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.

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 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.

Open-shell benzenoid polycyclic aromatic hydrocarbons, known as magnetic nanographenes, exhibit unconventional p-magnetism arising from topological frustration or strong electronic-electron (e-e) interaction. Imprinting multiple strongly entangled spins into polyradical nanographenes creates a major paradigm shift in realizing non-trivial collective quantum behaviors and exotic quantum phases in organic quantum materials. However, conventional design approaches are limited by a single magnetic origin, which can restrict the number of correlated spins or the type of magnetic ordering in open-shell nanographenes. Here, we present a novel design strategy combing topological frustration and e-e interactions to fabricate the largest fully-fused open-shell nanographene reported to date, a 'butterfly'-shaped tetraradical on Au(111). We employed bond-resolved scanning tunneling microscopy and spin excitation spectroscopy to unambiguously resolve the molecular backbone and reveal the strongly correlated open-shell character, respectively. This nanographene contains four unpaired electrons with both ferromagnetic and anti-ferromagnetic interactions, harboring a many-body singlet ground state and strong multi-spin entanglement, which can be well described by many-body calculations. Furthermore, we demonstrate that the nickelocene magnetic probe can sense highly-correlated spin states in nanographene. The ability to imprint and characterize many-body strongly correlated spins in polyradical nanographenes not only presents exciting opportunities for realizing non-trivial quantum magnetism and phases in organic materials but also paves the way toward high-density ultrafast spintronic devices and quantum information technologies.

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. Using a [2Fe-2S] model complex with FeII and FeIII oxidation states, which leads to different charges, i.e., [Fe2S2(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, [Fe2S2(SCys)4]2-, [Fe2S2(S-o-tol)4]2-, and [Fe2S2(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 FeIII/FeIII → FeII/FeIII (4.27 eV) and FeII/FIII → FeII/FII (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.

We have trained a new machine-learning (ML) model which predicts mutual information (MI) for strongly correlated systems. This is a complex quantity, which is much more difficult to predict than one-site entropies, but carries important information about the correlation structure inside electronic systems. In this work, we replaced the expensive density matrix renormalization group (DMRG) calculations by newly trained ML model for prediction of the mutual information. We show the performance of the model on two important tasks: (a) to determine the correlation structure and (b) to determine ordering of orbitals for accurate DMRG calculations. The results are compared with the MI obtained from accurate DMRG calculations.

Tensor algebra operations such as contractions in computational chemistry consume a significant fraction of the computing time on large-scale computing platforms. The widespread use of tensor contractions between large multi-dimensional tensors in describing electronic structure theory has motivated the development of multiple tensor algebra frameworks targeting heterogeneous computing platforms. In this paper, we present Tensor Algebra for Many-body Methods (TAMM), a framework for productive and performance-portable development of scalable computational chemistry methods. TAMM decouples the specification of the computation from the execution of these operations on available high-performance computing systems. With this design choice, the scientific application developers (domain scientists) can focus on the algorithmic requirements using the tensor algebra interface provided by TAMM, whereas high-performance computing developers can direct their attention to various optimizations on the underlying constructs, such as efficient data distribution, optimized scheduling algorithms, and efficient use of intra-node resources (e.g., graphics processing units). The modular structure of TAMM allows it to support different hardware architectures and incorporate new algorithmic advances. We describe the TAMM framework and our approach to the sustainable development of scalable ground- and excited-state electronic structure methods. We present case studies highlighting the ease of use, including the performance and productivity gains compared to other frameworks.

In the past decade, the quantum chemical version of the density matrix renormalization group method has established itself as the method of choice for strongly correlated molecular systems. However, despite its favorable scaling, in practice, it is not suitable for computations of dynamic correlation. Several approaches to include that in post-DMRG methods exist; in our group, we focused on the tailored coupled cluster (TCC) approach. This method works well in many situations; however, in exactly degenerate cases (with two or more determinants of equal weight), it exhibits a bias toward the reference determinant representing the Fermi vacuum. Although sometimes it is possible to use a compensation scheme to avoid this bias for energy differences, it is certainly a drawback. In order to overcome this bias of the TCC method, we have developed a Hilbert-space multireference version of tailored CC, which can treat several determinants on an equal footing. We have implemented and compared the performance of three Hilbert-space multireference coupled cluster (MRCC) variants-the state universal one and the Brillouin-Wigner and Mukherjee's state specific ones. We have assessed these approaches on the cyclobutadiene and tetramethyleneethane molecules, which are both diradicals with exactly degenerate determinants at a certain geometry. We have also investigated the sensitivity of the results on the orbital rotation of the highest occupied and lowest unoccupied molecular orbital (HOMO-LUMO) pair, as it is well known that Hilbert-space MRCC methods are not invariant to such transformations.

The new generation of proposed light-emitting molecules for organic light-emitting diodes (OLEDs) has raised considerable research interest due to its exceptional feature─a negative singlet-triplet (ST) gap violating Hund's multiplicity rule in the excited S1 and T1 states. We investigate the role of spin polarization in the mechanism of ST gap inversion. Spin polarization is associated with doubly excited determinants of certain types, whose presence in the wave function expansion favors the energy of the singlet state more than that of the triplet. Using a perturbation theory-based model for spin polarization, we propose a simple descriptor for prescreening of candidate molecules with negative ST gaps and prove its usefulness for heptazine-type molecules. Numerical results show that the quantitative effect of spin polarization decreases linearly with the increasing highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) exchange integral. Comparison of single- and multireference coupled-cluster predictions of ST gaps shows that the former methods provide good accuracy by correctly balancing the effects of doubly excited determinants and dynamic correlation. We also show that accurate ST gaps may be obtained using a complete active space model supplemented with dynamic correlation from multireference adiabatic connection theory.

Iron-sulfur clusters comprise an important functional motif in the catalytic centers of biological systems, capable of enabling important chemical transformations at ambient conditions. This remarkable capability derives from a notoriously complex electronic structure that is characterized by a high density of states that is sensitive to geometric changes. The spectral sensitivity to subtle geometric changes has received little attention from correlated, large active space calculations, owing partly to the exceptional computational complexity for treating these large and correlated systems accurately. To provide insight into this aspect, we report the first Complete Active Space Self Consistent Field (CASSCF) calculations for different geometries of the [Fe(II/III)4S4(SMe)4]-2 clusters using two complementary, correlated solvers: spin-pure Adaptive Sampling Configuration Interaction (ASCI) and Density Matrix Renormalization Group (DMRG). We find that the previously established picture of a double-exchange driven magnetic structure, with minute energy gaps (<1 mHa) between consecutive spin states, has a weak dependence on the underlying geometry. However, the spin gap between the singlet and the spin state 2S + 1 = 19, corresponding to a maximal number of Fe-d electrons being unpaired and of parallel spin, is strongly geometry dependent, changing by a factor of 3 upon slight deformations that are still within biologically relevant parameters. The CASSCF orbital optimization procedure, using active spaces as large as 86 electrons in 52 orbitals, was found to reduce this gap compared to typical mean-field orbital approaches. Our results show the need for performing large active space calculations to unveil the challenging electronic structure of these complex catalytic centers and should serve as accurate starting points for fully correlated treatments upon inclusion of dynamical correlation outside the active space.

The synthesis of novel polymeric materials with porphyrinoid compounds as key components of the repeating units attracts widespread interest from several scientific fields in view of their extraordinary variety of functional properties with potential applications in a wide range of highly significant technologies. The vast majority of such polymers present a closed-shell ground state, and, only recently, as the result of improved synthetic strategies, the engineering of open-shell porphyrinoid polymers with spin delocalization along the conjugation length has been achieved. Here, we present a combined strategy toward the fabrication of one-dimensional porphyrinoid-based polymers homocoupled via surface-catalyzed [3 + 3] cycloaromatization of isopropyl substituents on Au(111). Scanning tunneling microscopy and noncontact atomic force microscopy describe the thermal-activated intra- and intermolecular oxidative ring closure reactions as well as the controlled tip-induced hydrogen dissociation from the porphyrinoid units. In addition, scanning tunneling spectroscopy measurements, complemented by computational investigations, reveal the open-shell character, that is, the antiferromagnetic singlet ground state (S = 0) of the formed polymers, characterized by singlet-triplet inelastic excitations observed between spins of adjacent porphyrinoid units. Our approach sheds light on the crucial relevance of the π-conjugation in the correlations between spins, while expanding the on-surface synthesis toolbox and opening avenues toward the synthesis of innovative functional nanomaterials with prospects in carbon-based spintronics.

The synthesis of polycyclic aromatic hydrocarbons containing various non-benzenoid rings remains a big challenge facing contemporary organic chemistry despite a considerable effort made over the last decades. Herein, we present a novel route, employing on-surface chemistry, to synthesize nonalternant polycyclic aromatic hydrocarbons containing up to four distinct kinds of non-benzenoid rings. We show that the surface-induced mechanical constraints imposed on strained helical reactants play a decisive role leading to the formation of products, energetically unfavorable in solution, with a peculiar ring current stabilizing the aromatic character of the π-conjugated system. Determination of the chemical and electronic structures of the most frequent product reveals its closed-shell character and low band gap. The present study renders a new route for the synthesis of novel nonalternant polycyclic aromatic hydrocarbons or other hydrocarbons driven by internal stress imposed by the surface not available by traditional approaches of organic chemistry in solution.

Active space quantum chemical methods could provide very accurate description of strongly correlated electronic systems, which is of tremendous value for natural sciences. The proper choice of the active space is crucial but a nontrivial task. In this article, we present a neural network-based approach for automatic selection of active spaces, focused on transition metal systems. The training set has been formed from artificial systems composed of one transition metal and various ligands, on which we have performed the density matrix renormalization group and calculated the single-site entropy. On the selected set of systems, ranging from small benchmark molecules up to larger challenging systems involving two metallic centers, we demonstrate that our machine learning models could predict the active space orbitals with reasonable accuracy. We also tested the transferability on out-of-the-model systems, including bimetallic complexes and complexes with ligands, which were not involved in the training set. Also, we tested the correctness of the automatically selected active spaces on a Fe(II)-porphyrin model, where we studied the lowest states at the DMRG level and compared the energy difference between spin states or the energy difference between conformations of ferrocene with recent studies.

Author(s): Mejuto-Zaera, Carlos; Tzeli, Demeter; Williams-Young, David; Tubman, Norm M; Matousek, Mikulas; Brabec, Jiri; Veis, Libor; Xantheas, Sotiris S; Jong, Wibe A de | Abstract: Iron-sulfur clusters comprise an important functional motif of the catalytic centers of biological systems, capable of enabling important chemical transformations at ambient conditions. This remarkable capability derives from a notoriously complex electronic structure that is characterized by a high density of states that is sensitive to geometric changes. The spectral sensitivity to subtle geometric changes has received little attention from fully-correlated calculations, owing partly to the exceptional computational complexity for treating these large and correlated systems accurately. To provide insight into this aspect, we report the first Complete Active Space Self Consistent Field (CASSCF) calculations for different geometries of cubane-based clusters using two complementary, fully-correlated solvers: spin-pure Adaptive Sampling Configuration Interaction (ASCI) and Density Matrix Renormalization Group (DMRG). We find that the previously established picture of a double-exchange driven magnetic structure, with minute energy gaps (l 1 mHa) between consecutive spin states, has a weak dependence on the underlying geometry. However, the spin gap between the lowest singlet and the highest spin states is strongly geometry dependent, changing by an order of magnitude upon slight deformations that are still within biologically relevant parameters. The CASSCF orbital optimization procedure, using active spaces as large as 86 electrons in 52 orbitals, was found to reduce this gap by a factor of two compared to typical mean-field orbital approaches. Our results clearly demonstrate the need for performing highly correlated calculations to unveil the challenging electronic structure of these complex catalytic centers.

Carlos Mejuto-Zaera, 2, ∗ Demeter Tzeli, 4 David Williams-Young, Norm M. Tubman, † Mikuláš Matoušek, Jiri Brabec, Libor Veis, ‡ Sotiris S. Xantheas, 8, § and Wibe A. de Jong ¶ University of California, Berkeley, California 94720, United States Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA Laboratory of Physical Chemistry, Department of Chemistry, National and Kapodistrian University of Athens, Panepistimiopolis Zografou, Athens 15784, Greece Theoretical and Physical Chemistry Institute, National Hellenic Research Foundation, Vas. Constantinou 48, Athens 11635, Greece Quantum Artificial Intelligence Lab. (QuAIL), Exploration Technology Directorate, NASA Ames Research Center, Moffett Field, CA 94035, USA J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Doleǰskova 3, 18223 Prague 8, Czech Republic Advanced Computing, Mathematics and Data Division, Pacific Northwest National Laboratory, 902 Battelle Boulevard, P.O. Box 999, MS K1-83, Richland, WA 99352, USA Department of Chemistry, University of Washington, Seattle, WA 98185, USA (Dated: May 6, 2021)

We introduce a new database SC1MC-2020 of artificial mono transition metal complexes involving reference data (HF energy, orbitals, and integrals), and one- and two-site entropies obtained from corresponding DMRG calculations. The purpose of this database is to include all important metal - ligand interactions of strongly correlated systems and obtain as much as possible information about the electronic correlation structure, which could be exploited by machine learning models to estimate these important information almost immediately for any similar systems with high degree of transferability.

We introduce a new version of the database SC1MC (SC1MC-2022), obtained by extension of the recent SC1MC-2020, which includes artificial mono transition metal complexes. The database involves reference data used as inputs for training of machine learning models, one- and two-site entropies, and mutual information obtained at the DMRG level for canonical and split-localised orbitals. The purpose of this database is to obtain as much as possible information about the electronic correlation structure, which could be exploited by machine learning models to estimate these important information without a significant computational cost for any similar type of systems with some degree of transferability.

We present a new implementation of density matrix renormalization group based tailored coupled clusters method (TCCSD), which employs the domain-based local pair natural orbital approach (DLPNO). Compared to the previous local pair natural orbital (LPNO) version of the method, the new implementation is more accurate, offers more favorable scaling, and provides more consistent behavior across the variety of systems. On top of the singles and doubles, we include the perturbative triples correction (T), which is able to retrieve even more dynamic correlation. The methods were tested on three systems: tetramethyleneethane, oxo-Mn(Salen), and iron(II)-porphyrin model. The first two were revisited to assess the performance with respect to LPNO-TCCSD. For oxo-Mn(Salen), we retrieved between 99.8 and 99.9% of the total canonical correlation energy which is an improvement of 0.2% over the LPNO version in less than 63% of the total LPNO runtime. Similar results were obtained for iron(II)-porphyrin. When the perturbative triples correction was employed, irrespective of the active space size or system, the obtained energy differences between two spin states were within the chemical accuracy of 1 kcal/mol using the default DLPNO settings.