Chen Zhou

Charge-shift bonding (CSB), in which stabilization arises primarily from resonance between covalent and ionic structures rather than simple electron sharing, challenges the traditional covalent–ionic paradigm of chemical bonding. However, its identification has so far relied on either the resonance-energy-based analysis within valence bond theory (VBT) or electron-density-based analysis in molecular orbital theory (MOT), with no unified approach that directly connects the two perspectives. Although real-space descriptors such as density topology and the Laplacian provide qualitative connections, a direct quantitative link between resonance energy and electron density remains lacking. Here, we introduce information gain (IG) from density-based reactivity theory of density functional theory (DFT), defined as the Kullback–Leibler divergence between the actual electron density and a reference density, as a real-space descriptor of resonance-driven density reorganization that connects resonance with electron density. Two simple rules emerge. With the pure Lewis covalent density as the reference, negative IG in the bonding region characterizes regular covalent bonds, whereas positive IG signals charge-shift character. More generally, a sign reversal (“flip”) of IG upon switching between covalent and ionic reference densities reveals competition between resonance structures and provides the more robust diagnostic of charge-shift bonding. These features are consistently observed across homonuclear, heteronuclear, and geometrically constrained systems, and their evolution with bond length reveals a continuous transition between bonding regimes. IG thus provides a unified real-space measure of chemical bonding, establishing a direct link between resonance in VBT and the density-based descriptor in DFT.

Ambimodal reactions are characterized by a single transition structure that bifurcates toward multiple products, posing a fundamental challenge for understanding the origin of product selectivity. While selectivity emerges along post-transition-state pathways, a direct and chemically intuitive connection between transition-state electronic structure and product distribution remains elusive. Here, we demonstrate that product selectivity in ambimodal reactions can be quantitatively correlated with a purely electronic-structure descriptor derived from valence bond (VB) theory. By analyzing the relative weights of VB structures associated with reaction pathways leading to competing products at the ambimodal transition state, a VB-based descriptor is defined to quantify product selectivity. Across a diverse set of ambimodal reactions, this descriptor exhibits a robust linear correlation with the logarithm of the product ratio obtained from experiment or trajectory simulations. These findings reveal that, although selectivity manifests dynamically after the transition state, the transition-state electronic structure contains an intrinsic electronic bias that correlates strongly with product selectivity and influences subsequent pathway bifurcation. The VB analysis thus provides a chemically intuitive perspective on bifurcating reaction pathways and complements existing approaches on ambimodal reactions.

The valence bond (VB) theory offers a chemically intuitive, multiconfigurational framework for analyzing bonding, resonance, and reaction mechanisms. However, its broader application has been limited by high computational costs. In this paper, we present DLVB, a deep learning-based framework that integrates the VB theory with graph transformers through a chemically meaningful representation of VB structures. DLVB accurately predicts VB structural weights without the need for ab initio calculations and provides an efficient selected configuration interaction (SCI) scheme for identifying key configurations that enable the construction of compact VB wave functions. The DLVB-based SCI scheme can identify important VB structures from arbitrary structure sets within a given active space, outperforming traditional ionic-order-based selection methods in both accuracy and scalability. This approach offers a new pathway for extending the applicability of the VB theory to the bonding analysis of systems with larger active spaces and increased molecular complexity.

Covalent bonding and noncovalent interactions are fundamental concepts in chemistry, biology, and related fields, yet the energetic factors driving bond formation and bond rotation remain a subject of ongoing debate in the literature because different theoretical frameworks might provide different insights. In this study, we examine the energetics of bond formation and bond rotation with both density functional theory and valence bond theory. Our analysis spans a wide range of systems, including 40 diatomic molecules; six energy profiles for Ar2, H2, F2, NaF, (H2O)2, and Na2 molecules; and six rotational barriers for CH3CH3, CH3NH2, CH3OH, H2O2, NH2NH2, and NH2OH. We find that (i) electrostatic energy is the dominant contributor in most cases; (ii) within the electrostatic terms, nuclear–electron attraction is often, but not always, the leading contributor; (iii) during bond formation, different interactions dominate at different stages; and (iv) in multi-electron systems, steric effects consistently contribute positively to the total energy decrease due to the spatial constraints imposed by the Pauli exclusion principle. These findings are consistently supported by both theories. Overall, this work should help bridge a critical knowledge gap by providing a unified perspective on the energetics of fundamental bonding processes.

Based on the theory of symmetric group representations, we propose the symmetric group semiempirical valence bond (SGSVB) method for handling large molecular systems. In this approach, the bonded tableau functions are employed to directly construct the VB wave function rather than manipulating a large number of determinants. By truncating the overlap integrals between orbitals in the SGSVB method, efficient calculation of matrix elements is achieved. For the one-electron energy of the Hamiltonian matrix and the overlap matrix elements, the overlap integrals are truncated to first-order terms; for the computation of the two-electron energy, orbital orthogonality is assumed. We applied the SGSVB method to study the vertical excitation energies of the first covalent excited state 2¹A_g of linear polyenes C_2nH_2n+2, and found good agreement with experimental values. Extrapolation to infinite chain length yields limiting energies of ∼1.92 eV, in line with literature estimates. We further demonstrate the applicability of SGSVB by investigating the circumcoronene molecule (C₅₄H₁₈) with an active space of (54e, 54o). The method yields Kekulé structure weights that exhibit strong correlation with those obtained from wave function-based resonance theory (WFRT). The SGSVB method thus offers a novel and efficient computational tool for elucidating the π-electron structure of complex molecular systems using valence bond theory.

Strongly correlated systems, characterized by significant multiconfigurational character, pose a persistent challenge in quantum chemistry. While molecular orbital (MO)-based multiconfigurational self-consistent field methods such as CASSCF and CASPT2 have become standard tools for treating such systems, valence bond (VB) theory offers a conceptually distinct and chemically intuitive alternative. Rooted in the classical Lewis structure framework, VB theory provides a compact and localized description of electron pairing, making it especially well-suited for strongly correlated systems. This review presents a comprehensive overview of the methodological development and practical applications of ab initio VB approaches, including VB self-consistent field (VBSCF), breathing orbital VB (BOVB), VB configuration interaction (VBCI), VB perturbation theory (VBPT2), and density functional VB (DFVB) methods. Particularly, the VBPT2 and DFVB methods enable accurate treatment of bond dissociation, excitation energies, and reaction barriers. Benchmark comparisons demonstrate that VB-based methods achieve performance comparable to established MO-based methods. The findings highlight the promise of VB theory as a powerful and interpretable framework for advancing the theoretical understanding of strongly correlated systems.

Topochemical polymerization (TCP) represents an essential route to create regio- and stereoregular polymers through solid-state transformations. Herein, we present an innovative strategy for controlling topochemical polymerization pathways by tailoring the terminal group aromaticity in the para-azaquinodimethane (AQM) ring system. Substituting phenyl groups with less aromatic furyl units extends significant spin density delocalization across the conjugated core upon thermal activation, inducing significant diradicaloid characters at furyl positions and enabling unconventional reactivities in both solution and solid states. Thermal treatment in toluene yields a unique cyclophane dimer formed via furyl-methine C-C coupling, confirmed by X-ray crystallography, while solid-state reactions produce polymers formed via both intercolumnar furyl-methine coupling and intracolumnar methine-methine coupling. The spin-center-directed mechanism underlying these transformations is validated through theoretical modeling and isotopic labeling experiments. This study highlights the prowess of aromaticity modulation in functional pro-aromatic systems, which enables the synthesis of polymers with main chain structures that are otherwise difficult to access.

Valence bond (VB) theory is an ab initio approach that provides intuitive pictures and insights into chemical bonds and reaction mechanisms. This work integrates low-rank algorithms, including the resolution of the identity and the chain of spheres for exchange, into VB methods. These algorithms significantly improve the efficiency of VB calculations by reducing the computational expense and storage requirement of Fock matrix construction and integral transformations while preserving chemical accuracy. Historically, VB methods were limited to small or model systems due to these computational challenges. The adoption of low-rank techniques now enables efficient optimization of the full set of orbitals in ab initio VB theory, extending its applicability to molecular systems exceeding 100 atoms. The low-rank algorithm expands the scope of VB theory, allowing the study of larger and more realistic molecular systems from a VB perspective.

In this paper, a molecular dynamics (MD) approach based on ab initio classical valence bond (VB) theory, referred to as AIVBMD, is presented. To validate AIVBMD, a novel algorithm that enables efficient computation of energy gradients based on nonorthogonal orbitals is introduced. Taking the gas-phase S_N2 reaction as an example, a compact VB wave function gives reasonable accuracy with only 27 VB structures, compared to the full active space of 5292 VB structures. Furthermore, AIVBMD provides intuitive chemical insights into the reaction process, detailing the breaking and formation of chemical bonds, thereby elucidating the reaction mechanism. In summary, as the first attempt at the ab initio classical VB method-based MD approach, this paper demonstrates that VB theory offers a novel perspective and significant potential for investigating chemical reaction dynamics and mechanisms.

In this article the recent developments of the open-source OpenMolcas chemistry software environment, since spring 2020, are described, with the main focus on novel functionalities that are accessible in the stable branch of the package and/or via interfaces with other packages. These community developments span a wide range of topics in computational chemistry, and are presented in thematic sections associated with electronic structure theory, electronic spectroscopy simulations, analytic gradients and molecular structure optimizations, ab initio molecular dynamics, and other new features. This report represents a useful summary of these developments, and it offers a solid overview of the chemical phenomena and processes that OpenMolcas can address, while showing that OpenMolcas is an attractive platform for state-of-the-art atomistic computer simulations.