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.

Benchmark Study on the Calculation of 207Pb NMR Chemical Shifts.

A benchmark set for the computation of 207Pb nuclear magnetic resonance (NMR) chemical shifts is presented. The PbS50 set includes conformer ensembles of 50 lead-containing molecular compounds and their experimentally measured 207Pb NMR chemical shifts. Various bonding motifs at the Pb center with up to seven bonding partners are included. Six different solvents were used in the measurements. The respective shifts lie in the range between +10745 and -5030 ppm. Several calculation settings are assessed by evaluating computed 207Pb NMR shifts for the use with different density functional approximations (DFAs), relativistic approaches, treatment of the conformational space, and levels for geometry optimization. Relativistic effects were included explicitly with the zeroth order regular approximation (ZORA), for which only the spin-orbit variant was able to yield reliable results. In total, seven GGAs and three hybrid DFAs were tested. Hybrid DFAs significantly outperform GGAs. The most accurate DFAs are mPW1PW with a mean absolute deviation (MAD) of 429 ppm and PBE0 with an MAD of 446 ppm. Conformational influences are small as most compounds are rigid, but more flexible structures still benefit from Boltzmann averaging. Including explicit relativistic treatments such as SO-ZORA in the geometry optimization does not show any significant improvement over the use of effective core potentials (ECPs).

Improving Quantum Chemical Solvation Models by Dynamic Radii Adjustment for Continuum Solvation (DRACO).

We present the Dynamic Radii Adjustment for COntinuum solvation (DRACO) approach, which employs precomputed atomic partial charges and coordination numbers of the solute atoms to improve the solute cavity. As such, DRACO is compatible with major solvation models, improving their performance significantly and robustly at virtually no extra cost, especially for charged solutes. Combined with the purely electrostatic CPCM and COSMO models, DRACO reduces the mean absolute deviation (MAD) of the solvation free energy by up to 4.5 kcal mol-1 (67%) for a large data set of polar and ionic solutes. Even in combination with the highly empirical universal solvation model (SMD), DRACO substantially reduces the MAD for charged solutes by up to 1.5 kcal mol-1 (39%), while neutral solutes are slightly improved (0.2 kcal mol-1 or 16%). We present an interface of DRACO with two computationally efficient atomic charge models that enables fully automated, out-of-the-box calculations with the widely used program packages Orca and TurboMole.

Hybrid DFT Geometries and Properties for 17k Lanthanoid Complexes─The LnQM Data Set.

The unique properties of lanthanoids and their diverse applications make them an indispensable part of modern research and industry. While the field has garnered attention, there remains a gap in available molecule data sets that facilitate both classical quantum chemistry calculations and the burgeoning field of machine learning in data science applications. This research addresses the need for a comprehensive data set that allows for a comparative analysis of various lanthanoids. The herein presented, curated data set includes 17269 monolanthanoid complexes derived from 1205 distinct ligand motifs. Structures encompass all 15 lanthanoids in the +3 oxidation state and exhibit molecular charges ranging from -1 to +3, including structures with a high spin multiplicity up to 8. Starting from lanthanum complexes, samples were processed with a permutation of the central lanthanoid atom, resulting in highly comparable subsets, facilitating comparative studies in which the influence of the lanthanoid can be investigated independently of ligand effects. The data set provides a broad range of features such as PBE0-D4/def2-SVP optimized geometries and optimization trajectories, while also covering ωB97M-V/def2-SVPD energies, rotational constants, dipole moments, highest occupied molecular orbital-lowest-unoccupied molecular orbital (HOMO-LUMO) energies, and Mulliken, Löwdin, and Hirshfeld population analyses. Additionally, coordination numbers, polarizabilities, and partial charges from D4, electronegativity equilibration (EEQ), GFN2-xTB, and charge extended Hückel (CEH) calculations are included. The data set is openly accessible and may serve as a basis for further investigations into the properties of lanthanoids.

Machine learning-based correction for spin-orbit coupling effects in NMR chemical shift calculations.

As one of the most powerful analytical methods for molecular and solid-state structure elucidation, NMR spectroscopy is an integral part of chemical laboratories associated with a great research interest in its computational simulation. Particularly when heavy atoms are present, a relativistic treatment is essential in the calculations as these influence also the nearby light atoms. In this work, we present a Δ-machine learning method that approximates the contribution to 13C and 1H NMR chemical shifts that stems from spin-orbit (SO) coupling effects. It is built on computed reference data at the spin-orbit zeroth-order regular approximation (ZORA) DFT level for a set of 6388 structures with 38 740 13C and 64 436 1H NMR chemical shifts. The scope of the methods covers the 17 most important heavy p-block elements that exhibit heavy atom on the light atom (HALA) effects to covalently bound carbon or hydrogen atoms. Evaluated on the test data set, the approach is able to recover roughly 85% of the SO contribution for 13C and 70% for 1H from a scalar-relativistic PBE0/ZORA-def2-TZVP calculation at virtually no extra computational costs. Moreover, the method is transferable to other baseline DFT methods even without retraining the model and performs well for realistic organotin and -lead compounds. Finally, we show that using a combination of the new approach with our previous Δ-ML method for correlation contributions to NMR chemical shifts, the mean absolute NMR shift deviations from non-relativistic DFT calculations to experimental values can be halved.

Confined Lewis Pairs: Investigation of the X- →Si20 Interaction in Halogen-Encapsulating Silafulleranes.

A joint theoretical and experimental study on 32 endohedral silafullerane derivatives [X@Si20 Y20 ]- (X=F-I; Y=F-I, H, Me, Et) and T h ${T_h }$ -[Cl@Si20 H12 Y8 ]- (Y=F-I) is presented. First, we evaluated the structure-determining template effect of Cl- in a systematic series of concave silapolyquinane model systems. Second, we investigated the X- →Si20 interaction energy ( E int ${E_{{\rm{int}}} }$ ) as a function of X- and Y and found the largest E int ${E_{{\rm{int}}} }$ values for electron-withdrawing exohedral substituents Y. Given that X- ions can be considered as Lewis bases and empty Si20 Y20 clusters as Lewis acids, we classify our inseparable host-guest complexes [X@Si20 Y20 ]- as "confined Lewis pairs". Third, 35 Cl NMR spectroscopy proved to be highly diagnostic for an experimental assessment of the Cl- →Si20 interaction as the paramagnetic shielding and, in turn, δ ${\delta }$ (35 Cl) of the endohedral Cl- ion correlate inversely with E int ${E_{{\rm{int}}} }$ . Finally, we disclose the synthesis of [PPN][Cl@Si20 Y20 ] (Y=Me, Et, Br) and provide a thorough characterization of these new silafulleranes.

Influence of Steric and Dispersion Interactions on the Thermochemistry of Crowded (Fluoro)alkyl Compounds.

ConspectusAlkanes play a pivotal role in industrial, environmental, and biological processes. They are characterized by their carbon-carbon single-bond structure, remarkable stability, and conformational diversity. Fluorination of such compounds imparts unique physicochemical properties that often enhance pharmacokinetic profiles, metabolic stability, and receptor interactions while keeping beneficial properties. However, such per- and polyfluoroalkyl substances (PFAS) show a persistent presence in the environment and potential adverse health effects, which propelled them to the forefront of global environmental and health discussions. Alkyl compounds are also prototypical for stereoelectronic (SE) effects that are widely applied in chemistry. Substituents are typically described as electron-density-donating/withdrawing and/or responsible for sterically interacting with reagents or strategic groups in the molecule. That alkane branching can result in higher stability compared to less-branched isomers has been investigated in detail also by testing quantum chemical methods, in particular density functional theory (DFT). Alkane branching results in spatially compact structures with close intramolecular contacts so that at a specific size the detailed balance of attractive London dispersion and covalent versus repulsive Pauli exchange interactions shifts to new, chemically unfragile situations. This may lead to dissociation at room temperature and opens the central question: what is the smallest crowed alkane that cannot be made synthetically? In this Account, we try to shed light on the interplay among the various (free) energy components for crowded (fluoro)alkane dissociation. In this context, homolytic cleavage of the central C-C bond in a series of model alkanes of increasing size with tert-butyl (tBu), adamantyl (Ad), and [1.1.1]propellanyl (Prop) substituents is investigated. Reference energies are calculated at the PNO-LCCSD(T)-F12b level and used to benchmark the performance of contemporary DFT functionals. In line with previous conclusions, the application of dispersion corrections to density functionals is mandatory. For crowed structures, the accurate description of the midrange correlation effects, specifically repulsive van der Waals interactions, is crucial, and we observed that the density-dependent VV10 correction is superior to D4 in this context, although the asymptotic region is better described by the latter. The best available dispersion-inclusive functionals show systematic and reasonably small residual errors and can be safely applied to large systems (>100 atoms), for which coupled cluster methods with large basis sets are not computationally feasible anymore. For qualitatively correct predictions of synthetic accessibility under equilibrium conditions (free energy), the inclusion of thermostatistical (entropy) contributions is also essential. According to our results, tetra-tert-butylmethane (C17tBu) is the largest and most crowded system with a positive dissociation free energy and should be synthesizable. The difference between hydrogenated and perfluorinated systems originates from the increase in the steric repulsion of spatially close substituents, which is not compensated to the same extent by attractive orbital and dispersion interactions. A sometimes-assumed similar steric demand for fluorine and hydrogen atoms is not corroborated by our investigations on crowded systems. Perfluorination is found to substantially decrease thermal stability, rendering perfluorinated hexamethylethane (C8tBuF) the last potentially stable representative.

Dispersion-corrected r2SCAN based double-hybrid functionals.

The regularized and restored semi-local 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 adiabatic-connection-derived global double-hybrid functionals employing spin-opposite-scaled MP2. The 0-DH, CIDH, QIDH, and 0-2 type double-hybrid functionals are assessed as a starting point for further modification. Variants with 50% and 69% Hartree-Fock exchange (HFX) are empirically optimized (Pr2SCAN50 and Pr2SCAN69), and the effect of MP2-regularization (κPr2SCAN50) and range-separated HFX (ωPr2SCAN50) is evaluated. All optimized functionals are combined with the state-of-the-art London dispersion corrections D4 and NL. The resulting functionals are assessed comprehensively for their performance on main-group and metal-organic thermochemistry on 90 different benchmark sets containing 25 800 data points. These include the extensive GMTKN55 database, additional sets for main-group chemistry, and multiple sets for transition-metal complexes, including the ROST61, the MOR41, and the MOBH35 sets. As the main target of this study is the development of a broadly applicable, robust functional with low empiricism, special focus is put on variants with moderate amounts of HFX (50%), which are compared to the so far successful PWPB95-D4 (50% HFX, 20% MP2 correlation) functional. The overall best variant, ωPr2SCAN50-D4, performs well on main-group and metal-organic thermochemistry, followed by Pr2SCAN69-D4 that offers a slight edge for metal-organic thermochemistry and by the low HFX global double-hybrid Pr2SCAN50-D4 that performs robustly across all tested sets. All four optimized functionals, Pr2SCAN69-D4, Pr2SCAN50-D4, κPr2SCAN50-D4, and ωPr2SCAN50-D4, outperform the PWPB95-D4 functional.

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.

Modular Bicyclophane-Based Molecular Platforms.

The modular synthesis of a series of nanoscale phenylene bicyclophanes with an intraannular orthogonal pillar is described. The compounds are obtained by a Suzuki cross-coupling condensation and are characterized by mass spectrometry and NMR spectroscopy as well as in situ scanning tunneling microscopy at the solid/liquid interface of highly ordered pyrolytic graphite. In addition, their structures and conformations are supported by quantum chemical calculations, also after adsorption to the substrate. A set of two alkyl chain substitution patterns as well as a combination of both were investigated with respect to their ability to form extended 2D-crystalline superstructures on graphite. It shows that not the most densely packed surface coverage gives the most stable structure, but the largest number of alkyl chains per molecule determines the structural robustness to alterations at the pillar functionality.

ONIOM meets xtb: 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.

Brominated [20]silafulleranes: pushing the limits of steric loading.

Starting from the perhydrogenated silafullerane [nBu4N][Cl@Si20(SiH3)12H8], treatment with BBr3 leads to partially and exhaustively brominated clusters, [nBu4N][Cl@Si20(SiBr2H)12Br8] (120 eq. BBr3, room temperature, 30 min) and [nBu4N][Cl@Si20(SiBr3)12Br8] (300 eq. BBr3, 130 °C, 3 d). Perbromination is accompanied by a massively increased steric strain on the cluster surface, which explains why our approach achieves regioselective derivatization of the Si32 framework when mild conditions are maintained. Partial Br/H exchange on [nBu4N][Cl@Si20(SiBr2H)12Br8] (30 eq. iBu2AlH, room temperature, 16 h) affords [nBu4N][Cl@Si20(SiH3)12Br8].

Regioselective Derivatization of Silylated [20]Silafulleranes.

Silafulleranes with endohedral Cl- ions are a unique, scarcely explored class of structurally well-defined silicon clusters and host-guest complexes. Herein, we report regioselective derivatization reactions on the siladodecahedrane [nBu4N][Cl@Si20(SiCl3)12Cl8] ([nBu4N][1]), which has its cluster surface decorated with 12 SiCl3 and 8 Cl substituents in perfect Th symmetry. The room-temperature reaction of [nBu4N][1] with excess iBu2AlH in ortho-difluorobenzene (oDFB) furnishes perhydrogenated [nBu4N][Cl@Si20(SiH3)12H8] ([nBu4N][2]) in 50% yield; the non-pyrophoric [2]- is the largest structurally authenticated (by X-ray diffraction) hydridosilane known to date. A simple switch from pure oDFB to an oDFB/Et2O solvent mixture suppresses core hydrogenation and results in the formation of [nBu4N][Cl@Si20(SiH3)12Cl8] ([nBu4N][3]). In addition to the exhaustive Cl/H exchange at all 44 Si-Cl bonds of [1]- and the regioselective 36-fold silyl group hydrogenation, we achieved the simultaneous introduction of Me substituents at all 8 SiCl vertices along with the conversion of all 12 SiCl3 to SiH3 groups by treating [nBu4N][1] with Me2AlH/Me3Al in oDFB ([nBu4N][Cl@Si20(SiH3)12Me8], [nBu4N][4]; 73%). Quantum-chemical free-energy calculations find an SN2-Si-type hydrogenation of the exohedral SiCl3 moieties in [1]- (trigonal-bipyramidal intermediate) slightly preferred over metathesis-like SNi-Si substitutions (four-membered transition state). Cage hydrogenation likely occurs via SNi-Si processes. The experimentally demonstrated influence of an Et2O co-solvent, which drastically increases the respective reaction barriers, is attributed to the increased stability of the resulting iBu2AlH-OEt2 adduct and its higher steric bulk compared to free iBu2AlH.

London Dispersion Effects in a Distannene/Tristannane Equilibrium: Energies of their Interconversion and the Suppression of the Monomeric Stannylene Intermediate.

Reaction of {LiC6 H2 -2,4,6-Cyp3 ⋅Et2 O}2 (Cyp=cyclopentyl) (1) of the new dispersion energy donor (DED) ligand, 2,4,6-triscyclopentylphenyl with SnCl2 afforded a mixture of the distannene {Sn(C6 H2 -2,4,6-Cyp3 )2 }2 (2), and the cyclotristannane {Sn(C6 H2 -2,4,6-Cyp3 )2 }3 (3). 2 is favored in solution at higher temperature (345 K or above) whereas 3 is preferred near 298 K. Van't Hoff analysis revealed the 3 to 2 conversion has a ΔH=33.36 kcal mol-1 and ΔS=0.102 kcal mol-1 K-1 , which gives a ΔG300 K =+2.86 kcal mol-1 , showing that the conversion of 3 to 2 is an endergonic process. Computational studies show that DED stabilization in 3 is -28.5 kcal mol-1 per {Sn(C6 H2 -2,4,6-Cyp3 )2 unit, which exceeds the DED energy in 2 of -16.3 kcal mol-1 per unit. The data clearly show that dispersion interactions are the main arbiter of the 3 to 2 equilibrium. Both 2 and 3 possess large dispersion stabilization energies which suppress monomer dissociation (supported by EDA results).

Computational study of ground-state properties of µ2 -bridged group 14 porphyrinic sandwich complexes.

The structural properties of µ2 -bridged porphyrinic double-decker complexes are investigated and the influence of various ligands, metals, substituents, and bridging atoms on the dominant structural motif is elucidated. A variety of quantum chemical methods including semiempirical (SQM) methods and density functional theory (DFT) is assessed for the calculation of ecliptic and staggered conformational energies. Local coupled cluster (DLPNO-CCSD(T1)) data are generated for reference. The r2 SCAN-3c composite scheme as well as the B2PLYP-D4/def2-QZVPP approach are identified as reliable methods. Energy decomposition analyses (EDA) and localized molecular orbital analyses (LMO) are used to investigate the bonding situation and the nature of the inter-ligand interaction energy underlining the crucial role of attractive London dispersion interactions. Targeted modification of the bridging atom, e.g., by replacing O2- by S2- is shown to drastically change the major structural features of the investigated complexes. Further, the influence of different substituents of varying size at the phthalocyanine ligand regarding the dominant conformation is described.

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.

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.

Benchmark Study on the Calculation of 119Sn NMR Chemical Shifts.

A new benchmark set termed SnS51 for assessing quantum chemical methods for the computation of 119Sn NMR chemical shifts is presented. It covers 51 unique 119Sn NMR chemical shifts for a selection of 50 tin compounds with diverse bonding motifs and ligands. The experimental reference data are in the spectral range of ±2500 ppm measured in seven different solvents. Fifteen common density functional approximations, two scalar- and one spin-orbit relativistic approach are assessed based on conformer ensembles generated using the CREST/CENSO scheme and state-of-the-art semiempirical (GFN2-xTB), force field (GFN-FF), and composite DFT methods (r2SCAN-3c). Based on the results of this study, the spin-orbit relativistic method combinations of SO-ZORA with PBE0 or revPBE functionals are generally recommended. Both yield mean absolute deviations from experimental data below 100 ppm and excellent linear regression determination coefficients of ≤0.99. If spin-orbit calculations are not affordable, the use of SR-ZORA with B3LYP or X2C with ωB97X or M06 may be considered to obtain qualitative predictions if no severe spin-orbit effects, for example, due to heavy nuclei containing ligands, are expected. An empirical linear scaling correction is demonstrated to be applicable for further improvement, and respective empirical parameters are given. Conformational effects on chemical shifts are studied in detail but are mostly found to be small. However, in specific cases when the ligand sphere differs substantially between conformers, chemical shifts can change by up to several hundred ppm.

Designing a Solution-Stable Distannene: The Decisive Role of London Dispersion Effects in the Structure and Properties of {Sn(C6H2-2,4,6-Cy3)2}2 (Cy = Cyclohexyl).

The reaction of 1 equiv of the dimeric lithium salt of a new London dispersion effect donor ligand {Li(C6H2-2,4,6-Cy3)·OEt2}2 (Cy = cyclohexyl) with SnCl2 afforded the distannene {Sn(C6H2-2,4,6-Cy3)2}2 (1). The distannene remains dimeric in solution, as indicated by its room-temperature 119Sn NMR signal (δ = 361.3 ppm) and its electronic spectrum, which is invariant over the temperature range of -10 to 100 °C. The formation of the distannene, which has a short Sn-Sn distance of 2.7005(7) Å and greatly enhanced stability in solution compared to that of other distannenes, is due to increased interligand London dispersion (LD) attraction arising from multiple close approaches of ligand C-H moieties across the Sn-Sn bond. DFT-D4 calculations revealed a dispersion stabilization of dimer 1 of 38 kcal mol-1 and a dimerization free energy of ΔGdimer = -6 kcal mol-1. In contrast, the reaction of 2 equiv of the similarly shaped but less bulky, less hydrogen-rich Li(C6H2-2,4,6-Ph3)·(OEt2)2 with SnCl2 yielded the monomeric stannylene Sn(C6H2-2,4,6-Ph3)2 (2), which is unstable in solution at ambient temperature.