Activation and C-C Coupling of Aryl Iodides via Bismuth Photocatalysis

Within the emerging field of bismuth redox catalysis, the catalytic formation of C-C bonds using aryl halides would be highly desirable; yet such a process remains a synthetic challenge. Herein, we present a chemoselective bismuth-photocatalyzed activation and subsequent coupling of (hetero)aryl iodides with pyrrole derivatives to access C(sp2)-C(sp2) linkages through C-H functionalization. This unique reactivity is the result of the bismuth complex featuring two redox state-dependent interactions with light, which 1) activates the Bi(I) complex for oxidative addition via MLCT, and 2) promotes the homolytic cleavage of aryl Bi(III) intermediates through a LLCT process.

Varying Projection Quality of Good Local Electric Field Gradients of Monochlorobenzaldehydes

Rotational spectroscopy is an excellent tool for structure determination, which can provide additional insights into local electronic structure by investigating the hyperfine pattern due to nuclear quadrupole coupling. Jet-cooled molecules are good experimental benchmark targets for electronic structure calculations, as they are free of environmental effects. We report the rotational spectra of 2-chlorobenzaldehyde, 3-chlorobenzaldehyde, and 4-chlorobenzaldehyde, including a complete experimental description of the nuclear quadrupole coupling constants, which were previously not experimentally determined. We identified two conformers for 3-chlorobenzaldehyde and one conformer each for 2-chlorobenzaldehyde and 4-chlorobenzaldehyde. Rigorous structure fitting of 4-chlorobenzaldehyde was performed to determine bond lengths for r0, rs, rese, and rm(1) structures. Comparing experimental nuclear quadrupole coupling constants to computational results showed agreement in the nuclear axis system, but the accuracy of the projection into the principal axis system decreases in near-oblate 2-chlorobenzaldehyde. The experimental angle Θaz = 19.16° between the principal a-axis and nuclear z-axis is larger than predicted by multiple computational methods by ≥4°. It is attributed to the high sensitivity of 2-chlorobenzaldehyde to low-energy vibrational contributions.

Arene Ring Expansion by Ruthenium η6-Arene Complexes

Transition metal π-arene complexes enable the dearomatization of benzene rings to access diversified unsaturated carbocycles through multistep synthetic procedures involving sequential addition of nucleophiles and electrophiles. This work details a single-step dearomatization process by reaction of Ru(η6-arene) complexes with enolates derived from α-halo or α-(tosyloxy)esters to directly transform π-coordinated arenes to ring-expanded cycloheptatrienes.

Palladium-Catalyzed Ortho Alkoxylation of Oxazoline Derivatives: An Avenue to Reach Meta-Substituted Electron-Rich Arenes Exploiting Oxazoline as a Removeable Directing Group

An efficient and highly regioselective palladium-catalyzed oxazoline-directed alkoxylation is reported. The reaction proceeds under air and mild temperatures (60 °C). A series of alcohols can be used as alkoxylating agents and concomitantly act as reaction solvents, whereas primary and secondary alcohols are tolerated. Furthermore, fluorinated alcohols can be applied as well, introducing pharmaceutically relevant fluorine-containing groups. 1,3-Dialkoxylated products can be further subjected to hydrolysis transforming the oxazoline-directing group to a carboxylic acid, which can be removed by decarboxylation if desired. This approach demonstrates the capability to reverse the conventional site selectivity of electrophilic aromatic substitution reactions, since it allows the synthesis of arenes with two electron-donating groups in a 1,3-relationship.

What Determines the Lewis Acidity of a Bismuthane? Towards Bi-Based FLPs

Aiming at intramolecular frustrated Lewis pairs (FLPs) based on soft Lewis acidic bismuth centers, a phosphine function was combined with a dichloridobismuthane unit on a phenylene backbone utilizing a scrambling approach. The reaction between two equivalents of BiCl3 and (o-(Ph2P)C6H4)3Bi yielded (o-(Ph2P)C6H4)BiCl2(THF), the structure of which indicated Bi…P interactions and thus a pronounced Lewis acidity at the bismuth center that was confirmed by the Gutmann-Beckett method. However, the system turned out to be insufficient to be utilized for FLP reactivity. Hence, the chloride ligands were exchanged by iodide and C2F5 substituents, respectively. Despite a lower electronegativity the iodide compound exhibits a shorter Bi…P contact, while the C2F5 substituents led to a further decrease of the Lewis acidity, despite their high group electronegativity. DFT calculations rationalized this by a quenching of the Lewis acidity inherent to the σ*(Bi-C) orbital by negative hyperconjugation from occupied p-orbitals at the F atoms. Furthermore, it turned out that the strength of the covalent Bi-X σ-bond is a more important factor than the charge at Bi in determining the energetic accessibility and thus Lewis acidity of the antibonding σ*(Bi-C) orbital.

Extensive reference set and refined computational protocol for calculations of 57Fe Mössbauer parameters

Mössbauer spectroscopy is a powerful technique for probing the local electronic structure of iron compounds, because it reports in an element-selective manner on both the oxidation state and coordination environment of the Fe ion. Computational prediction of the two main Mössbauer parameters, isomer shift (δ) and quadrupole splitting (ΔEQ), has long been targeted by quantum chemical studies, and useful protocols based on density functional theory have been proposed. Here we present an extensive curated reference set of Fe compounds that is considerably larger and more diverse than literature precedents. We make a distinction between low-temperature and high-temperature experimental subgroups. This set is employed for optimizing a refined computational protocol utilizing the scalar version of the exact 2-component (X2C) Hamiltonian with the finite nucleus approximation. Attention is devoted to having an accurate and flexible all-electron basis set for Fe. We assess the performance of several DFT methods that cover all representative families and rungs of functionals and find that hybrid functionals with ca. 25-30% exact exchange offer the best accuracy for isomer shifts. The work establishes a refined general protocol of wide applicability that achieves good performance for the prediction of isomer shifts in a wider variety of systems than before, but the limitations of DFT for quadrupole splittings are also highlighted. Finally, comparison of calculated values with high-temperature experimental results shows that the use of an empirical correction factor is required to account for the second-order Doppler shift and to achieve the same quality of correlation as with the low-temperature data.

Application of the Adiabatic Connection Random Phase Approximation to Electron-Nucleus Hyperfine Coupling Constants

The electron-nucleus hyperfine coupling constant is a challenging property for density functional methods. For accurate results, hybrid functionals with a large amount of exact exchange are often needed and there is no clear "one-for-all" functional which describes the hyperfine coupling interaction for a large set of nuclei. To alleviate this unfavorable situation, we apply the adiabatic connection random phase approximation (RPA) in its post-Kohn-Sham fashion to this property as a first test. For simplicity, only the Fermi-contact and spin-dipole terms are calculated within the nonrelativistic and the scalar-relativistic exact two-component framework. This requires to solve a single coupled-perturbed Kohn-Sham equation to evaluate the relaxed density matrix, which comes with a modest increase in computational demands. RPA performs remarkably well and substantially improves upon its Kohn-Sham (KS) starting point while also reducing the dependence on the KS reference. For main-group systems, RPA outperforms global, range-separated, and local hybrid functionals─at similar computational costs. For transition-metal compounds and lanthanide complexes, a similar performance as for hybrid functionals is observed. In contrast, related post-Hartree-Fock methods such as Møller-Plesset perturbation theory or CC2 perform worse than semilocal density functionals.

Core-electron contributions to the magnetic response of molecules with heavy elements and their significance in aromaticity assessments

This study delves into the magnetic response of core electrons and their influence on the global magnetic response of planar and three-dimensional systems containing heavy elements, employing the removing valence electron (RVE) approximation. We also explore electronic aromaticity indices to understand the potential role of core electrons on electron delocalization in the absence of an external perturbation. The study reveals that core electrons significantly contribute to the overall magnetic response, especially to the magnetic shielding, affecting the interpretation of aromaticity. In contrast, the calculation of the electronic aromaticity indices suggests a negligible participation of the core electrons on electron delocalization. Despite their widespread use, the study emphasizes caution in labeling systems as strongly aromatic based solely on shielding function computations. It is noteworthy to emphasize the limitations associated with each aromaticity criterion; particularly in the context of magnetic shielding function calculations, the core-electron effect contamination is undeniable. Hence, the integration of various criteria becomes imperative for attaining a comprehensive understanding of magnetic responses within complex systems.

Valence-to-core X-ray emission spectroscopy of transition metal tetrahalides: mechanisms governing intensities

Valence-to-core (VtC) X-ray emission spectroscopy offers the opportunity to probe the valence electronic structure of a system filtered by selection rules. From this, the nature of its ligands can be inferred. While a preceding 1s ionization creates a core hole, in VtC XES this core hole is filled with electrons from mainly ligand based orbitals. In this work, we investigated the trends in the observed VtC intensities for a series of transition metal halides, which spans the first row transition metals from manganese to copper. Further, with the aid of computational studies, we corroborated these trends and identified the mechanisms and factors that dictate the observed intensity trends. Small amounts of metal p contribution to the ligand orbitals are known to give rise to intensity of a VtC transition. By employing an LCAO (linear combination of atomic orbitals) approach, we were able to assess the amount of metal p contribution to the ligand molecular orbitals, as well as the role of the transition dipole moment and correlate these factors to the experimentally observed intensities. Finally, by employing an ano (atomic natural orbital) basis set within the calculations, the nature of the metal p contribution (3p vs. 4p) was qualitatively assessed and their trends discussed within the same transition metal halide series.

Beyond Electrons: Correlation and Self-Energy in Multicomponent Density Functional Theory

Post-Kohn-Sham methods are used to evaluate the ground-state correlation energy and the orbital self-energy of systems consisting of multiple flavors of different fermions. Starting from multicomponent density functional theory, suitable ways to arrive at the corresponding multicomponent random-phase approximation and the multicomponent Green's functionG W ${GW}$ approximation, including relativistic effects, are outlined. Given the importance of both of this methods in the development of modern Kohn-Sham density functional approximations, this work will provide a foundation to design advanced multicomponent density functional approximations. Additionally, theG W ${GW}$ quasiparticle energies are needed to study light-matter interactions with the Bethe-Salpeter equation.

Unraveling the enigma of Craig-type Möbius-aromatic osmium compounds

Nuclear magnetic resonance (NMR) chemical shifts and the magnetically induced current density (MICD) susceptibility of four osmium containing molecules have been calculated at the density functional theory (DFT) level using three relativistic levels of theory. The calculations were performed at the quasi-relativistic level using an effective core potential (ECP) for Os, at the all-electron scalar exact two-component (X2C) relativistic level, and at the relativistic X2C level including spin-orbit coupling (SO-X2C). In earlier studies, the osmapentalene (1) and the osmapentalynes (2 and 3) were considered Craig-type Möbius aromatic and it was suggested that the analogous osmium compound (4) is Craig-type Möbius antiaromatic. Here, the ring-current strengths were obtained with the gauge including magnetically induced currents (GIMIC) method by integrating the MICD susceptibility passing through planes that intersect chemical bonds and by line integration of the induced magnetic field using Ampère-Maxwell's law. The ring-current calculations suggest that 1, 2 and 3 are weakly aromatic and that 4 is nonaromatic. The accuracy of the MICD susceptibility was assessed by comparing calculated NMR chemical shifts to available experimental data. Visualization of the MICD susceptibility shows that the ring current does not pass from one side of the molecular plane to the other, which means that the MICD susceptibility of the studied molecules does not exhibit any Möbius topology as one would expect for Craig-type Möbius aromatic and for Craig-type Möbius antiaromatic molecules. Thus, molecules 1-3 are not Craig-type Möbius aromatic and molecule 4 is not Craig-type Möbius antiaromatic as previously suggested. Calculations of the 1H NMR and 13C NMR chemical shifts of atoms near the Os atom show the importance of including spin-orbit effects. Overall, our study revisits the understanding of the aromaticity of organometallic molecules containing transition metals.

The aromatic nature of auracycles and diauracycles based on calculated ring-current strengths

We have calculated the magnetically induced current density susceptibility for gold-containing organometallic molecular rings using the gauge-including magnetically induced currents (GIMIC) method. The aromatic nature has been determined by calculating the strength of the magnetically induced ring current susceptibility, which is often called ring current. To our knowledge, we show here for the first time that gold-containing organometallic rings may be aromatic or antiaromatic sustaining ring currents in the presence of an external magnetic field. The calculated aromatic character of the rings agrees with the aromatic nature one expects when using Hückel's aromaticity rules. The studied auracycles and diauracycles with 4n electrons in the conjugated orbitals generally sustain a weak paratropic ring current, whereas those having 4n + 2 electrons in the conjugated orbitals sustain a diatropic ring current that is almost as strong as that of benzene. The number of electrons are obtained by assuming that each C, N and Au atom of the ring contribute one electron, and a H atom connected to a N atom in the ring increases the number of electrons by one. An electron-attracting ligand at Au removes one electron from the ring. Formation of a short Au-Au bonding diauracycles reduces the number of electrons in the ring by two.

A novel approach for estimating the strength of argentophilic and aurophilic interactions using QTAIM parameters

Metallophilic interactions, specifically argentophilic (Ag⋯Ag) and aurophilic (Au⋯Au) interactions, play a crucial role in stabilizing various molecular and solid-state structures. In this manuscript, we present a convenient method to estimate the strength of argentophilic and aurophilic interactions based on quantum theory of atoms in molecules (QTAIM) parameters evaluated at the bond critical points connecting the metal centres. We employ density functional theory (DFT) calculations and the QTAIM parameters to develop this energy predictor. To validate the reliability and applicability of our method, we test it using a selection of X-ray crystal structures extracted from the cambridge structural database (CSD), where argentophilic and aurophilic interactions are known to be significant in their solid-state arrangements. This method offers a distinct advantage in systems where multiple interactions, beyond metallophilic interactions, contribute to the overall stability of the structure. By employing our approach, researchers can distinctly quantify the strength of argentophilic and aurophilic interactions, facilitating a deeper understanding of their impact on molecular and solid-state properties. This method fills a critical gap in the existing literature, offering a valuable tool to researchers seeking to unravel the intricate interactions in metal-containing compounds.

Gas Uptake and Thermodynamics in Porous Liquids Elucidated by 129Xe NMR

We exploited 129Xe NMR to investigate xenon gas uptake and dynamics in a porous liquid formed by dissolving porous organic cages in a cavity-excluded solvent. Quantitative 129Xe NMR shows that when the amount of xenon added to the sample is lower than the amount of cages present (subsaturation), the porous liquid absorbs almost all xenon atoms from the gas phase, with 30% of the cages occupied with a Xe atom. A simple two-site exchange model enables an estimate of the chemical shift of 129Xe in the cages, which is in good agreement with the value provided by first-principles modeling. T2 relaxation times allow the determination of the exchange rate of Xe between the solvent and cage sites as well as the activation energies of the exchange. The 129Xe NMR analysis also enables determination of the free energy of confinement, and it shows that Xe binding is predominantly enthalpy-driven.

Molybdenum(VI) Nitrido Complexes with Tripodal Silanolate Ligands. Structure and Electronic Character of an Unsymmetrical Dimolybdenum μ-Nitrido Complex Formed by Incomplete Nitrogen Atom Transfer

In contrast to a tungsten nitrido complex endowed with a tripodal silanolate ligand framework, which was reported in the literature to be a dimeric species with a metallacyclic core, the corresponding molybdenum nitrides 3 are monomeric entities comprising a regular terminal nitride unit, as proven by single-crystal X-ray diffraction (SC-XRD). Their electronic character is largely determined by the constraints imposed on the metal center by the podand ligand architecture. 95Mo nuclear magnetic resonance (NMR) and, to a lesser extent, 14N NMR spectroscopy allow these effects to be studied, which become particularly apparent upon comparison with the spectral data of related molybdenum nitrides comprising unrestrained silanolate, alkoxide, or amide ligands. Attempted nitrogen atom transfer from these novel terminal nitrides to [(tBuArN)3Mo] (Ar = 3,5-dimethylphenyl) as the potential acceptor stopped at the stage of unsymmetric dimolybdenum μ-nitrido complex 13a as the first intermediate along the reaction pathway. SC-XRD, NMR, electron paramagnetic resonance, and ultraviolet-visible spectroscopy as well as magnetometry in combination with density functional theory allowed a clear picture of the geometric and electronic structure of this mixed-valent species to be drawn. 13a is formally best described as an adduct of the type [(Mo[O])+III-(μN)-III-(Mo[N])+VI], S = 1/2 complex with (Mo[O])+III in the low-spin configuration, whereas related complexes such as [(AdS)3Mo-(μN)-Mo(NtBuAr)3] (19; Ad = 1-adamantyl) have previously been regarded in the literature as mixed-valent Mo+IV/Mo+V species. The spin population at the two Mo centers is uneven and notably larger at the more reduced Mo[O] atom, whereas the only spin present at the (μN) bridge is derived from spin polarization.

[Tc(NO)(Cp)(PPh3)Cl] and [Tc(NO)(Cp)(PPh3)(NCCH3)](PF6), and Their Reactions with Pyridine and Chalcogen Donors

Reactions of the technetium(I) nitrosyl complex [Tc(NO)(Cp)(PPh3)Cl] with triphenylphosphine chalcogenides EPPh3 (E = O, S, Se), and Ag(PF6) in a CH2Cl2/MeOH mixture (v/v, 2/1) result in an exchange of the chlorido ligand and the formation of [Tc(NO)(Cp)(PPh3)(EPPh3)](PF6) compounds. The cationic acetonitrile complex [Tc(NO)(Cp)(PPh3)(NCCH3)]+ is formed when the reaction is conducted in NCCH3 without additional ligands. During the isolation of the corresponding PF6- salt a gradual decomposition of the anion was detected in the solvent mixture applied. The yields and the purity of the product increase when the BF4- salt is used instead. The acetonitrile ligand is bound remarkably strongly to technetium and exchange reactions readily proceed only with strong donors, such as pyridine or ligands with 'soft' donor atoms, such as the thioether thioxane. Substitutions on the cyclopentadienyl ring do not significantly influence the ligand exchange behavior of the starting material. 99Tc NMR spectroscopy is a valuable tool for the evaluation of reactions of the complexes of the present study. The extremely large chemical shift range of this method allows the ready detection of corresponding ligand exchange reactions. The observed 99Tc chemical shifts depend on the donor properties of the ligands. DFT calculations support the discussions about the experimental results and provide explanations for some of the unusual findings.

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.

Prediction of 19F NMR chemical shifts for organic compounds with ORCA

Accurate assignment of 19F NMR has long been a challenge, and quantum chemical methods are possible solutions. Herein we reported a scaling method for the prediction of 19F NMR chemical shift with freely available ORCA program package. Performance of 31 DFT functionals coupled with 11 basis sets were evaluated and influence of geometry optimization was also studied with five functionals coupled with three basis sets. The significance of geometry was further examined through the execution of relaxed surface scans of seven flexible compounds, and averaged shieldings of obtained conformers yielded notable improvement of the correlation between calculated isotropic shielidings and experimental chemical shifts. Utilization of the best scaling factor obtained successfully assigned of fluorine atoms in multifluorinated molecules with different conformations. The method reported here was computationally inexpensive, easily available with acceptable accuracy.

Zero-field splitting parameters within exact two-component theory and modern density functional theory using seminumerical integration

An efficient implementation of zero-field splitting parameters based on the work of Schmitt et al. [J. Chem. Phys. 134, 194113 (2011)] is presented. Seminumerical integration techniques are used for the two-electron spin-dipole contribution and the response equations of the spin-orbit perturbation. The original formulation is further generalized. First, it is extended to meta-generalized gradient approximations and local hybrid functionals. For these functional classes, the response of the paramagnetic current density is considered in the coupled-perturbed Kohn-Sham equations for the spin-orbit perturbation term. Second, the spin-orbit perturbation is formulated within relativistic exact two-component theory and the screened nuclear spin-orbit (SNSO) approximation. The accuracy of the implementation is demonstrated for transition-metal and diatomic main-group compounds. The efficiency is assessed for Mn and Mo complexes. Here, it is found that coarse integration grids for the seminumerical schemes lead to drastic speedups while introducing clearly negligible errors. In addition, the SNSO approximation substantially reduces the computational demands and leads to very similar results as the spin-orbit mean field Ansatz.

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.

TURBOMOLE: Today and Tomorrow

TURBOMOLE is a highly optimized software suite for large-scale quantum-chemical and materials science simulations of molecules, clusters, extended systems, and periodic solids. TURBOMOLE uses Gaussian basis sets and has been designed with robust and fast quantum-chemical applications in mind, ranging from homogeneous and heterogeneous catalysis to inorganic and organic chemistry and various types of spectroscopy, light-matter interactions, and biochemistry. This Perspective briefly surveys TURBOMOLE's functionality and highlights recent developments that have taken place between 2020 and 2023, comprising new electronic structure methods for molecules and solids, previously unavailable molecular properties, embedding, and molecular dynamics approaches. Select features under development are reviewed to illustrate the continuous growth of the program suite, including nuclear electronic orbital methods, Hartree-Fock-based adiabatic connection models, simplified time-dependent density functional theory, relativistic effects and magnetic properties, and multiscale modeling of optical properties.

Synthesis, Spectroscopy, and Structure of [FeRu(μ-dithiolate)(CN)2(CO)4]2

The salt [K(18-crown-6)]2[Ru(CN)2(CO)3] ([K(18-crown-6)]2[1]) was generated by the reaction of Ru(C2H4)(CO)4 with [K(18-crown-6)]CN. An initial thermal reaction gives [Ru(CN)(CO)4]-, which, upon ultraviolet (UV) irradiation, reacts with a second equiv of CN-. Protonation of [1]2- gave [HRu(CN)2(CO)3]- ([H1]-), which was isolated as a single isomer with mutually trans cyanide ligands. The complex cis,cis,cis-[Ru(pdt)(CN)2(CO)2]2- ([2]2-) was prepared by the UV-induced reaction of [1]2- with propanedithiol (pdtH2). The corresponding iron complex cis,cis,cis-[Fe(pdt)(CN)2(CO)2]2- ([3]2-) was prepared similarly. The pdt complexes [2]2- and [3]2- were treated with Fe(benzylideneacetone)(CO)3 to give, respectively, [RuFe (μ-pdt)(CN)2(CO)4]2- ([5]2-) and [Fe2(μ-pdt)(CN)2(CO)4]2- ([4]2-). The pathway from [3]2- to Fe2 complex [4]2- implicates intermetallic migration of CN-. In contrast, the formation of [5]2- leaves the Ru(CN)2(CO) center intact, as confirmed by X-ray crystallography. The structure of [5]2- features a "rotated" square-pyramidal Fe(CO)2(μ-CO) site. NMR measurements indicate that the octahedral Ru site is stereochemically rigid, whereas the Fe site dynamically undergoes turnstile rotation. 57Fe Mössbauer spectral parameters are very similar for rotated [5]2- and unrotated Fe2 complex [4]2-, indicating the insensitivity of that technique to both the geometry and the oxidation state of the Fe site. According to cyclic voltammetry, [5]2- oxidizes at E1/2 ∼ -0.8 V vs Fc+/0. Electron paramagnetic resonance (EPR) measurements show that 1e- oxidation of [5]2- gives an S = 1/2 rhombic species, consistent with the formulation Ru(II)Fe(I), related to the Hox state of the [FeFe] hydrogenases. Density functional theory (DFT) studies reproduce the structure, 1H NMR shifts, and infrared (IR) spectra observed for [5]2-. Related homometallic complexes with both cyanides on a single metal are predicted to not adopt rotated structures. These data suggest that [5]2- is best described as Ru(II)Fe(0). This conclusion raises the possibility that for some reduced states of the [FeFe]-hydrogenases, the [2Fe]H site may be better described as Fe(II)Fe(0) than Fe(I)Fe(I).

Tubular Magnetic Shielding Scan (TMSS): A New Technique for Molecular Space Exploration. (i) The Case of Aromaticity of Benzene and [n]Paracyclophanes

Both traditional and novel techniques were employed in this work for magnetic shielding evaluation to shed new light on the magnetic and aromaticity properties of benzene and 12 [n]paracyclophanes with n = 3-14. Density functional theory (DFT) with the B3LYP functional and all-electron Jorge-ATZP and x2c-TZVPPall-s basis sets was utilized for geometry optimization and magnetic shielding calculations, respectively. Additionally, the 6-311+G(d,p) basis set was incorporated for the purpose of comparing the magnetic shielding results. In addition to traditional evaluations such as NICS/NICSzz-Scan, and 2D-3D σiso(r)/σzz(r) maps, two new techniques were implemented: bendable grids (BGs) and cylindrical grids (CGs) of ghost atoms (Bqs). BGs allow for the recording of magnetic shielding from the bent ring levels of [n]pCPs, while CGs provide tubular magnetic shielding scan (TMSS) maps detailing the magnetic shielding from a cylindrical region above and below the ring frame. Our findings suggest that smaller [n]pCPs with n < 6 exhibit deviations in the magnetic shielding above and below the ring, indicating a broken electron delocalization under the ring. In contrast, larger [n]pCPs tend to behave similarly to benzene in terms of magnetic shielding. Moreover, we found that shorter polymethylene chains of [n]pCPs exhibit significantly higher magnetic shielding interactions with the ring. Both of the above techniques offer new and promising tools for characterizing nonplanar aromatic compounds, thereby contributing to a deeper understanding of their magnetic and electronic properties.

Synthesis and isolation of a triplet bismuthinidene with a quenched magnetic response

Large Spin-Orbit Coupling (SOC) is an intrinsic property of the heavy-elements that directly affects the electronic structures of the compounds. Herein we report the synthesis and characterization of a mono-coordinate bismuthinidene featuring a rigid and bulky ligand. All magnetic measurements (SQUID, NMR) point to a diamagnetic compound. However, multiconfigurational quantum chemical calculations predict the ground state of the compound to be dominated (76%) by a spin-triplet. The apparent diamagnetism is explained by an extremely large SOC induced positive zero-field-splitting of more than 4500 cm^-1 that leaves the M_S = 0 magnetic sublevel thermally isolated in the electronic ground state.

Reaching strong absorption up to 700 nm with new benzo[g]quinoxaline-based heteroleptic copper(I) complexes for light-harvesting applications

Heteroleptic copper(I) complexes, with a diimine as a chromophoric unit and a bulky diphosphine as an ancillary ligand, have the advantage of a reduced pseudo Jahn-Teller effect in their excited state over the corresponding homoleptic bis(diimine) complexes. Nevertheless, their lowest absorption lies generally between 350 to 500 nm. Aiming at a strong absorption in the visible by stable heteroleptic Cu(I) complexes, we designed a novel diimine based on 4-(benzo[g]quinoxal-2'-yl)-1,2,3-triazole derivatives. The large π-conjugation of the benzoquinoxaline moiety shifted bathochromically the absorption with regard to other diimine-based Cu(I) complexes. Adding another Cu(I) core broadened the absorption and extended it to considerably longer wavelengths. Moreover, by fine-tuning the structure of the dichelating ligand, we achieved a panchromatic absorption up to 700 nm with a high molar extinction coefficient of 8000 M^-1 cm^-1 at maximum (λ = 570 nm), making this compound attractive for light-harvesting antennae.

On the Utmost Importance of the Basis Set Choice for the Calculations of the Relativistic Corrections to NMR Shielding Constants

The investigation of the sensitivity of the relativistic corrections to the NMR shielding constants (σ) to the configuration of angular spaces of the basis sets used on the atoms of interest was carried out within the four-component density functional theory (DFT). Both types of relativistic effects were considered, namely the so-called heavy atom on light atom and heavy atom on heavy atom effects, though the main attention was paid to the former. As a main result, it was found that the dependence of the relativistic corrections to σ of light nuclei (exemplified here by 1H and 13C) located in close vicinity to a heavy atom (exemplified here by In, Sn, Sb, Te, and I) on the basis set used on the light spectator atom was very much in common with that of the Fermi-contact contribution to the corresponding nonrelativistic spin-spin coupling constant (J). In general, it has been shown that the nonrelativistic J-oriented and σ-oriented basis sets, artificially saturated in the tight s-region, provided much better accuracy than the standard nonrelativistic σ-oriented basis sets when calculating the relativistic corrections to the NMR shielding constants of light nuclei at the relativistic four-component level of the DFT theory.

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.

φ-Aromaticity in prismatic {Bi6}-based clusters

The occurrence of aromaticity in organic molecules is widely accepted, but its occurrence in purely metallic systems is less widespread. Molecules comprising only metal atoms (M) are known to be able to exhibit aromatic behaviour, sustaining ring currents inside an external magnetic field along M-M connection axes (σ-aromaticity) or above and below the plane (π-aromaticity) for cyclic or cage-type compounds. However, all-metal compounds provide an extension of the electrons' mobility also in other directions. Here, we show that regular {Bi₆} prisms exhibit a non-localizable molecular orbital of f-type symmetry and generate a strong ring current that leads to a behaviour referred to as φ-aromaticity. The experimentally observed heterometallic cluster [{CpRu}₃Bi₆]^-, based on a regular prismatic {Bi₆} unit, displays aromatic behaviour; according to quantum chemical calculations, the corresponding hypothetical Bi₆^2- prism shows a similar behaviour. By contrast, [{(cod)Ir}₃Bi₆] features a distorted Bi₆ moiety that inhibits φ-aromaticity.

Benchmarking the quadrupolar coupling tensor for chlorine to probe weak-bonding interactions

Rotational spectroscopy relies on quantum chemical calculations to interpret observed spectra. Among the most challenging molecules to assign are those with additional angular momenta coupling to the rotation, contributing to the complexity of the spectrum. This benchmark study of computational methods commonly used by rotational spectroscopists targets the nuclear quadrupole coupling constants of chlorine containing molecules and the geometry of its complexes and clusters. For each method, the quality of both structural and electronic parameter predictions is compared with the experimental values. Ab initio methods are found to perform best overall in predicting both the geometry of the complexes and the coupling constants of chlorine with moderate computational cost. This cost can be reduced by combining these methods with density functional theory structure optimization, which still yields adequate predictions. This work constitutes a first step in expanding Bailey's quadrupole coupling data set to encompass molecular clusters. [W. C. Bailey, Calculation of Nuclear Quadrupole Coupling Constants in Gaseous State Molecule, 2019, https://nqcc.wcbailey.net/].

Fully Tin-Coated Coinage Metal Ions: A Pincer-Type Bis-stannylene Ligand for Exclusive Tetrahedral Complexation

The synthesis of a novel bis-stannylene pincer ligand and its complexation with coinage metals (Cu^I , Ag^I and Au^I ) are described. All coinage metal centres are in tetrahedral coordination environments in the solid state and are exclusively coordinated by four neutral Sn^II donors. ¹¹⁹ Sn NMR provided information about the behaviour in solution. All of the isolated compounds have photoluminescent properties, and these were investigated at low and elevated temperatures. Compared to the free bis-stannylene ligand, coordination to coinage metals led to an increase in the luminescence intensity. The new compounds were investigated in detail through all-electron relativistic density functional theory (DFT) calculations.

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.

Unexpected NMR shieldings of sp- and sp2-hybridized carbon atoms in graphyne systems

Graphynes (GYs) are two-dimensional alloptropic forms of carbon consisting of periodically arranged sp- and sp²-hybridized carbon atoms in a planar structure. Graphynes can be formally created from graphene by inserting sp-hybridized carbon links into selected points of the graphene lattice. Depending on where the links are introduced, several forms of graphynes have been proposed with properties that make them potential candidates for new generation electronics or for applications in chemical processes. Since the applications of each form of GY depend on its structure, it is of interest to experimentally distinguish different forms of graphynes. In this paper we propose nuclear magnetic resonance (NMR) as a potential method of choice for such distinction. We computationally investigate on the DFT level the ¹³C-NMR chemical shifts for α-, β-, γ-, rhombic, and 6,6,12-graphynes, and α- and γ-graphdiynes. We perform the calculations both in periodic systems and with approximate finite models. The results show that NMR chemical shifts in graphynes are dependent on the structure and reflect the local bonding around the carbon nucleus. Interestingly, NMR shifts of several graphynes show anomalous values, differing significantly from shifts found in typical sp²-hybridized systems. We analyze these results in terms of local structural parameters and qualitatively investigate the possible origins of these anomalous NMR shifts. The results show that NMR is a viable method for determining the structure of graphynes and their finite precursor molecules.

Paramagnetic NMR Shielding Tensors Based on Scalar Exact Two-Component and Spin-Orbit Perturbation Theory

The temperature-dependent Fermi-contact and pseudocontact terms are important contributions to the paramagnetic NMR shielding tensor. Herein, we augment the scalar-relativistic (local) exact two-component (X2C) framework with spin-orbit perturbation theory including the screened nuclear spin-orbit correction for the EPR hyperfine coupling and g tensor to compute these temperature-dependent terms. The accuracy of this perturbative ansatz is assessed with the self-consistent spin-orbit two-component and four-component treatments serving as reference. This shows that the Fermi-contact and pseudocontact interaction is sufficiently described for paramagnetic NMR shifts; however, larger deviations are found for the EPR spectra and the principle components of the EPR properties of heavy elements. The impact of the perturbative treatment is further compared to that of the density functional approximation and the basis set. Large-scale calculations are routinely possible with the multipole-accelerated resolution of the identity approximation and the seminumerical exchange approximation, as shown for [CeTi₆O₃(OiPr)₉(salicylate)₆].

A Local Hybrid Exchange Functional Approximation from First Principles

Local hybrid functionals are a more flexible class of density functional approximations allowing for a position-dependent admixture of exact exchange. This additional flexibility, however, comes with a more involved mathematical form and a more complicated design. A common denominator for previously constructed local hybrid funtionals is usage of thermochemical benchmark data to construct these functionals. Herein, we design a local hybrid functional without relying on benchmark data. Instead, we construct it in a more ab initio manner, following the principles of modern meta-generalized gradient approximations and considering theoretical constrains. To achieve this, we make use of the density matrix expansion and a local mixing function based on an approximate correlation length. The accuracy of the developed density functional approximation is assessed for thermochemistry, excitation energies, polarizabilities, magnetizabilities, NMR spin-spincoupling constants, NMR shieldings and shifts, as well as EPR g-tensors and hyperfine coupling constants. Here, the new exchange functional shows a robust performance and is especially well suited for atomization energies, barrier heights, excitation energies, NMR coupling constants, and EPR properties, whereas it looses some ground for the NMR shifts.Therefore, the designed functional is a major step forwards for functionals that have been designed from first principles.

New pecS-n (n = 1, 2) basis sets for quantum chemical calculations of the NMR chemical shifts of H, C, N, and O nuclei

This paper demonstrates the performance of our previously suggested property-energy consistent method on the example of the generation of effective basis sets, pecS-1 and pecS-2, suited for the calculation of hydrogen, carbon, nitrogen, and oxygen chemical shifts. The new basis sets were successfully approbated in the GIAO-DFT calculations of the chemical shifts of 35 molecules using six different functionals. The pecS-1 basis set demonstrated very good accuracy, which makes this small basis set an effective means for the large-scale computations. At the same time, the pecS-2 basis set also gave very accurate results, thus putting it on a par with the other commensurate basis sets suited for the chemical shifts calculations.

Quantum Chemical Approaches to the Calculation of NMR Parameters: From Fundamentals to Recent Advances

Quantum chemical methods for the calculation of indirect NMR spin–spin coupling constants and chemical shifts are always in progress. They never stay the same due to permanently developing computational facilities, which open new perspectives and create new challenges every now and then. This review starts from the fundamentals of the nonrelativistic and relativistic theory of nuclear magnetic resonance parameters, and gradually moves towards the discussion of the most popular common and newly developed methodologies for quantum chemical modeling of NMR spectra.

Exact-Two-Component Multiconfiguration Pair-Density Functional Theory

Molecules containing late-row elements exhibit large relativistic effects. To account for both relativistic effects and electron correlation in a computationally inexpensive way, we derived a formulation of multiconfiguration pair-density functional theory with the relativistic exact-two-component Hamiltonian (X2C-MC-PDFT). In this new method, relativistic effects are included during variational optimization of a reference wave function by exact-two-component complete active-space self-consistent-field (X2C-CASSCF) theory, followed by an energy evaluation using pair-density functional theory. Benchmark studies of excited-state and ground-state fine-structure splitting of atomic species show that X2C-MC-PDFT can significantly improve the X2C-CASSCF results by introducing additional state-specific electron correlation.

Hyper-CEST NMR of metal organic polyhedral cages reveals hidden diastereomers with diverse guest exchange kinetics

Guest capture and release are important properties of self-assembling nanostructures. Over time, a significant fraction of guests might engage in short-lived states with different symmetry and stereoselectivity and transit frequently between multiple environments, thereby escaping common spectroscopy techniques. Here, we investigate the cavity of an iron-based metal organic polyhedron (Fe-MOP) using spin-hyperpolarized 129Xe Chemical Exchange Saturation Transfer (hyper-CEST) NMR. We report strong signals unknown from previous studies that persist under different perturbations. On-the-fly delivery of hyperpolarized gas yields CEST signatures that reflect different Xe exchange kinetics from multiple environments. Dilute pools with ~ 104-fold lower spin numbers than reported for directly detected hyperpolarized nuclei are readily detected due to efficient guest turnover. The system is further probed by instantaneous and medium timescale perturbations. Computational modeling indicates that these signals originate likely from Xe bound to three Fe-MOP diastereomers (T, C3, S4). The symmetry thus induces steric effects with aperture size changes that tunes selective spin manipulation as it is employed in CEST MRI agents and, potentially, impacts other processes occurring on the millisecond time scale.

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.

A 9.2-GHz clock transition in a Lu(II) molecular spin qubit arising from a 3,467-MHz hyperfine interaction

Spins in molecules are particularly attractive targets for next-generation quantum technologies, enabling chemically programmable qubits and potential for scale-up via self-assembly. Here we report the observation of one of the largest hyperfine interactions for a molecular system, A_iso = 3,467 ± 50 MHz, as well as a very large associated clock transition. This is achieved through chemical control of the degree of s-orbital mixing into the spin-bearing d orbital associated with a series of spin-½ La(II) and Lu(II) complexes. Increased s-orbital character reduces spin-orbit coupling and enhances the electron-nuclear Fermi contact interaction. Both outcomes are advantageous for quantum applications. The former reduces spin-lattice relaxation, and the latter maximizes the hyperfine interaction, which, in turn, generates a 9-GHz clock transition, leading to an increase in phase memory time from 1.0 ± 0.4 to 12 ± 1 μs for one of the Lu(II) complexes. These findings suggest strategies for the development of molecular quantum technologies, akin to trapped ion systems.

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.

NMR Coupling Constants Based on the Bethe-Salpeter Equation in the GW Approximation

We present the first steps to extend the Green's function GW method and the Bethe-Salpeter equation (BSE) to molecular response properties such as nuclear magnetic resonance (NMR) indirect spin-spin coupling constants. We discuss both a nonrelativistic one-component and a quasi-relativistic two-component formalism. The latter describes scalar-relativistic and spin-orbit effects and allows us to study heavy-element systems with reasonable accuracy. Efficiency is maintained by the application of the resolution of the identity approximation throughout. The performance is demonstrated using conventional central processing units (CPUs) and modern graphics processing units (GPUs) for molecules involving several thousand basis functions. Our results show that a large amount of Hartree-Fock exchange is vital to provide a sufficient Kohn-Sham starting point to compute the GW quasi-particle energies. As the GW-BSE approach is generally less accurate for triplet excitations or related properties such as the Fermi-contact interaction, the admixture of the Kohn-Sham correlation kernel through the contracted BSE (cBSE) method improves the results for NMR coupling constants. This leads to remarkable results when combined with the eigenvalue-only self-consistent variant (evGW) and Becke's half and half functional (BH&HLYP) or the CAM-QTP family. The developed methodology is used to calculate the Karplus curve of tin molecules, illustrating its applicability to extended chemically relevant molecules. Here, the GW-cBSE method improves upon the chosen BH&HLYP Kohn-Sham starting points.

Which DFT factors influence the accuracy of 1H, 13C and 195Pt NMR chemical shift predictions in organopolymetallic square-planar complexes? New scaling parameters for homo- and hetero-multimetallic compounds and their direct applications

Because of their chemical heterogeneity, stereochemical complexity and the presence of heavy atoms involving orbitals with high quantum number L, organopolymetallic complexes require considerable focus during their NMR spectral interpretation.

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.

Paramagnetic NMR Shielding Tensors and Ring Currents: Efficient Implementation and Application to Heavy Element Compounds

We present an efficient implementation of paramagnetic NMR shielding tensors and shifts in a nonrelativistic and scalar-relativistic density functional theory framework. For the latter, we make use of the scalar exact two-component Hamiltonian in its local approximation, and generally we apply the well established (multipole-accelerated) resolution of the identity approximation and the seminumerical exchange approximation. The perturbed density matrix of a paramagnetic NMR shielding calculation is further used to study the magnetically induced current density and ring currents of open-shell systems as illustrated for [U@Bi₁₂]^3-. [U@Bi₁₂]^3- features delocalized highest occupied molecular orbitals and sustains a net diatropic ring current of ca. 18 nA/T through the Bi₁₂ torus similar to the all-metal aromatic heavy-element cluster [Th@Bi₁₂]^4-.

Reliable TDDFT Protocol Based on a Local Hybrid Functional for the Prediction of Vibronic Phosphorescence Spectra Applied to Tris(2,2'-bipyridine)-Metal Complexes

An efficient computational protocol for the prediction of vibrationally resolved phosphorescence spectra is developed and validated for five tris(2,2'-bipyridine)-metal complexes ([M(bpy)₃]ⁿ⁺, where M = Zn, Ru, Rh, Os, Ir). The outstanding feature of this protocol is the use of full linear-response time-dependent density functional theory (TDDFT) for the excited-state triplet calculation, i.e., the commonly seen strategies employing the Tamm-Dancoff approximation (TDA) or unrestricted density functional theory (DFT) calculations for the T₁ state are not needed. This is achieved by the use of a local hybrid functional (LH12ct-SsirPW92) that features a real-space dependent admixture of exact exchange governed by a local mixing function. The excellent performance of this LH for triplet excitation energies known from previous studies transfers to a remarkable mean absolute error of 0.06 eV for the phosphorescence 0-0 energies investigated herein, while the popular B3PW91 functional gives an error of 0.27 eV in TDDFT and 0.09 eV in unrestricted DFT calculations, respectively. The advantages of the local hybrid are particularly apparent for excited states with a mixed-valence character. The influence of spin-orbit coupling was found to be significant for [Os(bpy)₃]²⁺ red-shifting the 0-0 energy for phosphorescence by 0.17 eV, while the effect is negligible for the other complexes (<0.03 eV). The influence of the basis-set and integration-grid sizes is evaluated, and a computationally lighter protocol is validated that leads to drastic savings in computation time with negligible loss in accuracy.

Highly Soluble Supertetrahedra upon Selective Partial Butylation of Chalcogenido Metalate Clusters in Ionic Liquids

Supertetrahedral clusters have been reported in two generally different types so far: one type possessing an organic ligand shell, no or low charges, and high solubility, while the other cluster type is ligand-free with usually high charges and low or no solubility in common solvents. The latter is a tremendous disadvantage regarding further use of the clusters in solution. However, as organic substituents usually broaden the HOMO-LUMO gaps, which cannot be overcompensated by the (limited) cluster sizes, a full organic shielding comes along with drawbacks regarding opto-electronic properties. We therefore sought to find a way of generating soluble clusters with a minimum number of organic substituents. Here, we present the synthesis and full characterization of two salts of [Sn10 O4 S16 (SBu)4 ]4- that are high soluble in CH2 Cl2 or CH3 CN, which includes first NMR and mass spectra obtained from solutions of such salts with mostly inorganic supertetrahedral clusters. The optical absorption properties of this new class of compounds indicates nearly unaffected band gaps. The synthetic approach and the spectroscopic findings were rationalized and explained by means of high-level quantum chemical studies.