We establish theoretical foundations for embedding a correlated wavefunction in an environment formed by Kohn-Sham orbitals. We show that introducing an approximation that equates two, in principle, distinct kinetic-energy functionals yields an embedding functional identical to the projection-based wavefunction-in-density functional theory (DFT) formulation of Miller and co-workers. We demonstrate that this functional is inherently nonvariational: its minimum is not guaranteed to coincide with the exact ground-state energy and remains bounded from above by it. Building on this formal framework, we analyze the dominant sources of error in projection-based density matrix renormalization group-in-DFT embedding with approximate exchange-correlation (xc) functionals. Using molecules with dissociating covalent bonds as a diagnostic example, we demonstrate that the primary source of error is the nonadditive exchange-correlation energy describing the nonclassical coupling between the active subsystem and its environment. Eliminating the fractional-spin error by employing a pair-density xc functional (pair-density functional theory) instead of a semilocal generalized gradient approximation (GGA) does not remedy this deficiency, because the inaccuracy stems from self-interaction effects at the subsystem-environment interface.

Strong coupling to the vacuum electromagnetic field of optical cavities has been proposed as a route to control ground-state chemical reactivity, enabling “photonic substituent effects.” Recent theoretical work predicted that cavity coupling can invert intrinsic regioselectivity in electrophilic aromatic substitution in nitrobenzene. Here, we revisit this prediction using correlated ab initio cavity quantum electrodynamics. QED-CCSD calculations reveal substantially enhanced energetic reordering of Wheland intermediates relative to previous approaches, indicating that regioselective control may be achievable under more experimentally feasible cavity-coupling strengths than previously predicted. QED-DMRG analysis shows that this effect arises from cavity-induced reweighting of resonance structures, reinforcing the idea of a photonic substituent effect that is similarly influential on molecular electronic structure as chemical substituents. Complementary ab initio molecular dynamics simulations driven by QED-DFT analytic gradients demonstrate that orientational fluctuations introduce a competing dynamical constraint on selectivity, suggesting conditions where canonical 100% meta selectivity could be modified to give mixtures of ortho and meta or para and meta electrophilic aromatic substitution products.

Excited-state electronic structure in strongly correlated systems remains challenging due to the exponential scaling of the many-body Hilbert space and the difficulty of constructing systematically controlled active spaces. Building on the stochastic cluster expansion (SCE) framework previously developed for ground-state correlation energies, we extend the formalism to excitation gaps by expressing energy differences directly as a hierarchy of orbital-space cluster contributions. In this formulation, excitation energies are reconstructed from reduced-rank calculations involving a minimal frontier chemical subspace (FCS), treated exactly, together with stochastic sampling of the remaining orbital environment. This approach greatly diminishes the dependence on large or chemically preselected active spaces. We demonstrate the method on charge-transfer complexes and polyacenes, where accurate singlet-triplet gaps are obtained that agree with full-system results. The method converges with low-order cluster terms and provides a systematically improvable framework for excited states in correlated systems.

Roaming, as an unconventional and ubiquitous class of reaction processes that bypass the minimum energy path (MEP), has increasingly become essential for understanding and regulating chemical reactions. In this context, despite the emerging consensus on the spin-polarized diradical roaming model for energetic molecules, it remains elusive to elucidate complex energy transfer and release processes, necessitating a deep insight into roaming radicals and their contributions to reactivity. Herein, we report the discovery of polyradical roaming reactions in a nitroaromatic energetic prototype, 2,4,6-trinitrotoluene (TNT). High-level ab initio calculations show that one-step polyradical roaming reaction yields NO molecules required for two-step MEP, with an energy barrier commensurate with that of the conventional two-step MEP. In particular, these polyradical systems formed during this reaction exhibit multispin entanglement arising from spin-symmetry breakings and aromatic ring fission, along with a nontrivial arrangement of ferromagnetic and antiferromagnetic coupling on distinct radicals, corroborated by many-body electronic structure calculations. Rate constant analyses then reveal that the contribution of the roaming reaction to the thermal dissociation is comparable to MEP for NO formation at detonation, underscoring its mechanistic significance. Such polyradical roaming reactions beyond diradical are also identified in other nitroaromatic energetic molecules, including 1,3,5-trinitrobenzene (TNB) and 2,4,6-trinitroaniline (MATB), suggesting that polyradical roaming might be an emerging reaction mechanism in nitroaromatic decomposition.

We establish the theoretical foundations for embedding a correlated wave function in an environment formed by Kohn-Sham orbitals. We show that introducing an approximation which equates two, in principle distinct, kinetic-energy functionals yields an embedding functional identical to the projection-based wavefunction-in-DFT formulation of Miller and co-workers. We demonstrate that this functional is inherently nonvariational: its minimum is not guaranteed to coincide with the exact ground-state energy and remains bounded from above by it. Building on this formal framework, we analyze the dominant sources of error in projection-based DMRG-in-DFT embedding with approximate exchange-correlation (xc) functionals. Using molecules with dissociating covalent bonds as a diagnostic example, we demonstrate that the primary source of error is the nonadditive exchange-correlation energy describing the nonclassical coupling between the active subsystem and its environment. Eliminating the fractional-spin error by employing a pair-density xc functional (PDFT) instead of a semilocal GGA does not remedy this deficiency, because the inaccuracy stems from self-interaction effects at the subsystem-environment interface.

Excited-state electronic structure in strongly correlated systems remains challenging due to the exponential scaling of the many-body Hilbert space and the difficulty of constructing systematically controlled active spaces. Building on the stochastic cluster expansion (SCE) framework previously developed for ground-state correlation energies, we extend the formalism to excitation gaps by expressing energy differences directly as a hierarchy of orbital-space cluster contributions. In this formulation, excitation energies are reconstructed from reduced-rank calculations involving a minimal frontier chemical subspace (FCS), treated exactly, together with stochastic sampling of the remaining orbital environment. This approach eliminates the need for large or chemically preselected active spaces. We demonstrate the method on charge-transfer complexes and polyacenes, where accurate singlet-triplet gaps are obtained that agree with full-system results. The method converges with low-order cluster terms and provides a systematically improvable framework for excited states in correlated systems.

Accurate many-body treatments of condensed-phase systems are challenging because correlated solvers such as the full configuration interaction (FCI) and the density matrix renormalization group (DMRG) scale exponentially with system size. Downfolding and embedding approaches mitigate this cost but typically require prior selection of a correlated subspace, which can be difficult to determine in heterogeneous or extended systems. Here, we introduce a stochastic cluster expansion framework for efficiently recovering the total correlation energy of large systems with near-DMRG accuracy and without the need to select an active space a priori. By combining correlation contributions from randomly sampled environment orbitals with an exactly treated subspace of interest, the method reproduces total energies for nonreacting and reactive systems while drastically reducing computational cost. The approach also provides a quantitative diagnostic for molecule-solvent correlation, guiding principled embedding decisions. This framework enables systematically improvable many-body calculations in extended systems, opening the door to high-accuracy studies of chemical processes in condensed phase environments.

The electron self-energy is central to quasiparticle theory, yet how an optical cavity enters it remains unclear. We address this question for a molecule in a single-mode cavity using the dipole-gauge Pauli-Fierz Hamiltonian and a coherent-state QED Hartree-Fock reference. The cavity enters through three channels: the static dipole self-energy (DSE) shift of reference orbital energies, direct DSE augmentation of the screened interaction, and the polariton pole carrying the bilinear electron-photon coupling. We benchmark QED-GW ionization potentials (IPs) and electron affinities (EAs) against a cavity Δ-method ladder from QED-HF to correlated wave-function methods, whose cavity-induced shifts agree within 1 meV where directly comparable. For closed-shell molecules with unbound anions, GW systematically overestimates cavity-induced IP redshifts, whereas EA shifts are reproduced nearly quantitatively, although this does not imply comparable accuracy for absolute EAs. For ionic molecules with bound anions, this ordering reverses, consistent with published QED coupled-cluster results. Coupling and detuning scans show that the error is predominantly quadratic in λ and DSE-driven rather than resonant. The spectral function develops a polariton-replica photoemission sideband with weight scaling as λ^2. In the static screened interaction used in the Bethe-Salpeter equation, bare-photon exchange cancels the matching DSE contribution to the direct interaction, while exchange and polariton-screening corrections remain. Their net effect on the lowest excitation is appreciable only for ammonia in the molecules studied. Exciton-binding energies involving unbound anions are strongly basis-dependent and should therefore be viewed as diagnostics of electron-hole interactions rather than basis-converged molecular quantities.

Quantum spin rings represent an intriguing platform for studying unconventional magnetic order and exotic quantum phases, and they are also promising materials for emerging quantum technologies. Conventional spin systems consist of a set of weakly interacting localized spins that are well described by the Heisenberg spin models. Here, we demonstrate that strong interactions between radical centers in macrocycles of different sizes lead to fluctuations in the total number of unpaired electrons and to non-trivial antiferromagnetic order that extends beyond the Heisenberg picture. We demonstrate that the electronic structure of these spin rings is governed by the concept of 4n/4n+2 Hückel (anti)aromaticity for even-membered rings, whereas odd-membered rings possess a highly degenerate frustrated magnetic ground state. The strongly coupled spin rings are experimentally realized through the on-surface synthesis of π-magnetic carbon-based macrocycles, which consist of [2]triangulene units. The close correlation between the electronic structure and the Hückel aromaticity rule is revealed by scanning tunneling spectroscopy and multireference calculations. This work establishes a novel design principle employing the concept of Hückel aromaticity for quantum spin macrocycles.

The projection-based wave function in density functional theory (WF-in-DFT) embedding enables an efficient description of both the energetics and properties of large and complex chemical systems, with accuracy exceeding that of pure DFT. Recently, we have proposed using the density matrix renormalization group (DMRG) as the WF method for molecules containing strongly correlated fragments [Beran, P. J. Phys. Chem. Lett. 2023, 14, 716-722]. In this work, we demonstrate that the accuracy of the DMRG-in-DFT approach is primarily limited by the approximate treatment of the coupling between the active component and its environment through nonadditive exchange-correlation functionals. To address this issue, we combine exact exchange to reduce the nonadditive exchange error with a multireference adiabatic connection (AC) scheme to recover nonadditive correlation. The performance of the improved DMRG-in-DFT embedding is illustrated on two prototypical strongly correlated systems: the dissociation of the H20 chain and the cleavage of a triple CN bond in propionitrile.

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.

The description of strongly correlated systems interacting with quantized cavity modes poses significant theoretical challenges due to the combinatorial scaling of the electronic and photonic degrees of freedom. Recent advances addressing this complexity include cavity quantum electrodynamics (QED) generalizations of complete active space configuration interaction and density matrix renormalization group methods. In this work, we introduce a QED extension of state-averaged complete active space self-consistent field theory, which incorporates cavity-induced correlations through a second-order orbital optimization framework with robust convergence properties. The method is implemented using both photon number state and coherent state representations, with the latter showing robust origin invariance in the energies, regardless of the completeness of the photonic Fock space. The implementation enables symmetry-free orbital relaxations to account for photon-mediated symmetry breaking in polaritonic systems. Numerical validation on lithium hydride, hydroxide anion, and magnesium hydride cation demonstrates that this method achieves significantly improved accuracy in modeling ground-state and polariton potential energy surfaces compared with QED-CASCI in a fixed orbital basis. In these studies, we reach sub kcal/mol accuracy in potential energy surface in much smaller active spaces than are required for QED-CASCI. This advancement provides a more robust approach for studying cavity-altered chemical landscapes for ground and excited strongly coupled systems.

This study integrates a Hermitian coupled-cluster downfolding technique with the Density Matrix Renormalization Group (DMRG) method to accurately treat both static and dynamic correlations in complex electronic systems. By calculating ground-state energies of active-space Hamiltonians via DMRG, we achieve efficient and accurate simulations of strongly correlated systems, demonstrated on molecular benchmarks including N2, benzene, porphyrin, and tetramethyleneethane. This combined approach offers a promising advancement in computational chemistry for complex chemical processes.

The use of machine learning (ML) to refine low-level theoretical calculations to achieve higher accuracy is a promising and actively evolving approach known as Δ-ML. The density matrix renormalization group (DMRG) is a powerful variational approach widely used for studying strongly correlated quantum systems. High computational efficiency can be achieved without compromising accuracy. Here, we demonstrate the potential of a simple ML model to significantly enhance the performance of the quantum chemical DMRG method.

The interpretation of experimental spatially resolved scanning tunneling spectroscopy (STS) maps of close-shell molecules on surfaces is usually interpreted within the framework of oneelectron molecular orbitals. Although this standard practice often gives relatively good agreement with experimental data, it contradicts one of the basic assumptions of quantum mechanics, postulating the impossibility of direct observation of the wavefunction, i.e., individual molecular orbitals. The scanning probe community often considers this contradiction about observing molecular orbitals as a philosophical question rather than a genuine problem. Moreover, in the case of polyradical strongly correlated molecules, the interpretation of STS maps based on one-electron molecular orbitals often fails. Thus, for a precise interpretation of STS maps and their connection to the electronic structure of molecules, a theoretical description, including non-equilibrium tunneling processes going beyond one-electron process, is required. In this contribution, we first show why, in selected cases, it is possible to achieve good agreement with experimental data based on one-electron canonical molecular orbitals and Tersoff-Hamann approximation. Next, we will show that for an accurate interpretation of strongly correlated molecules, it is necessary to describe the process of removing/adding an electron within the formalism of many-electron wavefunctions for the neutral and charged states. This can be accomplished by the concept of so-called Dyson orbitals.

Recent progress in on-surface chemistry has enabled the synthesis of novel polyradical molecules with interesting electronic structure, which are hardly available in solution chemistry. Moreover, the possibility to characterize their electronic structure with scanning tunneling spectroscopy (STS) with the unprecedented spatial resolution opens new possibilities to understand their nontrivial electronic structure. However, experimental STS maps of molecules on surfaces are interpreted using one-electron STM theory within the framework of one-electron molecular orbitals nowadays. Although this standard practice often gives relatively good agreement with experimental data for closed-shell molecules, it fails to address multireference polyradical molecules. In this manuscript, we provide multireference STM theory including out-of-equilibrium processes of removing/adding an electron within the formalism of many-electron wave functions for the neutral and charged states. This can be accomplished by the concept of so-called Dyson orbitals. We will discuss the examples where the concept of Dyson orbitals is mandatory to reproduce experimental STS maps of polyradical molecules. Finally, we critically review the possibility of the experimental verification of the so-called SOMO/HOMO inversion effect using STS maps in polyradical molecules. Namely, we will demonstrate that experimental STS measurements cannot provide any information in case of strongly correlated molecules about the ordering of one-electron molecular orbitals and, therefore neither about the SOMO/HOMO inversion effect.

We propose a general approach to reducing basis set incompleteness error in electron correlation energy calculations. The correction is computed alongside the correlation energy in a single calculation by modifying the electron interaction operator with an effective short-range electron-electron interaction. Our approach is based on a local mapping between the Coulomb operator projected onto a finite basis and a long-range interaction represented by the error function with a local range-separated parameter, originally introduced by Giner et al. [ J. Chem. Phys. 2018, 149, 194301]. Unlike the basis set incompleteness error correction proposed in that work, our method does not rely on short-range correlation density functionals. As a numerical demonstration, we apply the method with complete active space wave functions. Correlation energies are computed using two distinct approaches: the linearized adiabatic connection (AC0) method and n-electron valence state second-order perturbation theory (NEVPT2). We obtain encouraging results for the relative energies of test molecules, with accuracy in a triple-ζ basis set comparable to or exceeding that of uncorrected AC0 or NEVPT2 energies in a quintuple-ζ basis set.

The effective deployment and application of advanced methodologies for quantum chemistry is inherently linked to the optimal usage of emerging and highly diversified computational resources. This paper examines the synergistic utilization of Micron memory technologies and Azure Quantum Element cloud computing in Density Matrix Renormalization Group (DMRG) simulations leveraging coupled-cluster (CC) downfolded/effective Hamiltonians based on the double unitary coupled cluster (DUCC) Ansatz. We analyze the performance of the DMRG-DUCC workflow, emphasizing the proper choice of hardware that reflects the numerical overheads associated with specific components of the workflow. We report a hybrid approach that takes advantage of Micron CXL hardware for the memory capacity intensive CC downfolding phase while employing AQE cloud computing for the less resource-intensive DMRG simulations. Furthermore, we analyze the performance of the scalable ExaChem suite of electronic simulations conducted on Micron prototype systems.

Molecular ir-magnets based on single organic molecules have attracted increasing attention for their potential applications in optoelectronics and spintronics. Global aromaticity in conjugated macrocyclic polyradicaloids is still an open question that has only been tackled in molecules with an even number of electrons. Here, we report the on-surface synthesis of a cyclopenta-ring-fused oligo(m-phenylene) macrocycle, 9MC, with an odd number of electrons. The generated polyradicaloid undergoes a surface-induced distortion to a D3h symmetry with a fully delocalized doublet ground state. Interestingly, 9MC exhibits two aromatic annulene-within-an-annulene (AWA) ring currents in the inner and outer rings.

The character of the electronic structure of acenes has been the subject of the longstanding discussion. However, convincing experimental evidence of their open-shell character has so far been missing. Here, we present on surface synthesis of tridecacene molecule by thermal annealing of octahydrotridecacene on Au(111) surface. We characterized the electronic structure of the tridecacene by scanning probe microscopy, which reveals presence of the inelastic signal at 126 meV. We attribute the inelastic signal to the spin excitation from the singlet biradical ground state to triplet excited state. To rationalize the experimental findings we carried out many-body ab-initio calculations as well as model Hamiltonian to take into account the effect of metallic substrate. Moreover, we provide a detailed analysis how the dynamical electron correlation and virtual charge fluctuation between molecule and metallic surface reduces the singlet-triplet band gap. Therefore, this work provides first experimental confirmation of the magnetic character of tridecacene.