Calculation of Ligand Dissociation Energies in Large Transition-Metal Complexes

QUEST#4X: An Extension of QUEST#4 for Benchmarking Multireference Wave Function Methods

Given a number of data sets for evaluating the performance of single reference methods for the low-lying excited states of closed-shell molecules, a comprehensive data set for assessing the performance of multireference methods for the low-lying excited states of open-shell systems is still lacking. For this reason, we propose an extension (QUEST#4X) of the radical subset of QUEST#4 (J. Chem. Theory Comput. 2020, 16, 3720) to cover 110 doublet and 39 quartet excited states. Near-exact results obtained by iterative configuration interaction with selection and second-order perturbation correction (iCIPT2) are taken as benchmark to calibrate static-dynamic-static configuration interaction (SDSCI) and static-dynamic-static second-order perturbation theory (SDSPT2), which are minimal MRCI and CI-like perturbation theory, respectively. It is found that SDSCI is very close in accuracy to internally contracted multireference configuration interaction with singles and doubles (ic-MRCISD), although its computational cost is just that of one iteration of the latter. Unlike most variants of MRPT2, SDSPT2 treats single and multiple states in the same way and performs similarly to multistate n-electron valence second-order perturbation theory (MS-NEVPT2). These findings put SDSCI and SDSPT2 on a firm basis.

State-of-the-art local correlation methods enable affordable gold standard quantum chemistry for up to hundreds of atoms

In this feature, we review the current capabilities of local electron correlation methods up to the coupled cluster model with single, double, and perturbative triple excitations [CCSD(T)], which is a gold standard in quantum chemistry. The main computational aspects of the local method types are assessed from the perspective of applications, but the focus is kept on how to achieve chemical accuracy (i.e., <1 kcal mol-1 uncertainty), as well as on the broad scope of chemical problems made accessible. The performance of state-of-the-art methods is also compared, including the most employed DLPNO and, in particular, our local natural orbital (LNO) CCSD(T) approach. The high accuracy and efficiency of the LNO method makes chemically accurate CCSD(T) computations accessible for molecules of hundreds of atoms with resources affordable to a broad computational community (days on a single CPU and 10-100 GB of memory). Recent developments in LNO-CCSD(T) enable systematic convergence and robust error estimates even for systems of complicated electronic structure or larger size (up to 1000 atoms). The predictive power of current local CCSD(T) methods, usually at about 1-2 order of magnitude higher cost than hybrid density functional theory (DFT), has become outstanding on the palette of computational chemistry applicable for molecules of practical interest. We also review more than 50 LNO-based and other advanced local-CCSD(T) applications for realistic, large systems across molecular interactions as well as main group, transition metal, bio-, and surface chemistry. The examples show that properly executed local-CCSD(T) can contribute to binding, reaction equilibrium, rate constants, etc. which are able to match measurements within the error estimates. These applications demonstrate that modern, open-access, and broadly affordable local methods, such as LNO-CCSD(T), already enable predictive computations and atomistic insight for complicated, real-life molecular processes in realistic environments.

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.

Photochemical H2 activation by an Zn-Fe heterometallic: a mechanistic investigation

Addition of H2 to a Zn-Fe complex was observed to occur under photochemical conditions (390 or 428 nm LED) and leads to the formation of a heterometallic dihydride complex. The reaction does not occur under thermal conditions and DFT calculations suggest this is an endergonic, light driven process. Through a combined experimental and computational approach, the plausible mechanisms for H2 activation were investigated. Inhibition experiments, double-label cross-over experiments, radical trapping experiments, EPR spectroscopy and DFT calculations were used to gain insight into this system. The combined data are consistent with two plausible mechanisms, the first involving ligand dissociation followed by oxidative addition of H2 at the Fe centre, the second involving homolytic fragmentation of the Zn-Fe heterometallic and formation of radical intermediates.

Robustness of Threshold Collision-Induced Dissociation Simulations for Bond Dissociation Energies

The threshold collision-induced dissociation (T-CID) method is the workhorse for gas-phase bond dissociation energy (BDE) measurements. However, T-CID does not measure BDEs directly; instead, BDEs are obtained by fitting simulated data to the experimental data. We previously observed several large discrepancies between the computed and experimental BDEs. To analyze the reliability of the experimental values, we previously reported a study of the dissociation rate models in the simulation. Here, we report a study of the collision simulation part, specifically in the L-CID (ligand CID) program. We show that the BDE values are robust even to intentionally introduced mistakes in the simulations, varying in most cases by less than 3 kcal mol-1. The most significant exception is the collisional energy transfer (CET) simulation, which led to deviations larger than 10 kcal mol-1. However, we found that the BDEs obtained with explicitly simulated CET distributions deviated by only 3 kcal mol-1 from those simulated with the original model. Collectively, our results suggest that the T-CID-derived BDE values are robust and are likely to be accurate.

Cluster-in-Molecule Approach with Explicitly Correlated Methods for Large Molecules

In this article, we present a series of explicitly correlated local correlation methods developed under the cluster-in-molecule (CIM) framework, including explicitly correlated second-order Møller-Plesset perturbation (MP2), coupled-cluster singles and doubles (CCSD), domain-based local pair natural orbital CCSD (DLPNO-CCSD), and DLPNO-CCSD with perturbative triples (DLPNO-CCSD(T)). In these methods, F12 correction is decomposed into contributions from each occupied local molecular orbital and then evaluated independently in a given cluster, which consists of a subset of localized orbitals. These newly developed methods allow F12 calculations of large molecules (up to 145 atoms for quasi-one-dimensional systems) on a single node. We use these methods to investigate the relative stability between extended and folded alkane C30H62, the relative stability of four secondary structures of a polyglycine Ace(Gly)10NH2, and the binding energies of two host-guest complexes. The results demonstrate that the combination of CIM with F12 methods is a promising way to investigate large molecules with small basis set errors.

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.

Comparing Density Functional Theory Metal-Ligand Bond Dissociation Enthalpies with Experimental Solution-Phase Enthalpies of Activation for Bond Dissociation

The predictive ability of density functional theory is fundamental to its usefulness in chemical applications. Recent work has compared solution-phase enthalpies of activation for metal-ligand bond dissociation to enthalpies of reaction for bond dissociation, and the present work continues those comparisons for 43 density functional methods. The results for ligand dissociation enthalpies of 30 metal-ligand complexes tested in this work reveal significant inadequacies of some functionals as well as challenges from the dispersion corrections to some functionals. The analysis presented here demonstrates the excellent performance of a recent density functional, M11plus, which contains nonlocal rung-3.5 correlation. We also find a good agreement between theory and experiment for some functionals without empirical dispersion corrections such as M06, r2SCAN, M06-L, and revM11, as well as good performance for some functionals with added dispersion corrections such as ωB97X-D (which always has a correction) and BLYP, B3LYP, CAM-B3LYP, and PBE0 when the optional dispersion corrections are added.

Assessment of DLPNO-MP2 Approximations in Double-Hybrid DFT

The unfavorable scaling (N5) of the conventional second-order Møller-Plesset theory (MP2) typically prevents the application of double-hybrid (DH) density functionals to large systems with more than 100 atoms. A prominent approach to reduce the computational demand of electron correlation methods is the domain-based local pair natural orbital (DLPNO) approximation that is successfully used in the framework of DLPNO-CCSD(T). Its extension to MP2 [Pinski P.; Riplinger, C.; Valeev, E. F.; Neese, F. J. Chem. Phys. 2015, 143, 034108.] paved the way for DLPNO-based DH (DLPNO-DH) methods. In this work, we assess the accuracy of the DLPNO-DH approximation compared to conventional DHs on a large number of 7925 data points for thermochemistry and 239 data points for structural features, including main-group and transition-metal systems. It is shown that DLPNO-DH-DFT can be applied successfully to perform energy calculations and geometry optimizations for large molecules at a drastically reduced computational cost. Furthermore, PNO space extrapolation is shown to be applicable, similar to its DLPNO-CCSD(T) counterpart, to reduce the remaining error.

Bond-Dissociation Energies to Probe Pyridine Electronic Effects on Organogold(III) Complexes: From Methodological Developments to Application in π-Backdonation Investigation and Catalysis

In this work, we report on the synthesis of several organogold(III) complexes based on 4,4'-diterbutylbiphenyl (C^C) and 2,6-bis(4-terbutylphenyl)pyridine (C^N^C) ligands and bond with variously substituted pyridine ligands (pyrR). Altogether, 33 complexes have been prepared and studied with mass spectrometry using higher-energy collision dissociation (HCD) in an Orbitrap mass spectrometer. A complete methodology including the kinetic modeling of the dissociation process based on the Rice-Ramsperger-Kassel-Marcus (RRKM) statistical method is proposed to obtain critical energies E0 of the pyrR loss for all complexes. The capacity of these E0 values to describe the pyridine ligand effect is further explored, at the same time as more classical descriptors such as 1H pyridinic NMR shift variation upon coordination and Au-NpyrR bond length measured by X-ray diffraction. An extensive theoretical work, including density functional theory (DFT) and domain-based local pair natural orbital coupled-cluster theory (DLPNO-CCSD(T)) methods, is also carried out to provide bond-dissociation energies, which are compared to experimental results. Results show that dissociation energy outperforms other descriptors, in particular to describe ligand effects over a large electronic effect range as seen by confronting the results to the pyrR pKa values. Further insights into the Au-NpyrR bond are obtained through an energy decomposition analysis (EDA) study, which confirms the isolobal character of Au+ with H+. Finally, the correlation between the lability of the pyridine ligands toward the catalytic efficiency of the complexes could be demonstrated in an intramolecular hydroarylation reaction of alkyne. The results were rationalized considering both pre-catalyst activation and catalyst reactivity. This study establishes the possibility of correlating dissociation energy, which is a gas-phase descriptor, with condensed-phase parameters such as catalysis efficiency. It therefore holds great potential for inorganic and organometallic chemistry by opening a convenient and easy way to evaluate the electronic influence of a ligand toward a metallic center.

On the accuracy of orbital based multi-level approaches for closed-shell transition metal chemistry

In this work, we investigate the accuracy of the local molecular orbital molecular orbital (LMOMO) scheme and projection-based wave function-in-density functional theory (WF-in-DFT) embedding for the prediction of reaction energies and barriers of typical reactions involving transition metals. To analyze the dependence of the accuracy on the system partitioning, we apply a manual orbital selection for LMOMO as well as the so-called direct orbital selection (DOS) for both approaches. We benchmark these methods on 30 closed shell reactions involving 16 different transition metals. This allows us to devise guidelines for the manual selection as well as settings for the DOS that provide accurate results within an error of 2 kcal mol^-1 compared to local coupled cluster. To reach this accuracy, on average 55% of the occupied orbitals have to be correlated with coupled cluster for the current test set. Furthermore, we find that LMOMO gives more reliable relative energies for small embedded regions than WF-in-DFT embedding.

Computational Evaluation of Potential Molecular Catalysts for Nitrous Oxide Decomposition

Nitrous oxide (N₂O) is a potent greenhouse gas (GHG) with limited use as a mild anesthetic and underdeveloped reactivity. Nitrous oxide splitting (decomposition) is critical to its mitigation as a GHG. Although heterogeneous catalysts for N₂O decomposition have been developed, highly efficient, long-lived solid catalysts are still needed, and the details of the catalytic pathways are not well understood. Reported herein is a computational evaluation of three potential molecular (homogeneous) catalysts for N₂O splitting, which could aid in the development of more active and robust catalysts and provide deeper mechanistic insights: one Cu(I)-based, [(CF₃O)₄Al]Cu (A-1), and two Ru(III)-based, Cl(POR)Ru (B-1) and (NTA)Ru (C-1) (POR = porphyrin, NTA = nitrilotriacetate). The structures and energetic viability of potential intermediates and key transition states are evaluated according to a two-stage reaction pathway: (A) deoxygenation (DO), during which a metal-N₂O complex undergoes N-O bond cleavage to produce N₂ and a metal-oxo species and (B) (di)oxygen evolution (OER), in which the metal-oxo species dimerizes to a dimetal-peroxo complex, followed by conversion to a metal-dioxygen species from which dioxygen dissociates. For the (F-L)Cu(I) activator (A-1), deoxygenation of N₂O is facilitated by an O-bound (F-L)Cu-O-N₂ or better by a bimetallic N,O-bonded, (F-L)Cu-NNO-Cu(F-L) complex; the resulting copper-oxyl (F-L)Cu-O is converted exergonically to (F-L)Cu-(η²,η²-O₂)-Cu(F-L), which leads to dioxygen species (F-L)Cu(η²-O₂), that favorably dissociates O₂. Key features of the DO/OER process for (POR)ClRu (B-1) include endergonic N₂O coordination, facile N₂ evolution from LR'u-N₂O-RuL to Cl(POR)RuO, moderate barrier coupling of Cl(POR)RuO to peroxo Cl(POR)Ru(O₂)Ru(POR)Cl, and eventual O₂ dissociation from Cl(POR)Ru(η¹-O₂), which is nearly thermoneutral. N₂O decomposition promoted by (NTA)Ru(III) (C-1) can proceed with exergonic N₂O coordination, facile N₂ dissociation from (NTA)Ru-ON₂ or (NTA)Ru-N₂O-Ru(NTA) to form (NTA)Ru-O; dimerization of the (NTA)Ru-oxo species is facile to produce (NTA)Ru-O-O-Ru(NTA), and subsequent OE from the peroxo species is moderately endergonic. Considering the overall energetics, (F-L)Cu and Cl(POR)Ru derivatives are deemed the best candidates for promoting facile N₂O decomposition.

The transferability limits of static benchmarks

Every practical method to solve the Schrödinger equation for interacting many-particle systems introduces approximations. Such methods are therefore plagued by systematic errors. For computational chemistry, it is decisive to quantify the specific error for some system under consideration. Traditionally, the primary way for such an error assessment has been benchmarking data, usually taken from the literature. However, their transferability to a specific molecular system, and hence, the reliability of the traditional approach always remains uncertain to some degree. In this communication, we elaborate on the shortcomings of this traditional way of static benchmarking by exploiting statistical analyses using one of the largest quantum chemical benchmark sets available. We demonstrate the uncertainty of error estimates in the light of the choice of reference data selected for a benchmark study. To alleviate the issues with static benchmarks, we advocate to rely instead on a rolling and system-focused approach for rigorously quantifying the uncertainty of a quantum chemical result.

Since the errors of quantum chemical methods can strongly vary across chemical space, the transferability of traditional benchmarks is limited. This can be overcome by quantifying the uncertainty of quantum chemical results in a system-focused way.

Optimization of the r2SCAN-3c Composite Electronic-Structure Method for Use with Slater-Type Orbital Basis Sets

The "Swiss army knife" composite density functional electronic-structure method r²SCAN-3c (J. Chem. Phys. 2021, 154, 064103) is extended and optimized for the use with Slater-type orbital basis sets. The meta generalized-gradient approximation (meta-GGA) functional r²SCAN by Furness et al. is combined with a tailor-made polarized triple-ζ Slater-type atomic orbital (STO) basis set (mTZ2P), the semiclassical London dispersion correction (D4), and a geometrical counterpoise (gCP) correction. Relativistic effects are treated explicitly with the scalar-relativistic zeroth-order regular approximation (SR-ZORA). The performance of the new implementation is assessed on eight geometry and 74 energy benchmark sets, including the extensive GMTKN55 database as well as recent sets such as ROST61 and IONPI19. In geometry optimizations, the STO-based r²SCAN-3c is either on par with or more accurate than the hybrid density functional approximation M06-2X-D3(0)/TZP. In energy calculations, the overall accuracy is similar to the original implementation of r²SCAN-3c with Gaussian-type atomic orbitals (GTO), but basic properties, intermolecular noncovalent interactions, and barrier heights are better described with the STO approach, resulting in a lower weighted mean absolute deviation (WTMAD-2(STO) = 7.15 vs 7.50 kcal mol^-1 with the original method) for the GMTKN55 database. The STO-optimized r²SCAN-3c outperforms many conventional hybrid/QZ approaches in most common applications at a fraction of their cost. The reliable, robust, and accurate r²SCAN-3c implementation with STOs is a promising alternative to the original implementation with GTOs and can be generally used for a broad field of quantum chemical problems.

Dispersion corrected r2SCAN based global hybrid functionals: r2SCANh, r2SCAN0, and r2SCAN50

The regularized and restored semilocal meta-generalized gradient approximation (meta-GGA) exchange-correlation functional r²SCAN [Furness et al., J. Phys. Chem. Lett. 11, 8208-8215 (2020)] is used to create three global hybrid functionals with varying admixtures of Hartree-Fock "exact" exchange (HFX). The resulting functionals r²SCANh (10% HFX), r²SCAN0 (25% HFX), and r²SCAN50 (50% HFX) are combined with the semi-classical D4 London dispersion correction. The new functionals are assessed for the calculation of molecular geometries, main-group, and metalorganic thermochemistry at 26 comprehensive benchmark sets. These include the extensive GMTKN55 database, ROST61, and IONPI19 sets. It is shown that a moderate admixture of HFX leads to relative improvements of the mean absolute deviations for thermochemistry of 11% (r²SCANh-D4), 16% (r²SCAN0-D4), and 1% (r²SCAN50-D4) compared to the parental semi-local meta-GGA. For organometallic reaction energies and barriers, r²SCAN0-D4 yields an even larger mean improvement of 35%. The computation of structural parameters (geometry optimization) does not systematically profit from the HFX admixture. Overall, the best variant r²SCAN0-D4 performs well for both main-group and organometallic thermochemistry and is better or on par with well-established global hybrid functionals, such as PW6B95-D4 or PBE0-D4. Regarding systems prone to self-interaction errors (SIE4x4), r²SCAN0-D4 shows reasonable performance, reaching the quality of the range-separated ωB97X-V functional. Accordingly, r²SCAN0-D4 in combination with a sufficiently converged basis set [def2-QZVP(P)] represents a robust and reliable choice for general use in the calculation of thermochemical properties of both main-group and organometallic chemistry.

Direct orbital selection within the domain-based local pair natural orbital coupled-cluster method

Domain-based local pair natural orbital coupled cluster (DLPNO-CC) has become increasingly popular to calculate relative energies (e.g., reaction energies and reaction barriers). It can be applied within a multi-level DLPNO-CC-in-DLPNO-CC ansatz to reduce the computational cost and focus the available computational resources on a specific subset of the occupied orbitals. We demonstrate how this multi-level DLPNO-CC ansatz can be combined with our direct orbital selection (DOS) approach [M. Bensberg and J. Neugebauer, J. Chem. Phys. 150, 214106 (2019)] to automatically select orbital sets for any multi-level calculation. We find that the parameters for the DOS procedure can be chosen conservatively such that they are transferable between reactions. The resulting automatic multi-level DLPNO-CC method requires no user input and is extremely robust and accurate. The computational cost is easily reduced by a factor of 3 without sacrificing accuracy. We demonstrate the accuracy of the method for a total of 61 reactions containing up to 174 atoms and use it to predict the relative stability of conformers of a Ru-based catalyst.

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.

Assessing Density Functional Theory for Chemically Relevant Open-Shell Transition Metal Reactions

Due to the principle lack of systematic improvement possibilities of density functional theory, careful assessment of the performance of density functional approximations (DFAs) on well-designed benchmark sets, for example, for reaction energies and barrier heights, is crucial. While main-group chemistry is well covered by several available sets, benchmark data for transition metal chemistry is sparse. This is especially the case for larger, chemically relevant molecules. Addressing this issue, we recently introduced the MOR41 benchmark which covers chemically relevant reactions of closed-shell complexes. In this work, we extend these efforts to single-reference open-shell systems and introduce the "reactions of open-shell single-reference transition metal complexes" (ROST61) benchmark set. ROST61 includes accurate coupled-cluster reference values for 61 reaction energies with a mean reaction energy of -42.8 kcal mol^-1. Complexes with 13-93 atoms covering 20 d-block elements are included, but due to the restriction to single-reference open-shell systems, important elements such as iron or platinum could not be taken into account, or only to a small extent. We assess the performance of 31 DFAs in combination with three London dispersion (LD) correction schemes. Further, DFT-based composite methods, MP2, and a few semiempirical quantum chemical methods are evaluated. Consistent with the results for the MOR41 closed-shell benchmark, we find that the ordering of DFAs according to Jacob's ladder is preserved and that adding an LD correction is crucial, clearly improving almost all tested methods. The recently introduced r²SCAN-3c composite method stands out with a remarkable mean absolute deviation (MAD) of only 2.9 kcal mol^-1, which is surpassed only by hybrid DFAs with low amounts of Fock exchange (e.g., 2.3 kcal mol^-1 for TPSS0-D4/def2-QZVPP) and double-hybrid (DH) DFAs but at a significantly higher computational cost. The lowest MAD of only 1.6 kcal mol^-1 is obtained with the DH DFA PWPB95-D4 in the def2-QZVPP basis set approaching the estimated accuracy of the reference method. Overall, the ROST61 set adds important reference data to a sparsely sampled but practically relevant area of chemistry. At this point, it provides valuable orientation for the application and development of new DFAs and electronic structure methods in general.

Computational Discovery of Transition-metal Complexes: From High-throughput Screening to Machine Learning

Transition-metal complexes are attractive targets for the design of catalysts and functional materials. The behavior of the metal-organic bond, while very tunable for achieving target properties, is challenging to predict and necessitates searching a wide and complex space to identify needles in haystacks for target applications. This review will focus on the techniques that make high-throughput search of transition-metal chemical space feasible for the discovery of complexes with desirable properties. The review will cover the development, promise, and limitations of "traditional" computational chemistry (i.e., force field, semiempirical, and density functional theory methods) as it pertains to data generation for inorganic molecular discovery. The review will also discuss the opportunities and limitations in leveraging experimental data sources. We will focus on how advances in statistical modeling, artificial intelligence, multiobjective optimization, and automation accelerate discovery of lead compounds and design rules. The overall objective of this review is to showcase how bringing together advances from diverse areas of computational chemistry and computer science have enabled the rapid uncovering of structure-property relationships in transition-metal chemistry. We aim to highlight how unique considerations in motifs of metal-organic bonding (e.g., variable spin and oxidation state, and bonding strength/nature) set them and their discovery apart from more commonly considered organic molecules. We will also highlight how uncertainty and relative data scarcity in transition-metal chemistry motivate specific developments in machine learning representations, model training, and in computational chemistry. Finally, we will conclude with an outlook of areas of opportunity for the accelerated discovery of transition-metal complexes.

Assessment of the Accuracy of DFT-Predicted Li+-Nucleic Acid Binding Energies

Understanding how lithium interacts with complex biosystems is crucial for uncovering the roles of this alkali metal in biology and designing extraction techniques for battery production and environmental remediation. In this light, fundamental information about Li⁺ binding to nucleic acids is required. Herein, a new database of Li⁺-nucleic acid interactions is presented that contains CCSD(T)/CBS benchmark energies for all nucleobase and phosphate binding locations. Furthermore, the performance of 54 DFT functionals in combination with three triple-zeta (TZ) basis sets (6-311+G(3df,2p), aug-cc-pVTZ, and def2-TZVPP) is tested. The results identify a range of functionals across different families (B2-PLYP, PBE-QIDH, ωB97, ωB97X-D, MN15, B3PW91, B97-2, TPSS, BP86-D3(BJ), and PBE) that can accurately describe coordinated Li⁺-nucleic acid interactions, with the average mean percent error (AMPE) across binding positions and basis sets being below 2%. Nevertheless, only three functionals tested (B2-PLYP, PBE-QIDH, and ωB97X-D) preserve this accuracy for metal cation-π interactions, suggesting that caution is warranted when choosing a functional to describe a diverse range of Li⁺-nucleic acid complexes. Removal of counterpoise corrections has very little impact on the reliability of most functionals, while the effect of empirical dispersion corrections varies depending on the functional choice and interaction type. While increasing the basis set to quadruple-zeta quality had little impact on the AMPE, the accuracy of double-zeta basis sets varies with family. Importantly, DFT methods reproduce the CCSD(T)/CBS trend in the preferred binding position for a given nucleic acid component and the global trend across components (phosphate ≫ G > C ≫ A ∼ T = U), as well as the geometries of the metal-nucleic acid complexes. The overall top performing functional is PBE-QIDH, which results in deviations from CCSD(T)/CBS values as small as ∼0.1 kcal/mol for nucleobase contacts and ∼1 kcal/mol for phosphate interactions. The most accurate DFT methods identified in the present work are recommended for future investigations of lithium interactions in larger nucleic acid systems to provide insights into the biological roles of this metal and the design of novel biosensing strategies.

Multiwavelets applied to metal-ligand interactions: Energies free from basis set errors

Transition metal-catalyzed reactions invariably include steps where ligands associate or dissociate. In order to obtain reliable energies for such reactions, sufficiently large basis sets need to be employed. In this paper, we have used high-precision multiwavelet calculations to compute the metal-ligand association energies for 27 transition metal complexes with common ligands, such as H₂, CO, olefins, and solvent molecules. By comparing our multiwavelet results to a variety of frequently used Gaussian-type basis sets, we show that counterpoise corrections, which are widely employed to correct for basis set superposition errors, often lead to underbinding. Additionally, counterpoise corrections are difficult to employ when the association step also involves a chemical transformation. Multiwavelets, which can be conveniently applied to all types of reactions, provide a promising alternative for computing electronic interaction energies free from any basis set errors.

Modeling Gas-Phase Unimolecular Dissociation for Bond Dissociation Energies: Comparison of Statistical Rate Models within RRKM Theory

The Rice-Ramsperger-Kassel-Marcus (RRKM) theory provides a simple yet powerful rate theory for calculating microcanonical rate constants. In particular, it has found widespread use in combination with gas-phase kinetic experiments of unimolecular dissociations to extract experimental bond dissociation energies (BDEs). We have previously found several discrepancies between the computed BDE values and the respective experimental ones, obtained with our empirical rate model, named L-CID. To investigate the reliability of our rate model, we conducted a theoretical analysis and comparison of the performance of conventional rate models and L-CID within the RRKM framework. Using the previously published microcanonical rate data as well as reaction cross-section data, we show that the BDE values obtained with the L-CID model agree with the ones from the other rate models within the expected uncertainty bounds. Based on this agreement, we discuss the possible rationalization of the good performance of the L-CID model.

Asymmetric bis-PNP pincer complexes of zirconium and hafnium - a measure of hemilability

Asymmetrically-bound pyrrolide-based bis-PNP pincer complexes of zirconium and hafnium have been formed. The [κ2-PNPPh][κ3-PNPPh]MCl2 species are in direct contrast to previous zirconium PNP pincer complexes. The pincer ligands are fluxional in their binding and the energy barrier for exchange has been approximated using VT-NMR spectroscopy and the result validated by DFT calculations.

Mechanistic Study of the Production of NOx Gases from the Reaction of Copper with Nitric Acid

Copper dissolution in nitric acid is a historic reaction playing a central role in many industrial processes, particularly for metal recovery from the electronics to nuclear industries. The mechanism through which this process occurs is debated. In order to better understand this process, quantum chemical calculations were performed to elucidate the key steps in the mechanism of copper dissolution in nitric acid. We combine both Kohn-Sham density functional theory and ab initio molecular dynamics simulations to understand the mechanism of the formation of the key products: NO₂, HNO₂, and NO. Our calculations suggest that the mechanisms of formation of NO₂, HNO₂, and NO are interconnected.

Calculations of quantum tunnelling rates for muonium reactions with methane, ethane and propane

Thermal rate constants for Mu + CH₄, Mu + C₂H₆ and Mu + C₃H₈ and their equivalent reactions with H were evaluated with ab initio instanton rate theory. The potential-energy surfaces are fitted using Gaussian process regression to high-level electronic-structure calculations evaluated around the tunnelling pathway. This method was able to successfully reproduce various experimental measurements for the rate constant of these reactions. However, it was not able to reproduce the faster-than-expected rate of Mu + C₃H₈ at 300 K reported by Fleming et al. [Phys. Chem. Chem. Phys., 2015, 17, 19901 and Phys. Chem. Chem. Phys., 2020, 22, 6326]. Analysis of our results indicates that the kinetic isotope effect at this temperature is not significantly influenced by quantum tunnelling. We consider many possible factors for the discrepancy between theory and experiment but conclude that in each case, the instanton approximation is unlikely to be the cause of the error. This is in part based on the good agreement we find between the instanton predictions and new multiconfigurational time-dependent Hartree (MCTDH) calculations for Mu + CH₄ using the same potential-energy surface. Further experiments will therefore be needed to resolve this issue.

Modern quantum chemistry with [Open]Molcas

MOLCAS/OpenMolcas is an ab initio electronic structure program providing a large set of computational methods from Hartree-Fock and density functional theory to various implementations of multiconfigurational theory. This article provides a comprehensive overview of the main features of the code, specifically reviewing the use of the code in previously reported chemical applications as well as more recent applications including the calculation of magnetic properties from optimized density matrix renormalization group wave functions.

The Exploration of Chemical Reaction Networks

Modern computational chemistry has reached a stage at which massive exploration into chemical reaction space with unprecedented resolution with respect to the number of potentially relevant molecular structures has become possible. Various algorithmic advances have shown that such structural screenings must and can be automated and routinely carried out. This will replace the standard approach of manually studying a selected and restricted number of molecular structures for a chemical mechanism. The complexity of the task has led to many different approaches. However, all of them address the same general target, namely to produce a complete atomistic picture of the kinetics of a chemical process. It is the purpose of this overview to categorize the problems that should be targeted and to identify the principal components and challenges of automated exploration machines so that the various existing approaches and future developments can be compared based on well-defined conceptual principles.

M06-SX screened-exchange density functional for chemistry and solid-state physics

Screened-exchange hybrid density functionals are especially recommended for solid-state systems because they combine the advantages of hybrid functionals with the correct physics and lower computational cost associated with the attenuation of Hartree-Fock exchange at long range. We present a screened-exchange hybrid functional, M06-SX, that combines the functional form of the local revM06-L functional with a percentage of short-range nonlocal Hartree-Fock exchange. The M06-SX functional gives good results not only for a large set of training data but also for several databases quite different from the training data. The mean unsigned error (MUE) of the M06-SX functional is 2.85 kcal/mol for 418 atomic and molecular energies (AME418) in Minnesota Database 2019, which is better than all five other screened-exchange hybrid functionals tested in this work. The M06-SX functional also gives especially good results for semiconductor band gaps, molecular dissociation energies, noncovalent interactions, barrier heights, and electronic excitation energies excluding long-range charge transfer excitations. For the LC18 lattice constants database, the M06-SX functional gives an MUE of only 0.034 Å. Therefore, the M06-SX functional is well suited for studying molecular chemistry as well as solid-state physics.

Gaussian Process-Based Refinement of Dispersion Corrections

We employ Gaussian process (GP) regression to adjust for systematic errors in D3-type dispersion corrections. We refer to the associated, statistically improved model as D3-GP. It is trained on differences between interaction energies obtained from PBE-D3(BJ)/ma-def2-QZVPP and DLPNO-CCSD(T)/CBS calculations. We generated a data set containing interaction energies for 1248 molecular dimers, which resemble the dispersion-dominated systems contained in the S66 data set. Our systems represent not only equilibrium structures but also dimers with various relative orientations and conformations at both shorter and longer distances. A reparametrization of the D3(BJ) model based on 66 of these dimers suggests that two of its three empirical parameters, a₁ and s₈, are zero, whereas a₂ = 5.6841 bohr. For the remaining 1182 dimers, we find that this new set of parameters is superior to all previously published D3(BJ) parameter sets. To train our D3-GP model, we engineered two different vectorial representations of (supra-)molecular systems, both derived from the matrix of atom-pairwise D3(BJ) interaction terms: (a) a distance-resolved interaction energy histogram, histD3(BJ), and (b) eigenvalues of the interaction matrix ordered according to their decreasing absolute value, eigD3(BJ). Hence, the GP learns a mapping from D3(BJ) information only, which renders D3-GP-type dispersion corrections comparable to those obtained with the original D3 approach. They improve systematically if the underlying training set is selected carefully. Here, we harness the prediction variance obtained from GP regression to select optimal training sets in an automated fashion. The larger the variance, the more information the corresponding data point may add to the training set. For a given set of molecular systems, variance-based sampling can approximately determine the smallest subset being subjected to reference calculations such that all dispersion corrections for the remaining systems fall below a predefined accuracy threshold. To render the entire D3-GP workflow as efficient as possible, we present an improvement over our variance-based, sequential active-learning scheme [ J. Chem. Theory Comput. 2018 , 14 , 5238 ]. Our refined learning algorithm selects multiple (instead of single) systems that can be subjected to reference calculations simultaneously. We refer to the underlying selection strategy as batchwise variance-based sampling (BVS). BVS-guided active learning is an essential component of our D3-GP workflow, which is implemented in a black-box fashion. Once provided with reference data for new molecular systems, the underlying GP model automatically learns to adapt to these and similar systems. This approach leads overall to a self-improving model (D3-GP) that predicts system-focused and GP-refined D3-type dispersion corrections for any given system of reference data.

Multiple Anti-Kasha Emissions in Transition-Metal Complexes

In this Letter, we present first-principles evidence that several higher-lying excited states are responsible for the emission spectrum of [M(CO)4(bpy)] (M = Cr, Mo, W and bpy = 2,2'-bipyrimidine) complexes. These results highlight the violation of Kasha's rule, which states that after irradiation, molecules emit light with appreciable yield only from their lowest energy excited state. Furthermore, in [W(CO)4(bpy)] and [Mo(CO)4(bpy)], the breaking of Kasha's rule is two-fold because at least two different excited states besides T1 are involved in emission. To our knowledge, these are the first transition-metal complexes unambiguously demonstrated to display simultaneous equilibrated and nonequilibrated anti-Kasha emissions. This work also highlights the complexity of the emissive processes of tetracarbonyl-diimine transition-metal complexes, which are controlled via a subtle interplay of electronic and geometrical effects along the excited-state deactivation dynamics.

Structure Optimisation of Large Transition-Metal Complexes with Extended Tight-Binding Methods

Large transition-metal complexes are used in numerous areas of chemistry. Computer-aided theoretical investigations of such complexes are limited by the sheer size of real systems often consisting of hundreds to thousands of atoms. Accordingly, the development and thorough evaluation of fast semi-empirical quantum chemistry methods that are universally applicable to a large part of the periodic table is indispensable. Herein, we report on the capability of the recently developed GFNn-xTB method family for full quantum-mechanical geometry optimisation of medium to very large transition-metal complexes and organometallic supramolecular structures. The results for a specially compiled benchmark set of 145 diverse closed-shell transition-metal complex structures for all metals up to Hg are presented. Further the GFNn-xTB methods are tested on three established benchmark sets regarding reaction energies and barrier heights of organometallic reactions.

Designing in the Face of Uncertainty: Exploiting Electronic Structure and Machine Learning Models for Discovery in Inorganic Chemistry

Recent transformative advances in computing power and algorithms have made computational chemistry central to the discovery and design of new molecules and materials. First-principles simulations are increasingly accurate and applicable to large systems with the speed needed for high-throughput computational screening. Despite these strides, the combinatorial challenges associated with the vastness of chemical space mean that more than just fast and accurate computational tools are needed for accelerated chemical discovery. In transition-metal chemistry and catalysis, unique challenges arise. The variable spin, oxidation state, and coordination environments favored by elements with well-localized d or f electrons provide great opportunity for tailoring properties in catalytic or functional (e.g., magnetic) materials but also add layers of uncertainty to any design strategy. We outline five key mandates for realizing computationally driven accelerated discovery in inorganic chemistry: (i) fully automated simulation of new compounds, (ii) knowledge of prediction sensitivity or accuracy, (iii) faster-than-fast property prediction methods, (iv) maps for rapid chemical space traversal, and (v) a means to reveal design rules on the kilocompound scale. Through case studies in open-shell transition-metal chemistry, we describe how advances in methodology and software in each of these areas bring about new chemical insights. We conclude with our outlook on the next steps in this process toward realizing fully autonomous discovery in inorganic chemistry using computational chemistry.

Understanding and Quantifying London Dispersion Effects in Organometallic Complexes

Quantum chemical methods are nowadays able to determine properties of larger chemical systems with high accuracy and Kohn-Sham density functional theory (DFT) in particular has proven to be robust and suitable for everyday applications of electronic structure theory. A clear disadvantage of many established standard density functional approximations like B3LYP is their inability to describe long-range electron correlation effects. The inclusion of such effects, also termed London dispersion, into DFT has been extensively researched in recent years, resulting in some efficient and routinely used correction schemes. The well-established D3 method has demonstrated its efficiency and accuracy in numerous applications since 2010. Recently, it was improved by developing the successor (termed D4) which additionally includes atomic partial charge information for the generation of pairwise dispersion coefficients. These coefficients determine the leading-order (two-body) and higher-order (three- or many-body) terms of the D4 dispersion energy which is simply added to a standard DFT energy. With its excellent accuracy-to-cost ratio, the DFT-D4 method is well suited for the determination of structures and chemical properties for molecules of most kinds. While dispersion effects in organic molecules are nowadays well studied, much less is known for organometallic complexes. For such systems, there has been a growing interest in designing dispersion-controlled reactions especially in the field of homogeneous catalysis. Here, efficient electronic structure methods are necessary for screening of promising model complexes and quantifying dispersion effects. In this Account, we describe the quality of calculated structural and thermodynamic properties in gas-phase obtained with DFT-D4 corrected methods, specifically for organometallic complexes. The physical effects leading to London dispersion interactions are briefly discussed in the picture of second-order perturbation theory. Subsequently, basic theoretical aspects of the D4 method are introduced followed by selected case studies. Several chemical examples are presented starting with the analysis of transition metal thermochemistry and noncovalent interactions for small, heavy element containing main group compounds. Computed reaction energies can only match highly accurate reference values when all energy contributions are included in the DFT treatment, thus highlighting the major role of dispersion interactions for the accurate description of thermochemistry in gas-phase. Furthermore, the correlation between structural and catalytic properties is emphasized where the accessibility of high quality structures is essential for reaction planning and catalyst design. We present calculations for aggregates of organometallic systems with intrinsically large repulsive electrostatic interactions which can be stabilized by London dispersion effects. The newly introduced inclusion of atomic charge information in the DFT-D4 model robustly leads to quantitatively improved dispersion energies in particular for metallic systems. By construction it yields results which are easily understandable due to a clear separation into hybridization and charge (oxidation) state and two- and many-body effects, respectively. Due to its high computational efficiency, the D4 dispersion model is even applicable to low-cost classical and semiempirical theoretical methods.