A fast intrinsic localization procedure applicable for ab initio and semiempirical linear combination of atomic orbital wave functions

Reductive Elimination From Tetra-Alkyl Cuprates [MenCu(CF3)4-n]- (n=0-4): Beyond Simple Oxidation States

In recent years, the electronic structures of organocuprates in general and the complex [Cu(CF3)4]- in particular have attracted significant interest. A possible key indicator in this context is the reactivity of these species. Nonetheless, this aspect has received only limited attention. Here, we systematically study the series of tetra-alkyl cuprates [MenCu(CF3)4-n]- and their unimolecular reactivity in the gas phase, which includes concerted formal reductive eliminations as well as radical losses. Through computational studies, we characterize the electronic structures of the complexes and show how these are connected to their reactivity. We find that all [MenCu(CF3)4-n]- ions feature inverted ligand fields and that the distinct reactivity patterns of the individual complexes arise from the interplay of different effects.

Reduced Scaling Correlated Natural Transition Orbitals for Multilevel Coupled Cluster Calculations

Multilevel coupled cluster theory offers reduced scaling computation of intensive properties in systems that are too large for standard coupled cluster calculations. A significant benefit of the multilevel coupled cluster framework is the possibility of calculating intensive properties that are not tightly localized if an appropriate set of active orbitals is used. Correlated natural transition orbitals (CNTOs) are tailored to describe excitation processes. For multilevel coupled cluster singles and doubles (MLCCSD) and singles and perturbative doubles (MLCC2) calculations, the construction of CNTOs generally becomes the computational bottleneck. Here, we demonstrate how CNTOs can be obtained with O ( N 3 ) operations, eliminating the O ( N 5 ) -scaling steps involved in the original approach. This reduction in scaling moves the bottleneck of MLCC2 and MLCCSD calculations from the active orbital space preparation to the MLCC2 and MLCCSD equations with O ( N 4 ) -scaling.

Uncovering the reduction mechanism of Np(VI) with N,N-diethyl hydroxylamine: a scalar-relativistic DFT investigation

Salt-free reductants have been extensively studied in the plutonium uranium reduction extraction (PUREX) process for Np(VI) reduction. Hydroxylamine derivatives as a class of promising salt-free reductants can reduce Np(VI) to Np(V) in nitric acid solution. The reduction reaction and kinetic behavior of Np(VI) to Np(V) by diethylhydroxylamine (DEHA) were studied experimentally. Herein, we explored the reduction mechanism of Np(VI) by DEHA in aqueous solution using scalar-relativistic density functional theory. Four stages are included in the process of Np(VI) reduction to Np(V) by DEHA. The intermediate C2H5N(O)C2H4 is hydrolyzed to C2H5NHOH. The third and fourth stages of Np(VI) reduction are via two pathways due to different H atoms participating successively in the reduction process. The largest energy barrier for the four Np(VI) reduction processes is 12.3 kcal mol-1 for the third stage of Pathway I, consistent with the experimental observations. The Np-Oyl bond distances and spin density on Np elucidate the reduction essence including outer-sphere electron transfer or hydrogen atom transfer. The analyses of bonding nature reveal the bonding evolution during the reduction process. This work elucidates the reduction mechanism of Np(VI) by DEHA and provides new insights into the reduction of Np(VI) by hydroxylamine derivatives.

Periodic Local Coupled-Cluster Theory for Insulators and Metals

We describe the implementation details of periodic local coupled-cluster theory with single and double excitations (CCSD) and perturbative triple excitations [CCSD(T)] using local natural orbitals (LNOs) and k-point symmetry. We discuss and compare several choices for orbital localization, fragmentation, and LNO construction. By studying diamond and lithium, we demonstrate that periodic LNO-CC theory can be applied with equal success to both insulators and metals, achieving speedups of 2 to 3 orders of magnitude even for moderately sized k-point meshes. Our final predictions of the equilibrium cohesive energy, lattice constant, and bulk modulus for diamond and lithium are in good agreement with previous theoretical predictions and experimental results.

Restricted Open-Shell Cluster Mean-Field theory for Strongly Correlated Systems

The cluster-based Mean Field method (cMF) and it is second order perturbative correction was introduced by Jiménez-Hoyos and Scuseria to reduce the cost of modeling strongly correlated systems by dividing an active space up into small clusters, which are individually solved in the mean-field presence of each other. In that work, clusters with unpaired electrons are treated by allowing the α and β orbitals to spin polarize. While that provided significant energetic stabilization, the resulting cMF wave function was spin-contaminated, making it difficult to use as a reference state for spin-pure post-cMF methods. In this work, we propose the Restricted Open-shell cMF (RO-cMF) method, extending the cMF approach to systems with open-shell clusters, while not permitting spin-polarization. While the resulting RO-cMF energies are necessarily higher in energy than the unrestricted orbital cMF, the new RO-cMF provides a simple reference state for post-cMF methods that recover the missing intercluster correlations. We provide a detailed explanation of the method, and report demonstrative calculations of exchange coupling constants for three systems: a di-iron complex, a dichromium complex, and a dimerized organic radical. We also report the first perturbatively corrected RO-cMF-PT2 results as well.

Anisole-Water and Anisole-Ammonia Complexes in Ground and Excited (S1) States: A Multiconfigurational Symmetry-Adapted Perturbation Theory (SAPT) Study

Binary complexes of anisole have long been considered paradigm systems for studying microsolvation in both the ground and electronically excited states. We report a symmetry-adapted perturbation theory (SAPT) analysis of intermolecular interactions in anisole-water and anisole-ammonia complexes within the framework of the multireference SAPT(CAS) method. Upon the S1 ← S0 electronic transition, the hydrogen bond in the anisole-water dimer is weakened, which SAPT(CAS) shows to be determined by changes in the electrostatic energy. As a result, the water complex becomes less stable in the relaxed S1 state despite decreased Pauli repulsion. Stronger binding of the anisole-ammonia complex following electronic excitation is more nuanced and results from counteracting shifts in the repulsive (exchange) and attractive (electrostatic, induction and dispersion) forces. In particular, we show that the formation of additional binding N-H···π contacts in the relaxed S1 geometry is possible due to reduced Pauli repulsion in the excited state. The SAPT(CAS) interaction energies have been validated against the coupled cluster (CC) results and experimentally determined shifts of the S1 ← S0 anisole band. While for the hydrogen-bonded anisole-water dimer SAPT(CAS) and CC shifts are in excellent agreement, for ammonia SAPT(CAS) is only qualitatively correct.

Size-consistency and orbital-invariance issues revealed by VQE-UCCSD calculations with the FMO scheme

The fragment molecular orbital (FMO) scheme is one of the popular fragmentation-based methods and has the potential advantage of making the circuit shallow for quantum chemical calculations on quantum computers. In this study, we used a GPU-accelerated quantum simulator (cuQuantum) to perform the electron correlation part of the FMO calculation as unitary coupled-cluster singles and doubles (UCCSD) with the variational quantum eigensolver (VQE) for hydrogen-bonded (FH)  3 and (FH)  2 -H  2 O systems with the STO-3G basis set. VQE-UCCSD calculations were performed using both canonical and localized MO sets, and the results were examined from the point of view of size-consistency and orbital-invariance affected by the Trotter error. It was found that the use of localized MO leads to better results, especially for (FH)  2 -H  2 O. The GPU acceleration was substantial for the simulations with larger numbers of qubits, and was about a factor of 6.7-7.7 for 18 qubit systems.

Exploiting Non-Abelian Point-Group Symmetry to Estimate the Exact Ground-State Correlation Energy of Benzene in a Polarized Split-Valence Triple-Zeta Basis Set

Local electronic-structure methods in quantum chemistry operate on the ability to compress electron correlations more efficiently in a basis of spatially localized molecular orbitals than in a parent set of canonical orbitals. However, many typical choices of localized orbitals tend to be related by selected, near-exact symmetry operations whenever a molecule belongs to a point group, a feature which remains largely unexploited in most local correlation methods. The present Letter demonstrates how to leverage a recent unitary protocol for enforcing symmetry properties among localized orbitals to yield a high-accuracy estimate of the exact ground-state correlation energy of benzene (D6h) in correlation-consistent polarized basis sets of both double- and triple-ζ quality. Through an initial application to many-body expanded full configuration interaction (MBE-FCI) theory, we show how molecular point-group symmetry can lead to computational savings that are inversely proportional to the order of the point group in a manner generally applicable to the acceleration of modern local correlation methods.

Wannier Function Localization Using Bloch Intrinsic Atomic Orbitals

We extend the intrinsic atomic orbital (IAO) method for the localization of molecular orbitals to calculate well-localized generalized Wannier functions in crystals in the spirit of the Pipek-Mezey method. We furthermore present a one-shot diabatic Wannierization procedure that aligns the phases of the Bloch functions, providing immediate Wannier localization, which serves as an excellent initial guess for optimization. We test our Wannier localization implementation on a number of solid-state systems, highlighting the effectiveness of the diabatic preparation, especially for localizing core bands. Partial charges of Wannier functions generated using Bloch IAOs align well with chemical intuition, which we demonstrate through the example of the adsorption of CO on a MgO surface.

Mechanistic insights into copper-mediated benzylic C(sp3)-H bond trifluoromethylation

The mechanisms underlying copper-mediated trifluoromethylation of benzylic C(sp3)-H bonds were investigated using density functional theory (DFT) calculations. Two distinct pathways were identified: radical recombination/reductive elimination and single-electron transfer (SET). In the radical recombination/reductive elimination pathway, the CuII species recombines with benzyl radicals to generate a CuIII intermediate, which subsequently undergoes reductive elimination. Conversely, the SET pathway involves single-electron transfer from benzyl radicals to CuII species, forming a cationic benzylic intermediate and CuI species, followed by coupling with a CF3 group coordinated to Cu. DFT calculations revealed that the radical recombination/reductive elimination pathway is favoured for trifluoromethylation of primary and secondary benzylic C(sp3)-H bonds, with the reductive elimination step being rate-determining. In contrast, the SET pathway exhibits preference for trifluoromethylation of tertiary benzylic C(sp3)-H bonds. These mechanistic insights have significant implications for enhancing the selectivity of copper-mediated trifluoromethylation reactions.

Theoretical Study of the Isotope Effect in Optical Rotation

In this work, the isotope effect in optical rotation (OR) is examined by exploring structure-property relationships for H → D substitutions in chiral molecules. While electronic effects serve as the dominant source of optical activity, there is a non-negligible contribution from nuclear vibrations, which changes with isotopic substitution. We employ a test set of 50 small organic molecules: three-membered rings with varying heteroatoms (PCl, PH, S, NCl, NH, O, and NBr) and functional groups (Me, F), and simulations were run at the B3LYP/aug-cc-pVDZ level of theory. The objectives of this work are to determine locations of isotopic substitution that result in significant changes in the vibrational correction to the OR and to evaluate which vibrational modes and electronic response are the major contributors to the isotope effect. Molecules with more polarizable heteroatoms in the ring (e.g., S and P) have the largest change in the vibrational correction compared to the unsubstituted parent molecules. In many cases, isotopic substitution made to the hydrogens on the opposite side of the ring from the functional group provides the largest change in the OR. H/D wagging modes and C vibrations (for D-C centers) are the largest contributors to the isotope effect. This is explained with a molecular orbital decomposition analysis of the OR. The relevant vibrational modes affect the orbital transitions that are already significant at the equilibrium geometry. However, this effect is only large when polarizable heteroatoms are involved because the electron density surrounding them is diffuse enough to feel the subtle effect of change in mass due to isotopic substitution on the relevant vibrational modes.

Prominent Role of Charge Transfer in the Spectral Tuning of Photosynthetic Light-Harvesting I Complex

Purple bacteria possess two ring-shaped protein complexes, light-harvesting 1 (LH1) and 2 (LH2), both of which function as antennas for solar energy utilization for photosynthesis but exhibit distinct absorption properties. The two antennas have differing amounts of bacteriochlorophyll (BChl) a; however, their significance in spectral tuning remains elusive. Here, we report a high-precision evaluation of the physicochemical factors contributing to the variation in absorption maxima between LH1 and LH2, namely, BChl a structural distortion, protein electrostatic interaction, excitonic coupling, and charge transfer (CT) effects, as derived from detailed spectral calculations using an extended version of the exciton model, in the model purple bacterium Rhodospirillum rubrum. Spectral analysis confirmed that the electronic structure of the excited state in LH1 extended to the BChl a 16-mer. Further analysis revealed that the LH1-specific redshift (∼61% in energy) is predominantly accounted for by the CT effect resulting from the closer inter-BChl distance in LH1 than in LH2. Our analysis explains how LH1 and LH2, both with chemically identical BChl a chromophores, use distinct physicochemical effects to achieve a progressive redshift from LH2 to LH1, ensuring efficient energy transfer to the reaction center special pair.

Kohn-Sham fragment energy decomposition analysis

We introduce the concept of Kohn-Sham fragment localized molecular orbitals (KS-FLMOs), which are Kohn-Sham molecular orbitals (MOs) localized in specific fragments constituting a generic molecular system. In detail, we minimize the local electronic energies of various fragments, while maximizing the repulsion between them, resulting in the effective localization of the MOs. We use the developed KS-FLMOs to propose a novel energy decomposition analysis, which we name Kohn-Sham fragment energy decomposition analysis, which allows for rationalizing the main non-covalent interactions occurring in interacting systems both in vacuo and in solution, providing physical insights into non-covalent interactions. The method is validated against state-of-the-art energy decomposition analysis techniques and with high-level calculations.

DFT Modeling of Polyethylene Chains Cross-linked by Selected ns1 and ns2 Metal Atoms

We analyze the structures, stabilities, and thermochemical properties of polyethylene (PE) oligomer chains cross-linked by metal (M) atoms through C-M-C bonds. Representative PEn-Mm-PEn complexes contain between 7 and 15 carbon atoms in each oligomer and one to three Li, Be, Mg, Zn, Ag, or Au cross-linking metal elements. PEn-Mm-PEn complexes are quasiplanar with nearly parallel PE chains. Their stability is determined by covalent C-M-C bonds accompanied by noncovalent dispersion interactions between PEn chains. Using the CAM-B3LYP+D3BJ+ABC functional, the binding energies of PE15-M-PE15 with respect to two PE15 radicals and metal fragments are -225, -230, -322, -551, -289, and -303 kJ/mol for Li, Ag, Au, Be, Mg, and Zn atoms, respectively. Entropy contributions (109 to 121 kJ/mol at 298.15 K) destabilize all complexes significantly. With two cross-linking metal elements in PE15-M2-PE15 complexes, binding energies are about double. Complexes with several open-shell Li, Ag, or Au doublet atoms have spins located on separated C-M-C bonds. High-spin PE15-Mm1-PE15-Mm2-PE15 complexes of three PE oligomers cross-linked by up to five doublet metal atoms create parallel PE tubes, which are suggested as elementary cells for modeling magnetic polymer tubes.

A comprehensive electron wavefunction analysis toolbox for chemists, Multiwfn

Analysis of electron wavefunction is a key component of quantum chemistry investigations and is indispensable for the practical research of many chemical problems. After more than ten years of active development, the wavefunction analysis program Multiwfn has accumulated very rich functions, and its application scope has covered numerous aspects of theoretical chemical research, including charge distribution, chemical bond, electron localization and delocalization, aromaticity, intramolecular and intermolecular interactions, electronic excitation, and response property. This article systematically introduces the features and functions of the latest version of Multiwfn and provides many representative examples. Through this article, readers will be able to fully understand the characteristics and recognize the unique value of Multiwfn. The source code and precompiled executable files of Multiwfn, as well as the manual containing a detailed introduction to theoretical backgrounds and very rich tutorials, can all be downloaded for free from the Multiwfn website (http://sobereva.com/multiwfn).

Accurate and efficient open-source implementation of domain-based local pair natural orbital (DLPNO) coupled-cluster theory using a t1-transformed Hamiltonian

We present an efficient, open-source formulation for coupled-cluster theory through perturbative triples with domain-based local pair natural orbitals [DLPNO-CCSD(T)]. Similar to the implementation of the DLPNO-CCSD(T) method found in the ORCA package, the most expensive integral generation and contraction steps associated with the CCSD(T) method are linear-scaling. In this work, we show that the t1-transformed Hamiltonian allows for a less complex algorithm when evaluating the local CCSD(T) energy without compromising efficiency or accuracy. Our algorithm yields sub-kJ mol-1 deviations for relative energies when compared with canonical CCSD(T), with typical errors being on the order of 0.1 kcal mol-1, using our TightPNO parameters. We extensively tested and optimized our algorithm and parameters for non-covalent interactions, which have been the most difficult interaction to model for orbital (PNO)-based methods historically. To highlight the capabilities of our code, we tested it on large water clusters, as well as insulin (787 atoms).

Ensemble Generalization of the Perdew-Zunger Self-Interaction Correction: A Way Out of Multiple Minima and Symmetry Breaking

The Perdew-Zunger (PZ) self-interaction correction (SIC) is an established tool to correct unphysical behavior in density functional approximations. Yet, the PZ-SIC is well-known to sometimes break molecular symmetries. An example of this is the benzene molecule, for which the PZ-SIC predicts a symmetry-broken electron density and molecular geometry, since the method does not describe the two possible Kekulé structures on an even footing, leading to local minima [Lehtola et al. J. Chem. Theory Comput. 2016, 12, 3195]. The PZ-SIC is often implemented with Fermi-Löwdin orbitals (FLOs), yielding the FLO-SIC method, which likewise has issues with symmetry breaking and local minima [Trepte et al. J. Chem. Phys. 2021, 155, 224109]. In this work, we propose a generalization of the PZ-SIC─the ensemble PZ-SIC (E-PZ-SIC) method─which shares the asymptotic computational scaling of the PZ-SIC (albeit with an additional prefactor). The E-PZ-SIC is straightforwardly applicable to various molecules, merely requiring one to average the self-interaction correction over all possible Kekulé structures, in line with chemical intuition. We showcase the implementation of the E-PZ-SIC with FLOs, as the resulting E-FLO-SIC method is easy to realize on top of an existing implementation of the FLO-SIC. We show that the E-FLO-SIC indeed eliminates symmetry breaking, reproducing a symmetric electron density and molecular geometry for benzene. The ensemble approach suggested herein could also be employed within approximate or locally scaled variants of the PZ-SIC and its FLO-SIC versions.

Error Control and Automatic Detection of Reference Active Spaces in Many-Body Expanded Full Configuration Interaction

We present a wide-reaching revamp of the generalized many-body expanded full configuration interaction (MBE-FCI) method. First, we outline how to automatize the selection of reference active spaces, whereby the inherent bias introduced through a manual identification is reduced, also within the context of traditional complete active space methods. Second, we allow for the use of compact orbital clusters as expansion objects, which works to circumvent the unfavorable scaling with the number of orbitals included in the space complementary to the reference orbitals. Finally, we present a new algorithm for ensuring that many-body expansions can be efficiently terminated while conservatively accounting for resulting errors. These developments are all tested on a variety of molecular systems and different orbital representations to illustrate the abilities of our algorithm to produce correlation energies within predetermined error bounds, significantly broadening the overall applicability of the MBE-FCI method.

Probing σ-Aromaticity-Driven Ring Contraction of Metallabenzocyclobutadiene to Metallabenzocyclopropene

Ring contraction of metallacyclobutadiene to metallacyclopropene is rare because of the increasing strain from a four-membered ring to a three-membered one. Here we demonstrate a new series of reactions of metallabenzocyclobutadiene to metallabenzocyclopropene via density functional theory calculations. The results suggest that these reactions are thermodynamically favorable ranging from -17.4 to -29.4 kcal mol-1, and a low reaction barrier (10.3 kcal mol-1) is achieved when the metal center is Ru and the ligands are one cyanide and one chloride. Further analysis suggests that a strengthened binding energy helps stabilize the transition state in the protonation process. The aromaticity during the reaction was investigated using the electron density of delocalized bonds (EDDB), isomerization stabilization energy, and isodesmic reactions. The EDDB shows that the π-conjugation is disrupted in the intermediate, and then σ-aromaticity is generated and dominant in the products. Our findings could be helpful for experimentalists in developing novel ring contraction reactions driven by aromaticity.

Adsorption and vibrational spectroscopy of CO on the surface of MgO from periodic local coupled-cluster theory

The adsorption of CO on the surface of MgO has long been a model problem in surface chemistry. Here, we report periodic Gaussian-based calculations for this problem using second-order perturbation theory (MP2) and coupled-cluster theory with single and double excitations (CCSD) and perturbative triple excitations [CCSD(T)], with the latter two performed using a recently developed extension of the local natural orbital approximation to problems with periodic boundary conditions. The low cost of periodic local correlation calculations allows us to calculate the full CCSD(T) binding curve of CO approaching the surface of MgO (and thus the adsorption energy) and the two-dimensional potential energy surface (PES) as a function of the distance from the surface and the CO stretching coordinate. From the PES, we obtain the fundamental vibrational frequency of CO on MgO, whose shift from the gas phase value is a common experimental probe of surface adsorption. We find that CCSD(T) correctly predicts a positive frequency shift upon adsorption of +14.7 cm-1, in excellent agreement with the experimental shift of +14.3 cm-1. We use our CCSD(T) results to assess the accuracy of MP2, CCSD, and several density functional theory (DFT) approximations, including exchange correlation functionals and dispersion corrections. We find that MP2 and CCSD yield reasonable binding energies and frequency shifts, whereas many DFT calculations overestimate the magnitude of the adsorption energy by 5-15 kJ mol-1 and predict a negative frequency shift of about -20 cm-1, which we attribute to self-interaction-induced delocalization errors that are mildly ameliorated with hybrid functionals. Our findings highlight the accuracy and computational efficiency of the periodic local correlation for the simulation of surface chemistry with accurate wavefunction methods.

DOCSIC: A Mean-Field Method for Orbital-by-Orbital Self-Interaction Correction

We introduce a new method to remove the one-electron self-interaction error in approximate density functional calculations on an orbital-by-orbital basis, as originally proposed by Perdew and Zunger [Phys. Rev. B 1981, 23, 5048]. This method is motivated by a recent proposal by Pederson et al. [J. Chem. Phys. 2014, 140, 121103] to remove self-interaction that employs orbitals derived from the real-space density matrix, known as FLOSIC (Fermi Löwdin orbitals self-interaction correction). However, instead of Fermi Löwdin orbitals, our scheme utilizes columns of the density matrix to determine localized orbitals, like the localization procedure proposed by Fuemmeler et al. [J. Chem. Theory Comput. 2023, 19, 8572]. The new method, dubbed DOCSIC for density matrix as orbital coefficients self-interaction correction, contrasts with traditional Perdew-Zunger or FLOSIC in that it does not incorporate additional optimization parameters, and, unlike the average density self-interaction correction of Ciofini et al. [Chem. Phys. Lett. 2003, 380, 12], it makes use of localized orbitals. Another advantage of DOCSIC is that it can be implemented as a mean-field formalism. We show details of the self-consistent generalized Kohn-Sham implementation, some illustrative results, and we finally highlight its advantages and limitations.

Fragment Aligned Molecular Orbital Analysis: An Innovative Tool for Analyzing Atypical Chemical Bonding

In chemical research, it is a common practice to carry out quantum chemical calculations and analyze the canonical molecular orbitals (CMOs) obtained to study electronic structures of chemical systems. However, extensive orbital mixing of CMOs especially in molecular clusters significantly complicates our understanding of the electronic structures. In this paper, we have developed an innovative tool called fragment aligned molecular orbital (FAMO) analysis, which reconstructs our modular chemical picture by making use of the Procrustes analysis in statistical theory to align the occupied molecular orbitals of a molecular species against the occupied (molecular) orbitals of the constituting fragments of the cluster, and results in a set of chemically intuitive semilocalized orbitals. This alignment technique minimizes the extensive orbital mixing, thus allowing precise observation of bonding interactions in complex chemical systems. A few representative clusters have been selected as showcase examples to demonstrate the advantage of FAMO analysis in deciphering the distinct bonding interactions in cluster compounds.

The trials and triumphs of modelling X-ray absorption spectra of transition metal phthalocyanines

This study explores the electronic structure of Co, Fe and Mn phthalocyanines (TMPcs) as well as their perfluorinated counterparts through a series of electronic structure calculations utilizing multireference methods and by simulating their metal L-edge and ligand (nitrogen and fluorine) K-edge X-ray absorption spectra (XAS) in an angle-resolved manner. Simulations targeting different ground-state symmetries, where relevant, have been conducted to observe changes in the N K-edge lineshape. The applicability of the quasi-degenerate formulation of n-electron valence state perturbation theory (QD-NEVPT2) for L-edge X-ray absorption spectroscopy (XAS) is evaluated, alongside the use of a restricted active space (RAS) formalism to describe the final-state multiplets generated by L-shell X-ray processes. Our findings provide valuable insights into the electronic properties of TMPcs, in particular with respect to the effect of fluorination, and demonstrate the broad applicability of various formulations of NEVPT2 in spectral simulations. Moreover, this study highlights the utility of manual truncation of the configuration spaces in order to allow for large active orbital spaces in aforementioned calculations.

Quantum-Quantum and Quantum-Quantum-Classical Schemes for Near-Gap Excitations with Projection-Based-Embedded GW-Bethe-Salpeter Equation

We present quantum-quantum and quantum-quantum-classical schemes based on many-body Green's functions theory in the GW approximation with the Bethe-Salpeter equation (GW-BSE) employing projection-based-embedding (PbE). Such approaches allow defining active and inactive subsystems of larger, complex molecular systems, with only the smaller active subsystem being explicitly treated by GW-BSE offering significant computational advantages. However, as PbE can modify the single-particle states in the Kohn-Sham (KS) ground state calculation and screening effects from the inactive region are not automatically included in GW-BSE, results from such PbE-GW-BSE calculations can deviate from a full-system reference. Here, we scrutinize in detail, e.g., the individual and combined effects of different choices of active regions, the influence of omitting the screening from the inactive region, and strategies for basis set truncation on frontier orbital and near-gap electron-hole excitation energies. As prototypical systems, we consider a diketopyrrolopyrrole bicyclic ring including side-chains, a polarity-sensitive dye (prodan) in aqueous environment, and a π-stacked dimer of benzene and tetracyanoethylene in water, respectively, covering a variety of excitation characters in molecular systems with complex chemical environments and photoinduced processes. Our results suggest that to obtain agreement of approximately 0.1 eV between near-gap excitation energies from embedded and full calculations, the active region should be chosen based on the Mulliken population of the full highest-occupied molecular orbital and that careful benchmarking should be done on the KS level before the actual GW-BSE steps when basis set truncation is used. We find that PbE-GW-BSE offers significant reductions in computation times and, more importantly, memory requirements, making calculations for considerably larger systems tractable.

Performant automatic differentiation of local coupled cluster theories: Response properties and ab initio molecular dynamics

In this work, we introduce a differentiable implementation of the local natural orbital coupled cluster (LNO-CC) method within the automatic differentiation framework of the PySCFAD package. The implementation is comprehensively tuned for enhanced performance, which enables the calculation of first-order static response properties on medium-sized molecular systems using coupled cluster theory with single, double, and perturbative triple excitations [CCSD(T)]. We evaluate the accuracy of our method by benchmarking it against the canonical CCSD(T) reference for nuclear gradients, dipole moments, and geometry optimizations. In addition, we demonstrate the possibility of property calculations for chemically interesting systems through the computation of bond orders and Mössbauer spectroscopy parameters for a [NiFe]-hydrogenase active site model, along with the simulation of infrared spectra via ab initio LNO-CC molecular dynamics for a protonated water hexamer.

Restricted Open-Shell Hartree-Fock Method for a General Configuration State Function Featuring Arbitrarily Complex Spin-Couplings

In this work, we present a general spin restricted open-shell Hartree-Fock (ROHF) implementation that is able to generate self-consistent field (SCF) wave functions for an arbitrary configuration state function (CSF). These CSFs can contain an arbitrary number of unpaired electrons in arbitrary spin-couplings. The resulting method is named CSF-ROHF. We demonstrate that starting from the ROHF energy expression, for example, the one given by Edwards and Zerner, it is possible to obtain the values of the ROHF vector-coupling coefficients by setting up an open-shell for each group of consecutive parallel-coupled spins dictated by the unique spin-coupling pattern of any given CSF. To achieve this important and nontrivial goal, we employ the machinery of the iterative configuration expansion configuration interaction (ICE-CI) method, which is able to tackle general CI problems on the basis of spin-adapted CSFs. This development allows for the efficient generation of SCF spin-eigenfunctions for systems with complex spin-coupling patterns, such as polymetallic chains and metal clusters, while maintaining SCF scaling with system size (quadratic or less, depending on the specific algorithm and approximations chosen).

Modeling One-Electron Oxidation Potentials and Hole Delocalization in Double-Stranded DNA by Multilayer and Dynamic Approaches

The number of innovative applications for DNA nowadays is growing quickly. Its use as a nanowire or electrochemical biosensor leads to the need for a deep understanding of the charge-transfer process along the strand, as well as its redox properties. These features are computationally simulated and analyzed in detail throughout this work by combining molecular dynamics, multilayer schemes, and the Marcus theory. One-electron oxidation potential and hole delocalization have been analyzed for six DNA double strands that cover all possible binary combinations of nucleotides. The results have revealed that the one-electron oxidation potential decreases with respect to the single-stranded DNA, giving evidence that the greater rigidity of a double helix induces an increase in the capacity of storing the positive charge generated upon oxidation. In addition, the hole is mainly stored in nucleobases with large reducer character, i.e., purines, especially when those are arranged in a stacked configuration in the same strand. From the computational point of view, the sampling needed to describe biological systems implies a significant computational cost. Here, we show that a small number of representative conformations generated by clustering analysis provides accurate results when compared with those obtained from sampling, reducing considerably the computational cost.

Maximization of linear independence of basis function products

Basis sets consisting of functions that form linearly independent products (LIPs) have remarkable applications in quantum chemistry but are scarce because of mathematical limitations. We show how to linearly transform a given set of basis functions to maximize the linear independence of their products by maximizing the determinant of the appropriate Gram matrix. The proposed method enhances the utility of the LIP basis set technology and clarifies why canonical molecular orbitals form LIPs more readily than atomic orbitals. The same approach can also be used to orthogonalize basis functions themselves, which means that various orthogonalization techniques may be viewed as special cases of a certain nonlinear optimization problem.

Revisiting the quasi-aromaticity in polynuclear metal chalcogenide clusters and their derivative "cluster-assembly" crystalline structures

The concept of aromaticity is primarily invented to account for the high stability of conjugated organic compounds that possess a specific structural and chemical stability with (4n + 2) π electrons. In 1988, quasi-aromaticity was theoretically proposed for the Mo3S44+ core in the Mo3(μ3-S)(μ-S)3(χ-dtp)3(μ-dtp) L compound (χ: chelating ligand; dtp: (EtO)2PS2-) illustrated by canonical molecular orbitals. However, the origin of the quasi-aromaticity and chemical bonding remains ambiguous, lacking a thorough analysis in terms of stability and quantitative measurement of the aromatic character. Thus, in this work, we systematically reported the electronic structure and aromaticity of a series of polynuclear metal chalcogenide clusters [M3X4(H2O)9]4+ (M = Cr, Mo, W, and Sg; X = O, S, Se, and Te) to explore an efficient tool of NICS index values at specific points to measure the quasi-aromaticity and to figure out the (d-p-d) π three-center bonding as the predominant origin from the arrangement of three Mo atoms and three bridged X atoms. Interestingly, derived from the Mo3⋯S3 quasi-plane, the extended sandwich cluster model of a S3⋯Mo3⋯S3 (Mo3S6) structure can be seen as the seed unit of the popular MoS2 nanomaterials, with the resemblance between both molecular and periodic systems regarding geometries, electronic structures, and chemical bonding. Additionally, the highly symmetric Mo3S4 core in [Mo3X4(H2O)9]4+ can be arranged in a staggered and stacked manner to create the Mo6S82- building block, corresponding to the crystalline structures in BaMo6S8 Chevrel phases, albeit with slight deformations. But the neutral Mo6S8 cluster can be seen as the seed structure for the Mo3S4 periodic materials for the high resemblance in terms of geometry, electronic structures and chemical bonding. Drawing upon the observed similarities between cluster models and materials, we propose a new concept termed "cluster-assembly" materials. This concept involves the expansion from a high-symmetry and/or aromatic stable cluster seed unit to form the corresponding derivative materials, presenting an alternative paradigm for investigating crystals and enriching our comprehension of the stabilities exhibited by both gas-phase clusters and solid-state materials. The concept of "cluster-assembly" materials not only contributes to the formulation of design strategies for novel materials or stable clusters but also provides valuable insights into the extension of periodic aromaticity.

Chelate Complexes of 3d Transition Metal Ions─A Challenge for Electronic-Structure Methods?

Different electronic-structure methods were assessed for their ability to predict two important properties of the industrially relevant chelating agent nitrilotriacetic acid (NTA): its selectivity with respect to six different first-row transition metal ions and the spin-state energetics of its complex with Fe(III). The investigated methods encompassed density functional theory (DFT), the random phase approximation (RPA), coupled cluster (CC) theory, and the auxiliary-field quantum Monte Carlo (AFQMC) method, as well as the complete active space self-consistent field (CASSCF) method and the respective on-top methods: second-order N-electron valence state perturbation theory (NEVPT2) and multiconfiguration pair-density functional theory (MC-PDFT). Different strategies for selecting active spaces were explored, and the density matrix renormalization group (DMRG) approach was used to solve the largest active spaces. Despite somewhat ambiguous multi-reference diagnostics, most methods gave relatively good agreement with experimental data for the chemical reactions connected to the selectivity, which only involved transition-metal complexes in their high-spin state. CC methods yielded the highest accuracy followed by range-separated DFT and AFQMC. We discussed in detail that even higher accuracies can be obtained with NEVPT2, under the prerequisite that consistent active spaces along the entire chemical reaction can be selected, which was not the case for reactions involving Fe(III). A bigger challenge for electronic-structure methods was the prediction of the spin-state energetics, which additionally involved lower spin states that exhibited larger multi-reference diagnostics. Conceptually different, typically accurate methods ranging from CC theory via DMRG-NEVPT2 in combination with large active spaces to AFQMC agreed well that the high-spin state is energetically significantly favored over the other spin states. This was in contrast to most DFT functionals and RPA which yielded a smaller stabilization and some common DFT functionals and MC-PDFT even predicting the low-spin state to be energetically most favorable.

MBE-CASSCF Approach for the Accurate Treatment of Large Active Spaces

We present a novel implementation of the complete active space self-consistent field (CASSCF) method that makes use of the many-body expanded full configuration interaction (MBE-FCI) method to incrementally approximate electronic structures within large active spaces. On the basis of a hybrid first-order algorithm employing both Super-CI and quasi-Newton strategies for the optimization of molecular orbitals, we demonstrate both computational efficacy and high accuracy of the resulting MBE-CASSCF method. We assess the performance of our implementation on a set of established numerical tests before applying MBE-CASSCF in the investigation of the triplet-quintet spin gap of iron(II) porphyrin with active spaces as large as 50 electrons in 50 orbitals.

Reducing the Runtime of Fault-Tolerant Quantum Simulations in Chemistry through Symmetry-Compressed Double Factorization

Quantum phase estimation based on qubitization is the state-of-the-art fault-tolerant quantum algorithm for computing ground-state energies in chemical applications. In this context, the 1-norm of the Hamiltonian plays a fundamental role in determining the total number of required iterations and also the overall computational cost. In this work, we introduce the symmetry-compressed double factorization (SCDF) approach, which combines a CDF of the Hamiltonian with the symmetry shift technique, significantly reducing the 1-norm value. The effectiveness of this approach is demonstrated numerically by considering various benchmark systems, including the FeMoco molecule, cytochrome P450, and hydrogen chains of different sizes. To compare the efficiency of SCDF to other methods in absolute terms, we estimate Toffoli gate requirements, which dominate the execution time on fault-tolerant quantum computers. For the systems considered here, SCDF leads to a sizable reduction of the Toffoli gate count in comparison to other variants of DF or even tensor hypercontraction, which is usually regarded as the most efficient approach for qubitization.

Toward Reliable Dipole Moments without Single Excitations: The Role of Orbital Rotations and Dynamical Correlation

The dipole moment is a crucial molecular property linked to a molecular system's bond polarity and overall electronic structure. To that end, the electronic dipole moment, which results from the electron density of a system, is often used to assess the accuracy and reliability of new electronic structure methods. This work analyses electronic dipole moments computed with the pair coupled cluster doubles (pCCD) ansätze and its linearized coupled cluster (pCCD-LCC) corrections using the canonical Hartree-Fock and pCCD-optimized (localized) orbital bases. The accuracy of pCCD-based dipole moments is assessed against experimental and CCSD(T) reference values using relaxed and unrelaxed density matrices and different basis set sizes. Our test set comprises molecules of various bonding patterns and electronic structures, exposing pCCD-based methods to a wide range of electron correlation effects. Additionally, we investigate the performance of pCCD-in-DFT dipole moments of some model complexes. Finally, our work indicates the importance of orbital relaxation in the pCCD model and shows the limitations of the linearized couple cluster corrections in predicting electronic dipole moments of multiple-bonded systems. Most importantly, pCCD with a linearized CCD correction can reproduce the dipole moment surfaces in singly bonded molecules, which are comparable to the multireference ones.

Propagated (fragment) Pipek-Mezey Wannier functions in real-time time-dependent density functional theory

Localization procedures are an important tool for analysis of complex systems in quantum chemistry, since canonical molecular orbitals are delocalized and can, therefore, be difficult to align with chemical intuition and obscure information at the local level of the system. This especially applies to calculations obeying periodic boundary conditions. The most commonly used approach to localization is Foster-Boys Wannier functions, which use a unitary transformation to jointly minimize the second moment of the orbitals. This procedure has proven to be robust and fast but has a side effect of often mixing σ- and π-type orbitals. σ/π-separation is achieved by the Pipek-Mezey Wannier function (PMWF) approach [Lehtola and Jónsson, J. Chem. Theory Comput. 10, 642 (2014) and Jónsson et al., J. Chem. Theory Comput. 13, 460 (2017)], which defines the spread functional in terms of partial charges instead. We have implemented a PMWF algorithm in the CP2K software package using the Cardoso-Souloumiac algorithm to enable their application to real-time time-dependent density functional theory. The method is demonstrated on stacked CO2 molecules, linear acetylenic carbon, boron and nitrogen co-doped graphene, and nitrogen-vacancy doped diamond. Finally, we discuss its computational scaling and recent efforts to improve it with fragment approaches.

Photochemical Formation and Electronic Structure of an Alkane σ-Complex from Time-Resolved Optical and X-ray Absorption Spectroscopy

C-H bond activation reactions with transition metals typically proceed via the formation of alkane σ-complexes, where an alkane C-H σ-bond binds to the metal. Due to the weak nature of metal-alkane bonds, σ-complexes are challenging to characterize experimentally. Here, we establish the complete pathways of photochemical formation of the model σ-complex Cr(CO)5-alkane from Cr(CO)6 in octane solution and characterize the nature of its metal-ligand bonding interactions. Using femtosecond optical absorption spectroscopy, we find photoinduced CO dissociation from Cr(CO)6 to occur within the 100 fs time resolution of the experiment. Rapid geminate recombination by a fraction of molecules is found to occur with a time constant of 150 fs. The formation of bare Cr(CO)5 in its singlet ground state is followed by complexation of an octane molecule from solution with a time constant of 8.2 ps. Picosecond X-ray absorption spectroscopy at the Cr L-edge and O K-edge provides unique information on the electronic structure of the Cr(CO)5-alkane σ-complex from both the metal and ligand perspectives. Based on clear experimental observables, we find substantial destabilization of the lowest unoccupied molecular orbital upon coordination of the C-H bond to the undercoordinated Cr center in the Cr(CO)5-alkane σ-complex, and we define this as a general, orbital-based descriptor of the metal-alkane bond. Our study demonstrates the value of combining optical and X-ray spectroscopic methods as complementary tools to study the stability and reactivity of alkane σ-complexes in their role as the decisive intermediates in C-H bond activation reactions.

Projected Atomic Orbitals As Optimal Virtual Space for Excited State Projection-Based Embedding Calculations

The projected atomic orbital (PAO) technique is presented for the construction of virtual orbital spaces in projection-based embedding (PbE) applications. The proposed straightforward procedure produces a set of virtual orbitals that are used in the final, high-level calculation of the embedded active subsystem. The PAO scheme is demonstrated on intermolecular potentials of bimolecular complexes in ground and excited states, including Rydberg excitations. The results show the outstanding performance of the PbE method when used with PAO virtual orbitals compared with those produced using common orbital localization techniques. The good agreement of the resulting PbE potential curves with those from high-level ab initio dimer calculations, also in diffuse basis sets, confirms that the PAO technique can be suggested for future applications using top-down embedding methods.

Analytical Gradient Using Cluster-in-Molecule RI-MP2 Method for the Geometry Optimizations of Large Systems

We present an efficient analytical energy gradient algorithm for the cluster-in-molecule resolution-of-identity second-order Møller-Plesset perturbation (CIM-RI-MP2) method based on the Lagrange multiplier method. Our algorithm independently constructs the Lagrangian formalism within each cluster, avoiding the solution of the coupled-perturbed Hartree-Fock (CPHF) equation for the whole system. Due to this feature, the computational cost of the CIM-RI-MP2 gradients is much lower than that of other local MP2 algorithms. Benchmark calculations of several molecules containing up to 312 atoms demonstrate the general applicability of our CIM-RI-MP2 gradient algorithm. The optimized structure of a 244-atom molecule using the CIM-RI-MP2 method with the cc-pVDZ basis set is in good agreement with the corresponding crystal structure. A single-point gradient calculation conducted for a molecular cage containing 972 atoms and 9612 basis functions takes 48 h on 25 nodes, utilizing a total of 600 CPU cores. The present CIM-RI-MP2 gradient program is applicable for obtaining the optimized geometries of large systems with hundreds of atoms.

Pt-S Bond-Enabled Temperature-Dependent Phosphorescence in S-Heteroaryl Tetradentate Pt(S^C^N^O) Complexes

This study presents the rare examples of S-heteroaryl tetradentate Pt(S^C^N^O) luminescent complexes (PtSZ and PtSZtBu) containing a Pt-S bond. The presence of the Pt-S bond allows the novel Pt(S^C^N^O) complexes to exhibit temperature-dependent phosphorescent emission behavior. The PtSZtBu exhibits dual-emission phenomena and biexponential transient decay spectra above 250 K, indicating the presence of two minimal excited states in the potential energy surface (PES) of the T1 state. Through complementary experimental and computational studies, we have identified changes in orbital composition between Pt(dxy)-S(px) and Pt(dyz)-S(pz) in excited states with increasing temperature. This results in two energy minima, enabling the excited states to decay selectively and radiatively at different temperatures. Consequently, this leads to remarkable steady-state and transient emission spectra changes. Our work not only provides valuable insights for the development of novel Pt-S bond-based tetradentate Pt(II) complexes but also enhances our understanding of the distinctive properties governed by the Pt-S bond.

The p-block challenge: assessing quantum chemistry methods for inorganic heterocycle dimerizations

The elements of the p-block of the periodic table are of high interest in various chemical and technical applications like frustrated Lewis-pairs (FLP) or opto-electronics. However, high-quality benchmark data to assess approximate density functional theory (DFT) for their theoretical description are sparse. In this work, we present a benchmark set of 604 dimerization energies of 302 "inorganic benzenes" composed of all non-carbon p-block elements of main groups III to VI up to polonium. This so-called IHD302 test set comprises two classes of structures formed by covalent bonding and by weaker donor-acceptor (WDA) interactions, respectively. Generating reliable reference data with ab initio methods is challenging due to large electron correlation contributions, core-valence correlation effects, and especially the slow basis set convergence. To compute reference values for these dimerization reactions, after thorough testing, we applied a computational protocol using state-of-the-art explicitly correlated local coupled cluster theory termed PNO-LCCSD(T)-F12/cc-VTZ-PP-F12(corr.). It includes a basis set correction at the PNO-LMP2-F12/aug-cc-pwCVTZ level. Based on these reference data, we assess 26 DFT methods in combination with three different dispersion corrections and the def2-QZVPP basis set, five composite DFT approaches, and five semi-empirical quantum mechanical methods. For the covalent dimerizations, the r2SCAN-D4 meta-GGA, the r2SCAN0-D4 and ωB97M-V hybrids, and the revDSD-PBEP86-D4 double-hybrid functional are found to be the best-performing methods among the evaluated functionals of the respective class. However, since def2 basis sets for the 4th period are not associated to relativistic pseudo-potentials, we obtained significant errors in the covalent dimerization energies (up to 6 kcal mol-1) for molecules containing p-block elements of the 4th period. Significant improvements were achieved for systems containing 4th row elements by using ECP10MDF pseudopotentials along with re-contracted aug-cc-pVQZ-PP-KS basis sets introduced in this work with the contraction coefficients taken from atomic DFT (PBE0) calculations. Overall, the IHD302 set represents a challenge to contemporary quantum chemical methods. This is due to a large number of spatially close p-element bonds which are underrepresented in other benchmark sets, and the partial covalent bonding character for the WDA interactions. The IHD302 set may be helpful to develop more robust and transferable approximate quantum chemical methods in the future.

Computational Comparative Study of the Binding of Americium with N-Donor Ligands

The accessibility of multiple valence states of americium (Am) inspired redox-based protocols aimed at efficient separation of trivalent Am (Am3+) from trivalent lanthanides (Ln3+) alternative to the traditional liquid-liquid extraction. This requires an extensive understanding of the coordination chemistry of Am in its various accessible valence states in the aqueous phase. In this work, by means of DFT calculations, the coordination of AmIII-VI with five typical N-donor ligands, i.e., terpyridine (tpy), bispyrazinylpyridine (dpp), bistriazinylpyridine (BTP), bistriazinyl bipyridine (BTBP), and bistrazinyl phenanthroline (BTPhen), was studied in terms of energy and topological analysis. The results show that the exchange of aqua ligands of hydrated ions by N-donor ligands is an entropy-driven process and enthalpically unfavorable. Topological analysis suggests a distinct mechanism of BTP to modulate the redox potential of Am(III) in that BTP can assist the relay of the leaving electron of AmIII, while the other N-donor ligands can detain the oxidation of Am by offering their electron instead. This comparative study enriches our understanding of the coordination chemistry of high-valent Am with N-donor ligands and recommends the ligand design toward the modulation of redox potentials of hydrated Am(III) ions.

Bond analysis in meta- and para-substituted thiophenols: overlap descriptors, local mode analysis, and QTAIM

CONTEXT

This study delves into the chemical nuances of thiophenols and their derivatives through a comprehensive computational analysis, moving beyond traditional energetic perspectives such as bond dissociation enthalpy and S-H dissociation dynamics. By employing the overlap model along with its topological descriptors (OP/TOP), quantum theory of atoms in molecules (QTAIM), and local vibrational mode (LVM) theories, the research provides a deeper understanding of the S-H and C-S bonding scenarios in substituted thiophenols. The investigation follows the electron-donating capacity of S-H substituent variation with the nature and positioning of other ring substituents. Energy profile analyses indicate distinct stability differences in the cis and trans conformations of meta- and para-PhSH systems, influenced by the electron-donating strength of these substituents. The study also uncovers significant variations in S-H bond distances and descriptor values, particularly in para-substituted PhSH, reflecting the influence of electron-donating or withdrawing substituents. In contrast, alterations at the meta-position show minimal effects on C-S bond descriptors, while para-substitutions markedly influence C-S bond characteristics, demonstrating a clear correlation with the electron-donating or withdrawing capabilities of the substituents. This research sheds light on the intricate bond dynamics in aromatic systems with diverse substituents, highlighting the complex interaction between electronic effects and molecular conformation.

METHODS

The study employs the ω B97X-D/Def2TZVP level of theory for molecular geometries, ensuring accurate characterization of structures as true minima via analytical harmonic frequency determination. The electronic properties of S-H and C-S bonds in variously substituted thiophenols were analyzed using OP/TOP, QTAIM, and LVM methodologies. Computational processes, including conformational scans, geometry optimizations, and vibrational frequency calculations, were conducted using Gaussian 09, with ultra-fine integration grids and tight convergence criteria for the SCF procedure. Bond descriptors were computed utilizing ChemBOS, Multiwfn, and LModeA software, providing a robust and detailed examination of bond properties.

Synthesis and characterization of iron clusters with an icosahedral [Fe@Fe12]16+ Core

Iron-metal clusters are crucial in a variety of critical biological and material systems, including metalloenzymes, catalysts, and magnetic storage devices. However, a synthetic high-nuclear iron cluster has been absent due to the extreme difficulty in stabilizing species with direct iron-iron bonding. In this work, we have synthesized, crystallized, and characterized a (Tp*)4W4S12(Fe@Fe12) cluster (Tp* = tris(3,5-dimethyl-1-pyrazolyl)borate(1-)), which features a rare trideca-nuclear, icosahedral [Fe@Fe12] cluster core with direct multicenter iron-iron bonding between the interstitial iron (Fei) and peripheral irons (Fep), as well as Fep···Fep ferromagnetic coupling. Quantum chemistry studies reveal that the stability of the cluster arises from the 18-electron shell-closing of the [Fe@Fe12]16+ core, assisted by its bonding interactions with the peripheral tridentate [(Tp*)WS3]4- ligands which possess both S→Fe donation and spin-polarized Fe-W σ bonds. The ground-state electron spin is theoretically predicted to be S = 32/2 for the cluster. The existence of low oxidation-state (OS ∼ +1.23) iron in this compound may find interesting applications in magnetic storage, spintronics, redox chemistry, and cluster catalysis.

Theoretical insight into the doubly antiaromatic carbon allotrope cyclo[16]carbon

A new carbon allotrope, cyclo[16]carbon (C16), has recently been successfully synthesized. It is hypothesized to exhibit double antiaromatic properties owing to the 4n π electrons. Theoretical calculations are a feasible method for systematically studying the structures and properties of unstable antiaromatic molecules. The results show that C16 has a planar structure characterized by alternating long and short bonds with D8h, and a strong antiaromatic characteristic originates from the two perpendicular π systems. We performed an extensive comparative analysis of C16 and the aromatic cyclo[18]carbon, C18. This study offers valuable insight into the structural and electronic characteristics of C16 and could inspire innovative applications and avenues for its utilization in various fields.

Unraveling Atomic Contributions to the London Dispersion Energy: Insights into Molecular Recognition and Reactivity

We present a general framework that enables quantification with atomic resolution of the overall London dispersion energy, which can be readily integrated with currently available energy decomposition schemes. This approach can be used to determine the contribution of individual atoms and functional groups to molecular recognition, conformational preferences, molecular stability, and reactivity. Its efficacy across diverse realms of molecular chemistry and biology is demonstrated with application to molecular balances in solution, asymmetric organocatalytic transformations, and a subcomplex of the F1FO ATP synthase.

Renormalized-Residue-Based Multireference Configuration Interaction Method for Strongly Correlated Systems

The implementation of multireference configuration interaction (MRCI) methods in quantum systems with large active spaces is hindered by the expansion of configuration bases or the intricate handling of reduced density matrices (RDMs). In this work, we present a spin-adapted renormalized-residue-based MRCI (RR-MRCI) approach that leverages renormalized residues to effectively capture the entanglement between active and inactive orbitals. This approach is reinforced by a novel efficient algorithm, which also facilitates an efficient deployment of spin-adapted matrix product state MRCI (MPS-MRCI). The RR-MRCI framework possesses several advantages: (1) It considers the orbital entanglement and utilizes highly compressed MPS structure, improving computational accuracy and efficiency compared with internally contracted (ic) MRCI. (2) Utilizing small-sized buffer environments of a few external orbitals as probes based on quantum information theory, it enhances computational efficiency over MPS-MRCI and offers potential application to large molecular systems. (3) The RR framework can be implemented in conjunction with ic-MRCI, eliminating the need for high-rank RDMs, by using distinct renormalized residues. We evaluated this method across nine diverse molecular systems, including Cu2O22+ with an active space of (24e,24o) and two complexes of lanthanide and actinide with active space (38e,36o), demonstrating the method's versatility and efficacy.

Protein3D: Enabling analysis and extraction of metal-containing sites from the Protein Data Bank with molSimplify

Metalloenzymes catalyze a wide range of chemical transformations, with the active site residues playing a key role in modulating chemical reactivity and selectivity. Unlike smaller synthetic catalysts, a metalloenzyme active site is embedded in a larger protein, which makes interrogation of electronic properties and geometric features with quantum mechanical calculations challenging. Here we implement the ability to fetch crystallographic structures from the Protein Data Bank and analyze the metal binding sites in the program molSimplify. We show the usefulness of the newly created protein3D class to extract the local environment around non-heme iron enzymes containing a two histidine motif and prepare 372 structures for quantum mechanical calculations. Our implementation of protein3D serves to expand the range of systems molSimplify can be used to analyze and will enable high-throughput study of metal-containing active sites in proteins.

Anisotropic Metal-Metal Pauli Repulsion in Polynuclear d10 Metal Clusters

Metallophilicity has been widely considered to be the driving force for self-assembly of closed-shell d10 metal complexes, but this view has been challenged by recent studies showing that metallophilicity in linear d10-d10 dimers is repulsive. This is due to strong metal-metal (M-M') Pauli repulsion (Wan, Q., Proc. Natl. Acad. Sci. U. S. A. 2021, 118, e2019265118). Here, we study M-M' Pauli repulsion in d10 metal clusters. Our results show that M-M' Pauli repulsion in d10 polynuclear clusters is 6-52% weaker than in similar linear d10 complexes due to the anisotropic shape of (n+1)s-nd hybridized orbitals. The overall M-M' interactions in closed-shell d10 polynuclear metal clusters remain repulsive. The effects of coordination geometry, relativistic effects, and the ligand's electronegativity on M-M' Pauli repulsion in polynuclear d10 clusters have been explored. These findings provide valuable guidance for the design and development of ligands and coordination geometries that alleviate M-M' Pauli repulsion in d10 metal cluster systems.

Ultrasound-activated piezo-hot carriers trigger tandem catalysis coordinating cuproptosis-like bacterial death against implant infections

Implant-associated infections due to the formation of bacterial biofilms pose a serious threat in medical healthcare, which needs effective therapeutic methods. Here, we propose a multifunctional nanoreactor by spatiotemporal ultrasound-driven tandem catalysis to amplify the efficacy of sonodynamic and chemodynamic therapy. By combining piezoelectric barium titanate with polydopamine and copper, the ultrasound-activated piezo-hot carriers transfer easily to copper by polydopamine. It boosts reactive oxygen species production by piezoelectrics, and facilitates the interconversion between Cu2+ and Cu+ to promote hydroxyl radical generation via Cu+ -catalyzed chemodynamic reactions. Finally, the elevated reactive oxygen species cause bacterial membrane structure loosening and DNA damage. Transcriptomics and metabolomics analysis reveal that intracellular copper overload restricts the tricarboxylic acid cycle, promoting bacterial cuproptosis-like death. Therefore, the polyetherketoneketone scaffold engineered with the designed nanoreactor shows excellent antibacterial performance with ultrasound stimulation and promotes angiogenesis and osteogenesis on-demand in vivo.

Three-Coordinate Nickel and Metal-Metal Interactions in a Heterometallic Iron-Sulfur Cluster

Biological multielectron reactions often are performed by metalloenzymes with heterometallic sites, such as anaerobic carbon monoxide dehydrogenase (CODH), which has a nickel-iron-sulfide cubane with a possible three-coordinate nickel site. Here, we isolate the first synthetic iron-sulfur clusters having a nickel atom with only three donors, showing that this structural feature is feasible. These have a core with two tetrahedral irons, one octahedral tungsten, and a three-coordinate nickel connected by sulfide and thiolate bridges. Electron paramagnetic resonance (EPR), Mössbauer, and superconducting quantum interference device (SQUID) data are combined with density functional theory (DFT) computations to show how the electronic structure of the cluster arises from strong magnetic coupling between the Ni, Fe, and W sites. X-ray absorption spectroscopy, together with spectroscopically validated DFT analysis, suggests that the electronic structure can be described with a formal Ni1+ atom participating in a nonpolar Ni-W σ-bond. This metal-metal bond, which minimizes spin density at Ni1+, is conserved in two cluster oxidation states. Fe-W bonding is found in all clusters, in one case stabilizing a local non-Hund state at tungsten. Based on these results, we compare different M-M interactions and speculate that other heterometallic clusters, including metalloenzyme active sites, could likewise store redox equivalents and stabilize low-valent metal centers through metal-metal bonding.

Vinylic C-H Activation of Styrenes by an Iron-Aluminum Complex

The oxidative addition of sp2 C-H bonds of alkenes to single-site transition-metal complexes is complicated by the competing π-coordination of the C═C double bond, limiting the examples of this type of reactivity and onward applications. Here, we report the C-H activation of styrenes by a well-defined bimetallic Fe-Al complex. These reactions are highly selective, resulting in the (E)-β-metalation of the alkene. For this bimetallic system, alkene binding appears to be essential for the reaction to occur. Experimental and computational insights suggest an unusual reaction pathway in which a (2 + 2) cycloaddition intermediate is directly converted into the hydrido vinyl product via an intramolecular sp2 C-H bond activation across the two metals. The key C-H cleavage step proceeds through a highly asynchronous transition state near the boundary between a concerted and a stepwise mechanism influenced by the resonance stabilization ability of the aryl substituent. The metalated alkenes can be further functionalized, which has been demonstrated by the (E)-selective phosphination of the employed styrenes.