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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Fast methods for multisite charge transfer processes. I. Constrained, state averaged CASSCF(1,n) and CASSCF(2n − 1,n) simulations

We design a dynamically weighted state-averaged constrained complete active space self-consistent field (DW-SA-cCASSCF) algorithm to treat electrons or holes moving between n molecular fragments (where n can be larger than 2). Within such a so-called eDSCn/hDSCn approach, we consider configurations that are mutually single excitations of each other, and we apply a generalized set of constraints to tailor the method for studying charge transfer problems. The constrained optimization problem is efficiently solved using a DIIS-SQP algorithm, thus maintaining computational efficiency. We demonstrate the method for a finite Su–Schrieffer–Heeger chain, successfully reproducing the expected exponential decay of diabatic couplings with distance. When combined with a gradient, the current extension immediately enables efficient nonadiabatic dynamics simulations of complex multi-state charge transfer processes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Accurate energies for ππ* excited states via exchange scaling: the XS-CASSCF method

The state-averaged complete-active space self-consistent field method (SA-CASSCF) is a widely employed electronic structure method used for studying photochemistry and dynamics owing to its ability to provide a reliable description even of complicated cases while still retaining computational efficiency. However, SA-CASSCF suffers from one Achilles heel, related to the description of ionic ππ* excited states, whose energy is often overestimated by 1–2 eV. In light of this challenge, we present the XS-CASSCF method, a new approach based on the idea of exchange scaling (XS) that screens the involved energy terms to improve the excitation energies of singlet ionic ππ* states. First, we illustrate the power of the XS-CASSCF method using hexatriene and para-quinodimethane as examples, showing that it corrects the targeted ionic states while leaving the other states largely unaffected, giving root-mean-square errors (RMSE) below 0.2 eV for the four lowest states in both cases. Subsequently, XS-CASSCF vertical excitation energies are tested against theoretical best estimates for a set of 11 molecules and 56 excited states. XS-CASSCF performs exceptionally well for the ππ* states of hydrocarbons, reducing the RMSE over 21 excitation energies from 0.96 to 0.27 eV. In the challenging subset of molecules with heteroatoms and a larger number of ππ* and nπ* states, we find that improvements can also be obtained, albeit not as pronounced. We conclude with an outlook into more realistic molecular materials focusing on their singlet–triplet (S 1 /T 1 ) gaps, finding that significant improvements can be obtained along the whole range of S 1 /T 1 gaps studied, going from 0.1 eV to more than 1.5 eV. Owing to notable improvements across significant classes of molecules combined with its conceptual simplicity, we believe that XS-CASSCF is a promising addition to the electronic structure toolbox, serving both as a standalone electronic structure method and as a starting point for further correlated treatment.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

A Cautionary Tale: Failure of the Valence CASSCF to Describe the Hallmark of Hydrogen Bonding

Valence CASSCF (vCAS) calculations for the hydrogen-bonded (H2O)2, (HF)2, and HF–H2O dimers fail to predict the lengthening of the hydrogen donor bond and the corresponding red shift in the donor bond vibrational stretching frequency. Analysis of the active orbitals in the vCAS calculation reveals that one of the weakly occupied orbitals in each dimer is used to correlate the electrons in the acceptor lone pairs rather than those in the donor bonding orbitals. This has significant implications for subsequent treatments of the dynamical correlation that are based on the vCAS wavefunction.

Nguyen, Long H.↗
DOE OSTI2024

Importance of Electron Correlation on the Geometry and Electronic Structure of [2Fe–2S] Systems: A Benchmark Study of the [Fe 2 S 2 (SCH 3 ) 4 ] 2–,3–,4– , [Fe 2 S 2 (SCys) 4 ] 2– , [Fe 2 S 2 (S- p -tol) 4 ] 2– , and [Fe 2 S 2 (S- o -xyl) 4 ] 2– Complexes

Iron–sulfur clusters are crucial for biological electron transport and catalysis. Obtaining accurate geometries, energetics, manifolds of their excited electronic states, and reduction energies is important to understand their role in these processes. Here, using a [2Fe–2S] model complex with Fe II and Fe III oxidation states, which leads to different charges, i.e., [Fe 2 S 2 (SMe) 4 ] 2–,3–,4– , we benchmarked a variety of computational methodologies ranging from density functional theory (DFT) to post-Hartree–Fock methods, including complete active space self-consistent field (CASSCF), multireference configuration interaction, the second-order N-electron valence state perturbation theory (NEVPT2), and the linearized integrand approximation of adiabatic connection (AC0) approaches. Additionally, we studied three experimentally well-characterized complexes, [Fe 2 S 2 (SCys) 4 ] 2– , [Fe 2 S 2 (S-o-tol) 4 ] 2– , and [Fe 2 S 2 (S-o-xyl) 4 ] 2– , via DFT methods. We conclude that the dynamic electron correlation is important for accurately predicting the geometry of these complexes. Broken symmetry (BS) DFT correctly predicts experimental geometries of low-spin multiplicity, while CASSCF does not. However, BS-DFT significantly overestimates the difference between the low- and high-spin electronic states for a given oxidation state. At the same time, CASSCF underestimates it but provides relative energies closer to the reference NEVPT2 results. Finally, AC0 provides energetics of NEVPT2 quality with the additional advantage of being able to use large CASSCF sizes. NEVPT2 gives the best estimates of the Fe III /Fe III → Fe II /Fe III (4.27 eV) and Fe II /F III → Fe II /F II (7.72 eV) reduction energies. The results provide insight into the electronic structure of these complexes and assist in the understanding of their physical properties.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Role of Electron Correlation beyond the Active Space in Achieving Quantitative Predictions of Spin-Phonon Relaxation

Single-molecule magnets (SMMs) are promising candidates for molecular-scale data storage and processing due to their strong magnetic anisotropy and long spin relaxation times. However, as temperature rises, interactions between electronic states and lattice vibrations accelerate spin relaxation, significantly limiting their practical applications. Recently, ab initio simulations have made it possible to advance our understanding of phonon-induced magnetic relaxation, but significant deviations from experiments have often been observed. The description of molecules’ electronic structure has been mostly based on complete active space self-consistent field (CASSCF) calculations, and the impact of electron correlation beyond the active space remains largely unexplored. In this study, we provide the first systematic investigation of spin-phonon relaxation in SMMs with post-CASSCF multiconfigurational methods, specifically CAS followed by second-order perturbation theory and multiconfiguration pair-density functional theory. Taking Co(II)- and Dy(III)-based SMMs as case studies, we analyze how electron correlation influences spin-phonon relaxation rates across a range of temperatures, comparing theoretical predictions with experimental observations. Our findings demonstrate that post-CASSCF treatments make it possible to achieve quantitative predictions for Co(II)-based SMMs. For Dy(III)-based systems, however, accurate predictions require consideration of additional effects, underscoring the urgent necessity of further advancing the study of the effects of electronic correlation in these complex systems.

Energy↗
DOE OSTI2025

Computational Investigation of the Chemical Bond between An(III) Ions and Soft-Donor Ligands

The chemical bonding of actinide ions with arene and borohydride ligands is explored via quantum chemical methods to understand how the transuranium elements interact with softdonor ligands. Specifically, the [An(C 6 Me 6 )(BH 4 ) 3 ] complexes (An = U, Np, and Pu) and their reduced congeners are studied. Density functional theory (DFT) shows that the metal–ligand interactions in the neutral complexes are governed by electrostatic interactions. Both DFT and complete active space (CASSCF) results show that as one moves from U to Pu, the 5f-orbitals are stabilized leading to a poorer energy match with the ligand orbitals. This contributes to progressively weaker metal-arene and metal-borohydride interactions across the series due to a decrease in energy-driven covalency. A reduction in orbital contributions to bonding is obtained for the transuranium-arene interactions as well. Upon reduction, the arene is reduced, forming a δ-bond. This causes the An–arene distances to contract by 0.1–0.2 Å compared to the neutral complexes. The ground state is assigned as the intermediate-spin state where the arene radical is antiferromagnetically coupled to the metal-centered f-electrons in Np and Pu. On the other hand, the ferromagnetically and antiferromagnetically coupled states are close in energy in the uranium complex, but do not mix when spin– orbit coupling is included using a state-interaction approach (SO-CASPT2). The population of the CASSCF δ*-antibonding natural orbital increases from U to Pu consistent with the increased An–arene distances, weaker interactions, and decreasing covalency across the series. Although the An–B distance increases by ca. 0.06 Å upon reduction, both the neutral and reduced species involve an An(III)–borohydride bond and as such are qualitatively similar. The Np complexes can be assigned to have slightly weaker bonding than the uranium analogs but are overall “uranium-like”. The Pu complexes are predicted to have less covalent contributions to bonding in both the Pu–arene and Pu–borohydride interactions; however, the Pu–arene interaction is predicted to be particularly weak.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Exact-Two-Component Complete Active Space Method with Variational Treatment of Magnetic Field and Spin–Orbit Coupling: Application to X-ray Magnetic Circular Dichroism Spectroscopy

We introduce an exact-two-component complete active space self-consistent-field (X2C-CASSCF) method formulated under the restricted-magnetic-balance condition. This framework allows for the nonperturbative treatment of static magnetic fields using gauge-including atomic orbitals (GIAOs). The GIAO-X2C-CASSCF methodology effectively captures all microstates within the same 2J + 1-degenerate manifold and their splitting in a static magnetic field, which are not accessible through single-reference-based methods. We also present mathematical recursive expressions for evaluating one-electron relativistic integrals by using GIAOs in the presence of a finite magnetic field. Benchmark studies include oxygen and nitrogen K-edge X-ray magnetic circular dichroism spectroscopy (XMCD) for closed-shell organic compounds, as well as L-edge XMCD spectroscopy for the high-spin open-shell transition metal ion Mn 2+ and the tetrahedral Mn(II)O 4 6– complex.

Chemical calculations↗
DOE OSTI2024

Properties of NoO and YbO

Bond dissociation energies (BDEs) and spectroscopic parameters for the ground states of YbO and NoO were calculated at the Brueckner doubles (BD(T)) level and for NoO at the coupled cluster CCSD(T) level based on the closed-shell configurations Yb 2+ (4f 14 )O 2 – (2p 6 ) and No 2+ (5f 14 )O 2 – (2p 6 ). For YbO, the BD(T) BDE (3.93 eV) and vibrational frequency (686.3 cm –1 ) are consistent with the experiment; the BD(T) bond distance was 1.8492 Å, about 0.04 Å longer than the experiment. For NoO, the calculated BDEs are 3.07 eV (BD(T)) and 3.08 eV (CCSD(T)) and are expected to be good to ±3 kcal/mol (±0.13 eV). Potential energy curves (PECs) for the spin–orbit (Ω) states associated with the f 13 s 1 configurations of YbO and NoO were calculated at the SA-CASSCF/SO-CASPT2/aQ-DK level. PECs considering both the f 13 s 1 and f 14 configurations were calculated at this level, as the ground states are expected to contain both configurations. Due to a bias in the SA-CASSCF to the f 13 s 1 configurations, the f 14 configurations could not be properly described simultaneously with the f 13 s 1 ones. Finally, the natural population analysis based on the natural bond orbitals shows that YbO and NoO are quite ionic, with 5d orbitals being more important in YbO than the 6d orbitals in NoO.

basis sets↗
DOE OSTI2025

Perspective on Many-Body Methods for Molecular Polaritonic Systems

Recent advances in strong light–matter interactions have revealed a wealth of new physical phenomena in molecules embedded in optical cavities, including modified chemical reactivity, altered excitation spectra, and novel quantum correlations. To describe these effects from first-principles, the field of ab initio quantum electrodynamics (QED) has emerged as a compelling extension of quantum chemistry that treats electronic and photonic degrees of freedom on equal footing. In this Perspective, we review the growing landscape of many-body QED methods, including Hartree–Fock, density functional theory (QEDFT), time-dependent DFT (QED-TDDFT), configuration interaction (QED-CI), complete active space (QED-CASSCF), coupled cluster (QED-CC), quantum Monte Carlo (QED-QMC), and density matrix renormalization group (QED-DMRG), highlighting recent developments and implementations. We further explore real-time methods, gradient and Hessian formalisms, and the integration of nonadiabatic nuclear dynamics. Applications range from benchmark simulations of polaritonic chemistry to quantum simulations on emerging quantum hardware. We conclude by outlining future directions for theory development and interdisciplinary efforts at the interface of quantum chemistry, condensed matter, and quantum optics.

36 MATERIALS SCIENCE↗
DOE OSTI2026

NOCI-F Electronic Couplings in Assemblies of Indolonaphthyridine Molecules: From Dimers to the Full Stack

Key electronic processes related to molecular excitonic states of finite stacks of indolonaphthyridine molecules are analyzed via the non-orthogonal configuration interaction with fragments (NOCI-F) method. Indolonaphthyridine is an organic chromophore that can undergo several electronic photoexcitation-related intermolecular processes, such as exciton and electron transfer. The structures studied here are noncrystalline arrangements built as either ordered stacks of indolonaphthyridine or stacks extracted from molecular dynamics simulations including thermal disorder. Taking dimers or trimers from either model, we performed CASSCF and NOCI-F calculations to quantify the intermolecular electronic couplings governing singlet fission, excited singlet and triplet diffusion, and hole and electron diffusion processes. Also, comparing the results for the different models, we studied the effect of structural disorder and distortion on these couplings. Finally, we present a newly developed, advanced postanalysis tool. It takes the NOCI-F data as input to carry out a multifragment full Hamiltonian procedure that involves the complete stack, providing physical information not available from the dimer/trimer models, hence giving access to additional insight into the material’s properties.

coupling reactions↗
DOE OSTI2025

Nonunitary Variational Quantum Eigensolver with the Localized Active Space Method and Cost Mitigation

Accurately describing strongly correlated systems with affordable quantum resources remains a central challenge for quantum chemistry applications on near and intermediate term quantum computers. The localized active space self-consistent field (LASSCF) approximates the complete active space self-consistent field (CASSCF) by generating active space-based wave functions within specific fragments while treating interfragment correlation with mean-field approach, hence is computationally less expensive. Hardware-efficient ansatzes (HEA) offer affordable and shallower circuits, yet they often fail to capture the necessary correlation. Previously, Jastrow-factor-inspired nonunitary qubit operators were proposed to use with HEA for variational quantum eigensolver (VQE) calculations (so-called nuVQE), as they do not increase circuit depths and recover correlation beyond the mean-field level for Hartree–Fock initial states. Here, in this study, we explore running nuVQE with LASSCF as the initial state. The method, named LAS-nuVQE, is shown to recover interfragment correlations, reach chemical accuracy with a small number of gates (<70) in both H 4 and square cyclobutadiene (C 4 H 4 ), and produces more accurate energetics than its HEA counterparts at all circuit depths. To further address the inherent symmetry-breaking in HEA, we implemented spin-constrained LAS-nuVQE to extend the capabilities of HEA further and show spin-pure results for square cyclobutadiene. We also mitigate the increased measurement overhead of nuVQE via Pauli grouping and shot-frugal sampling, reducing measurement costs by up to 2 orders of magnitude compared to ungrouped operator, and show that one can achieve better accuracy with a small number of shots (10 3–4 ) per one expectation value calculation compared to noiseless simulations with one or two orders of magnitude more shots. Finally, wall clock time estimates show that, with our measurement mitigation protocols, nuVQE becomes a cheaper and more accurate alternative than vanilla VQE with HEA. Taken together, these developments illustrate a practical pathway toward performing multireference chemical simulations with accuracy and affordable resources on today’s quantum hardware, achieving both accuracy and affordability in challenging correlated systems.

Wang, Qiaohong [Univ. of Chicago, IL (United State↗
DOE OSTI2025

Excited electronic states of Na 2 and K 2 : The potential for long-lived “reservoir” states leading to collision induced population inversions

Potential energy curves (PECs) for the spin-free (ΛS) and spin–orbit (Ω) states associated with the four lowest-lying dissociation channels of Na 2 and K 2 were calculated at the SA-CASSCF/SO-CASPT2/aug-cc-pwCVQZ-DK level. The PECs of Na 2 were consistent with the experimental data and with the FS-CCSD (2,0) calculations, reproducing the double-well and the “shelf” character for some of the potentials of the excited states. For K 2 , the PECs behaved in a similar way and the spectroscopic parameters for the ground and the excited states are in good agreement with the available experimental values. The dissociation energy of K 2 was predicted to be D e = 4454 cm −1 , within an agreement of 5 cm −1 with the experiments. For Na 2 , D e = 5789 cm −1 compared to the experimental value of 6022 cm −1 . The inclusion of spin–orbit coupling effects resulted in avoided crossings, which affect the PECs. Spin–orbit changes the predicted curves for some excited Ω states arising from ΛS states that overlap each other, affecting their associated vibrational frequencies and bond distances. Here, the current studies of the low-lying states in K 2 reveal a similar structure to those of Na 2 , which suggests the accessibility of long-lived energy storing reservoir states and possible population inversions in K 2 following prior experimental work on the reaction of halogen atoms with Na 3 to produce excited states of Na 2 .

Ab-initio methods↗
DOE OSTI2025

Fast methods for multisite charge transfer. Processes II. Analytic nuclear gradients and nonadiabatic dynamics for cCASSCF(1,n) and cCASSCF(2n-1,n) wavefunctions

In this work we derive and implement analytic nuclear gradients and derivative couplings for a constrained complete active space self-consistent field with a small active space designed to model electron or hole transfer. Using a Lagrangian formalism, we are able to differentiate both the CASSCF energy and the constraint (which is required for smooth surfaces over a wide range of parameter space), and the resulting efficient algorithm can be immediately applied to nonadiabatic dynamics simulations of charge transfer processes. Here, we run initial surface-hopping simulations of a proton coupled electron transfer event for a phenoxyl–phenol system.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Many roads to the seam: How conformational flexibility drives nonadiabatic relaxation in a prototypical tetrapyrrolic chromophore

Large and structurally flexible chromophores pose challenges for in silico modeling of photodeactivation due to the many vibrational modes that can funnel the system toward energy degeneracy. In this work, we examine how the multiple degrees of freedom in biliverdin, a prototypical tetrapyrrolic chromophore, cooperate to drive access to the S 1 /S 0 intersection seam in vacuo. We begin by mapping the ground-state potential energy surface to identify representative biliverdin conformers relevant to photoexcitation. We then use a CASSCF-based framework to map the excited-state landscape and characterize the intersection seam, identifying distinct conical-intersection types. Finally, we employ ab initio multiple spawning to resolve the dynamical pathways by which the system accesses these regions. DFT potential-energy and free-energy mappings indicate that, although several conformers are relevant, the “locked-helix” ZsZsZs conformer predominates in the ground state. The intersection seam comprises numerous geometrically distinct regions characterized by varying degrees and combinations of dihedral torsion, pyramidalization, and bond-length alternation. Yet only select regions lie within energetic reach, and moderate barriers separate them from the S 1 minimum. Nonadiabatic dynamics combined with multivariate analyses show that, despite extensive mode coupling during deactivation that guides the system toward multiple regions of the seam, a single dihedral torsion, together with bond-length alternation, predominantly drives energy degeneracy. This work offers new insight into biliverdin’s intrinsic photochemical response and underscores a general feature of flexible chromophores: many modes may participate during photorelaxation, but only a limited subset ultimately dictates seam accessibility.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Activation of methane by U + studied by guided ion beam tandem mass spectrometry and quantum chemistry

Reaction pathways of all products formed in the U + + CH 4 (CD 4 ) reaction were explored as a function of kinetic energy using guided ion beam tandem mass spectrometry and quantum chemical calculations. UH + , UC + , UCH + , UCH 2 + , and UCH 3 + (and their perdeuterated analogues) are formed in endothermic reactions. In both systems, the UCH 2 + (UCD 2 + ) dehydrogenated product was the dominant product in the low-energy region, whereas the UH + (UD + ) hydride product became predominant at high energies. The kinetic energy behavior of the various products is consistent with a common intermediate of H–U + –CH 3 (D–U + –CD 3 ). Here, the kinetic energy dependence of all product cross sections was modeled to obtain experimental bond dissociation energies at 0 K (in eV): D 0 (U + –H) = 2.42 ± 0.10, D 0 (U + –C) = 3.95 ± 0.12, D 0 (U + –CH) = 4.91 ± 0.09, D 0 (U + –CH 2 ) = 4.11 ± 0.04, and D 0 (U + –CH 3 ) = 2.41 ± 0.09. Quantum chemical calculations using the UCCSD(T) and UB3LYP approaches with the cc-pwCVXZ-PP basis set with MDF-60 pseudopotential for U + and the aug-cc-pCVXZ and aug-cc-pVXZ (X = T, Q) basis set for carbon and hydrogen, respectively, validate the experimental bond dissociation energies and outline the potential energy surface for all reactions observed. In addition, spin–orbit corrections of the bond energies for all products were calculated at a CASSCF-CASPT2-RASSI level.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

ELECTRONIC STRUCTURE METHODS AND PROTOCOLS WITH APPLICATION TO DYNAMICS, KINETICS AND THERMOCHEMISTRY

Hydrocarbon combustion involves the reaction dynamics of a tremendous number of species beginning with many-component fuel mixtures and proceeding via a complex system of intermediates to form primary and secondary products. Combustion conditions corresponding to new advanced engines and/or alternative fuels rely increasingly on autoignition and low-temperature-combustion chemistry. In these regimes various transient radical species such as HO2, ROO·, ·QOOH, HCO, NO2, HOCO, and Criegee intermediates play important roles in determining the detailed as well as more general dynamics. A clear understanding and accurate representation of these processes is needed for effective modeling. Given the difficulties associated with making reliable experimental measurements of these systems, computation can play an important role in developing these energy technologies. Accurate calculations have their own challenges since even within the simplest dynamical approximations such as transition state theory, the rates depend exponentially on critical barrier heights and these may be sensitive to the level of quantum chemistry. Moreover, it is well-known that in many cases it is necessary to go beyond statistical theories and consider the dynamics. Quantum tunneling, resonances, radiative transitions, and non-adiabatic effects governed by spin-orbit or derivative coupling can be determining factors in those dynamics. Building upon progress made during a period of prior support through the DOE Early Career Program, this project combines developments in the areas of potential energy surface (PES) fitting and multistate multireference quantum chemistry to allow spectroscopically and dynamically/kinetically accurate investigations of key molecular systems (such as those mentioned above), many of which are radicals with strong multireference character and have the possibility of multiple electronic states contributing to the observed dynamics. An ongoing area of investigation is to develop general strategies for robustly convergent electronic structure theory for global multichannel reactive surfaces including diabatization of energy and other relevant surfaces such as dipole transition. Combining advances in ab initio methods with automated interpolative PES fitting allows the construction of high-quality PESs (incorporating thousands of high-level data) to be done rapidly through parallel processing on high-performance computing (HPC) clusters. In addition, new methods and approaches to electronic structure theory will be developed and tested through applications. This project will explore limitations in traditional multireference calculations (e.g., MRCI) such as those imposed by internal contraction, lack of high-order correlation treatment and poor scaling. Methods such as DMRG-based extended active-space CASSCF and various Quantum Monte Carlo (QMC) methods will be applied (including VMC/DMC and FCIQMC). Insight into the relative significance of different orbital spaces and the robustness of application of these approaches on leadership class computing architectures will be gained. Synergy with other components of this research program such as automated PES fitting and multireference quantum chemistry will be used to address challenges encountered by the standard approaches to computational thermochemistry (those being single-reference quantum chemistry and perturbative treatments of the anharmonic vibrational energy, which break down for some cases of electronic structure or floppy strongly coupled vibrational modes).

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2026

Frontiers in divalent $f$-block chemistry

Divalent f-block chemistry has undergone rapid expansion in recent years, driven by advances in the stabilization of low-valent lanthanide and actinide complexes. Although f-elements were historically accessed in the +3 or higher oxidation states, the isolation of +2 species has revealed unusual spectroscopic signatures, distinct bonding motifs, and multiple accessible electronic configurations that influence their chemical and physical properties. These developments have generated opportunities in areas including quantum information science, molecular magnetism, catalysis, and luminescence. Computational chemistry has played a pivotal role in interpreting the electronic structure and reactivity of these systems. However, accurately modeling divalent f-block complexes remains challenging because of strong electronic correlation, multiconfigurational character, and the presence of close-in-energy competing electronic states. As experimental capabilities and theoretical methodologies continue to advance, a comprehensive assessment of divalent chemistry is both timely and needed. In this Review, we integrate experimental and theoretical perspectives to provide a systematic analysis of divalent lanthanide and actinide complexes across the f-block series. We critically assess the role of ligands in determining competing ground-state configurations (f n d 1 vs. f n+1 ) resulting in their distinct spectroscopic, magnetic, and bonding properties. Finally, we discuss emerging strategies for predictive modeling and rational design of low-valent f-block molecular systems, with potential applications ranging from dinitrogen reduction to quantum technologies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗