Assessment of DFT Methods for Transition Metals with the TMC151 Compilation of Data Sets and Comparison with Accuracies for Main-Group Chemistry

Quasi-Hydrogen Bond and Charge-Trapping Effect Originating from Polar Side Group Lead to Significantly Suppressed Charge Transport in Polypropylene

How to fundamentally suppress charge transport is one of the essential issues in polymer dielectrics. This work reports significant charge transport suppression by glycidyl methacrylate (GMA) side group modification on polypropylene (PP). Experimental and computational investigations discover for the first time a quasi-hydrogen bond effect generated by carbonyl and epoxide of GMA in PP inter/intramolecular structure, while introducing trap energy levels within the HOMO-LUMO gap. These energy levels suppress the leakage current of GMA-modified PP thanks to the charge-trapping effect. The quasi-hydrogen bond originating from the interaction between the high-polar GMA group and flexible PP chain raises the thermostability while averaging the electron distribution between hydrogen and acceptor oxygen, which is conducive to lessening electric weak points, suppressing charge transport, and finally enhancing the electrical breakdown strength. This work provides new thinking on polymer dielectric design and charge transport regulation utilizing electron structure and weak interaction at the molecular scale.

Clusters of solvated ferrous ion in water-ammonia mixture: Structures and noncovalent interactions

The behavior of metal ions is commonly studied in pure solvent although, in our daily life, these metals are involved in mixtures of solvents. In the present study, we investigated structures, relative stabilities and temperature dependance of solvated ferrous ion in water-ammonia mixture solvent at 0K and at various temperatures ranging from 25K to 400K. All the calculations are performed at the MN15 level of theory associated with the aug-cc-pVDZ basis set. For deep understanding of binding patterns in solvated ferrous ion in water-ammonia mixture solvent, noncovalent interactions are presented based on the QTAIM analysis using AIMAll. Our results prove that the ferrous ion is more stable when it is solvated by ammonia instead of water. In addition, hydrogen bonds are weakened by the presence of ammonia molecules. The temperature dependence of the different obtained geometries indicates that from s=6 (s is the sum of water and ammonia molecules around the ferrous ion), when the number of water molecules is almost equal to that of ammonia, the structures with coordination number 5 are dominant. However, the coordination number is six when there are a maximum water molecules (rich water solution) or maximum ammonia molecules (rich ammonia solution) around the ferrous ion (for s≥6). The QTAIM analysis shows that there are two coordination bondings and four hydrogen bondings. Furthermore, it is found that the Fe2+⋯N coordination bondings are stronger than the Fe2+⋯O confirming that the ferrous ion prefers to be solvated by ammonia instead of water.

Interaction characteristics and mechanism of Cr(VI)/Cr(III) with microplastics: Influence factor experiment and DFT calculation

The coexistence of highly toxic heavy metal chromium and new pollutants microplastics has been widely present, and the interaction behavior and mechanism of the two are crucial for their environmental effects in coexisting environments, which urgently need to be further explored. Firstly, the interaction characteristics of polyamide (PA) and polyethylene (PE) with Cr(VI)/Cr(III) were investigated, where PA exhibited higher adsorption capacity of both Cr(VI) and Cr(III) than PE among various environmental conditions. The higher adsorption energy of PA on Cr(VI)/Cr(III) was also achieved by DFT calculation, and the bending configuration of PA during the adsorption process may be beneficial for its interaction with Cr. Then, the combination of characterization analysis and DFT calculation showed that significant chemical bonding occurred in the interaction between CO bond of PA and Cr(III), weak chemical interactions occurred in the adsorption of PE with Cr(III) and PA with Cr(VI), while the adsorption of PE with Cr(VI) was mainly physical effects. This study provides theoretical support for pollution control of microplastics and chromium in co-existing environment.

Intersystem Crossing Control of the Nb+ + CO2 → NbO+ + CO Reaction

The transfer of an oxygen atom from carbon dioxide (CO2) to a transition metal cation in the gas phase offers atomic level insights into single-atom catalysis for CO2 activation. Given that these reactions often involve open-shell transition metals, they may proceed through intersystem crossing between different spin manifolds. However, a definitive understanding of such spin-forbidden reaction requires dynamical calculations on multiple global potential energy surfaces (PESs) coupled by spin-orbit couplings. In this work, we report global PESs and spin-orbit couplings for three low-lying spin (quintet, triplet, and singlet) states for the reaction between the niobium cation (Nb+) and CO2, which are used to investigate the nonadiabatic reaction dynamics and kinetics. Comparison with experimental data of kinetics and collision dynamics shows satisfactory agreement. This reaction is found to be very similar to that between Ta+ + CO2. Specifically, our theoretical findings suggest that the rate-limiting step in this reaction is intersystem crossing, rather than potential barriers.

Femtosecond Core-Level Spectroscopy Reveals Involvement of Triplet States in the Gas-Phase Photodissociation of Fe(CO)5

Excitation of iron pentacarbonyl [Fe(CO)5], a prototypical photocatalyst, at 266 nm causes the sequential loss of two CO ligands in the gas phase, creating catalytically active, unsaturated iron carbonyls. Despite numerous studies, major aspects of its ultrafast photochemistry remain unresolved because the early excited-state dynamics have so far eluded spectroscopic observation. This has led to the long-held assumption that ultrafast dissociation of gas-phase Fe(CO)5 proceeds exclusively on the singlet manifold. Herein, we present a combined experimental-theoretical study employing ultrafast extreme ultraviolet transient absorption spectroscopy near the Fe M2,3-edge, which features spectral evolution on 100 fs and 3 ps time scales, alongside high-level electronic structure theory, which enables characterization of the molecular geometries and electronic states involved in the ultrafast photodissociation of Fe(CO)5. We assign the 100 fs evolution to spectroscopic signatures associated with intertwined structural and electronic dynamics on the singlet metal-centered states during the first CO loss and the 3 ps evolution to the competing dissociation of Fe(CO)4 along the lowest singlet and triplet surfaces to form Fe(CO)3. Calculations of transient spectra in both singlet and triplet states as well as spin-orbit coupling constants along key structural pathways provide evidence for intersystem crossing to the triplet ground state of Fe(CO)4. Thus, our work presents the first spectroscopic detection of transient excited states during ultrafast photodissociation of gas-phase Fe(CO)5 and challenges the long-standing assumption that triplet states do not play a role in the ultrafast dynamics.

Machine learning for accuracy in density functional approximations

Machine learning techniques have found their way into computational chemistry as indispensable tools to accelerate atomistic simulations and materials design. In addition, machine learning approaches hold the potential to boost the predictive power of computationally efficient electronic structure methods, such as density functional theory, to chemical accuracy and to correct for fundamental errors in density functional approaches. Here, recent progress in applying machine learning to improve the accuracy of density functional and related approximations is reviewed. Promises and challenges in devising machine learning models transferable between different chemistries and materials classes are discussed with the help of examples applying promising models to systems far outside their training sets.

Identifying and embedding transferability in data-driven representations of chemical space

Transferability, especially in the context of model generalization, is a paradigm of all scientific disciplines. However, the rapid advancement of machine learned model development threatens this paradigm, as it can be difficult to understand how transferability is embedded (or missed) in complex models developed using large training data sets. Two related open problems are how to identify, without relying on human intuition, what makes training data transferable; and how to embed transferability into training data. To solve both problems for ab initio chemical modelling, an indispensable tool in everyday chemistry research, we introduce a transferability assessment tool (TAT) and demonstrate it on a controllable data-driven model for developing density functional approximations (DFAs). We reveal that human intuition in the curation of training data introduces chemical biases that can hamper the transferability of data-driven DFAs. We use our TAT to motivate three transferability principles; one of which introduces the key concept of transferable diversity. Finally, we propose data curation strategies for general-purpose machine learning models in chemistry that identify and embed the transferability principles.

Application of a modern theoretical approach to the study of the interaction of KR-12 peptides derived from human cathelicidins with Cu(II) ions

The human cationic antimicrobial protein (hCAP) corresponding to the overlapping sequences of 151-162 of hCAP named KR-12 peptide is the smallest portion of the only type of human Cathelicidin, which has been shown to be modifiable into a more effective antimicrobial. In this study, an in silico analysis, supported by potentiometric titration and isothermal titration calorimetry techniques, was performed to identify potential Cu(II) binding sites of KR-12. The analysis of the presented data at the given theoretical level (GFN2-xTB/ALPB) revealed which peptide chain fragments are involved in the most favourable KR-12-Cu(II) binding mode. Based on a quantum chemical approach, the most favourable coordination modes of Cu(II) to peptides are proposed together with the discussion of the chemical nature of the interactions. The presented results demonstrated that KR-12 interacts with metal ions mostly via the main chain's oxygen atoms; however, the two types of amino acids that are expected to be vital for the interaction of Cu(II) are D (aspartic acid) and R29 (arginine). It was demonstrated that in order to explain the complexity of the interaction process in peptide-metal ion systems, the use of theoretical methods is sometimes necessary to explain the details of the experimental results and provide an in-depth understanding of these dynamic systems.

Copper-catalysed electrophilic carboamination of terminal alkynes with benzyne looked at through the computational lens

A detailed computational mechanistic study of the copper-catalysed three-component-type electrophilic carboamination of terminal alkynes with benzyne and an archetypal O-benzoylhydroxylamine electrophile is presented. Probing various plausible pathways for relevant elementary steps and scrutinising performance degradation pathways, with the aid of a reliable computational protocol applied to a realistic catalyst model combined with kinetic analysis, identified the pathways preferably traversed in productive catalysis. It entails rapid alkynylcupration of in situ generated benzyne to deliver the arylcopper nucleophile that undergoes amination with the O-benzoylhydroxylamine electrophile to afford copper benzoate. Umpolung-enabled electrophilic amination favours a multistep SN2-type oxidative addition/N-C bond-forming reductive elimination sequence involving a short-lived formal {P^P}CuIII carboxylate amido aryl intermediate. SN2-type displacement of the benzoate leaving group at the arylcopper nucleophile, which represents the catalyst resting state, is predicted to be the turnover limiting step. Alkynolysis transforms copper benzoate back to catalytically competent alkynylcopper. The computational probe of a wider range of substrates reveals that only severely ring-strained C6-arynes, C6-cycloalkynes and electron-deficient cyclopropenes featuring a highly reactive C≡C linkage could replace benzyne. Moreover, strict control of stationary benzyne concentration is indispensable for electrophilic carboamination to ever become achievable.

Deep Mind 21 functional does not extrapolate to transition metal chemistry

The development of density functional approximations stands at a crossroads: while machine-learned functionals show potential to surpass their human-designed counterparts, their extrapolation to unseen chemistry lags behind. Here we assess how well the recent Deep Mind 21 (DM21) machine-learned functional [Science, 2021, 374, 1385-1389], trained on main-group chemistry, extrapolates to transition metal chemistry (TMC). We show that DM21 demonstrates comparable or occasionally superior accuracy to B3LYP for TMC, but consistently struggles with achieving self-consistent field convergence for TMC molecules. We also compare main-group and TMC machine-learning DM21 features to shed light on DM21's challenges in TMC. We finally propose strategies to overcome limitations in the extrapolative capabilities of machine-learned functionals in TMC.

Formation of negative ions from cobalt tricarbonyl nitrosyl Co(CO)3NO clusters

Electron attachment and corresponding dissociative electron attachment (DEA) to cobalt tricarbonyl nitrosyl (Co(CO)3NO) clusters have been studied by co-expansion with Ar gas into a high vacuum. A monochromatic electron beam was utilized to generate negative ions and the resulting reaction products were identified using mass spectrometry. The ion fragments corresponding to Co(CO)3NO monomers closely resemble results from earlier gas phase experiments and studies conducted on Co(CO)3NO in He nanodroplets. However, contrary to the gas phase or He nanodroplet ion yields, a resonance structure comprising several peaks at energies above ∼4 eV was observed both in the case of molecular clusters [Co(CO)3NO]n- (with n = 1, 2, 3) and clusters comprising DEA fragments. Additionally, the ion yields of numerous other clusters such as ions without nitrosyl ([Co(CO)4]-, [Co2(CO)5]-), clusters consisting of two fragments such as ([Co2(CO)NO]-, [Co2(CO)(NO)2]-, [Co2(CO)2NO]-, [Co2(CO)2(NO)2]-, [Co3(CO)(NO)3]-, [Co3(CO)8(NO)3]-, [Co3(CO)(NO)2]-, [Co3(CO)3(NO)2]-, and [Co3(CO)5(NO)2]-) were recorded. Moreover, NO bond dissociation was confirmed with the [Co(CO)2N]-ion and with N- or O-retaining cluster ions, such as [Co2(CO)(NO)N]-, [Co2(CO)2(NO)N]-, [Co3(CO)2(NO)N]-, [Co3(CO)3(NO)N]- and [Co3(CO)(NO)2N]-, or [Co2(CO)2O]-, [Co2(CO)3O]-, [Co3(CO)3O]-, [Co3(CO)4O]-and [Co3(CO)2(NO)O]- respectively.

Quantum chemical modeling of hydrogen binding in metal-organic frameworks: validation, insight, predictions and challenges

A detailed chemical understanding of H2 interactions with binding sites in the nanoporous crystalline structure of metal-organic frameworks (MOFs) can lay a sound basis for the design of new sorbent materials. Computational quantum chemical calculations can aid in this quest. To set the stage, we review general thermodynamic considerations that control the usable storage capacity of a sorbent. We then discuss cluster modeling of H2 ligation at MOF binding sites using state-of-the-art density functional theory (DFT) calculations, and how the binding can be understood using energy decomposition analysis (EDA). Employing these tools, we illustrate the connections between the character of the MOF binding site and the associated adsorption thermodynamics using four experimentally characterized MOFs, highlighting the role of open metal sites (OMSs) in accessing binding strengths relevant to room temperature storage. The sorbents are MOF-5, with no open metal sites, Ni2(m-dobdc), containing Lewis acidic Ni(II) sites, Cu(I)-MFU-4l, containing π basic Cu(I) sites and V2Cl2.8(btdd), also containing π-basic V(II) sites. We next explore the potential for binding multiple H2 molecules at a single metal site, with thermodynamics useful for storage at ambient temperature; a materials design goal which has not yet been experimentally demonstrated. Computations on Ca2+ or Mg2+ bound to catecholate or Ca2+ bound to porphyrin show the potential for binding up to 4 H2; there is precedent for the inclusion of both catecholate and porphyrin motifs in MOFs. Turning to transition metals, we discuss the prediction that two H2 molecules can bind at V(II)-MFU-4l, a material that has been synthesized with solvent coordinated to the V(II) site. Additional calculations demonstrate binding three equivalents of hydrogen per OMS in Sc(I) or Ti(I)-exchanged MFU-4l. Overall, the results suggest promising prospects for experimentally realizing higher capacity hydrogen storage MOFs, if nontrivial synthetic and desolvation challenges can be overcome. Coupled with the unbounded chemical diversity of MOFs, there is ample scope for additional exploration and discovery.

DAPD Set of Pd-Containing Diatomic Molecules: Accurate Molecular Properties and the Great Lengths to Obtain Them

In the present study, we obtained reliable bond energy, bond length, and zero-point vibrational frequency for a set of diatomic Pd species (the DAPD set). It includes PdH, Pd2, and PdX (X = B, C, N, O, F, Al, Si, P, S, and Cl). Our highest-level protocol (W4X-L) represents scalar and spin-orbit relativistic, valence- and inner-valence correlated, extrapolated CCSDTQ(5) energy. The DAPD set of molecules is challenging for computational chemistry methods in different manners; for Pd2, the spin-orbit contribution to the bond energy is fairly large, whereas for PdC and PdSi, the post-CCSD(T) correlation components are considerable. The diverse range of requirements represents a significant challenge for lower-level methods. While density functional theory (DFT) methods generally yield good agreements for bond lengths and vibrational frequencies, large deviations are found for bond energies. In general, hybrid DFT methods are more accurate than nonhybrid functionals, but the agreement in individual cases varies. This illustrates the critical role that new high-quality reference data would play in the continual development of lower-cost methods.

Applying Large Graph Neural Networks to Predict Transition Metal Complex Energies Using the tmQM_wB97MV Data Set

Machine learning (ML) methods have shown promise for discovering novel catalysts but are often restricted to specific chemical domains. Generalizable ML models require large and diverse training data sets, which exist for heterogeneous catalysis but not for homogeneous catalysis. The tmQM data set, which contains properties of 86,665 transition metal complexes calculated at the TPSSh/def2-SVP level of density functional theory (DFT), provided a promising training data set for homogeneous catalyst systems. However, we find that ML models trained on tmQM consistently underpredict the energies of a chemically distinct subset of the data. To address this, we present the tmQM_wB97MV data set, which filters out several structures in tmQM found to be missing hydrogens and recomputes the energies of all other structures at the ωB97M-V/def2-SVPD level of DFT. ML models trained on tmQM_wB97MV show no pattern of consistently incorrect predictions and much lower errors than those trained on tmQM. The ML models tested on tmQM_wB97MV were, from best to worst, GemNet-T > PaiNN ≈ SpinConv > SchNet. Performance consistently improves when using only neutral structures instead of the entire data set. However, while models saturate with only neutral structures, more data continue to improve the models when including charged species, indicating the importance of accurately capturing a range of oxidation states in future data generation and model development. Furthermore, a fine-tuning approach in which weights were initialized from models trained on OC20 led to drastic improvements in model performance, indicating transferability between ML strategies of heterogeneous and homogeneous systems.

Theoretical Insights into the Generation Mechanism of the Tyr122 Radical Catalyzed by Intermediate X in Class Ia Ribonucleotide Reductase

Ribonucleotide reductase (RNR) catalyzes the reduction of ribonucleotides to deoxyribonucleotides in all organisms. There is an ∼35 Å long-range electron-hole transfer pathway during the catalytic process of class Ia RNR, which can be described as Tyr122β ↔ [Trp48β]? ↔ Tyr356β ↔ Tyr731α ↔ Tyr730α ↔ Cys439α. The formation of the Y122• radical initiates this long-range radical transfer process. However, the generation mechanism of Y122• is not yet clear due to confusion over the intermediate X structures. Based on the two reported X structures, we examined the possible mechanisms of Y122• generation by density functional theory (DFT) calculations. Our examinations revealed that the generation of the Y122• radical from the two different core structures of X was via a similar two-step reaction, with the first step of proton transfer for the formation of the proton receptor of Y122 and the second step of a proton-coupled long-range electron transfer reaction with the proton transfer from the Y122 hydroxyl group to the terminal hydroxide ligand of Fe1III and simultaneously electron transfer from the side chain of Y122 to Fe2IV. These findings provide an insight into the formation mechanism of Y122• catalyzed by the double-iron center of the β subunit of class Ia RNR.

A step toward density benchmarking-The energy-relevant "mean field error"

Since the development of generalized gradient approximations in the 1990s, approximations based on density functional theory have dominated electronic structure theory calculations. Modern approximations can yield energy differences that are precise enough to be predictive in many instances, as validated by large- and small-scale benchmarking efforts. However, assessing the quality of densities has been the subject of far less attention, in part because reliable error measures are difficult to define. To this end, this work introduces the mean-field error, which directly assesses the quality of densities from approximations. The mean-field error is contextualized within existing frameworks of density functional error analysis and understanding and shown to be part of the density-driven error. It is demonstrated in several illustrative examples. Its potential use in future benchmarking protocols is discussed, and some conclusions are drawn.

Benchmarking Density Functional Theory Methods for Metalloenzyme Reactions: The Introduction of the MME55 Set

We present a new benchmark set of metalloenzyme model reaction energies and barrier heights that we call MME55. The set contains 10 different enzymes, representing eight transition metals, both open and closed shell systems, and system sizes of up to 116 atoms. We use four DLPNO-CCSD(T)-based approaches to calculate reference values against which we then benchmark the performance of a range of density functional approximations with and without dispersion corrections. Dispersion corrections improve the results across the board, and triple-ζ basis sets provide the best balance of efficiency and accuracy. Jacob's ladder is reproduced for the whole set based on averaged mean absolute (percent) deviations, with the double hybrids SOS0-PBE0-2-D3(BJ) and revDOD-PBEP86-D4 standing out as the most accurate methods for the MME55 set. The range-separated hybrids ωB97M-V and ωB97X-V also perform well here and can be recommended as a reliable compromise between accuracy and efficiency; they have already been shown to be robust across many other types of chemical problems, as well. Despite the popularity of B3LYP in computational enzymology, it is not a strong performer on our benchmark set, and we discourage its use for enzyme energetics.

Benchmarks for transition metal spin-state energetics: why and how to employ experimental reference data?

Accurate prediction of energy differences between alternative spin states of transition metal complexes is essential in computational (bio)inorganic chemistry-for example, in characterization of spin crossover materials and in the theoretical modeling of open-shell reaction mechanisms-but it remains one of the most compelling problems for quantum chemistry methods. A part of this challenge is to obtain reliable reference data for benchmark studies, as even the highest-level applicable methods are known to give divergent results. This Perspective discusses two possible approaches to method benchmarking for spin-state energetics: using either theoretically computed or experiment-derived reference data. With the focus on the latter approach, an extensive general review is provided for the available experimental data of spin-state energetics and their interpretations in the context of benchmark studies, targeting the possibility of back-correcting the vibrational effects and the influence of solvents or crystalline environments. With a growing amount of experience, these effects can be now not only qualitatively understood, but also quantitatively modeled, providing the way to derive nearly chemically accurate estimates of the electronic spin-state gaps to be used as benchmarks and advancing our understanding of the phenomena related to spin states in condensed phases.

Generation of an accurate CCSD(T)/CBS data set and assessment of DFT methods for the binding strengths of group I metal-nucleic acid complexes

Accurate information about interactions between group I metals and nucleic acids is required to understand the roles these metals play in basic cellular functions, disease progression, and pharmaceuticals, as well as to aid the design of new energy storage materials and nucleic acid sensors that target metal contaminants, among other applications. From this perspective, this work generates a complete CCSD(T)/CBS data set of the binding energies for 64 complexes involving each group I metal (Li+, Na+, K+, Rb+, or Cs+) directly coordinated to various sites in each nucleic acid component (A, C, G, T, U, or dimethylphosphate). This data have otherwise been challenging to determine experimentally, with highly accurate information missing for many group I metal-nucleic acid combinations and no data available for the (charged) phosphate moiety. Subsequently, the performance of 61 DFT methods in combination with def2-TZVPP is tested against the newly generated CCSD(T)/CBS reference values. Detailed analysis of the results reveals that functional performance is dependent on the identity of the metal (with increased errors as group I is descended) and nucleic acid binding site (with larger errors for select purine coordination sites). Over all complexes considered, the best methods include the mPW2-PLYP double-hybrid and ωB97M-V RSH functionals (≤1.6% MPE; <1.0 kcal/mol MUE). If more computationally efficient approaches are required, the TPSS and revTPSS local meta-GGA functionals are reasonable alternatives (≤2.0% MPE; <1.0 kcal/mol MUE). Inclusion of counterpoise corrections to account for basis set superposition error only marginally improves the computed binding energies, suggesting that these corrections can be neglected with little loss in accuracy when using larger models that are necessary for describing biosystems and biomaterials. Overall, the most accurate functionals identified in this study will permit future works geared towards uncovering the impact of group I metals on the environment and human biology, designing new ways to selectively sense harmful metals, engineering modern biomaterials, and developing improved computational methods to more broadly study group I metal-nucleic acid interactions.

On the Prediction of Spectroscopic Fingerprints of Co2+ Complexes Relevant for the ZIF Nucleation Process

The nucleation process of zeolitic imidazolate frameworks (ZIFs) is to date not completely understood. Recently, it has been found that, during the formation of Co-ZIF-67, after mixing imidazole-type ligands with octahedral precursors containing oxygen-coordinated ligands, a metal-organic pool with a diversity of transition metal complexes (TMCs) is formed showing fingerprints of octahedral and tetrahedral Co2+ complexes with both types of ligands [Filez, M. Cell Rep. Phys. Sci. 2021, 2, 100680]. In order to further unravel this process, we aim to characterize the d-d transitions of the TMCs and focus on their number, intensity, and position, which change during the process and can thus serve as a fingerprint for the formed species. It was previously shown that the number of ligands and symmetry has a detrimental influence on the ground state properties of Co2+ TMCs. Herein, we investigate how far excited state properties of TMCs relevant during nanoporous formation processes can be predicted by time-dependent density functional theory (TDDFT) and ligand field density functional theory (LFDFT). As TMCs are known to be challenging systems with possibly degenerate ground states and double excitations, we first investigate the performance of both techniques on first-row octahedral aqua-complexes. With this knowledge, we then focus on tetrahedral Co2+ complexes with aqua and imidazole-type ligands in order to investigate in how far we can propose a spectroscopic fingerprint that allows us to follow the Co2+ complexes during the formation of Co-ZIF-67. The results of TDDFT and LFDFT are qualitatively in agreement and provide complementary information. We found that various features can be used to distinguish between the species. However, as LFDFT is not suited for TMCs possessing the extended imidazole-type ligands and double and spin-flip states are not included in TDDFT, both techniques need to be complemented with more advanced methods to obtain complete insight into the d-d excitations of TMCs with imidazole ligands. Therefore, we particularly explored ab initio ligand field theory, which is capable of describing double excitations and is, in contrast to LFDFT, suitable for TMCs with extended ligands.

Even Faster Exact Exchange for Solids via Tensor Hypercontraction

Hybrid density functional theory (DFT) remains intractable for large periodic systems due to the demanding computational cost of exact exchange. We apply the tensor hypercontraction (THC) (or interpolative separable density fitting) approximation to periodic hybrid DFT calculations with Gaussian-type orbitals using the Gaussian plane wave approach. This is done to lower the computational scaling with respect to the number of basis functions (N) and k-points (Nk) at a fixed system size. Additionally, we propose an algorithm to fit only occupied orbital products via THC (i.e., a set of points, NISDF) to further reduce computation time and memory usage. This algorithm has linear scaling cost with k-points, no explicit dependence of NISDF on basis set size, and overall cubic scaling with unit cell size. Significant speedups and reduced memory usage may be obtained for moderately sized k-point meshes, with additional gains for large k-point meshes. Adequate accuracy can be obtained using THC-oo-K for self-consistent calculations. We perform illustrative hybrid density function theory calculations on the benzene crystal in the basis set and thermodynamic limits to highlight the utility of this algorithm.

Assessment of DFT functionals for a minimal nitrogenase [Fe(SH)4H]- model employing state-of-the-art ab initio methods

We have designed a [Fe(SH)4H]- model with the fifth proton binding either to Fe or S. We show that the energy difference between these two isomers (∆E) is hard to estimate with quantum-mechanical (QM) methods. For example, different density functional theory (DFT) methods give ∆E estimates that vary by almost 140 kJ/mol, mainly depending on the amount of exact Hartree-Fock included (0%-54%). The model is so small that it can be treated by many high-level QM methods, including coupled-cluster (CC) and multiconfigurational perturbation theory approaches. With extrapolated CC series (up to fully connected coupled-cluster calculations with singles, doubles, and triples) and semistochastic heat-bath configuration interaction methods, we obtain results that seem to be converged to full configuration interaction results within 5 kJ/mol. Our best result for ∆E is 101 kJ/mol. With this reference, we show that M06 and B3LYP-D3 give the best results among 35 DFT methods tested for this system. Brueckner doubles coupled cluster with perturbaitve triples seems to be the most accurate coupled-cluster approach with approximate triples. CCSD(T) with Kohn-Sham orbitals gives results within 4-11 kJ/mol of the extrapolated CC results, depending on the DFT method. Single-reference CC calculations seem to be reasonably accurate (giving an error of ∼5 kJ/mol compared to multireference methods), even if the D1 diagnostic is quite high (0.25) for one of the two isomers.

Assessment of Density Functional Theory Methods for the Structural Prediction of Transition and Post-Transition Metal-Nucleic Acid Complexes

Understanding the structure of metal-nucleic acid systems is important for many applications such as the design of new pharmaceuticals, metal detection platforms, and nanomaterials. Herein, we explore the ability of 20 density functional theory (DFT) functionals to reproduce the crystal structure geometry of transition and post-transition metal-nucleic acid complexes identified in the Protein Data Bank and Cambridge Structural Database. The environmental extremes of the gas phase and implicit water were considered, and analysis focused on the global and inner coordination geometry, including the coordination distances. Although gas-phase calculations were unable to describe the structure of 12 out of the 53 complexes in our test set regardless of the DFT functional considered, accounting for the broader environment through implicit solvation or constraining the model truncation points to crystallographic coordinates generally afforded agreement with the experimental structure, suggesting that functional performance for these systems is likely due to the models rather than the methods. For the remaining 41 complexes, our results show that the reliability of functionals depends on the metal identity, with the magnitude of error varying across the periodic table. Furthermore, minimal changes in the geometries of these metal-nucleic acid complexes occur upon use of the Stuttgart-Dresden effective core potential and/or inclusion of an implicit water environment. The overall top three performing functionals are ωB97X-V, ωB97X-D3(BJ), and MN15, which reliably describe the structure of a broad range of metal-nucleic acid systems. Other suitable functionals include MN15-L, which is a cheaper alternative to MN15, and PBEh-3c, which is commonly used in QM/MM calculations of biomolecules. In fact, these five methods were the only functionals tested to reproduce the coordination sphere of Cu²⁺-containing complexes. For metal-nucleic acid systems that do not contain Cu²⁺, ωB97X and ωB97X-D are also suitable choices. These top-performing methods can be utilized in future investigations of diverse metal-nucleic acid complexes of relevance to biology and material science.

Compilation of Ionic Clusters with the Rock Salt Structure: Accurate Benchmark Thermochemical Data, Assessment of Quantum Chemistry Methods, and the Convergence Behavior of Lattice Energies

In the present study, computational quantum chemistry is used to obtain lattice energies (LEs) for a range of ionic clusters with the NaCl structure. Specifically, the compounds include NaF, NaCl, MgO, MgS, KF, CaO, and CaS clusters, (MX)_n, with n = 1, 2, 4, 6, 8, 12, 16, 24, 32, 40, 50, 60, 75, 90, and 108. The highest-level W2 and W1X-2 methods are applied to the small clusters with n = 1 to 8 (the MX35 data set). The assessment with MX35 shows that, for the calculation of geometries and vibrational frequencies, the PBE0-D3(BJ) and PBE-D3(BJ) DFT methods are reasonable, but the calculation of atomization energies is more challenging. This is a result of different systematic deviations for clusters of different species. Thus, species-specific adjustments are applied for larger clusters, which are calculated with the DuT-D3 double-hybrid DFT method, the MN15 DFT method, and the PM7 semi-empirical method. They yield smoothly converging LEs to the bulk values. It is also found that, for the alkali-metal species, the LEs for a single molecule are ∼70% of the bulk values, while for the alkali-earth species, they are ∼80%. This has enabled a straightforward means to the first-principles estimation of LEs for similarly structured ionic compounds.

Insights into the coordination chemistry of antineoplastic doxorubicin with 3d-transition metal ions Zn2+, Cu2+, and VO2+: a study using well-calibrated thermodynamic cycles and chemical interaction quantum chemistry models

We present a computational strategy based on thermodynamic cycles to predict and describe the chemical equilibrium between the 3d-transition metal ions Zn²⁺, Cu²⁺, and VO²⁺ and the widely used antineoplastic drug doxorubicin. Our method involves benchmarking a theoretical protocol to compute gas-phase quantities using DLPNO Coupled-Cluster calculations as reference, followed by estimating solvation contributions to the reaction Gibbs free energies using both explicit partial (micro)solvation steps for charged solutes and neutral coordination complexes, as well as a continuum solvation procedure for all solutes involved in the complexation process. We rationalized the stability of these doxorubicin-metal complexes by inspecting quantities obtained from the topology of their electron densities, particularly the bond critical points and non-covalent interaction index. Our approach allowed us to identify representative species in solution phase, infer the most likely complexation process for each case, and identify key intramolecular interactions involved in the stability of these compounds. To the best of our knowledge, this is the first study reporting thermodynamic constants for the complexation of doxorubicin with transition metal ions. Unlike other methods, our procedure is computationally affordable for medium-sized systems and provides valuable insights even with limited experimental data. Furthermore, it can be extended to describe the complexation process between 3d-transition metal ions and other bioactive ligands.

The Good, the Bad, and the Ugly: Pseudopotential Inconsistency Errors in Molecular Applications of Density Functional Theory

The pseudopotential (PP) approximation is one of the most common techniques in computational chemistry. Despite its long history, the development of custom PPs has not tracked with the explosion of different density functional approximations (DFAs). As a result, the use of PPs with exchange/correlation models for which they were not developed is widespread, although this practice is known to be theoretically unsound. The extent of PP inconsistency errors (PPIEs) associated with this practice has not been systematically explored across the types of energy differences commonly evaluated in chemical applications. We evaluate PPIEs for a number of PPs and DFAs across 196 chemically relevant systems of both transition-metal and main-group elements, as represented by the W4-11, TMC34, and S22 data sets. Near the complete basis set limit, these PPs are found to cleanly approach all-electron (AE) results for noncovalent interactions but introduce root-mean-squared errors (RMSEs) upwards of 15 kcal mol^-1 into predictions of covalent bond energies for a number of popular DFAs. We achieve significant improvements through the use of empirical atom- and DFA-specific PP corrections, indicating considerable systematicity of the PPIEs. The results of this work have implications for chemical modeling in both molecular contexts and for DFA design, which we discuss.

Activation of Methane by Zr+: A Deep-Dive into the Potential Surface via Pressure- and Temperature-Dependent Kinetics with Statistical Modeling

The kinetics of Zr⁺ + CH₄ are measured using a selected-ion flow tube apparatus over the temperature range 300-600 K and the pressure range 0.25-0.60 Torr. Measured rate constants are small, never exceeding 5% of the Langevin capture value. Both collisionally stabilized ZrCH₄⁺ and bimolecular ZrCH₂⁺ products are observed. A stochastic statistical modeling of the calculated reaction coordinate is used to fit the experimental results. The modeling indicates that an intersystem crossing from the entrance well, necessary for the bimolecular product to be formed, occurs faster than competing isomerization and dissociation processes. That sets an upper limit on the lifetime of the entrance complex to crossing of 10^-11 s. The endothermicity of the bimolecular reaction is derived to be 0.09 ± 0.05 eV, in agreement with a literature value. The observed ZrCH₄⁺ association product is determined to be primarily HZrCH₃⁺ not Zr⁺(CH₄), indicating that bond activation has occurred at thermal energies. The energy of HZrCH₃⁺ relative to separated reactants is determined to be -0.80 ± 0.25 eV. Inspection of the statistical modeling results under best-fit conditions reveals reaction dependences on impact parameter, translation energy, internal energy, and angular momentum. Reaction outcomes are heavily affected by angular momentum conservation. Additionally, product energy distributions are predicted.

Adsorption behavior of hierarchical porous biochar from shrimp shell for tris(2-chloroethyl) phosphate (TCEP): Sorption experiments and DFT calculations

Tris(2-chloroethyl) phosphate (TCEP) as a new type of flame retardant exists in various water environments, causing great risks to humans and the environment. In this study, shrimp shell was used to prepare an economical and environmental-friendly adsorbent for the efficient removal of TCEP. The systematic studies including characterization, removal performance, and adsorption mechanism of shrimp shell biochar toward TCEP were carried out. Adsorption kinetics and thermodynamics showed that fast equilibrium reached within 30 min, the maximum adsorption capacity q_m was 108 μmol g^-1 at 298 K, and the adsorption process is spontaneous and exothermic. The environmental factor, such as temperature, pH, inorganic anions and organic matter hardly affected the adsorption performance. Structural characterization indicated that the hierarchical porous structure of shrimp shell biochar is the key to excellent adsorption performance. The adsorption mechanisms were further revealed using density functional theory (DFT) calculations, and the hydrogen bond, van der Waals interactions, Cl-H interactions, and pi-H interactions were identified as potential interaction mechanisms between TCEP and specific biochar structures. The calculated binding energy between TCEP and simplified biochar structure suggested that oxygen-containing groups especially carboxyl, hydroxyl and aldehyde facilitate the adsorption. Our work not only provides a novel strategy for the quick remediation of organophosphate-contaminated water environments but also offers new opportunities for crustacean waste biomass valorization.

Supervised learning of a chemistry functional with damped dispersion

Kohn-Sham density functional theory is widely used in chemistry, but no functional can accurately predict the whole range of chemical properties, although recent progress by some doubly hybrid functionals comes close. Here, we optimized a singly hybrid functional called CF22D with higher across-the-board accuracy for chemistry than most of the existing non-doubly hybrid functionals by using a flexible functional form that combines a global hybrid meta-nonseparable gradient approximation that depends on density and occupied orbitals with a damped dispersion term that depends on geometry. We optimized this energy functional by using a large database and performance-triggered iterative supervised training. We combined several databases to create a very large, combined database whose use demonstrated the good performance of CF22D on barrier heights, isomerization energies, thermochemistry, noncovalent interactions, radical and nonradical chemistry, small and large systems, simple and complex systems and transition-metal chemistry.

Faster Exact Exchange for Solids via occ-RI-K: Application to Combinatorially Optimized Range-Separated Hybrid Functionals for Simple Solids with Pseudopotentials Near the Basis Set Limit

In this work, we developed and showcased the occ-RI-K algorithm to compute the exact exchange contribution in density functional calculations of solids near the basis set limit. Within the Gaussian planewave (GPW) density fitting, our algorithm achieves a 1-2 orders of magnitude speedup compared to conventional GPW algorithms. Since our algorithm is well suited for simulations with large basis sets, we applied it to 12 hybrid density functionals with pseudopotentials and a large uncontracted basis set to assess their performance on band gaps of 25 simple solids near the basis set limit. The largest calculation performed in this work involves 16 electrons and 350 basis functions in the unit cell utilizing a 6 × 6 × 6 k-mesh. With 20-27% exact exchange, global hybrid functionals (B3LYP, PBE0, revPBE0, B97-3, SCAN0) perform similarly with a root-mean-square deviation (RMSD) of 0.61-0.77 eV, while other global hybrid functionals such as M06-2X (2.02 eV) and MN15 (1.05 eV) show higher RMSD due to their increased fraction of exact exchange. A short-range hybrid functional, HSE achieves a similar RMSD (0.76 eV) but shows a notable underestimation of band gaps due to the complete lack of long-range exchange. We found that two combinatorially optimized range-separated hybrid functionals, ωB97X-rV (3.94 eV) and ωB97M-rV (3.40 eV), and the two other range-separated hybrid functionals, CAM-B3LYP (2.41 eV) and CAM-QTP01 (4.16 eV), significantly overestimate the band gap because of their high fraction of long-range exact exchange. Given the failure of ωB97X-rV and ωB97M-rV, we have yet to find a density functional that offers consistent performance for both molecules and solids. Our algorithm development and density functional assessment will serve as a stepping stone toward developing more accurate hybrid functionals and applying them to practical applications.

Mechanistic views and computational studies on transition-metal-catalyzed reductive coupling reactions

Transition-metal-catalyzed reductive coupling reactions have been considered as a powerful tool to convert two electrophiles into value-added products. Numerous related reports have shown the fascinating potential. Mechanistic studies, especially theoretical studies, can provide important implications for the design of novel reductive coupling reactions. In this review, we summarize the representative advancements in theoretical studies on transition-metal-catalyzed reductive coupling reactions and systematically elaborate the mechanisms for the key steps of reductive coupling reactions. The activation modes of electrophiles and the deep insights of selectivity generation are mechanistically discussed. In addition, the mechanism of the reduction of high-oxidation-state catalysts and further construction of new chemical bonds are also described in detail.

Prediction of Multiple Hydrogen Ligation at a Vanadium(II) Site in a Metal-Organic Framework

Densifying hydrogen in a metal-organic framework (MOF) at moderate pressures can circumvent challenges associated with high-pressure compression. The highly tunable structural and chemical composition in MOFs affords vast possibilities to optimize binding interactions. At the heart of this search are the nanoscale characteristics of molecular adsorption at the binding site(s). Using density functional theory (DFT) to model binding interactions of hydrogen to the exposed metal site of cation-exchanged MFU-4l, we predict multiple hydrogen ligation of H₂ at the first coordination sphere of V(II) in V(II)-exchanged MFU-4l. We find that the strength of this binding between the metal site and H₂ molecules can be tuned by altering the halide counterion adjacent to the metal site and that the fluoride containing node affords the most favorable interactions for high-density H₂ storage. Using energy decomposition analysis, we delineate electronic contributions that enable multiple hydrogen ligation and demonstrate its benefits for hydrogen adsorption and release at modest pressures.

Dynamic Intramolecular Cap for Preserving Metallodrug Integrity─A Case of Catalytic Fluoroquinolones

A library of eight new fluoroquinolone-nuclease conjugates containing a guanidinoethyl or aminoethyl auxiliary pendant on the cyclen moiety was designed and synthesized to investigate their potential for overcoming the general issue of "metallodrug vulnerability" under physiological conditions. The Cu(II) and Co(III) complexes of the new designer compounds were synthesized, and their potential to operate a dynamic, intramolecular cap with DNase activity was explored. The lead Co(III)-cyclen-ciprofloxacin conjugate showed excellent in vitro hydrolytic DNase activity, which was retained in the presence of strong endogenous chelators and exhibited enhanced antibacterial activity relative to the metal-free ligand (in the absence of any adjuvants), thereby demonstrating a "proof of concept" in vitro and ex vivo, respectively, for the dynamic cap hypothesis. The lead conjugate nicked supercoiled plasmid DNA within the fluoroquinolone-gyrase-DNA ternary complex and thereby disabled the function of gyrase, a new mode of action not previously reported for any fluoroquinolone.

Theoretical Study of the Structure and Binding Energies of Dimers of Zn(II)-Porphyrin Derivatives

Zinc-complexed porphyrin and chlorophyll derivatives form functional aggregates with remarkable photophysical and optoelectronic properties. Understanding the type and strength of intermolecular interactions between these molecules is essential for designing new materials with desired morphology and functionality. The dimer interactions of a molecular set composed of porphyrin derivatives obtained by substitutional changes starting from free-base porphyrin is studied. It is found that the B97M-rV/def2-TZVP level of theory provides a good compromise between the accuracy and cost to get the dimer geometries and interaction energies (IEs). The neglect of the relaxation energy due to the change in the monomer configurations upon complex formation causes a more significant error than the basis set superposition error. The metal complexation increases the binding energy by about -6 to -8 kcal/mol, and the introduction of keto and hydroxy groups further stabilizes the dimers by about -20 kcal/mol. Although the saturation of one of the pyrrol double bonds does not change the IE, the addition of R groups increases it.

The role of the intermediate triplet state in iron-catalyzed multi-state C-H activation

Efficient activation and functionalization of the C-H bond under mild conditions are of a great interest in chemical synthesis. We investigate the previously proposed spin-accelerated activation of the C(sp²)-H bond by a Fe(II)-based catalyst to clarify the role of the intermediate triplet state in the reaction mechanism. High-level electronic structure calculations on a small model of a catalytic system utilizing the coupled cluster with the single, double, and perturbative triple excitations [CCSD(T)] are used to select the density functional for the full-size model. Our analysis indicates that the previously proposed two-state quintet-singlet reaction pathway is unlikely to be efficient due to a very weak spin-orbit coupling between these two spin states. We propose a more favorable multi-state quintet-triplet-singlet reaction pathway and discuss the importance of the intermediate triplet state. This triplet state facilitates a spin-accelerated reaction mechanism by strongly coupling to both quintet and singlet states. Our calculations show that the C-H bond activation through the proposed quintet-triplet-singlet reaction pathway is more thermodynamically favorable than the single-state quintet and two-state singlet-quintet mechanisms.

Assessment of DLPNO-CCSD(T)-F12 and its use for the formulation of the low-cost and reliable L-W1X composite method

In the present study, we have investigated the performance of RIJCOSX DLPNO-CCSD(T)-F12 methods for a wide range of systems. Calculations with a high-accuracy option ["DefGrid3 RIJCOSX DLPNO-CCSD(T₁ )-F12"] extrapolated to the complete-basis-set limit using the maug-cc-pV[D+d,T+d]Z basis sets provides fairly good agreements with the canonical CCSD(T)/CBS reference for a diverse set of thermochemical and kinetic properties [with mean absolute deviations (MADs) of ~1-2 kJ mol^-1 except for atomization energies]. On the other hand, the low-cost "RIJCOSX DLPNO-CCSD(T)-F12D" option leads to substantial deviations for certain properties, notably atomization energies (MADs of up to tens of kJ mol^-1 ). With the high-accuracy CBS approach, we have formulated the L-W1X method, which further includes a low-cost core-valence plus scalar-relativistic term. It shows generally good accuracy. For improved accuracies in specific cases, we advise replacing maug-cc-pV(n+d)Z with jun-cc-pV(n+d)Z for the calculation of electron affinities, and using well-constructed isodesmic-type reactions to obtain atomization energies. For medium-sized systems, DefGrid3 RIJCOSX DLPNO-CCSD(T₁ )-F12 calculations are several times faster than the corresponding canonical computation; the use of the local approximations (RIJCOSX and DLPNO) leads to a better scaling than that for the canonical calculation (from ~6-7 down to ~2-4 for our test systems). Thus, the DefGrid3 RIJCOSX DLPNO-CCSD(T₁ )-F12 method, and the L-W1X protocol that based on it, represent a useful means for obtaining accurate thermochemical quantities for larger systems.

Chemoton 2.0: Autonomous Exploration of Chemical Reaction Networks

Fueled by advances in hardware and algorithm design, large-scale automated explorations of chemical reaction space have become possible. Here, we present our approach to an open-source, extensible framework for explorations of chemical reaction mechanisms based on the first-principles of quantum mechanics. It is intended to facilitate reaction network explorations for diverse chemical problems with a wide range of goals such as mechanism elucidation, reaction path optimization, retrosynthetic path validation, reagent design, and microkinetic modeling. The stringent first-principles basis of all algorithms in our framework is key for the general applicability that avoids any restrictions to specific chemical systems. Such an agile framework requires multiple specialized software components of which we present three modules in this work. The key module, Chemoton, drives the exploration of reaction networks. For the exploration itself, we introduce two new algorithms for elementary-step searches that are based on Newton trajectories. The performance of these algorithms is assessed for a variety of reactions characterized by a broad chemical diversity in terms of bonding patterns and chemical elements. Chemoton successfully recovers the vast majority of these. We provide the resulting data, including large numbers of reactions that were not included in our reference set, to be used as a starting point for further explorations and for future reference.

Experimental and Theoretical Study of N2 Adsorption on Hydrogenated Y2C4H− and Dehydrogenated Y2C4− Cluster Anions at Room Temperature

The adsorption of atmospheric dinitrogen (N₂) on transition metal sites is an important topic in chemistry, which is regarded as the prerequisite for the activation of robust N≡N bonds in biological and industrial fields. Metal hydride bonds play an important part in the adsorption of N₂, while the role of hydrogen has not been comprehensively studied. Herein, we report the N₂ adsorption on the well-defined Y₂C₄H_0,1⁻ cluster anions under mild conditions by using mass spectrometry and density functional theory calculations. The mass spectrometry results reveal that the reactivity of N₂ adsorption on Y₂C₄H⁻ is 50 times higher than that on Y₂C₄⁻ clusters. Further analysis reveals the important role of the H atom: (1) the presence of the H atom modifies the charge distribution of the Y₂C₄H⁻ anion; (2) the approach of N₂ to Y₂C₄H⁻ is more favorable kinetically compared to that to Y₂C₄⁻; and (3) a natural charge analysis shows that two Y atoms and one Y atom are the major electron donors in the Y₂C₄⁻ and Y₂C₄H⁻ anion clusters, respectively. This work provides new clues to the rational design of TM-based catalysts by efficiently doping hydrogen atoms to modulate the reactivity towards N₂.

Revisiting the Bonding Model for Gold(I) Species: The Importance of Pauli Repulsion Revealed in a Gold(I)-Cyclobutadiene Complex

Understanding the bonding of gold(I) species has been central to the development of gold(I) catalysis. Herein, we present the synthesis and characterization of the first gold(I)-cyclobutadiene complex, accompanied with bonding analysis by state-of-the-art energy decomposition analysis methods. Analysis of possible coordination modes for the new species not only confirms established characteristics of gold(I) bonding, but also suggests that Pauli repulsion is a key yet hitherto overlooked element. Additionally, we obtain a new perspective on gold(I)-bonding by comparison of the gold(I)-cyclobutadiene to congeners stabilized by p-, d-, and f-block metals. Consequently, we refine the gold(I) bonding model, with a delicate interplay of Pauli repulsion and charge transfer as the key driving force for various coordination motifs. Pauli repulsion is similarly determined as a significant interaction in AuI -alkyne species, corroborating this revised understanding of AuI bonding.

Calculation of Metallocene Ionization Potentials via Auxiliary Field Quantum Monte Carlo: Toward Benchmark Quantum Chemistry for Transition Metals

The accurate ab initio prediction of ionization energies is essential to understanding the electrochemistry of transition metal complexes in both materials science and biological applications. However, such predictions have been complicated by the scarcity of gas phase experimental data, the relatively large size of the relevant molecules, and the presence of strong electron correlation effects. In this work, we apply all-electron phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) utilizing multideterminant trial wave functions to six metallocene complexes to compare the computed adiabatic and vertical ionization energies with experimental results. We find that ph-AFQMC yields mean absolute errors (MAEs) of 1.69 ± 1.02 kcal/mol for the adiabatic energies and 2.85 ± 1.13 kcal/mol for the vertical energies. We also carry out density functional theory (DFT) calculations using a variety of functionals, which yields MAEs of 3.62-6.98 kcal/mol and 3.31-9.88 kcal/mol, as well as one variant of localized coupled cluster calculations (DLPNO-CCSD(T0) with moderate PNO cutoffs), which has MAEs of 4.96 and 6.08 kcal/mol, respectively. We also test the reliability of DLPNO-CCSD(T0) and DFT on acetylacetonate (acac) complexes for adiabatic energies measured in the same manner experimentally, and we find higher MAEs, ranging from 4.56 to 10.99 kcal/mol (with a different ordering) for DFT and 6.97 kcal/mol for DLPNO-CCSD(T0). Finally, by utilizing experimental solvation energies, we show that accurate reduction potentials in solution for the metallocene series can be obtained from the AFQMC gas phase results.

Revisiting the Performance of Time-Dependent Density Functional Theory for Electronic Excitations: Assessment of 43 Popular and Recently Developed Functionals from Rungs One to Four

In this paper, the performance of more than 40 popular or recently developed density functionals is assessed for the calculation of 463 vertical excitation energies against the large and accurate QuestDB benchmark set. For this purpose, the Tamm-Dancoff approximation offers a good balance between computational efficiency and accuracy. The functionals ωB97X-D and BMK are found to offer the best performance overall with a root-mean square error (RMSE) of around 0.27 eV, better than the computationally more demanding CIS(D) wave function method with a RMSE of 0.36 eV. The results also suggest that Jacob's ladder still holds for time-dependent density functional theory excitation energies, though hybrid meta generalized-gradient approximations (meta-GGAs) are not generally better than hybrid GGAs. Effects of basis set convergence, gauge invariance correction to meta-GGAs, and nonlocal correlation (VV10) are also studied, and practical basis set recommendations are provided.

Effect of Intersystem Crossings on the Kinetics of Thermal Ion-Molecule Reactions: Ti+ + O2, CO2, and N2O

A selected-ion flow tube apparatus has been used to measure rate constants and product branching fractions of ²Ti⁺ reacting with O₂, CO₂, and N₂O over the range of 200-600 K. Ti⁺ + O₂ proceeds at near the Langevin capture rate constant of 6-7 × 10^-10 cm³ s^-1 at all temperatures to yield ⁴TiO⁺ + O. Reactions initiated on doublet or quartet surfaces are formally spin-allowed; however, the 50% of reactions initiated on sextet surfaces must undergo an intersystem crossing (ISC). Statistical theory is used to calculate the energy and angular momentum dependences of the specific rate constants for the competing isomerization and dissociation channels. This acts as an internal clock on the lifetime to ISC, setting an upper limit on the order of τ_ISC < 1e^-11 s. ²Ti⁺ + CO₂ produces ⁴TiO⁺ + CO less efficiently, with a rate constant fit as 5.5 ± 1.3 × 10^-11 (T/300)^{-1.1 ± 0.2} cm³ s^-1. The reaction is formally spin-prohibited, and statistical modeling shows that ISC, not a submerged transition state, is rate-limiting, occurring with a lifetime on the order of 10^-7 s. Ti⁺ + N₂O proceeds at near the capture rate constant. In this case, both Ti⁺ON₂ and Ti⁺N₂O entrance channel complexes are formed and can interconvert over a barrier. The main product is >90% TiO⁺ + N₂, and the remainder is TiN⁺ + NO. Both channels need to undergo ISC to form ground-state products but TiO⁺ can be formed in an excited state exothermically. Therefore, kinetic information is obtained only for the TiN⁺ channel, where ISC occurs with a lifetime on the order of 10^-9 s. Statistical modeling indicates that the dipole-preferred Ti⁺ON₂ complex is formed in ∼80% of collisions, and this value is reproduced using a capture model based on the generic ion-dipole + quadrupole long-range potential.

Oxidation State Localized Orbitals: A Method for Assigning Oxidation States Using Optimally Fragment-Localized Orbitals and a Fragment Orbital Localization Index

Oxidation states represent the ionic distribution of charge in a molecule and are significant in tracking redox reactions and understanding chemical bonding. While effective algorithms already exist based on formal Lewis structures as well as using localized orbitals, they exhibit differences in challenging cases where effects such as redox noninnocence are at play. Given a density functional theory (DFT) calculation with chosen total charge and spin multiplicity, this work reports a new approach to obtaining fragment-localized orbitals that is termed oxidation state localized orbitals (OSLO), together with an algorithm for assigning the oxidation state using the OSLOs and an associated fragment orbital localization index (FOLI). Evaluating the FOLI requires fragment populations, and for this purpose a new version of the intrinsic atomic orbital (IAO) scheme is introduced in which the IAOs are evaluated using a reference minimal basis formed from on-the-fly superposition of atomic density (IAO-AutoSAD) calculations in the target basis set and at the target level of theory. The OSLO algorithm is applied to a range of challenging cases including high valent metal oxide complexes, redox noninnocent NO and dithiolate transition metal complexes, a range of carbene-containing TM complexes, and other examples including the potentially inverted ligand field in [Cu(CF₃)₄]^-. Across this range of cases, OSLO produces generally satisfactory results. Furthermore, in borderline cases, the OSLOs and associated FOLI values provide direct evidence of the emergence of covalent interactions between fragments that nicely complements existing approaches.

BH9, a New Comprehensive Benchmark Data Set for Barrier Heights and Reaction Energies: Assessment of Density Functional Approximations and Basis Set Incompleteness Potentials

The calculation of accurate reaction energies and barrier heights is essential in computational studies of reaction mechanisms and thermochemistry. To assess methods regarding their ability to predict these two properties, high-quality benchmark sets are required that comprise a reasonably large and diverse set of organic reactions. Due to the time-consuming nature of both locating transition states and computing accurate reference energies for reactions involving large molecules, previous benchmark sets have been limited in scope, the number of reactions considered, and the size of the reactant and product molecules. Recent advances in coupled-cluster theory, in particular local correlation methods like DLPNO-CCSD(T), now allow the calculation of reaction energies and barrier heights for relatively large systems. In this work, we present a comprehensive and diverse benchmark set of barrier heights and reaction energies based on DLPNO-CCSD(T)/CBS called BH9. BH9 comprises 449 chemical reactions belonging to nine types common in organic chemistry and biochemistry. We examine the accuracy of DLPNO-CCSD(T) vis-a-vis canonical CCSD(T) for a subset of BH9 and conclude that, although there is a penalty in using the DLPNO approximation, the reference data are accurate enough to serve as a benchmark for density functional theory (DFT) methods. We then present two applications of the BH9 set. First, we examine the performance of several density functional approximations commonly used in thermochemical and mechanistic studies. Second, we assess our basis set incompleteness potentials regarding their ability to mitigate basis set incompleteness errors. The number of data points, the diversity of the reactions considered, and the relatively large size of the reactant molecules make BH9 the most comprehensive thermochemical benchmark set to date and a useful tool for the development and assessment of computational methods.

Coupled Cluster Benchmark of New DFT and Local Correlation Methods: Mechanisms of Hydroarylation and Oxidative Coupling Catalyzed by Ru(II, III) Chloride Carbonyls

We have evaluated a set of accurate canonical CCSD(T) energies for stationary points on the potential energy surface for Ru(II, III) chloride carbonyl catalysis of two competing reactions between benzene and methyl acrylate (MA), namely, hydroarylation and oxidative coupling. We have then applied this set to evaluate the performance of localized orbital coupled-cluster methods and several new and common density functionals. We find that (a) DLPNO-CCSD(T) with TightPNO cutoffs is an acceptable substitute for full canonical CCSD(T) calculations on this system; (b) for the closed-shell systems where it could be applied, LNO-CCSD(T) with tight convergence criteria is very close to the canonical results; (c) the recent ωB97X-V and ωB97M-V functionals exhibit superior performance to commonly used DFT functionals in both closed- and open-shell calculations; (d) the revDSD-PBEP86 revision of the DSD-PBEP86 double hybrid represents an improvement over the original, even though transition metals were not involved in its parametrization; and (e) DSD-SCAN and DOD-SCAN show comparable efficiency. Most tested (meta)-GGA and hybrid density functionals perform better for open-shell than for closed-shell complexes; this is not the case for the double hybrids considered.

Conversion of carbon dioxide to a novel molecule NCNBO- mediated by NbBN2- anions at room temperature

The activation of carbon dioxide (CO₂) mediated by NbBN₂^- cluster anions under the conditions of thermal collision has been investigated by time-of-flight mass spectrometry combined with density functional theory calculations. Two CO double bonds in the CO₂ molecule are completely broken and two C-N bonds are further generated to form the novel molecule NCNBO^-. To the best of our knowledge, this new molecule is synthesized and reported for the first time. In addition, one oxygen atom transfer channel produces another product, NbBN₂O^-. Both of the Nb and B atoms in NbBN₂^- donate electrons to reduce CO₂, and the carbon atom originating from CO₂ serves as an electron reservoir. The reaction of NbB^- with N₂ was also investigated theoretically, and the formation of NbBN₂^- from this reaction is thermodynamically and kinetically quite favorable, indicating that NCNBO^- might be produced from the coupling of N₂ and CO₂ mediated by NbB^- anions.

Machine Learning-Assisted Selection of Active Spaces for Strongly Correlated Transition Metal Systems

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.