/Tait-Bryan angles are prone to gimbal-lock singularities, both the Rodrigues' rotation formula and quaternion-based parametrizations consistently generate smooth, stable diabatic states with well-localized chemical character.

Energy decomposition analysis(EDA)has become a powerful approach for elucidating chemi-cal bonding and non-covalent interactions,especially in com-plex and multiscale systems.Embedding strategies combin-ing high-level quantum chemi-cal methods with more approxi-mate treatments of the environ-ment provide a promising bal-ance between accuracy and effi-ciency,yet existing embedding schemes of EDA approaches im-plementations are often frag-mented and software-depen-dent.To address this challenge,we present PyMEDA,a unified,open-source interface framework for multiscale energy decomposition analysis.Through a modular design,PyMEDA standardizes interfaces to diverse quantum mechanical,molecular mechanics,and semi-empirical backends(initially XEDA,OpenMM,and xtb),enabling the unified implementation of workflows for both conventional and embedding-type EDA schemes,such as DM-EDA(QM/MM)and DM-EDA(EB).By providing extensibility,repro-ducibility,and automation,PyMEDA offers a flexible environment to advance multiscale in-teraction analysis and facilitates the future development of embedding-based EDA methods.

The crucial role of ligands in modulating metallophilic interactions, primarily through attractive dispersion and electrostatic forces, has already been widely recognized. However, while most theoretical investigations have focused on intermolecular models, much less attention has been given to intramolecular metallophilic interactions, where metal centers are connected by covalent ligand bridges. In this work, a combination of quantum-chemical approaches was employed to elucidate the intrinsic nature of argentophilic interactions in a series of intra- and intermolecular Ag(I) complexes. The intramolecular systems feature ligand-supported argentophilic interactions bridged by phenylene or pyridylene linkers; substitution of the phenylene bridge by a pyridylene unit exerts only a minor effect on the geometry and interaction strength. Both inter- and intramolecular complex interactions are governed predominantly by ligand-stacking effects, whereas direct Ag-Ag' contributions are minimal. Energy decomposition analysis (EDA) and the independent gradient model based on Hirshfeld partition (IGMH) show that dispersion interactions provide the major attractive component, followed by electrostatics, while orbital contributions are comparatively small. The isolated Ag-Ag' interactions are intrinsically weak and can be either slightly attractive or repulsive. Overall, this study highlights that the ligand frameworks play a decisive role in stabilizing both intra- and intermolecular argentophilic interactions, providing fundamental insights for the design of ligand architectures that promote controlled metallophilic aggregation.

Atomically precise metal nanoclusters (NCs) offer a unique platform for efficiently converting CO2 into highvalue chemicals, yet their performance is hindered by high energy barriers and complex pathways. Herein, we creatively employed a precise ligand-engineering strategy to synthesize a series of highly stable Cu$ NCs served as demonstrative models to elucidate the role of copper kernel along with electronic modulation in determining C2+ production. Modifying the ligands with electron-donating groups significantly enhanced C2+ production on Cu8-3, which exhibited an impressive C2+ Faradaic efficiency of 64.9 % at -1.3 V vs. RHE. Furthermore, to the best of our knowledge, Cu8-3 is the first copper cluster reported to produce a C3 product (n-PrOH). Experimental results and theoretical calculations reveal that electron-donating ligands induce the formation of electron-rich Cu$ centers, modulating the Cu d-band center closer to the Fermi level and facilitating proton-coupled electron transfer (PCET) process, thus stabilizing the key C2+ intermediates via electrostatic interactions and thermodynamically controlling product selectivity. Furthermore, steric effects introduced via ligand engineering in Cu8-4 demonstrated that multicore Cu sites are critical for generating C2+ products. This study underscores the potential of NCs with precise structural regulation as advanced electrocatalysts for enhancing CO2 reduction efficiency.

Asymmetric organocatalysis represents a pivotal yet challenging concept in modern organic chemistry education. To enhance interdisciplinary learning, we designed an interdisciplinary instructional project focusing on the l-proline-catalyzed asymmetric Mannich reaction. In the whole schedule, the experimental section includes the synthesis, purification, and characterization of the products, while the computational chemistry section involves the computation for the reaction potential energy surface and the energy decomposition analysis (EDA)-based quantification of noncovalent interactions. It cultivates key skills in molecular modeling and data analysis while offering students insights into fundamental organic concepts, such as stereoselectivity, steric effects, and electronic effects. Implemented as a capstone project in advanced organic chemistry courses, this project effectively introduces theoretical concepts of intermolecular interactions and provides a practical and easy way for teaching catalytic mechanisms.

Atomically precise metal nanoclusters (NCs) offer a unique platform for efficiently converting CO2 into high-value chemicals, yet their performance is hindered by high energy barriers and complex pathways. Herein, we creatively employed a precise ligand-engineering strategy to synthesize a series of highly stable Cu8 NCs served as demonstrative models to elucidate the role of copper kernel along with electronic modulation in determining C2+ production. Modifying the ligands with electron-donating groups significantly enhanced C2+ production on Cu8-3, which exhibited an impressive C2+ Faradaic efficiency of 64.9 % at −1.3 V vs. RHE. Furthermore, to the best of our knowledge, Cu8-3 is the first copper cluster reported to produce a C3 product (n-PrOH). Experimental results and theoretical calculations reveal that electron-donating ligands induce the formation of electron-rich Cu8 centers, modulating the Cu d-band center closer to the Fermi level and facilitating proton-coupled electron transfer (PCET) process, thus stabilizing the key C2+ intermediates via electrostatic interactions and thermodynamically controlling product selectivity. Furthermore, steric effects introduced via ligand engineering in Cu8-4 demonstrated that multicore Cu sites are critical for generating C2+ products. This study underscores the potential of NCs with precise structural regulation as advanced electrocatalysts for enhancing CO2 reduction efficiency.

Many-body effects play a governing role in molecular assembly and recognition, yet their physical origins are not fully elucidated. In this work, we extend the recently developed real-space energy decomposition analysis method, called DM-EDA(RS), to enable the direct visualization and atomic-level quantification of three-body interaction energies. By projection of energy components onto three-dimensional grids, this method uniquely bridges the gap between integrated energy numbers and spatially resolved chemical insight. The results show that three-body cooperativity is driven by highly localized, counterdirectional flows of polarization energy localized on specific atoms. DM-EDA(RS) identifies the real-space energy distribution, directly mapping how interaction terms are transferred across molecular networks. Remarkably, even in systems with nearly zero net cooperativity, intense local energy redistributions are revealed that cancel out globally. This work establishes DM-EDA(RS) as a transformative approach that bridges integrated energy numbers with chemical intuition, providing a spatially resolved tool for probing many-body interactions in complex chemical and biological environments.

The construction of diabatic representations is important for understanding nonadiabatic processes. Significant efforts have been devoted to developing robust and generalizable methodologies for diabatization, aiming to improve numerical accuracy, computational efficiency, and transferability across diverse systems. However, while substantial progress has been made on the methodological front, the fundamental chemical significance inherent to the diabatic representation itself has received less attention. In this study, we move beyond these technical performance metrics to decode the chemical meaning of diabatic representations in a series of nonlinear (bent) hydrogen atom transfer (HAT) systems. Using classical valence bond (VB) theory, we explicitly analyze the bonding nature (e.g., covalent, ionic) embodied by diabatic representation in model HAT systems (H3, H2F, NaH2, NaHF, BeH2+), revealing the specific electronic reorganization captured during the reaction. This mechanistic insight extends the traditional diabatic state representation and underscores the role of dynamic bonding pattern mixing.

Within the framework of many-body perturbation theory based on Green's functions, the GW approximation has emerged as a pivotal method for computing quasiparticle energies and excitation spectra. However, its high computational cost and steep scaling present significant challenges for applications to large molecular systems. In this work, we extend the block tensor decomposition (BTD) algorithm, recently developed in our previous work [Zhang et al., J. Chem. Phys. 163, 174109 (2025)] for low-rank tensor compression, to enable a formally O(N-3)-scaling GW algorithm. By integrating BTD with an imaginary-time GW formalism and introducing a real space screening strategy for the polarizability, we achieve an observed scaling of approximately O(N-2) in test systems. Key parameters of the algorithm are optimized on the S66 dataset using the JADE algorithm, ensuring a balanced compromise between accuracy and efficiency. Our BTD-based random phase approximation also exhibits O(N-2) scaling, and eigenvalue-self-consistent GW calculations become feasible for systems with over 3000 basis functions. This work establishes BTD as an efficient and scalable approach for large-scale GW calculations in molecular systems.

Block tensor decomposition (BTD) and canonical polyadic decomposition (CPD) are combined into a unified O(N^3)-scaling framework for second-order perturbation theory (PT2), demonstrated on MP2 and renormalized PT2 (rPT2). BTD constructs the tensor hyper-contraction kernel at O(N^3) via a dual-grid scheme; CPD factorizes the exchange channel through a block-based two-stage ALS. An asymmetric half-kernel design applies bare Coulomb to one vertex and coupling-constant-averaged screening to the other, capturing the SOSEX component of rPT2 without a frequency-dependent CPD. For MP2, BTD-CPD reproduces canonical RI-MP2 to 0.058 kcal/mol per heavy atom. For rPT2@PBE0 on the S66x8 benchmark, the mean absolute error is 0.36 kcal/mol (ME -0.19, RMSE 0.46) over 528 data points. The CPD-compressed intermediates yield O(N^2) storage alongside O(N^3) scaling.

The accurate and efficient treatment of electron-electron interactions remains a central challenge in electronic structure theory. Post-Hartree-Fock (HF) methods are often hindered by high computational costs, primarily due to the need to compute four-index electron repulsion integrals. To address this issue, low-rank approaches, such as tensor hyper-contraction (THC) and interpolative separable density fitting, have been developed to accelerate the computation of HF exchange and dynamic correlation energies in post-HF frameworks. Nevertheless, these methods remain inefficient for molecular systems, mainly because of the quartic-scaling computational cost associated with constructing the THC kernel with respect to the number of basis functions. In this work, we present a new algorithm, named block tensor decomposition (BTD), based on a dual-grid scheme. By integrating Hilbert sorting with pivoted Cholesky decomposition, BTD generates compact and non-redundant interpolative grids, achieving formal O(N3) scaling for kernel building. Key parameters of the method are optimized via differential evolution, ensuring an effective balance between computational efficiency and accuracy. We further demonstrate the application of BTD in scaled opposite-spin second-order Møller-Plesset perturbation theory, where sparse mapping in real space enables O(N2) scaling for both electron correlation and exchange evaluations. Test examples show that BTD is a robust, low-scaling framework for accurate electronic structure calculations in molecular systems.

The pumpkin-like supra-molecular container Cucurbit[8]uril (CB8) is a promising drug carrier and detoxifier that stably coordinates a series of structurally diverse guests with high association constants. Despite the good biocompatibility of CB8, its practical use is limited by the poor solubility, which could be resolved by methyl substitution Me4CB8. However, this comes with additional difficulties in molecular modelling due to the breaking of the D8h symmetry (to C2v and even lower). The binding-mode space is further complicated by complex structural features of abused drugs (e.g., Fentanyl with multiple aromatic rings). In this work, we present a thorough characterization of cucurbiturils host-guest coordinations on a batch of practical detoxification situations with advanced enhanced sampling techniques in conjunction with the most accurate fixed-charge parameter set, where the water-soluble methylated Me4CB8 is parametrized at B97-3c and the 10 abused drugs are fitted at r2SCAN-3c, achieving a practical accuracy limit of current fixed-charge modelling for cucurbiturils host-guest binding. While the predicted binding thermodynamics agree with experimental values, additional all-atom insights into the binding modes and the nature of host-guest interactions that are absent in experimental measurements are presented in great detail, using a combination of force-field energetics and advanced quantum mechanics-based energy decomposition analysis.

In this work, an automatic diabatization approach based on valence-bond (VB) wave functions, called VBADA, is proposed. Compared with the original VB based diabatization implementation [Zhang, Y.; et al. J. Phys. Chem. Lett. 2020, 11, 5295-5301; Zhang, Y.; et al. J. Phys. Chem. Lett. 2021, 12, 1885-1892], VBADA introduces two critical advancements: (1) the improved framework enables rigorous treatment of three-state diabatization, and (2) it relies on VB adiabatic wave functions rather than explicit Hamiltonian matrix operations. These are achieved by a novel criterion, which maximizes both the diversity of adiabatic VB wave functions and the trace of the adiabatic-to-diabatic (ATD) transformation matrix. The diabatic representations of two prototype hydrogen atom transfer (HAT) reactions, including Na + H2 → NaH + H and H + HCl → Cl + H2, is studied by employing VBADA. The computational results demonstrate that VBADA enables rigorous construction of three-state diabatic state, with benchmark validation showing exact numerical equivalence to conventional VB based diabatization implementation in two-state systems.

The accurate description of excited states is crucial for the development of electronic structure theory. In addition to determining excitation energies, strong state interactions arise when electronic states with the same symmetry are degenerate or nearly degenerate, often requiring a multi-state treatment. These strong correlation effects and state interactions can be effectively handled by the Hamiltonian matrix correction-based density functional valence bond (hc-DFVB) method, a multi-reference density functional theory capable of accurately describing electronic state interactions. In this paper, we explore the low-lying excited states of four isoelectronic systems (C2H, CN, CO+, BO) using valence bond methods, including the valence bond self-consistent field (VBSCF) and hc-DFVB methods. Our results show that the hc-DFVB method provides significantly better excitation energies compared to VBSCF. Furthermore, hc-DFVB can reliably predict the correct ordering of excited states, whereas VBSCF shows some ordering inconsistencies. By categorizing the VB structures into groups based on point group symmetry, we can extract the key structural contributions and bonding pictures of each state from the weight distribution of these groups. Additionally, we study the potential energy curves for lithium fluoride (LiF) and a mixed-valence spiro cation, demonstrating the superior performance of hc-DFVB when applied to the study of near-degenerate excited states in the avoided crossing region.

Noncovalent through-space conjugation (TSC), a unique property of π-charge delocalization, has emerged as a powerful strategy for modulating the optoelectronic properties of organic materials. However, the quantitative relationship among the molecular structure, the strength of TSC, and optoelectronic properties has not yet been established. Here, using typical conjugated aromatic compounds as model systems, it is revealed that TSC arises from the interaction of π-orbitals, and a molecular descriptor, composed of geometric parameters, is proposed to characterize the strength of TSC. This descriptor exhibits a strong linear correlation with the orbital splitting energy of symmetric and antisymmetric π-orbitals, achieving a linear fit coefficient (R2) as high as 0.935. More importantly, A shows a strong positive correlation with the spectral red-shift of organic materials, suggesting that TSC can effectively tune the luminescent properties of organic materials. The descriptor is helpful for the rational design and machine-learning-based high-throughput screening of advanced organic luminescent materials.

The selective reduction of the unsaturated substrates in green solvent is highly desired yet however, remains a long-standing challenge. Especially the selective desulfurization of thioamides usually requires hazardous highly reactive reagents or transition metal catalysts in high-pressure conditions. Herein, a novel protocol of selective desulfurization of thioamides to amines with dimethylaminoborane (DMAB) without catalysts, operating in neat water under an open system, is presented. Notably, the selectivity of the reaction is effectively controlled with a simple Lewis acid additive through computational design. The combination of density functional theory and experimental mechanism studies reveals the important synergistic cooperation by DMAB and Lewis acid additive to facilitate the hydrogenative desulfurization process in an aqueous solution.

Accurate and fast treatment of electron-electron interactions remains a central challenge in electronic structure theory because post-Hartree-Fock methods often suffered from the computational cost for 4-index electron repulsion integrals (ERIs). Low-rank approaches such as tensor hyper-contraction (THC) and interpolative separable density fitting (ISDF) have been proposed for Hartree-Fock exchange and correlation's calculations. Their application to molecular systems remains inefficient due to the construction of THC kernel whose time scale increases as quartic with the number of basis functions. In this work, we present an algorithm named block tensor decomposition (BTD) based on a dual grid scheme that combines Hilbert sort and pivoted Cholesky decomposition to generate compact interpolative grids, allowing strict O(N^3) scaling for THC/ISDF kernel construction. The key parameters in BTD are optimized via differential evolution, balancing efficiency and accuracy. Furthermore, we apply BTD in scaled opposite-spin MP2 (SOS-MP2), leveraging sparse mapping in real space to achieve quadratic scaling for electron correlation calculation and linear scaling for exchange calculation. This work advances low-scaling THC/ISDF methodologies for molecular systems, offering a robust framework for efficient and accurate electronic structure computations.

The green reductive transformation of thioamides is highly desired yet faces challenges in broad substrate scope and selectivity for C 00000000 00000000 00000000 00000000 11111111 00000000 11111111 00000000 00000000 00000000 S and C-N cleavage. Existing catalytic hydrogenation methods are still limited and require harsh reaction conditions. Here, computation-aided design discovered a catalyst-free protocol for thioamides' reductive desulfurization with ammonia borane (AB). The system uses dimethylamine-borane (DMAB) to directly reduce thioamides to amines under catalyst-free, practical, economical, green, and easy-to-handle conditions. It covers a broad scope for primary, secondary, and tertiary thioamides. The experimental and theoretical studies revealed a concerted double-hydrogen transfer mechanism for this catalyst-free system, in which DMAB was found to play an important self-catalytic role in the reaction. This practical and selective protocol provides an important example for designing catalyst-free reductive systems.

In this work, an energy decomposition analysis (EDA) method, termed DM-EDA(EB), is introduced to explore intermolecular interactions in large systems by employing a DFT-in-xTB embedding scheme. DM-EDA(EB) integrates density matrix-based EDA (DM-EDA) with the GFNn-xTB method to decompose the total interaction energy into electrostatic, exchange-repulsion, polarization, and correlation terms. Test cases demonstrate that DM-EDA(EB) can accurately analyze total interaction energies in large systems with the computational efficiency comparable to GFNn-xTB. Notably, by using the appropriate partition strategy, DM-EDA(EB) is able to provide quantificational knowledge of individual interactions in large assemblies.

Solar-driven photocatalytic dehalogenation and mineralization of halogenated organic pollutants (HOPs) remain a significant challenge. In this study, we develop a dual-site confined g-C3N4 (CN)-based catalyst, incorporating cerium doping and nitrogen vacancies (Ce-FCNV), for a sequential anaerobic-aerobic photocatalytic system designed for the deep treatment of HOPs-contaminated wastewater. The Ce-FCNV catalyst demonstrates a remarkable 36.04-fold increase in photocatalytic activity for 4-chlorophenol (4-CP) degradation compared to pristine CN. Notably, it achieves near-complete dechlorination (99.45 %) and mineralization (99.21 %) efficiencies in the anaerobic-aerobic system, significantly outperforming single-aerobic, single-anaerobic, and combined aerobic-anaerobic systems. Kinetic and mechanistic studies reveal that the dual catalytic sites and pore confinement effects of Ce-FCNV enhance the generation of reactive species (e.g., •OHbulk, surface-bound, •O2⁻, and electrons) and accelerate 4-CP degradation. Experimental and computational analyses further indicate that the dual-sites lower the C-Cl bond dissociation energy, promote •OH generation, and improve carrier separation. The system exhibits broad applicability, effectively degrading various HOPs and adapting to diverse water matrices, even in real occurrence ranges. This work highlights a novel strategy leveraging the synergistic effects of dual sites within a multi-level pore structure of CN, offering a promising approach for the efficient purification of HOPs-contaminated wastewater in anaerobic-aerobic photocatalytic systems.