Semiautomated Transition State Localization for Organometallic Complexes with Semiempirical Quantum Chemical Methods

A remarkably simple dispersion damping scheme and the DH24 double hybrid density functional

In recent papers, Becke et al. [J. Chem. Phys. 158, 151103 (2023)] and then Becke [J. Chem. Phys. 159, 241101 (2023)] have developed a novel double hybrid density functional, "DH23," whose terms are based on good local physics. Its 12 coefficients are trained on the GMTKN55 (general main-group thermochemistry, kinetics, and noncovalent interactions) chemical database of Goerigk et al. [Phys. Chem. Chem. Phys. 19, 32184 (2017)]. The lowest GMTKN55 "WTMAD2" error to date for any hybrid or double hybrid density functional was obtained (1.73 kcal/mol for the revDH23 variant). Here, we simplify DH23 by introducing a dispersion damping scheme involving atomic numbers only and one global parameter. The resulting new functional, "DH24," performs as well as its predecessors.

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

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

Improved CPS and CBS Extrapolation of PNO-CCSD(T) Energies: The MOBH35 and ISOL24 Data Sets

Computation of heats of reaction of large molecules is now feasible using the domain-based pair natural orbital (PNO)-coupled-cluster singles, doubles, and perturbative triples [CCSD(T)] theory. However, to obtain agreement within 1 kcal/mol of experiment, it is necessary to eliminate basis set incompleteness error, which comprises both the AO basis set error and the PNO truncation error. Our investigation into the convergence to the canonical limit of PNO-CCSD(T) energies with the PNO truncation threshold T shows that errors follow the model E ( T ) = E + A T 1 / 2 . Therefore, PNO truncation errors can be eliminated using a simple two-point CPS extrapolation to the canonical limit so that subsequent CBS extrapolation is not limited by the residual PNO truncation error. Using the ISOL24 and MOBH35 data sets, we find that PNO truncation errors are larger for molecules with significant static correlation and that it is necessary to use very tight thresholds of T = 10 - 8 to ensure that errors do not exceed 1 kcal/mol. We present a lower-cost extrapolation scheme that uses information from small basis sets to estimate the PNO truncation errors for larger basis sets. In this way, the canonical limit of CCSD(T) calculations on sizable molecules with large basis sets can be reliably estimated in a practical way. Using this approach, we report near complete basis set (CBS)-CCSD(T) reaction energies for the full ISOL24 and MOBH35 data sets.

GFN-xTB-Based Computations Provide Comprehensive Insights into Emulsion Radiation-Induced Graft Polymerization

In this article, a deep insight into emulsion radiation-induced graft polymerization (RIGP) was obtained by computing explicit solvation free energies, conformational entropy, monomer radius and dipole moments with the state-of-the-art Conformer-Rotamer Ensemble Sampling Tool (CREST) package primarily at semiempirical GFN-xTB level. By leveraging the robustness of the CREST package, above parameters provided dynamic nature of methacrylate monomers with the consideration of realistic emulsion conditions. With the chemical and physical importance of the above results, CREST-determined explanatory variables sufficiently led to the building of the prediction models for the RIGP of methacrylate monomers. The machine learning model building resulted in effective reactivity predictions and unveiled important factors for the radiation-induced graft polymerization in a chemically interpretable fashion.

Synthesis of Functionalized Tetrasubstituted Allenes by the Addition of Bis(trimethylsilyl)ketene Acetals to Ynones Catalyzed by Gold(I)

We have developed a straightforward and rapid methodology for the synthesis of tetrasubstituted allenes bearing carboxylic acids in the 1,3-position through the gold(I)-catalyzed nucleophilic addition of bis(trimethylsilyl)ketene acetals to ynones. The reaction was evaluated with several substrates, and 21 allenes were obtained in moderate to good yields. Using DFT calculations, we studied the mechanism of the reaction, which suggested a nucleophilic 1,4-addition pathway. The potential of allenes to act as a source of highly functionalized lactones was also explored.

Doubling down on density-functional theory

In a recent paper, Becke et al. [J. Chem. Phys. 158, 151103 (2023)] presented a novel double hybrid density functional, "DH23," whose terms are based on good physics. Its 12 coefficients were trained on the GMTKN55 (general main-group thermochemistry, kinetics, and noncovalent interactions) chemical database of Goerigk et al. [Phys. Chem. Chem. Phys. 19, 32184 (2017)]. The lowest GMTKN55 "WTMAD2" error to date for any hybrid or double hybrid density functional was obtained (1.76 kcal/mol). Here, we make some revisions to DH23 and test its efficacy on reference data beyond GMTKN55, namely, organometallic reaction energies and barrier heights. The results confirm that DH23 is robust outside its training set. In the process, a slightly smaller GMTKN55 WTMAD2 of 1.73 kcal/mol is achieved.

Toward a correct treatment of core properties with local hybrid functionals

In local hybrid functionals (LHs), a local mixing function (LMF) determines the position-dependent exact-exchange admixture. We report new LHs that focus on an improvement of the LMF in the core region while retaining or partly improving upon the high accuracy in the valence region exhibited by the LH20t functional. The suggested new pt-LMFs are based on a Padé form and modify the previously used ratio between von Weizsäcker and Kohn-Sham local kinetic energies by different powers of the density to enable flexibly improved approximations to the correct high-density and iso-orbital limits relevant for the innermost core region. Using TDDFT calculations for a set of K-shell core excitations of second- and third-period systems including accurate state-of-the-art relativistic orbital corrections, the core part of the LMF is optimized, while the valence part is optimized as previously reported for test sets of atomization energies and reaction barriers (Haasler et al., J Chem Theory Comput 2020, 16, 5645). The LHs are completed by a calibration function that minimizes spurious nondynamical correlation effects caused by the gauge ambiguities of exchange-energy densities, as well as by B95c meta-GGA correlation. The resulting LH23pt functional relates to the previous LH20t functional but specifically improves upon the core region.

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.

High-throughput screening of spin states for transition metal complexes with spin-polarized extended tight-binding methods

The semiempirical GFNn-xTB ( n = 1 , 2 ) tight-binding methods are extended with a spin-dependent energy term (spin-polarization), enabling the fast and efficient screening of different spin states for transition metal complexes. While GFNn-xTB methods inherently can not differentiate properly between high-spin (HS) and low-spin (LS) states, this shortcoming is corrected with the presented methods termed spGFNn-xTB. The performance of spGFNn-xTB methods for spin state energy splittings is evaluated on a newly compiled benchmark set of 90 complexes (27 HS and 63 LS complexes) containing 3d, 4d, and 5d transition metals (termed TM90S) employing DFT references at the TPSSh-D4/def2-QZVPP level of theory. The challenging TM90S set contains complexes with charges between - 4 and +3, spin multiplicities between 1 and 6, and spin-splitting energies that range from - 47.8 to 146.6 kcal/mol with a mean average of 32.2 kcal/mol. On this set the (sp)GFNn-xTB methods, the PM6-D3H4 method, and the PM7 method are evaluated with spGFN1-xTB yielding the lowest MAD of 19.6 kcal/mol followed by spGFN2-xTB with 24.8 kcal/mol. While for the 4d and 5d subsets small or no improvements are observed with spin-polarization, large improvements are obtained for the 3d subset with spGFN1-xTB yielding the smallest MAD of 14.2 kcal/mol followed by spGFN2-xTB with 17.9 kcal/mol and PM6-D3H4 with 28.4 kcal/mol. The correct sign of the spin state splittings is obtained with spGFN2-xTB in 89% of all cases closely followed by spGFN1-xTB with 88%. On the full set, a pure semiempirical vertical spGFN2-xTB//GFN2-xTB-based workflow for screening purposes yields a slightly better MAD of 22.2 kcal/mol due to error compensation, while being qualitative correct for one additional case. In combination with their low computational cost (scanning spin states in seconds), the spGFNn-xTB methods represent robust tools for pre-screening steps of spin state calculations and high-throughput workflows.

Theoretical investigation of hydroxylated analogues of valinomycin as potassium transporter

Valinomycin is a potent ionophore known for its ability to transport potassium ions across biological membranes. The study focuses on the hydroxylated analogues of valinomycin (HyVLMs) and compares their energy profiles and capabilities for transporting potassium ions across phospholipid membranes. Using metadynamics, we investigated the energy profiles of wildtype valinomycin (VLM_1) and its three hydroxylated analogues (VLM_2, VLM_3, and VLM_4). We observed that all analogues exhibited energy maxima in the centre of the membrane and preferred positions below the phospholipid heads. Furthermore, the entry barriers for membrane penetration were similar among the analogues, suggesting that the hydroxyl group did not significantly affect their passage through the membrane. Transition state calculations provided insights into the ability of valinomycin analogues to capture potassium ions, with VLM_4 showing the lowest activation energy and VLM_2 displaying the highest. Our findings contribute to understanding the mechanisms of potassium transport by valinomycin analogues and highlight their potential as ionophores. The presence of the hydroxyl group is of particular importance because it paves the way for subsequent chemical modifications and the synthesis of new antiviral agents with reduced intrinsic toxicity.

ONIOM meets : efficient, accurate, and robust multi-layer simulations across the periodic table

The computational treatment of large molecular structures is of increasing interest in fields of modern chemistry. Accordingly, efficient quantum chemical approaches are needed to perform sophisticated investigations on such systems. This engaged the development of the well-established "Our own N-layered integrated molecular orbital and molecular mechanics" (ONIOM) multi-layer scheme [L. W. Chung et al., Chem. Rev., 2015, 115, 5678-5796]. In this work, we present the specific implementation of the ONIOM scheme into the xtb semi-empirical extended tight-binding program package and its application to challenging transition-metal complexes. The efficient and broadly applicable GFNn-xTB and -FF methods are applied in the ONIOM framework to elucidate reaction energies, geometry optimizations, and explicit solvation effects for metal-organic systems with up to several hundreds of atoms. It is shown that an ONIOM-based combination of density functional theory, semi-empirical, and force-field methods can be used to drastically reduce the computational costs and thus enable the investigation of huge systems at almost no significant loss in accuracy.

Unraveling Binding Mechanism and Stability of Urease Inhibitors: A QM/MM MD Study

Soil bacteria can produce urease, which catalyzes the hydrolysis of urea to ammonia (NH3) and carbamate. A variety of urease inhibitors have been proposed to reduce NH3 volatilization by interfering with the urease activity. We report a quantum mechanics/molecular mechanics molecular dynamics (QM/MM MD) study on the mechanism employed for the inhibition of urease by three representative competitive inhibitors; namely, acetohydroxamic acid (AHA), hydroxyurea (HU), and N-(n-butyl)phosphorictriamide (NBPTO). The possible connections between the structural and thermodynamical properties and the experimentally observed inhibition efficiency were evaluated and characterized. We demonstrate that the binding affinity decreases in the order NBPTO >> AHA > HU in terms of the computed activation and reaction free energies. This trend also indicates that NBPTO shows the highest inhibitory activity and the lowest IC50 value of 2.1 nM, followed by AHA (42 μM) and HU (100 μM). It was also found that the X=O moiety (X = carbon or phosphorous) plays a crucial role in the inhibitor binding process. These findings not only elucidate why the potent urease inhibitors are effective but also have implications for the design of new inhibitors.

Exploring the Accuracy Limits of PNO-Based Local Coupled-Cluster Calculations for Transition-Metal Complexes

While the domain-based local pair natural orbital coupled-cluster method with singles, doubles, and perturbative triples (DLPNO-CCSD(T)) has proven instrumental for computing energies and properties of large and complex systems accurately, calculations on first-row transition metals with a complex electronic structure remain challenging. In this work, we identify and address the two main error sources that influence the DLPNO-CCSD(T) accuracy in this context, namely, (i) correlation effects from the 3s and 3p semicore orbitals and (ii) dynamic correlation-induced orbital relaxation (DCIOR) effects that are not described by the local MP2 guess. We present a computational strategy that allows us to completely eliminate the DLPNO error associated with semicore correlation effects, while increasing, at the same time, the efficiency of the method. As regards the DCIOR effects, we introduce a diagnostic for estimating the deviation between DLPNO-CCSD(T) and canonical CCSD(T) for systems with significant orbital relaxation.

A Practical Algorithm to Solve the Near-Congruence Problem for Rigid Molecules and Clusters

We present an improved algorithm to solve the near-congruence problem for rigid molecules and clusters based on the iterative application of assignment and alignment steps with biased Euclidean costs. The algorithm is formulated as a quasi-local optimization procedure with each optimization step involving a linear assignment (LAP) and a singular value decomposition (SVD). The efficiency of the algorithm is increased by up to 5 orders of magnitude with respect to the original unbiased noniterative method and can be applied to systems with hundreds or thousands of atoms, outperforming all state-of-the-art methods published so far in the literature. The Fortran implementation of the algorithm is available as an open source library (https://github.com/qcuaeh/molalignlib) and is suitable to be used in global optimization methods for the identification of local minima or basins.

Full Implementation, Optimization, and Evaluation of a Range-Separated Local Hybrid Functional with Wide Accuracy for Ground and Excited States

We report the first full and efficient implementation of range-separated local hybrid functionals (RSLHs) into the TURBOMOLE program package. This enables the computation of ground-state energies and nuclear gradients as well as excitation energies. Regarding the computational effort, RSLHs scale like regular local hybrid functionals (LHs) with system or basis set size and increase timings by a factor of 2-3 in total. An advanced RSLH, ωLH22t, has been optimized for atomization energies and reaction barriers. It is an extension of the recent LH20t local hybrid and is based on short-range PBE and long-range HF exchange-energy densities, a pig2 calibration function to deal with the gauge ambiguity of exchange-energy densities, and reoptimized B95c correlation. ωLH22t has been evaluated for a wide range of ground-state and excited-state quantities. It further improves upon the already successful LH20t functional for the GMTKN55 main-group energetics test suite, and it outperforms any global hybrid while performing close to the top rung-4 functional, ωB97M-V, for these evaluations when augmented by D4 dispersion corrections. ωLH22t performs excellently for transition-metal reactivity and provides good balance between delocalization errors and left-right correlation for mixed-valence systems, with a somewhat larger bias toward localized states compared to LH20t. It approaches the accuracy of the best local hybrids to date for core, valence singlet and triplet, and Rydberg excitation energies while improving strikingly on intra- and intermolecular charge-transfer excitations, comparable to the most successful range-separated hybrids available.

Thermal Degradation and Carbonization Mechanism of Fe-Based Metal-Organic Frameworks onto Flame-Retardant Polyethylene Terephthalate

Currently, the metal-organic framework (MOF) is a promising candidate for flame-retardant polymers. In this study, a Fe-based MOF, MIL-88B(Fe), was introduced to polyethylene terephthalate (PET) and 3-hydroxyphenylphosphinyl-propanoic acid copolymer (P-PET) to reduce the fire hazard involved in using PET. The limiting oxygen indexes (LOIs) of MIL-PET and MIL-P-PET improved by 27% and 30%, respectively. The UL-94 level achieved for MIL-P-PET was V-0 rating. The thermal degradation and carbonization mechanisms of MIL-PET and MIL-P-PET were systematically investigated through thermogravimetric analysis coupled with a Fourier transform infrared spectroscopy (TG-IR), pyrolysis-gas chromatography-mass spectrometry (Py-GC-MS), x-ray photoelectron spectroscopy (XPS), and Raman spectrum combined with quantum chemical molecular dynamics simulation. With the addition of MIL-88B(Fe), high graphitization and a hard flammability char residual were generated. Compared with neat PET, the ferric ions efficiently catalyzed the homolytic cleavage and dehydrogenation of PET to produce a large amount of CO₂ and terephthalic acid for MIL-PET in gas phase. Rough and hierarchical char residual with ferric oxide was also generated when temperatures exceeded 600 °C. However, the carbonization process was inhibited due to the coordinated complex between phosphorus and ferric ions in MIL-P-PET, invaliding the decarboxylation and generating more benzoic acid and its precursor, which led to heavy smoke.

High-throughput computational workflow for ligand discovery in catalysis with the CSD

A novel semi-automated, high-throughput computational workflow for ligand/catalyst discovery based on the Cambridge Structural Database is reported.

Best-Practice DFT Protocols for Basic Molecular Computational Chemistry

Nowadays, many chemical investigations are supported by routine calculations of molecular structures, reaction energies, barrier heights, and spectroscopic properties. The lion's share of these quantum-chemical calculations applies density functional theory (DFT) evaluated in atomic-orbital basis sets. This work provides best-practice guidance on the numerous methodological and technical aspects of DFT calculations in three parts: Firstly, we set the stage and introduce a step-by-step decision tree to choose a computational protocol that models the experiment as closely as possible. Secondly, we present a recommendation matrix to guide the choice of functional and basis set depending on the task at hand. A particular focus is on achieving an optimal balance between accuracy, robustness, and efficiency through multi-level approaches. Finally, we discuss selected representative examples to illustrate the recommended protocols and the effect of methodological choices.

Theoretical calculations of formation and reactivity of o-quinomethide derivatives of resorcin[4]arene with reference to empirical data

This paper describes theoretical reaction pathways of alkoxybenzyl derivatives of resorcin[4]arene leading to the formation of o-quinomethide derivatives of resorcin[4]arene (o-QMR[4]A). For each case, the activation energies for the formation of one o-QMR[4]A unit and the activation energies for the backward reaction were calculated. Based on the calculated reaction pathways, the reaction mechanism of o-QMR[4]A formation was proposed. Using the example of o-QMR[4]A generated from a methoxy derivative of resorcin[4]arene, the activation energies with selected nucleophiles were calculated and the reaction mechanisms discussed. Reaction path calculations were performed using the nudged elastic band method and semiempirical extended tight-binding method (GFN2-xTB). Using hydroxybenzyl derivatives of resorcin[4]arene as an example, a comparison of calculated activation energies by selected density-functional theory methods with GFN2-xTB and B97-3c geometries was performed. B97-3c and wB97XD methods were used to calculate the energies of the reactants (R), transition states (TS) and products (P) of the analysed reactions. Theoretical reaction mechanisms were discussed with respect to the orbital-weighted Fukui dual descriptor (Δfw ) and experimental data.

In Silico Optimization of Charge Separating Dyes for Solar Energy Conversion

Dye-sensitized photoelectrochemical cells are promising devices in solar energy conversion. However, several limitations still have to be addressed, such as the major loss pathway through charge recombination at the dye-semiconductor interface. Charge separating dyes constructed as push-pull systems can increase the spatial separation of electron and hole, decreasing the recombination rate. Here, a family of dyes, consisting of polyphenylamine donors, fluorene bridges, and perylene monoimide acceptors, was investigated in silico using a combination of semi-empirical nuclear dynamics and a quantum propagation of photoexcited electron and hole. To optimize the charge separation, several molecular design strategies were investigated, including modifying the donor molecule, increasing the π-bridge length, and decoupling the molecular components through steric effects. The combination of a triphenylamine donor, using an extended 2-fluorene π-bridge, and decoupling the different components by steric hindrance from side groups resulted in a dye with significantly improved charge separation properties in comparison to the original supramolecular complex.

Benchmarking various types of partial atomic charges for classical all-atom simulations of metal-organic frameworks

The density derived electrostatic and chemical (DDEC) approach for calculating the charges of atoms in a metal-organic framework (MOF) is considered to be the most accurate (yet computationally costly) one among many charge-assignment methods. Here, we conducted a comparative study on five different types of atomic partial charges (namely CM5, Mulliken, Qeq, EQeq and PACMOF) prepared for a subset of MOFs with affordable computational costs and benchmarked them with respect to the DDEC charges, which is particularly relevant because currently most databases lack MOFs with pre-calculated DDEC charges. To find a suitable charge type alternative to the DDEC approach, we statistically ranked the five charge types based on two metrics, the relative standard deviation of charges and relative dipole moment difference, based on which we provide general guidance as well as suggestions for specific MOFs according to bond polarity analyses. Finally, we recommend a possible and more accurate parametrization scheme for future studies.

The MOBH35 Metal–Organic Barrier Heights Reconsidered: Performance of Local-Orbital Coupled Cluster Approaches in Different Static Correlation Regimes

We have revisited the MOBH35 (Metal–Organic Barrier Heights, 35 reactions) benchmark [Iron, Janes, J. Phys. Chem. A, 2019, 123 ( (17), ), 3761−378130973722; ibid. 2019, 123, 6379–6380] for realistic organometallic catalytic reactions, using both canonical CCSD(T) and localized orbital approximations to it. For low levels of static correlation, all of DLPNO-CCSD(T), PNO-LCCSD(T), and LNO-CCSD(T) perform well; for moderately strong levels of static correlation, DLPNO-CCSD(T) and (T₁) may break down catastrophically, and PNO-LCCSD(T) is vulnerable as well. In contrast, LNO-CCSD(T) converges smoothly to the canonical CCSD(T) answer with increasingly tight convergence settings. The only two reactions for which our revised MOBH35 reference values differ substantially from the original ones are reaction 9 and to a lesser extent 8, both involving iron. For the purpose of evaluating density functional theory (DFT) methods for MOBH35, it would be best to remove reaction 9 entirely as its severe level of static correlation makes it just too demanding for a test. The magnitude of the difference between DLPNO-CCSD(T) and DLPNO-CCSD(T₁) is a reasonably good predictor for errors in DLPNO-CCSD(T₁) compared to canonical CCSD(T); otherwise, monitoring all of T₁, D₁, max|t_i^A|, and 1/(ε_LUMO – ε_HOMO) should provide adequate warning for potential problems. Our conclusions are not specific to the def2-SVP basis set but are largely conserved for the larger def2-TZVPP, as they are for the smaller def2-SV(P): the latter may be an economical choice for calibrating against canonical CCSD(T). Finally, diagnostics for static correlation are statistically clustered into groups corresponding to (1) importance of single excitations in the wavefunction; (2a) the small band gap, weakly separated from (2b) correlation entropy; and (3) thermochemical importance of correlation energy, as well as the slope of the DFT reaction energy with respect to the percentage of HF exchange. Finally, a variable reduction analysis reveals that much information on the multireference character is provided by T₁, I_ND/I_tot, and the exchange-based diagnostic A₁₀₀[TPSS].

Surface tension of liquids and binary mixtures from molecular dynamics simulations

In this work we assess and extend strategies for calculating surface tension of complex liquids from molecular dynamics simulations: the mechanical route and the instantaneous liquid interface (ILI) approach. The former employs the connection between stress tensor and surface tension, whereas the latter involves computation of instantaneous density field. Whereas the mechanical route is general, the ILI method involves system-dependent parameters restricting its original application to liquid water only. Here we generalize the approach to complex molecular liquids using atomic van der Waals radii. The performance of the approaches is evaluated on two liquid systems: acetonitrile and water-methanol mixture. In addition, we compare the effect of the computational models for interaction potentials based on semi-empirical electronic structure theory and classical force fields on the estimate of the surface tension within both stress tensor and ILI approaches.

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.

Efficient workflow for the investigation of the catalytic cycle of water oxidation catalysts: Combining GFN-xTB and density functional theory

Photocatalytic water oxidation remains the bottleneck in many artificial photosynthesis devices. The efficiency of this challenging process is inherently linked to the thermodynamic and electronic properties of the chromophore and the water oxidation catalyst (WOC). Computational investigations can facilitate the search for favorable chromophore‐catalyst combinations. However, this remains a demanding task due to the requirements on the computational method that should be able to correctly describe different spin and oxidation states of the transition metal, the influence of solvation and the different rates of the charge transfer and water oxidation processes. To determine a suitable method with favorable cost/accuracy ratios, the full catalytic cycle of a molecular ruthenium based WOC is investigated using different computational methods, including density functional theory (DFT) with different functionals (GGA, Hybrid, Double Hybrid) as well as the semi‐empirical tight binding approach GFN‐xTB. A workflow with low computational cost is proposed that combines GFN‐xTB and DFT and provides reliable results. GFN‐xTB geometries and frequencies combined with single‐point DFT energies give free energy changes along the catalytic cycle that closely follow the full DFT results and show satisfactory agreement with experiment, while significantly decreasing the computational cost. This workflow allows for cost efficient determination of energetic, thermodynamic and dynamic properties of WOCs.

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.

[Cl@Si20H20]-: Parent Siladodecahedrane with Endohedral Chloride Ion

Fullerenes and diamondoids are at the core of nanoscience. Comparable monodisperse silicon analogues are scarce. Herein, we report the synthesis of the parent siladodecahedrane, which represents the largest Platonic solid. It shares its pattern of pentagonal faces with the smallest fullerene, C₂₀, and its saturated, H-terminated skeleton with diamondoids. Similar to endofullerenes, the silicon cage encapsulates a chloride ion ([Cl@Si₂₀H₂₀]^-); similar to diamondoids, its Si-H termini offer a wealth of opportunities for further functionalization. Mere treatment with chloromethanes leads to the perchlorinated cluster [Cl@Si₂₀Cl₂₀]^-. Both compounds were characterized by mass spectrometry, X-ray crystallography, NMR spectroscopy, and quantum-chemical calculations. The experimentally determined ³⁵Cl resonances of the endohedral chloride ions are particularly diagnostic to probe the Cl^- → Si₂₀ interaction strength as a function of the different surface substituents, as we have proven by high-level computational analyses.

From QCEIMS to QCxMS: A Tool to Routinely Calculate CID Mass Spectra Using Molecular Dynamics

Mass spectrometry (MS) is a powerful tool in chemical research and substance identification. For the computational modeling of electron ionization MS, we have developed the quantum-chemical electron ionization mass spectra (QCEIMS) program. Here, we present an extension of QCEIMS to calculate collision-induced dissociation (CID) spectra. The more general applicability is accounted for by the new name QCxMS, where "x" refers to EI or CID. To this end, fragmentation and rearrangement reactions are computed "on-the-fly" in Born-Oppenheimer molecular dynamics (MD) simulations with the semiempirical GFN2-xTB Hamiltonian, which provides an efficient quantum mechanical description of all elements up to Z = 86 (Rn). Through the explicit modeling of multicollision processes between precursor ions and neutral gas atoms as well as temperature-induced decomposition reactions, QCxMS provides detailed insight into the collision kinetics and fragmentation pathways. In combination with the CREST program to determine the preferential protonation sites, QCxMS becomes the first standalone MD-based program that can predict mass spectra based solely on molecular structures as input. We demonstrate this for six organic molecules with masses ranging from 159 to 296 Da, for which QCxMS yields CID spectra in reasonable agreement with experiments.

Simultaneously improving reaction coverage and computational cost in automated reaction prediction tasks

Automated reaction prediction has the potential to elucidate complex reaction networks for applications ranging from combustion to materials degradation, but computational cost and inconsistent reaction coverage are still obstacles to exploring deep reaction networks. Here we show that cost can be reduced and reaction coverage can be increased simultaneously by relatively straightforward modifications of the reaction enumeration, geometry initialization and transition state convergence algorithms that are common to many prediction methodologies. These components are implemented in the context of yet another reaction program (YARP), our reaction prediction package with which we report reaction discovery benchmarks for organic single-step reactions, thermal degradation of a γ-ketohydroperoxide, and competing ring-closures in a large organic molecule. Compared with recent benchmarks, YARP (re)discovers both established and unreported reaction pathways and products while simultaneously reducing the cost of reaction characterization by nearly 100-fold and increasing convergence of transition states. This combination of ultra-low cost and high reaction coverage creates opportunities to explore the reactivity of larger systems and more complex reaction networks for applications such as chemical degradation, where computational cost is a bottleneck.

Titanocene-Catalyzed [2+2] Cycloaddition of Bisenones and Comparison with Photoredox Catalysis and Established Methods

Cp2 Ti(TFA) is a broadly applicable catalyst for the [2+2] cycloaddition of bisenones by inner-sphere electron transfer. The attractiveness of this mechanism is shown by comparison with outer-sphere ET methods. DFT calculations show that the reaction proceeds through a unique unfavorable 5-exo (the rate-determining step) and a favorable 4-exo cyclization.

Exploring Avenues beyond Revised DSD Functionals: II. Random-Phase Approximation and Scaled MP3 Corrections

For revDSD double hybrids, the Görling–Levy second-order perturbation theory component is an Achilles’ heel when applied to systems with significant near-degeneracy (“static”) correlation. We have explored its replacement by the direct random phase approximation (dRPA), inspired by the SCS-dRPA75 functional of Kállay and co-workers. The addition to the final energy of both a D4 empirical dispersion correction and of a semilocal correlation component lead to significant improvements, with DSD-PBEdRPA₇₅-D4 approaching the performance of revDSD-PBEP86-D4 and the Berkeley ωB97M(2). This form appears to be fairly insensitive to the choice of the semilocal functional but does exhibit stronger basis set sensitivity than the PT2-based double hybrids (due to much larger prefactors for the nonlocal correlation). As an alternative, we explored adding an MP3-like correction term (in a medium-sized basis set) to a range-separated ωDSD-PBEP86-D4 double hybrid and found it to have significantly lower WTMAD2 (weighted mean absolute deviation) for the large and chemically diverse GMTKN55 benchmark suite; the added computational cost can be mitigated through density fitting techniques.

Exploring Avenues beyond Revised DSD Functionals: I. Range Separation, with xDSD as a Special Case

We have explored the use of range separation as a possible avenue for further improvement on our revDSD minimally empirical double hybrid functionals. Such ωDSD functionals encompass the XYG3 type of double hybrid (i.e., xDSD) as a special case for ω → 0. As in our previous studies, the large and chemically diverse GMTKN55 benchmark suite was used for evaluation. Especially when using the D4 rather than D3BJ dispersion model, xDSD has a slight performance advantage in WTMAD2. As in previous studies, PBEP86 is the winning combination for the semilocal parts. xDSDn-PBEP86-D4 marginally outperforms the previous "best in class" ωB97M(2) Berkeley double hybrid but without range separation and using fewer than half the number of empirical parameters. Range separation turns out to offer only marginal further improvements on GMTKN55 itself. While ωB97M(2) still yields better performance for small-molecule thermochemistry, this is compensated in WTMAD2 by the superior performance of the new functionals for conformer equilibria. Results for two external test sets with pronounced static correlation effects may indicate that range-separated double hybrids are more resilient to such effects.

Efficient Computation of Geometries for Gold Complexes

Computationally obtaining structural parameters along a reaction coordinate is commonly performed with Kohn‐Sham density functional theory which generally provides a good balance between speed and accuracy. However, CPU times still range from inconvenient to prohibitive, depending on the size of the system under study. Herein, the tight binding GFN2‐xTB method [C. Bannwarth, S. Ehlert, S. Grimme, J. Chem. Theory Comput. 2019, 15, 1652] is investigated as an alternative to produce reasonable geometries along a reaction path, that is, reactant, product and transition state structures for a series of transformations involving gold complexes. A small mean error (1 kcal/mol) was found, with respect to an efficient composite hybrid‐GGA exchange‐correlation functional (PBEh‐3c) paired with a double‐ζ basis set, which is 2–3 orders of magnitude slower. The outlined protocol may serve as a rapid tool to probe the viability of proposed mechanistic pathways in the field of gold catalysis.

Oxidation Under Reductive Conditions: From Benzylic Ethers to Acetals with Perfect Atom-Economy by Titanocene(III) Catalysis

Described here is a titanocene‐catalyzed reaction for the synthesis of acetals and hemiaminals from benzylic ethers and benzylic amines, respectively, with pendant epoxides. The reaction proceeds by catalysis in single‐electron steps. The oxidative addition comprises an epoxide opening. An H‐atom transfer, to generate a benzylic radical, serves as a radical translocation step, and an organometallic oxygen rebound as a reductive elimination. The reaction mechanism was studied by high‐level dispersion corrected hybrid functional DFT with implicit solvation. The low‐energy conformational space was searched by the efficient CREST program. The stereoselectivity was deduced from the lowest lying benzylic radical structures and their conformations are controlled by hyperconjugative interactions and steric interactions between the titanocene catalyst and the aryl groups of the substrate. An interesting mechanistic aspect is that the oxidation of the benzylic center occurs under reducing conditions.

Improvement of d-d interactions in density functional tight binding for transition metal ions with a ligand field model: assessment of a DFTB3+U model on nickel coordination compounds

To improve the description of interactions among the localized d, f electrons in transition metals, we have introduced a ligand-field motivated contribution into the Density Functional Tight Binding (DFTB) model. Referred to as DFTB3+U, the approach treats the d, f electron repulsions with rotationally invariant orbital-orbital interactions and a Hartree-Fock model; this represents a major conceptual improvement over the original DFTB3 approach, which treats the d, f-shell interactions in a highly averaged fashion without orbital level of description. The DFTB3+U approach is tested using a series of nickel compounds that feature Ni(ii) and Ni(iii) oxidation states. By using parameters developed with the original DFTB3 Hamiltonian and empirical +U parameters (F0/2/4 Slater integrals), we observe that the DFTB3+U model indeed provides substantial improvements over the original DFTB3 model for a number of properties of the nickel compounds, including the population and spin polarization of the d-shell, nature of the frontier orbitals, ligand field splitting and the energy different between low and high spin states at OPBE optimized structures. This proof-of-concept study suggests that with self-consistent parameterization of the electronic and +U parameters, the DFTB3+U model can develop into a promising model that can be used to efficiently study reactive events involving transition metals ion condensed phase systems. The methodology can be integrated with other approximate QM methods as well, such as the extended tight binding (xTB) approach.