Self-Consistent Field Calculation of Nuclear Magnetic Resonance Chemical Shielding Constants Using Gauge-Including Atomic Orbitals and Approximate Two-Electron Integrals

1.3 Å Crystal Structure of E. coli Peptidyl-Prolyl Isomerase B with Uniform Substitution of Valine by (2S,3S)-4-Fluorovaline Reveals Structure Conservation and Multiple Staggered Rotamers of CH2F Groups

(2S,3S)-4-Fluorovaline (FVal) is an analogue of valine, where a single CH3 group is substituted by a CH2F group. In the absence of valine, E. coli valyl-tRNA synthetase uses FVal as a substitute, enabling the production of proteins uniformly labeled with FVal. Here, we describe the production and analysis of E. coli peptidyl-prolyl isomerase B where all 16 valine residues have been replaced by FVal synthesized with a 13C-labeled CH2F group. Although the melting temperature is lower by about 11 °C relative to the wild-type protein, the three-dimensional protein structure is almost completely conserved, as shown by X-ray crystallography. The CH2F groups invariably populate staggered rotamers. Most CH2F groups populate two different rotamers. The increased space requirement of fluorine versus hydrogen does not prohibit rotamers that position fluorine next to a backbone carbonyl carbon. 19F NMR spectra show a signal dispersion over 25 ppm. The most high-field shifted 19F resonances correlate with large 3JHF coupling constants, confirming the impact of the γ-gauche effect on the signal dispersion. The present work is the second experimental verification of the effect and extends its validity to fluorovaline. The abundance of valine in proteins and structural conservation with FVal renders this valine analogue attractive for probing proteins by 19F NMR spectroscopy.

Catalytic Upgrading of Acetaldehyde to Acetoin Using a Supported N-Heterocyclic Carbene Catalyst

We report the catalytic synthesis of 3-hydroxy-2-butanon (acetoin) from acetaldehyde as a key step in the synthesis of C4-molecules from ethanol. Facile C-C bond formation at the α-carbon of the C2 building block is achieved using an N-heterocyclic carbene (NHC) catalyst. The immobilization of the catalyst on a Merrifield's peptide resin and its spectroscopic characterisation using solid-state Nuclear Magnetic Resonance (NMR) is described herein. The immobilization of the NHC catalyst allows for process intensification steps and the reported catalytic system was subjected to batch recycling as well as continuous flow experiments. The robustness of the catalytic system was shown over a maximum of 10 h time-on-stream. Overall, high selectivity S>90 % was observed. The observed deactivation of the catalyst with increasing time-on-stream is explained by ex-situ 1H solution-state, as well as 13C and 15N solid-state NMR spectra allowing us to develop a deeper understanding of the underlying decomposition mechanism of the catalyst.

Investigation of Ln3+ complexation by a DOTA derivative substituted by an imidazothiadiazole: synthesis, solution structure, luminescence and relaxation properties

We investigated the coordination properties of original macrocyclic Ln3+ complexes comprising an imidazothiadiazole heterocycle. The thermodynamic stability of the Gd3+ complex was determined by a combination of potentiometric and photophysical measurements. The kinetic inertness was assessed in highly acidic media. The solution structure of the Ln3+ complex was unambiguously determined by a set of photophysical measurements and 1H, 13C, 89Y NMR data in combination with DFT calculations, which proved coordination of the heterocycle to Ln3+. The ability of the imidazothiadiazole moiety to sensitize Tb3+ luminescence was investigated. Finally, the relaxation properties were investigated by recording 1H nuclear magnetic relaxation dispersion (NMRD) profiles and 17O measurements. The water exchange rate is similar to that of GdDOTA as the less negative charge of the ligand is compensated for by the presence of a bulky heterocycle. Relaxivity is constant over a large range of pH values, demonstrating the favorable properties of the complex for imaging purposes.

Salophen-type Organocatalysts for the Cycloaddition of CO2 and Epoxides under Solvent, Halide, and Metal-Free Conditions

8-Formyl-7-hydroxycoumarin (A) and their derived salophen-type organocatalysts L1, L2, and L3 were used for the synthesis of cyclic carbonates from carbon dioxide (CO2) and epoxides under solvent-, halide-, and metal-free conditions. According to previous optimization tests, L1 and L2 had the best catalytic activity presenting 89 and 92% conversion toward the synthesis of 3-chloropropylene carbonate (2c) using 8 bar CO2, 100 °C at 9 h. Therefore, they were used as organocatalysts to complete the catalytic screening with 11 terminal epoxides (1a-k) exhibiting the highest TOF values of 20 and 22 h-1 using 1c and 1b, respectively. Similarly, they were tested with an internal epoxide, such as cyclohexene oxide (1l) exhibiting 72% conversion, becoming the first salophen organocatalyst to obtain cis-cyclohexane carbonate (2l) in the absence of a cocatalyst. In addition, a reaction mechanism was proposed for the formation of cyclic carbonates based on experimental data and computational techniques; these contributed in establishing a probable role of CO2 pressure along the catalysis and the hydrogen bonds that favor the stabilization of the different intermediates of the reaction.

Implementation and First Evaluation of Strong-Correlation-Corrected Local Hybrid Functionals for the Calculation of NMR Shieldings and Shifts

Local hybrid functionals containing strong-correlation factors (scLHs) and range-separated local hybrids (RSLHs) have been integrated into an efficient coupled-perturbed Kohn-Sham implementation for the calculation of nuclear shielding constants. Several scLHs and the ωLH22t RSLH have then been evaluated for the first time for the extended NS372 benchmark set of main-group shieldings and shifts and the TM70 benchmark of 3d transition-metal shifts. The effects of the strong-correlation corrections have been analyzed with respect to the spatial distribution of the sc-factors, which locally diminish exact-exchange admixture at certain regions in a molecule. The scLH22t, scLH23t-mBR, and scLH23t-mBR-P functionals, which contain a "damped" strong-correlation factor to retain the excellent performance of the underlying LH20t functional for weakly correlated situations, tend to make smaller corrections to shieldings and shifts than the "undamped" scLH22ta functional. While the latter functional can also deteriorate agreement with the reference data in certain weakly correlated cases, it provides overall better performance, in particular for systems where static correlation is appreciable. This pertains only to a minority of systems in the NS372 main-group test set but to many more systems in the TM70 transition-metal test set, in particular for high-oxidation-state complexes, e.g., Cr(+VI) complexes and other systems with stretched bonds. Another undamped scLH, the simpler LDA-based scLH21ct-SVWN-m, also tends to provide significant improvements in many cases. The differences between the functionals and species can be rationalized on the basis of one-dimensional plots of the strong-correlation factors, augmented by isosurface plots of the fractional orbital density (FOD). Position-dependent exact-exchange admixture is thus shown to provide substantial flexibility in treating response properties like NMR shifts for both weakly and strongly correlated systems.

High throughput selection of organic cathode materials

Efficient and affordable batteries require the design of novel organic electrode materials to overcome the drawbacks of the traditionally used inorganic materials, and the computational screening of potential candidates is a very efficient way to identify prospective solutions and minimize experimental testing. Here we present a DFT high-throughput computational screening where 86 million molecules contained in the PUBCHEM database have been analyzed and classified according to their estimated electrochemical features. The 5445 top-performing candidates were identified, and among them, 2306 are expected to have a one-electron reduction potential higher than 4 V versus (Li/Li+ ). Analogously, one-electron energy densities higher than 800 Whkg-1 have been predicted for 626 molecules. Explicit calculations performed for certain materials show that at least 69 candidates with a two-electron energy density higher than 1300 Whkg-1 . Successful molecules were sorted into several families, some of them already commonly used electrode materials, and others still experimentally untested. Most of them are small systems containing conjugated CO, NN, or NC functional groups. Our selected molecules form a valuable starting point for experimentalists exploring new materials for organic electrodes.

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.

Paramagnetic Nuclear Magnetic Resonance Shifts for Triplet Systems and Beyond with Modern Relativistic Density Functional Methods

An efficient framework for the calculation of paramagnetic NMR (pNMR) shifts within exact two-component (X2C) theory and (current-dependent) density functional theory (DFT) up to the class of local hybrid functionals (LHFs) is presented. Generally, pNMR shifts for systems with more than one unpaired electron depend on the orbital shielding contribution and a temperature-dependent term. The latter includes zero-field splitting (ZFS), hyperfine coupling (HFC), and the g-tensor. For consistency, we calculate these three tensors at the same level of theory, i.e., using scalar-relativistic X2C augmented with spin-orbit perturbation theory. Results for pNMR chemical shifts of transition-metal complexes reveal that this X2C-DFT framework can yield good results for both the shifts and the individual tensor contributions of metallocenes and related systems, especially if the HFC constant is large. For small HFC constants, the relative error is often large, and sometimes the sign may be off. 4d and 5d complexes with more complicated structures demonstrate the limitations of a fully DFT-based approach. Additionally, a Co-based complex with a very large ZFS and pronounced multireference character is not well described. Here, a hybrid DFT-multireference framework is necessary for accurate results. Our results show that X2C is sufficient to describe relativistic effects and computationally cheaper than a fully relativistic approach. Thus, it allows use of large basis sets for converged HFCs. Overall, current-dependent meta-generalized gradient approximations and LHFs show some potential; however, the currently available functionals leave a lot to be desired, and the predictive power is limited.

Elucidating the Electronic Nature of Rh-based Paddlewheel Catalysts from 103 Rh NMR Chemical Shifts: Insights from Quantum Mechanical Calculations

The tremendous importance of dirhodium paddlewheel complexes for asymmetric catalysis is largely the result of an empirical optimization of the chiral ligand sphere about the bimetallic core. It was only recently that a H(C)Rh triple resonance 103 Rh NMR experiment provided the long-awaited opportunity to examine - with previously inconceivable accuracy - how variation of the ligands impacts on the electronic structure of such catalysts. The recorded effects are dramatic: formal replacement of only one out of eight O-atoms surrounding the metal centers in a dirhodium tetracarboxylate by an N-atom results in a shielding of the corresponding Rh-site of no less than 1000 ppm. The current paper provides the theoretical framework that allows this and related experimental observations made with a set of 19 representative rhodium complexes to be interpreted. In line with symmetry considerations, it is shown that the shielding tensor responds only to the donor ability of the equatorial ligands along the perpendicular principal axis. Axial ligands, in contrast, have no direct effect on shielding but may come into play via the electronicc i s ${cis}$ -effect that they exert onto the neighboring equatorial sites. On top of these fundamental interactions, charge redistribution within the core as well as the electronict r a n s ${trans}$ -effect of ligands of different donor strengths is reflected in the recorded 103 Rh NMR shifts.

Revisiting Gauge-Independent Kinetic Energy Densities in Meta-GGAs and Local Hybrid Calculations of Magnetizabilities

In a recent study [J. Chem. Theory Comput. 2021, 17, 1457-1468], some of us examined the accuracy of magnetizabilities calculated with density functionals representing the local density approximation (LDA), generalized gradient approximation (GGA), meta-GGA (mGGA), as well as global hybrid (GH) and range-separated (RS) hybrid functionals by assessment against accurate reference values obtained with coupled-cluster theory with singles, doubles, and perturbative triples [CCSD(T)]. Our study was later extended to local hybrid (LH) functionals by Holzer et al. [J. Chem. Theory Comput. 2021, 17, 2928-2947]; in this work, we examine a larger selection of LH functionals, also including range-separated LH (RSLH) functionals and strong-correlation LH (scLH) functionals. Holzer et al. also studied the importance of the physically correct handling of the magnetic gauge dependence of the kinetic energy density (τ) in mGGA calculations by comparing the Maximoff-Scuseria formulation of τ used in our aforementioned study to the more physical current-density extension derived by Dobson. In this work, we also revisit this comparison with a larger selection of mGGA functionals. We find that the newly tested LH, RSLH, and scLH functionals outperform all of the functionals considered in the previous studies. The various LH functionals afford the seven lowest mean absolute errors while also showing remarkably small standard deviations and mean errors. Most strikingly, the best two functionals are scLHs that also perform remarkably well in cases with significant multiconfigurational character, such as the ozone molecule, which is traditionally excluded from statistical error evaluations due to its large errors with common density functionals.

Exact two-component theory becoming an efficient tool for NMR shieldings and shifts with spin-orbit coupling

We present a gauge-origin invariant exact two-component (X2C) approach within a modern density functional framework, supporting meta-generalized gradient approximations such as TPSS and range-separated hybrid functionals such as CAM-B3LYP. The complete exchange-correlation kernel is applied, including the direct contribution of the field-dependent basis functions and the reorthonormalization contribution from the perturbed overlap matrix. Additionally, the finite nucleus model is available for the electron-nucleus potential and the vector potential throughout. Efficiency is ensured by the diagonal local approximation to the unitary decoupling transformation in X2C as well as the (multipole-accelerated) resolution of the identity approximation for the Coulomb term (MARI-J, RI-J) and the seminumerical exchange approximation. Errors introduced by these approximations are assessed and found to be clearly negligible. The applicability of our implementation to large-scale calculations is demonstrated for a tin pincer-type system as well as low-valent tin and lead complexes. Here, the calculation of the Sn nuclear magnetic resonance shifts for the pincer-type ligand with about 2400 basis functions requires less than 1 h for hybrid density functionals. Further, the impact of spin-orbit coupling on the nucleus-independent chemical shifts and the corresponding ring currents of all-metal aromatic systems is studied.

Computation of CCSD(T)-Quality NMR Chemical Shifts via Δ-Machine Learning from DFT

NMR spectroscopy undoubtedly plays a central role in determining molecular structures across different chemical disciplines, and the accurate computational prediction of NMR parameters is highly desirable. In this work, a new Δ-machine learning approach is presented to correct DFT-computed NMR chemical shifts using input features from the calculation and in addition highly accurate reference data at the CCSD(T)/pcSseg-2 level of theory with a basis set extrapolation scheme. The model is trained on a data set containing 1000 optimized and geometrically distorted structures of small organic molecules comprising most elements of the first three periods and containing data for 7090 ¹H and 4230 ¹³C NMR chemical shifts. Applied to the PBE0/pcSseg-2 method, the mean absolute deviation (MAD) on the internal NMR shift test set is reduced by 81% for ¹H and 92% for ¹³C at virtually no additional computational cost. For 12 different DFT functional and basis set combinations, the MAD of the ML-corrected NMR shifts ranges from 0.021 to 0.039 ppm (¹H) and from 0.38 to 1.07 ppm (¹³C). Importantly, the new method consistently outperforms the simple and widely used linear regression correction technique. This behavior is reproduced on three different external benchmark sets, confirming the generality and robustness of the correction scheme, which can easily be applied in DFT-based spectral simulations.

Tristhiolato Pseudopeptides Bind Arsenic(III) in an AsS3 Coordination Environment Imitating Metalloid Binding Sites in Proteins

The AsIII binding of two NTA-based tripodal pseudopeptides, possessing three cysteine (ligand L1) or d-penicillamine residues (ligand L2) as potential coordinating groups for soft semimetals or metal ions, was studied by experimental (UV, CD, NMR, and ESI-MS) and theoretical (DFT) methods. All of the experimental data, obtained with the variation of the AsIII:ligand concentration ratios or pH values in some instances, evidence the exclusive formation of species with an AsS3-type coordination mode. The UV-monitored titration of the ligands with arsenous acid at pH = 7.0 provided an absorbance data set that allowed for the determination of apparent stability constants of the forming species. The obtained stabilities (logK' = 5.26 (AsL1) and logK' = 3.04 (AsL2)) reflect high affinities, especially for the sterically less restricted cysteine derivative. DFT calculated structures correlate well with the spectroscopic results and, in line with the 1H NMR data, indicate a preference for the all-endo conformers resembling the AsIII environment at the semimetal binding sites in various metalloproteins.

An in-silico NMR laboratory for nuclear magnetic shieldings computed via finite fields: Exploring nucleus-specific renormalizations of MP2 and MP3

We developed and implemented a method-independent, fully numerical, finite difference approach to calculating nuclear magnetic resonance shieldings, using gauge-including atomic orbitals. The resulting capability can be used to explore non-standard methods, given only the energy as a function of finite-applied magnetic fields and nuclear spins. For example, standard second-order Møller-Plesset theory (MP2) has well-known efficacy for 1H and 13C shieldings and known limitations for other nuclei such as 15N and 17O. It is, therefore, interesting to seek methods that offer good accuracy for 15N and 17O shieldings without greatly increased compute costs, as well as exploring whether such methods can further improve 1H and 13C shieldings. Using a small molecule test set of 28 species, we assessed two alternatives: κ regularized MP2 (κ-MP2), which provides energy-dependent damping of large amplitudes, and MP2.X, which includes a variable fraction, X, of third-order correlation (MP3). The aug-cc-pVTZ basis was used, and coupled cluster with singles and doubles and perturbative triples [CCSD(T)] results were taken as reference values. Our κ-MP2 results reveal significant improvements over MP2 for 13C and 15N, with the optimal κ value being element-specific. κ-MP2 with κ = 2 offers a 30% rms error reduction over MP2. For 15N, κ-MP2 with κ = 1.1 provides a 90% error reduction vs MP2 and a 60% error reduction vs CCSD. On the other hand, MP2.X with a scaling factor of 0.6 outperformed CCSD for all heavy nuclei. These results can be understood as providing renormalization of doubles amplitudes to partially account for neglected triple and higher substitutions and offer promising opportunities for future applications.

Reducing Exact Two-Component Theory for NMR Couplings to a One-Component Approach: Efficiency and Accuracy

The self-consistent and complex spin-orbit exact two-component (X2C) formalism for NMR spin-spin coupling constants [ J. Chem. Theory Comput. 17, 2021, 3874-3994] is reduced to a scalar one-component ansatz. This way, the first-order response term can be partitioned into the Fermi-contact (FC) and spin-dipole (SD) interactions as well as the paramagnetic spin-orbit (PSO) contribution. The FC+SD terms are real and symmetric, while the PSO term is purely imaginary and antisymmetric. The relativistic one-component approach is combined with a modern density functional treatment up to local hybrid functionals including the response of the current density. Computational demands are reduced by factors of 8-24 as shown for a large tin compound consisting of 137 atoms. Limitations of the current ansatz are critically assessed for Sn, Pb, Pd, and Pt compounds, i.e. the one-component treatment is not sufficient for tin compounds featuring a few heavy halogen atoms.

The structure of pathogenic huntingtin exon 1 defines the bases of its aggregation propensity

Huntington's disease is a neurodegenerative disorder caused by a CAG expansion in the first exon of the HTT gene, resulting in an extended polyglutamine (poly-Q) tract in huntingtin (httex1). The structural changes occurring to the poly-Q when increasing its length remain poorly understood due to its intrinsic flexibility and the strong compositional bias. The systematic application of site-specific isotopic labeling has enabled residue-specific NMR investigations of the poly-Q tract of pathogenic httex1 variants with 46 and 66 consecutive glutamines. Integrative data analysis reveals that the poly-Q tract adopts long α-helical conformations propagated and stabilized by glutamine side chain to backbone hydrogen bonds. We show that α-helical stability is a stronger signature in defining aggregation kinetics and the structure of the resulting fibrils than the number of glutamines. Our observations provide a structural perspective of the pathogenicity of expanded httex1 and pave the way to a deeper understanding of poly-Q-related diseases.

The SHARK integral generation and digestion system

In this paper, the SHARK integral generation and digestion engine is described. In essence, SHARK is based on a reformulation of the popular McMurchie/Davidson approach to molecular integrals. This reformulation leads to an efficient algorithm that is driven by BLAS level 3 operations. The algorithm is particularly efficient for high angular momentum basis functions (up to L = 7 is available by default, but the algorithm is programmed for arbitrary angular momenta). SHARK features a significant number of specific programming constructs that are designed to greatly simplify the workflow in quantum chemical program development and avoid undesirable code duplication to the largest possible extent. SHARK can handle segmented, generally and partially generally contracted basis sets. It can be used to generate a host of one- and two-electron integrals over various kernels including, two-, three-, and four-index repulsion integrals, integrals over Gauge Including Atomic Orbitals (GIAOs), relativistic integrals and integrals featuring a finite nucleus model. SHARK provides routines to evaluate Fock like matrices, generate integral transformations and related tasks. SHARK is the essential engine inside the ORCA package that drives essentially all tasks that are related to integrals over basis functions in version ORCA 5.0 and higher. Since the core of SHARK is based on low-level basic linear algebra (BLAS) operations, it is expected to not only perform well on present day but also on future hardware provided that the hardware manufacturer provides a properly optimized BLAS library for matrix and vector operations. Representative timings and comparisons to the Libint library used by ORCA are reported for Intel i9 and Apple M1 max processors.

Molecular Dynamics and Structural Studies of Zinc Chloroquine Complexes

Chloroquine (CQ) is a first-choice drug against malaria and autoimmune diseases. It has been co-administered with zinc against SARS-CoV-2 and soon dismissed because of safety issues. The structural features of Zn-CQ complexes and the effect of CQ on zinc distribution in cells are poorly known. In this study, state-of-the-art computations combined with experiments were leveraged to solve the structural determinants of zinc-CQ interactions in solution and the solid state. NMR, ESI-MS, and X-ray absorption and diffraction methods were combined with ab initio molecular dynamics calculations to address the kinetic lability of this complex. Within the physiological pH range, CQ binds Zn²⁺ through the quinoline ring nitrogen, forming [Zn(CQH)Cl_x(H₂O)_3-x]^(3+)-x (x = 0, 1, 2, and 3) tetrahedral complexes. The Zn(CQH)Cl₃ species is stable at neutral pH and at high chloride concentrations typical of the extracellular medium, but metal coordination is lost at a moderately low pH as in the lysosomal lumen. The pentacoordinate complex [Zn(CQH)(H₂O)₄]³⁺ may exist in the absence of chloride. This in vitro/in silico approach can be extended to other metal-targeting drugs and bioinorganic systems.

Electron Correlation or Basis Set Quality: How to Obtain Converged and Accurate NMR Shieldings for the Third-Row Elements?

The quality of theoretical NMR shieldings calculated at the quantum-chemical level depends on various theoretical aspects, of which the basis set type and size are among the most important factors. Nevertheless, not much information is available on the basis set effect on theoretical shieldings of the NMR-active nuclei of the third row. Here, we report on the importance of proper basis set selection to obtain accurate and reliable NMR shielding parameters for nuclei from the third row of the periodic table. All calculations were performed on a set of eleven compounds containing the elements Na, Mg, Al, Si, P, S, or Cl. NMR shielding tensors were calculated using the SCF-HF, DFT-B3LYP, and CCSD(T) methods, combined with the Dunning valence aug-cc-pVXZ, core-valence aug-cc-pCVXZ, Jensen polarized-convergent aug-pcSseg-n and Karlsruhe x2c-Def2 basis set families. We also estimated the complete basis set limit (CBS) values of the NMR parameters. Widely scattered nuclear shieldings were observed for the Dunning polarized-valence basis set, which provides irregular convergence. We show that the use of Dunning core-valence or Jensen basis sets effectively reduces the scatter of theoretical NMR results and leads to their exponential-like convergence to CBS. We also assessed the effect of vibrational, temperature, and relativistic corrections on the predicted shieldings. For systems with single bonds, all corrections are relatively small, amounting to less than 4% of the CCSD(T)/CBS value. Vibrational and temperature corrections were less reliable for H3PO and HSiCH due to the high anharmonicity of the molecules. An abnormally high relativistic correction was observed for phosphorus in PN, reaching ~20% of the CCSD(T)/CBS value, while the correction was less than 7% for other tested molecules.

In Situ Ternary Adduct Formation of Yttrium Polyaminocarboxylates Leads to Small Molecule Capture and Activation

In this work the chemistry of yttrium complexes is exploited for small molecule capture and activation. Nuclear magnetic resonance (NMR) and density functional theory (DFT) studies were used to investigate the in situ formation of solution state ternary yttrium-acetate, yttrium-bicarbonate, and yttrium-pyruvate adducts with a range of polyaminocarboxylate chelates. These studies reveal that [Y(DO3A)(H₂ O)₂ ] (H₃ DO3A - 1,4,7,10-tetraazacyclododecane-1,4,7-tricarboxylic acid) and [Y(EDTA)(H₂ O)_q ]^- (H₄ EDTA - ethylenediaminetetraacetic acid, q = 2 and 3) are able to form ternary adducts with bicarbonate and pyruvate. In the latter, unusual decarboxylation of pyruvate to form acetic acid and CO₂ was observed and further studied using SABRE-hyperpolarised ¹³ C NMR (SABRE - signal amplification by reversible exchange) to provide information about the reaction timescale and lifetime of intermediates involved in this conversion. The work presented demonstrates that yttrium complexes can capture and activate small molecules, which may lead to novel and useful applications of this metal in catalysis and medical imaging.

Between Two Chairs: Combination of Theory and Experiment for the Determination of the Conformational Dynamics of Xylosides

The conformational properties of monosaccharides constitute fundamental features of oligosaccharides. While the energy landscape of monosaccharides can be altered by a specific biochemical environment or by chemical modifications, the analysis of resulting dynamic conformational equilibria is not feasible by experimental means alone. In this work, a series of β-d-xylopyranosides is used to outline how a combination of experimental NMR parameters and computed molecular properties can be used to determine conformers and quantify the composition of conformational equilibria. We demonstrate that identifying the most stable conformers using energy calculations is challenging and computing of NMR shieldings is typically not sensitive enough. On the other hand, computed spin-spin coupling constants for the xyloside ring can be used to unambiguously assign experimental NMR data of dynamic conformational equilibria and quantify the ratio of different conformers in the mixture. As a proof of principle, this procedure allowed to analyze a hitherto unknown dynamic equilibrium of a diamino-xyloside as a precursor of a molecular switch.

Detailed Density Functional Theory Study of the Cationic Zirconocene Compound [Cp(C5H4CMe2C6H4F)ZrMe]. ACS OMEGA 2022;7:35136-35152. [PMID: 36211080 PMCID: PMC9535714 DOI: 10.1021/acsomega.2c04053]

Detailed density functional theory studies at the B3LYP and PBE-D3 levels of theory were performed on the cationic compound [Cp(C5H4CMe2C6H4F)ZrMe]+, with the F atom occupying either the ortho, meta, or para positions of the arene ring. In all cases, the arene ring coordinates with the cationic zirconium metal. The nature of this coordination is such that for the meta- or para-substituted arene ring, it is predominantly the ortho carbon atom of the C-H bond which interacts with the metal, as evident from noncovalent interaction studies. This is further corroborated by the natural bond orbital and quantum theory of atoms in molecular studies. In the case of the F atom being in the ortho position, we obtained clear-cut evidence for a Zr-F coordination.

Accurate Prediction of Nuclear Magnetic Resonance Parameters via the XYG3 Type of Doubly Hybrid Density Functionals

Nuclear magnetic resonance (NMR) spectroscopy is one of the most powerful and versatile tools in elucidating molecular structures. To eliminate ambiguities of experimental assignments, accurate calculations of NMR spectra are of great importance. Here, a method for theoretical evaluation of the NMR shielding constants by analytic derivatives using gauge including atomic orbitals (GIAO) has been implemented for the XYG3 type of doubly hybrid density functionals (xDH), namely, the GIAO-xDH method. Benchmark calculations on shielding constants and chemical shifts demonstrate the remarkable accuracy of the GIAO-xDH method, compared to the accurate CCSD(T) references. It is shown here that the XYGJ-OS functional is able to give a mean absolute deviation (MAD) of ∼3.0 ppm in the calculated shielding constants for ¹³C, ¹⁵N, ¹⁷O, ¹⁹F, while both XYGJ-OS and xDH-PBE0 functionals are able to provide a satisfactory estimation of chemical shifts with MADs of ∼0.03 and 1.0 ppm for ¹H and ¹³C, respectively. The basis set influence upon the method has been examined and a computational scheme considering both accuracy and efficiency has been proposed and tested to predict the experimental ¹³C chemical shifts of five medium-sized natural product molecules, yielding a MAD of ∼1.0 ppm, which demonstrates the practical feasibility of the GIAO-xDH method.

Versatile Macrocyclic Platform for the Complexation of [natY/90Y]Yttrium and Lanthanide Ions

We report a macrocyclic ligand (H3L6) based on a 3,6,10,13-tetraaza-1,8(2,6)-dipyridinacyclotetradecaphane platform containing three acetate pendant arms and a benzyl group attached to the fourth nitrogen atom of the macrocycle. The X-ray structures of the YL6 and TbL6 complexes reveal nine coordination of the ligand to the metal ions through the six nitrogen atoms of the macrocycle and three oxygen atoms of the carboxylate pendants. A combination of NMR spectroscopic studies (1H, 13C, and 89Y) and DFT calculations indicated that the structure of the YL6 complex in the solid state is maintained in an aqueous solution. The detailed study of the emission spectra of the EuL6 and TbL6 complexes revealed Ln3+-centered emission with quantum yields of 7.0 and 60%, respectively. Emission lifetime measurements indicate that the ligand offers good protection of the metal ions from surrounding water molecules, preventing the coordination of water molecules. The YL6 complex is remarkably inert with respect to complex dissociation, with a lifetime of 1.7 h in 1 M HCl. On the other hand, complex formation is fast (∼1 min at pH 5.4, 2 × 10-5 M). Studies using the 90Y-nuclide confirmed fast radiolabeling since [90Y]YL6 is nearly quantitatively formed (radiochemical yield (RCY) > 95) in a short time over a broad range of pH values from ca. 2.4 to 9.0. Challenging experiments in the presence of excess ethylenediaminetetraacetic acid (EDTA) and in human serum revealed good stability of the [90Y]YL6 complex. All of these experiments combined suggest the potential application of H3L6 derivatives as Y-based radiopharmaceuticals.

Statistical evaluation of simulated NMR data of flexible molecules

A new probability score-named χ-probability-is introduced for evaluating the fit of mixed NMR datasets to calculate molecular model ensembles, in order to answer challenging structural questions such as the determination of stereochemical configurations. Similar to the DP4 parameter, the χ-probability is based on Bayes theorem and expresses the probability that an experimental NMR dataset fits to a given individual within a finite set of candidate structures or configurations. Here, the χ-probability is applied to single out the correct configuration in four example cases, with increasing complexity and conformational mobility. The NMR data (which include RDCs, NOE distances and ³J couplings) are calculated from MDOC (Molecular Dynamics with Orientational Constraints) trajectories and are investigated against experimentally measured data. It is demonstrated that this approach singles out the correct stereochemical configuration with probabilities more than 98%, even for highly mobile molecules. In more demanding cases, a decisive χ-probability test requires that the datasets include high-quality NOE distances in addition to RDC values.

High Level Electronic Structure Calculation of Molecular Solid-State NMR Shielding Constants

In this work, we present a quantum mechanics/molecular mechanics (QM/MM) approach for the computation of solid-state nuclear magnetic resonance (SS-NMR) shielding constants (SCs) for molecular crystals. Besides applying standard-DFT functionals like GGAs (PBE), meta-GGAs (TPSS), and hybrids (B3LYP), we apply a double-hybrid (DSD-PBEP86) functional as well as MP2, using the domain-based local pair natural orbital (DLPNO) formalism, to calculate the NMR SCs of six amino acid crystals. All the electronic structure methods used exhibit good correlation of the NMR shieldings with respect to experimental chemical shifts for both 1H and 13C. We also find that local electronic structure is much more important than the long-range electrostatic effects for these systems, implying that cluster approaches using all-electron/Gaussian basis set methods might offer great potential for predictive computations of solid-state NMR parameters for organic solids.

Quasi-Relativistic Calculation of EPR g Tensors with Derivatives of the Decoupling Transformation, Gauge-Including Atomic Orbitals, and Magnetic Balance

We present an exact two-component (X2C) ansatz for the EPR g tensor using gauge-including atomic orbitals (GIAOs) and a magnetically balanced basis set expansion. In contrast to previous X2C and four-component relativistic ansätze for the g tensor, this implementation results in a gauge-origin-invariant formalism. Furthermore, the derivatives of the relativistic decoupling matrix are incorporated to form the complete analytical derivative of the X2C Hamiltonian. To reduce the associated computational costs, we apply the diagonal local approximation to the unitary decoupling transformation (DLU). The quasi-relativistic X2C and DLU-X2C Hamiltonians accurately reproduce the results of the parent four-component relativistic theory when accounting for two-electron picture-change effects with the modified screened nuclear spin-orbit approximation in the respective one-electron integrals and integral derivatives. According to our benchmark studies, the uncontracted Dyall and segmented-contracted Karlsruhe x2c-type basis sets perform well when compared to large even-tempered basis sets. Moreover, (range-separated) hybrid density functional approximations such as LC-ωPBE and ωB97X-D are needed to match the experimental findings. The impact of the GIAOs depends on the distribution of the spin density, and their use may change the Δg shifts by 10-50% as shown for [(C₅Me₅)₂Y(μ-S)₂Mo(μ-S)₂Y(C₅Me₅)₂]^-. Routine calculations of large molecules are possible with widely available and comparably low-cost hardware as demonstrated for [Pt(C₆Cl₅)₄]^- with 3003 basis functions and three spin-(1/2) La(II) and Lu(II) compounds, for which we observe good agreement with the experimental findings.

An Investigation of the Predominant Structure of Antibiotic Azithromycin in Chloroform Solution through NMR and Thermodynamic Analysis

Azithromycin (AZM) is a well-known macrolide-type antibiotic that has been used in the treatment of infections and inflammations. Knowledge of the predominant molecular structure in solution is a prerequisite for...

Systematic Evaluation of Modern Density Functional Methods for the Computation of NMR Shifts of 3d Transition-Metal Nuclei

A wide range of density functionals from all rungs of Jacob's ladder have been evaluated systematically for a set of experimental 3d transition-metal NMR shifts of 70 complexes encompassing 12 × ⁴⁹Ti, 10 × ⁵¹V, 10 × ⁵³Cr, 11 × ⁵⁵Mn, 9 × ⁵⁷Fe, 9 × ⁵⁹Co, and 9 × ⁶¹Ni shift values, as well as a diverse range of electronic structure characteristics. The overall 39 functionals evaluated include one LDA, eight GGAs, seven meta-GGAs (including their current-density-functional─CDFT─versions), nine global hybrids, four range-separated hybrids, eight local hybrids, and two double hybrids, and we also include Hartree-Fock and MP2 calculations. While recent evaluations of the same functionals for a very large coupled-cluster-based benchmark of main-group shieldings and shifts achieved in some cases aggregate percentage mean absolute errors clearly below 2%, the best results for the present 3d-nuclei set are in the range between 4 and 5%. Strikingly, the overall best-performing functionals are the recently implemented CDFT versions of two meta-GGAs, namely cM06-L (4.0%) and cVSXC (4.3%), followed by cLH14t-calPBE (4.9%), B3LYP (5.0%), and cLH07t-SVWN (5.1%), i.e., the previously best-performing global hybrid and two local hybrids. A number of further functionals achieve aggregate deviations in the range 5-6%. Range-separated hybrids offer no particular advantage over global hybrids. Due to the overall poor performance of Hartree-Fock theory for all systems except the titanium complexes, MP2 and double-hybrid functionals are unsuitable for these 3d-nucleus shifts and provide large errors. Global hybrid functionals with larger EXX admixtures, such as BHLYP or M06-2X, also perform poorly, and some other highly parametrized global hybrids also are unsuitable. For many functionals depending on local kinetic energy τ, their CDFT variants perform much better than their "non-CDFT" versions. This holds notably also for the above-mentioned M06-L and VSXC, while the effect is small for τ-dependent local hybrids and can even be somewhat detrimental to the agreement with experiment for a few other cases. The separation between well-performing and more poorly performing functionals is mainly determined by their results for the most critical nuclei ⁵⁵Mn, ⁵⁷Fe, and ⁵⁹Co. Here either moderate exact-exchange admixtures or CDFT versions of meta-GGAs are beneficial for the accuracy. The overall deviations of the better-performing global or local hybrids are then typically dominated by the ⁵³Cr shifts, where triplet instabilities appear to disfavor exact-exchange admixture. Further detailed analyses help to pinpoint specific nuclei and specific types of complexes that are challenges for a given functional.

Hyperfine Coupling Constants in Local Exact Two-Component Theory

We present a highly efficient implementation of the electron-nucleus hyperfine coupling matrix within the one-electron exact two-component (X2C) theory. The complete derivative of the X2C Hamiltonian is formed, that is, the derivatives of the unitary decoupling transformation are considered. This requires the solution of the response and Sylvester equations, consequently increasing the computational costs. Therefore, we apply the diagonal local approximation to the unitary decoupling transformation (DLU). The finite nucleus model is employed for both the scalar potential and the vector potential. Two-electron picture-change effects are modeled with the (modified) screened nuclear spin-orbit approach. Our implementation is fully integral direct and OpenMP-parallelized. An extensive benchmark study regarding the Hamiltonian, the basis set, and the density functional approximation is carried out for a set of 12-17 transition-metal compounds. The error introduced by DLU is negligible, and the DLU-X2C Hamiltonian accurately reproduces its four-component "fully" relativistic parent results. Functionals with a large amount of Hartree-Fock exchange such as CAM-QTP-02 and ωB97X-D are generally favorable. The pure density functional r²SCAN performs remarkably and even outperforms the common hybrid functionals TPSSh and CAM-B3LYP. Fully uncontracted basis sets or contracted quadruple-ζ bases are required for accurate results. The capability of our implementation is demonstrated for [Pt(C₆Cl₅)₄]^- with more than 4700 primitive basis functions and four rare-earth single-molecule magnets: [La(OAr*)₃]^-, [Lu(NR₂)₃]^-, [Lu(OAr*)₃]^-, and [TbPc₂]^-. Here, the results with the spin-orbit DLU-X2C Hamiltonian are in an excellent agreement with the experimental findings of all Pt, La, Lu, and Tb molecules.

Extended Benchmark Set of Main-Group Nuclear Shielding Constants and NMR Chemical Shifts and Its Use to Evaluate Modern DFT Methods

An extended theoretical benchmark set, NS372, for light main-group nuclear shieldings and NMR shifts has been constructed based on high-level GIAO-CCSD(T)/pcSseg-3//CCSD(T)/cc-pVQZ reference data. After removal of the large static-correlation cases O₃, F₃^-, and BH from the statistical evaluations for the ¹⁷O, ¹⁹F, and ¹¹B subsets, the benchmark comprises overall 372 shielding values in 117 molecules with a wide range of electronic-structure situations, containing 124 ¹H, 14 ¹¹B, 93 ¹³C, 43 ¹⁵N, 31 ¹⁷O, 47 ¹⁹F, 14 ³¹P, and 6 ³³S shielding constants. The CCSD(T)/pcSseg-3 data are shown to be close to the basis-set and method limit and thus provide an excellent benchmark to evaluate more approximate methods, such as density functional approaches. This dataset has been used to evaluate Hartree-Fock (HF) and MP2, and a wide range of exchange-correlation functionals from local density approximation (LDA) to generalized gradient approximations (GGAs) and meta-GGAs (focusing on their current-density functional implementations), as well as global hybrid, range-separated hybrid, local hybrid, and double-hybrid functionals. Starting with absolute shielding constants, the DSD-PBEP86 double hybrid is confirmed to provide the highest accuracy, with an aggregate relative mean absolute error (rel. MAE) of only 0.9%, followed by MP2 (1.1%). MP2 and double hybrids only show larger errors for a few systems with the largest static-correlation effects. The double-hybrid B2GP-PLYP, the two local hybrids cLH12ct-SsirPW92 and cLH12ct-SsifPW92, and the current-density functional meta-GGA cB97M-V follow closely behind (all 1.5%), as do some further functionals, cLH20t and cMN15-L (both 1.6%), as well as B2PLYP and KT3 (both 2.0%). Functionals on the lower rungs of the usual ladder offer the advantage of lower computational cost and access to larger molecules. Closer examination also reveals the best-performing methods for individual nuclei in the test set. Different ways of treating τ-dependent functionals are evaluated. When moving from absolute shielding constants to chemical shifts, some of the methods can benefit from systematic error compensation, and the overall error range somewhat narrows. Further methods now achieve the 2% threshold of relative MAEs, including functionals based on TPSS (TPSSh, cmPSTS).

Surprising Complexity of the [Gd(AAZTA)(H2O)2]- Chelate Revealed by NMR in the Frequency and Time Domains

Typically, Ln(III) complexes are isostructural along the series, which enables studying one particular metal chelate to derive the structural features of the others. This is not the case for [Ln(AAZTA)(H₂O)_x]⁻ (x = 1, 2) systems, where structural variations along the series cause changes in the hydration number of the different metal complexes, and in particular the loss of one of the two metal-coordinated water molecules between Ho and Er. Herein, we present a ¹H field-cycling relaxometry and ¹⁷O NMR study that enables accessing the different exchange dynamics processes involving the two water molecules bound to the metal center in the [Gd(AAZTA)(H₂O)₂]⁻ complex. The resulting picture shows one Gd-bound water molecule with an exchange rate ∼6 times faster than that of the other, due to a longer metal–water distance, in accordance with density functional theory (DFT) calculations. The substitution of the more labile water molecule with a fluoride anion in a diamagnetic-isostructural analogue of the Gd-complex, [Y(AAZTA)(H₂O)₂]⁻, allows us to follow the chemical exchange process by high-resolution NMR and to describe its thermodynamic behavior. Taken together, the variety of tools offered by NMR (including high-resolution ¹H, ¹⁹F NMR as a function of temperature, ¹H longitudinal relaxation rates vs B₀, and ¹⁷O transverse relaxation rates vs T) provides a complete description of the structure and exchange dynamics of these Ln-complexes along the series.

Herein, we present a ¹H field−cycling relaxometry and ¹⁷O NMR study that enables accessing the different exchange dynamics processes involving the two water molecules bound to the metal center in the [Gd(AAZTA)(H₂O)₂]⁻ complex.

A new protocol for the identification of singlet fission sensitizers through computational screening

Although singlet fission presents deep advantages or the generation of solar energy, the list of efficient singlet fission sensitizers is still very short, encouraging the theoreticians to focus their efforts on selecting and designing new candidates. Here, it is presented a computational protocol for the efficient screening of databases to select those species matching the energy requirements for singlet fission. Hence, out of the initial 29,123 species, 254 molecules (0.87%) were found to match singlet fission energy conditions. The consideration of practical concerns such as availability or stability reduced the number to just 24 (0.08%), among which the aminoanthraquinone derivatives are found particularly promising. The proposed protocol correct the deficiencies of the preceding ones, reaching DFT accuracy and minimizing the risk of getting false negatives especially at the early stages of the screening. In addition, this protocol can be used in future high-throughput investigations using datasets composed of millions of species.

An improved chain of spheres for exchange algorithm

In the present work, we describe a more accurate and efficient variant of the chain-of-spheres algorithm (COSX) for exchange matrix computations. Higher accuracy for the numerical integration is obtained with new grids that were developed using global optimization techniques. With our new default grids, the average absolute energy errors are much lower than 0.1 kcal/mol, which is desirable to achieve "chemical accuracy." Although the size of the new grids is increased by roughly a factor of 2.5, the excellent efficiency of the original COSX implementation is still further improved in most cases. The evaluation of the analytic electrostatic potential integrals was significantly accelerated by a new implementation of rolled-out versions of the Dupuis-Rys-King and Head-Gordon-Pople algorithms. Compared to our earlier implementation, a twofold speedup is obtained for the frequently used triple-ζ basis sets, while up to a 16-fold speedup is observed for quadruple-ζ basis sets. These large gains are a consequence of both the more efficient integral evaluation and the intermediate exchange matrix computation in a partially contracted basis when generally contracted shells occur. With our new RIJCOSX implementation, we facilitate accurate self-consistent field (SCF) binding energy calculations on a large supra-molecular complex composed of 320 atoms. The binding-energy errors with respect to the fully analytic results are well below 0.1 kcal/mol for the cc-pV(T/Q)Z basis sets and even smaller than for RIJ with fully analytic exchange. At the same time, our RIJCOSX SCF calculation even with the cc-pVQZ basis and the finest grid is 21 times faster than the fully analytic calculation.

NMR chemical shift computations at second-order Møller-Plesset perturbation theory using gauge-including atomic orbitals and Cholesky-decomposed two-electron integrals

We report on a formulation and implementation of a scheme to compute nuclear magnetic resonance (NMR) shieldings at second-order Møller-Plesset (MP2) perturbation theory using gauge-including atomic orbitals (GIAOs) to ensure gauge-origin independence and Cholesky decomposition (CD) to handle unperturbed and perturbed two-electron integrals. We investigate the accuracy of the CD for the derivatives of the two-electron integrals with respect to an external magnetic field and for the computed NMR shieldings, before we illustrate the applicability of our CD-based GIAO-MP2 scheme in calculations involving up to about 100 atoms and more than 1000 basis functions.

Triple Resonance Experiments for the Rapid Detection of 103Rh NMR Shifts: A Combined Experimental and Theoretical Study into Dirhodium and Bismuth-Rhodium Paddlewheel Complexes

A H(C)Rh triple resonance NMR experiment makes the rapid detection of ¹⁰³Rh chemical shifts possible, which were previously beyond reach. It served to analyze a series of dirhodium and bismuth–rhodium paddlewheel complexes of the utmost importance for metal–carbene chemistry. The excellent match between the experimental and computed ¹⁰³Rh shifts in combination with a detailed analysis of the pertinent shielding tensors forms a sound basis for a qualitative and quantitative interpretation of these otherwise (basically) inaccessible data. The observed trends clearly reflect the influence exerted by the equatorial ligands (carboxylate versus carboxamidate), the axial ligands (solvents), and the internal “metalloligand” (Rh versus Bi) on the electronic estate of the reactive Rh(II) center.

Investigation of cobalt(III)-phenylalanine complexes for hypoxia-activated drug delivery

Four cobalt(iii)-phenylalanine complexes, [Co(Phe)(py2en)](ClO4)2·H2O (1), [Co(Phe)(TPA)](ClO4)2·H2O (2), [Co(Phe)(py2enMe2)](ClO4)2·H2O (3) and [Co(bipy)2(Phe)](ClO4)2·H2O (4), were investigated as prototype models for hypoxia-activated delivery of melphalan - a phenylalanine derivative anticancer drug of the class of nitrogen mustards. Single crystal X-ray diffraction analysis provided the molecular structures of 1-4, as a single isomer/conformer. According with NMR and theoretical calculations, the solid-state structures of 2 and 4 are maintained in solutions. For complexes 1 and 3, though, a mixture of isomers was found in DMSO solutions: Λ-cisα(exo,exo) and Δ-cisβ1(exo,exo) for 1 (3 : 2 ratio), and Λ-cisα(exo,exo) and Δ-cisα(exo,exo) for 3 (5 : 1 ratio). Theoretical calculations point to a re-equilibration reaction of the solid-state Λ-cisβ1 isomer of 1 in solution. Electrochemical analysis revealed a correlation between the electron-donor capacity of the ancillary ligands and the redox potentials of the complexes. The potentials varied from +0.01 for 1 to +0.31 V vs. SHE for 4 in aqueous media and indicate that reduction should be achieved in biological media. The integrity of the complexes in pH 5.5 and 7.4 buffered solutions was confirmed by UV-Vis monitoring up to 24 h at 25 °C. Reduction by ascorbic acid (AA) shows an O2-dependent dissociation of the l-Phe for complexes 1-3, with higher conversion rates at pH 7.4. For complex 4, a fast dissociation of l-Phe was observed, with conversion rates unaffected by the pH and presence of O2.

Mössbauer Spectroscopic and Computational Investigation of An Iron Cyclopentadienone Complex

(Cyclopentadienone)iron carbonyl complexes have recently received particular attention for their use as catalysts in hydrogenation or transfer hydrogenation reactions including the N-alkylation of amines with alcohols. This is due to their easy synthesis from simple and cheap materials, air and water stabilities, and the crucial metal-ligand cooperation giving rise to unique catalytic properties. Here, we report a Mössbauer spectroscopic and computational investigation of such a complex and its corresponding activated species for dehydrogenation and hydrogenation reactions. This study affords a deeper understanding of the species formed by the reaction with Me₃NO and their distribution upon the added amount of an oxidant.

Assessing the Accuracy of Local Hybrid Density Functional Approximations for Molecular Response Properties

A comprehensive overview of the performance of local hybrid functionals for molecular properties like excited states, ionization potentials within the GW framework, polarizabilities, magnetizabilities, NMR chemical shifts, and NMR spin-spin coupling constants is presented. We apply the generalization of the kinetic energy, τ, with the paramagnetic current density to all magnetic properties and the excitation energies from time-dependent density functional theory. This restores gauge invariance for these properties. Different ansätze for local mixing functions such as the iso-orbital indicator, the correlation length, the Görling-Levy second-order limit, and the spin polarization are compared. For the latter, we propose a modified version of the corresponding hyper-generalized gradient approximation functional of Perdew, Staroverov, Tao, and Scuseria (PSTS) [Phys. Rev. A 2008, 78, 052513] to allow for a numerically stable evaluation of the exchange-correlation kernel and hyperkernel. The PSTS functional leads to a very consistent improvement compared to the related TPSSh functional. It is further shown that the "best" choice of the local mixing function depends on the studied property and molecular class. While functionals based on the iso-orbital indicator lead to rather accurate excitation energies and ionization energies, the results are less impressive for NMR properties, for which a considerable dependence on the considered molecular test set and nuclei is observed. Johnson's local hybrid functional based on the correlation length yields remarkable results for NMR shifts of compounds featuring heavy elements and also for the excitation energies of organic compounds.

Implementation and Validation of Local Hybrid Functionals with Calibrated Exchange-Energy Densities for Nuclear Shielding Constants

A recently reported coupled-perturbed Kohn-Sham implementation to compute nuclear shielding constants with gauge-including atomic orbitals and local hybrid functionals has been extended to cover higher derivatives of the density in the local mixing function (LMF) of the local hybrid as well as the calibration function (CF) needed to deal with the ambiguity of exchange-energy densities. This allowed the first evaluation of state-of-the-art local hybrids with "calibrated" exchange-energy densities for nuclear shieldings. Compared to previously evaluated simpler local hybrids without a CF, appreciable improvements are found for proton shieldings. Furthermore, the recent LH20t functional is still competitive with the outstanding performance of the uncalibrated LH12ct-SsirSVWN and LH12ct-SsifSVWN LHs for heavier nuclei, suggesting that LH20t is possibly the most robust choice of any rung-four functional for computing the nuclear shieldings of main-group nuclei so far. Interestingly, the presence of a CF in the functional significantly reduces the number of artifacts introduced by the widely used Maximoff-Scuseria framework to treat the local kinetic energy τ. The latter occurs in so-called t-LMFs used in many of the present local hybrids. In any case, the use of Dobson's current-density functional framework is also recommended with more advanced calibrated τ-dependent local hybrid functionals.

Benchmarking Magnetizabilities with Recent Density Functionals

We have assessed the accuracy of the magnetic properties of a set of 51 density functional approximations, including both recently published and already established functionals. The accuracy assessment considers a series of 27 small molecules and is based on comparing the predicted magnetizabilities to literature reference values calculated using coupled-cluster theory with full singles and doubles and perturbative triples [CCSD(T)] employing large basis sets. The most accurate magnetizabilities, defined as the smallest mean absolute error, are obtained with the BHandHLYP functional. Three of the six studied Berkeley functionals and the three range-separated Florida functionals also yield accurate magnetizabilities. Also, some older functionals like CAM-B3LYP, KT1, BHLYP (BHandH), B3LYP, and PBE0 perform rather well. In contrast, unsatisfactory performance is generally obtained with Minnesota functionals, which are therefore not recommended for calculations of magnetically induced current density susceptibilities and related magnetic properties such as magnetizabilities and nuclear magnetic shieldings. We also demonstrate that magnetizabilities can be calculated by numerical integration of magnetizability density; we have implemented this approach as a new feature in the gauge-including magnetically induced current (GIMIC) method. Magnetizabilities can be calculated from magnetically induced current density susceptibilities within this approach even when analytical approaches for magnetizabilities as the second derivative of the energy have not been implemented. The magnetizability density can also be visualized, providing additional information that is not otherwise easily accessible on the spatial origin of magnetizabilities.

Lanthanide(III) Complexes Based on an 18-Membered Macrocycle Containing Acetamide Pendants. Structural Characterization and paraCEST Properties

We report a detailed investigation of the coordination properties of macrocyclic lanthanide complexes containing a 3,6,10,13-tetraaza-1,8(2,6)-dipyridinacyclotetradecaphane scaffold functionalized with four acetamide pendant arms. The X-ray structures of the complexes with the large Ln³⁺ ions (La and Sm) display 12- and 10-coordinated metal ions, where the coordination sphere is fulfilled by the six N atoms of the macrocycle, the four O atoms of the acetamide pendants, and a bidentate nitrate anion in the La³⁺ complex. The analogous Yb³⁺ complex presents, however, a 9-coordinated metal ion because one of the acetamide pendant arms remains uncoordinated. ¹H NMR studies indicate that the 10-coordinated form is present in solution throughout the lanthanide series from La to Tb, while the smaller lanthanides form 9-coordinated species. ¹H and ⁸⁹Y NMR studies confirm the presence of this structural change because the two species are present in solution. Analysis of the ¹H chemical shifts observed for the Tb³⁺ complex confirms its D₂ symmetry in aqueous solution and evidences a highly rhombic magnetic susceptibility tensor. The acetamide resonances of the Pr³⁺ and Tb³⁺ complexes provided sizable paraCEST effects, as demonstrated by the corresponding Z-spectra recorded at different temperatures and studies on tube phantoms recorded at 22 °C.

Probing the generality of spin crossover complex T½vs. ligand 15N NMR chemical shift correlations: towards predictable tuning

A study of 6 families (42 members) demonstrates that within a family the easily calculated 15N-NMR values of ligands enable predictable tuning of T1/2 in the corresponding complexes, except for 2 families with weakly influencing meta-substituents.

Comprehensive Benchmark Study on the Calculation of 29Si NMR Chemical Shifts

A comprehensive and diverse benchmark set for the calculation of ²⁹Si NMR chemical shifts is presented. The SiS146 set includes 100 silicon containing compounds with 146 experimentally determined reference ²⁹Si NMR chemical shifts measured in nine different solvents in a range from -400 to +828 ppm. Silicon atoms bound to main group elements as well as transition metals with coordination numbers of 2-6 in various bonding patterns including multiple bonds and coordinative and aromatic bonding are represented. The performance of various common and specialized density functional approximations including (meta-)GGA, hybrid, and double-hybrid functionals in combination with different AO basis sets and for differently optimized geometries is evaluated. The role of scalar-relativistic effects is further investigated by inclusion of the zeroth order regular approximation (ZORA) method into the calculations. GGA density functional approximations (DFAs) are found to outperform hybrid DFAs with B97-D3 performing best with an MAD of 7.2 ppm for the subset including only light atoms (Z < 18), while TPSSh is the best tested hybrid functional with an MAD of 10.3 ppm. For ²⁹Si cores in the vicinity of heavier atoms, the application of ZORA proved indispensable. Inclusion of spin-orbit effects into the ²⁹Si NMR chemical shift calculation decreases the mean absolute deviations by up to 74% compared to calculations applying effective core potentials.

Aromaticity of Even-Number Cyclo[n]carbons (n = 6-100)

The recently synthesized cyclo[18]carbon molecule has been characterized in a number of studies by calculating electronic, spectroscopic, and mechanical properties. However, cyclo[18]carbon is only one member of the class of cyclo[n]carbons—standalone carbon allotrope representatives. Many of the larger members of this class of molecules have not been thoroughly investigated. In this work, we calculate the magnetically induced current density of cyclo[n]carbons in order to elucidate how electron delocalization and aromatic properties change with the size of the molecular ring (n), where n is an even number between 6 and 100. We find that the Hückel rules for aromaticity (4k + 2) and antiaromaticity (4k) become degenerate for large C_n rings (n > 50), which can be understood as a transition from a delocalized electronic structure to a nonaromatic structure with localized current density fluxes in the triple bonds. Actually, the calculations suggest that cyclo[n]carbons with n > 50 are nonaromatic cyclic polyalkynes. The influence of the amount of nonlocal exchange and the asymptotic behavior of the exchange–correlation potential of the employed density functionals on the strength of the magnetically induced ring current and the aromatic character of the large cyclo[n]carbons is also discussed.

Halogen Bond of Halonium Ions: Benchmarking DFT Methods for the Description of NMR Chemical Shifts

Because of their anisotropic electron distribution and electron deficiency, halonium ions are unusually strong halogen-bond donors that form strong and directional three-center, four-electron halogen bonds. These halogen bonds have received considerable attention owing to their applicability in supramolecular and synthetic chemistry and have been intensely studied using spectroscopic and crystallographic techniques over the past decade. Their computational treatment faces different challenges to those of conventional weak and neutral halogen bonds. Literature studies have used a variety of wave functions and DFT functionals for prediction of their geometries and NMR chemical shifts, however, without any systematic evaluation of the accuracy of these methods being available. In order to provide guidance for future studies, we present the assessment of the accuracy of 12 common DFT functionals along with the Hartree-Fock (HF) and the second-order Møller-Plesset perturbation theory (MP2) methods, selected from an initial set of 36 prescreened functionals, for the prediction of 1H, 13C, and 15N NMR chemical shifts of [N-X-N]+ halogen-bond complexes, where X = F, Cl, Br, and I. Using a benchmark set of 14 complexes, providing 170 high-quality experimental chemical shifts, we show that the choice of the DFT functional is more important than that of the basis set. The M06 functional in combination with the aug-cc-pVTZ basis set is demonstrated to provide the overall most accurate NMR chemical shifts, whereas LC-ωPBE, ωB97X-D, LC-TPSS, CAM-B3LYP, and B3LYP to show acceptable performance. Our results are expected to provide a guideline to facilitate future developments and applications of the [N-X-N]+ halogen bond.

Computation of NMR Shielding Constants for Solids Using an Embedded Cluster Approach with DFT, Double-Hybrid DFT, and MP2

In this work, we explore the accuracy of post-Hartree–Fock (HF) methods and double-hybrid density functional theory (DFT) for the computation of solid-state NMR chemical shifts. We apply an embedded cluster approach and investigate the convergence with cluster size and embedding for a series of inorganic solids with long-range electrostatic interactions. In a systematic study, we discuss the cluster design, the embedding procedure, and basis set convergence using gauge-including atomic orbital (GIAO) NMR calculations at the DFT and MP2 levels of theory. We demonstrate that the accuracy obtained for the prediction of NMR chemical shifts, which can be achieved for molecular systems, can be carried over to solid systems. An appropriate embedded cluster approach allows one to apply methods beyond standard DFT even for systems for which long-range electrostatic effects are important. We find that an embedded cluster should include at least one sphere of explicit neighbors around the nuclei of interest, given that a sufficiently large point charge and boundary effective potential embedding is applied. Using the pcSseg-3 basis set and GIAOs for the computation of nuclear shielding constants, accuracies of 1.6 ppm for ⁷Li, 1.5 ppm for ²³Na, and 5.1 ppm for ³⁹K as well as 9.3 ppm for ¹⁹F, 6.5 ppm for ³⁵Cl, 7.4 ppm for ⁷⁹Br, and 7.5 ppm for ²⁵Mg as well as 3.8 ppm for ⁶⁷Zn can be achieved with MP2. Comparing various DFT functionals with HF and MP2, we report the superior quality of results for methods that include post-HF correlation like MP2 and double-hybrid DFT.