Efficient implementation of one- and two-component analytical energy gradients in exact two-component theory

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.

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.

Investigation of Isolated IrF5 -, IrF6 - Anions and M[IrF6] (M=Na, K, Rb, Cs) Ion Pairs by Matrix-Isolation Spectroscopy and Relativistic Quantum-Chemical Calculations

The molecular IrF5 -, IrF6 - anions and M[IrF6] (M=Na, K, Rb, Cs) ion pairs were prepared by co-deposition of laser-ablated alkali metal fluorides MF with IrF6 and isolated in solid neon or argon matrices under cryogenic conditions. The free anions were obtained as well by co-deposition of IrF6 with laser-ablated metals (Ir or Pt) as electron sources. The products were characterized in a combined analysis of matrix IR spectroscopy and electronic structure calculations using two-component quasi-relativistic DFT methods accounting for spin-orbit coupling (SOC) effects as well as multi-reference configuration-interaction (MRCI) approaches with SOC. Inclusion of SOC is crucial in the prediction of spectra and properties of IrF6 - and its alkali-metal ion pairs. The observed IR bands and the computations show that the IrF6 - anion adopts an Oh structure in a nondegenerate ground state stabilized by SOC effects, and not a distorted D4h structure in a triplet ground state as suggested by scalar-relativistic calculations. The corresponding "closed-shell" M[IrF6] ion pairs with C3v symmetry are stabilized by coordination of an alkali metal ion to three F atoms, and their structural change in the series from M=Na to Cs was proven spectroscopically. There is no evidence for the formation of IrF7, IrF7 - or M[IrF7] (M=Na, K, Rb, Cs) ion pairs in our experiments.

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.

Consistent Analytical Second Derivatives of the Kohn-Sham DFT Energy in the Framework of the Conductor-Like Screening Model through Gaussian Charge Distributions

The use of implicit solvation models such as the conductor-like screening model (COSMO) in quantum chemical calculations is very common, as both a rough estimate of solvation effects as well as a general tool for stabilizing ionic molecular structures. In order to generate a smooth potential energy surface as well as consistent gradients, it is necessary to apply the Gaussian charge model (GCM) for the COSMO charges. This work introduces an efficient implementation for consistent analytical second derivatives of the electronic energy with COSMO-GCM in the framework of the Kohn-Sham density functional theory. This is used to investigate the infrared spectroscopy of amino acids in aqueous solution, where the impact of pH on the molecular structure and vibrational spectra is examined. Furthermore, the structure and stability of selected all-metal aromatic cluster ions are assessed.

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.

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.

Electronic spectroscopy of homo- and heterometallic binuclear coinage metal phosphine complexes in isolation

Binuclear coinage metal phosphine complexes are examined under ion trap isolation in order to elucidate their noncovalent binding, structural properties and intrinsic electronic spectra. Our survey shows an intriguing order of electronic transitions obtained by in situ synthesis and mass-spectrometrically supported UV photodissociation spectroscopy on a series of six isolated homo- and heterobinuclear complexes of type [MM'(dcpm)2]2+ (M, M' = CuI, AgI, AuI; dcpm = bis(dicyclohexyl-phosphino)methane). This approach provides the unique opportunity to study all possible coinage metal interactions within a fixed ligand framework. A successive blue-shift (33 700-38 500 cm-1; 297-260 nm) of the lowest-energy bright electronic transition energy in gas phase was observed in the order of Cu2 < CuAu < CuAg < Au2 < AgAu < Ag2. This order was reproduced by quantum chemical calculations using a scalar-relativistic GW-Bethe-Salpeter-equation (GW-BSE) approach. Theory ascribes the electronic bands of all complexes to metal-centered 1MC(dσ*-pσ) transitions revealing a strengthening of metal-metal' (M-M') binding upon excitation, in agreement to mass spetrometric results. A test of the correlation of transition energies with M-M' distance by quantum chemical calculations of single point energies as a function of intermetallic distance indicates qualitative agreement with experimental results. However, the experimentally observed high sensitivity of spectroscopic shifts towards metal composition cannot be accounted for solely by M-M' distance variation. The differences in electronic transitions are qualitatively rationalized by the varying (n + 1)s (n = 3, 4, 5) orbital contributions (increase from Cu2via CuAu/CuAg to Au2/AgAu/Ag2) within the nd(n + 1)s/p-hybridization for the ground electronic state of the different complexes, whereas the excited state (of (n + 1)p orbital character) shows significantly less variation in energy. In particular, the observed spectroscopic and mass spectrometric sequence for the Ag/Au complexes is traced back to the interplay of Pauli repulsion and variation in metal-ligand bond strength within the orbital hybridization model.

Robust relativistic many-body Green's function based approaches for assessing core ionized and excited states

A two-component contour deformation (CD) based GW method that employs frequency sampling to drastically reduce the computational effort when assessing quasiparticle states far away from the Fermi level is outlined. Compared to the canonical CD-GW method, computational scaling is reduced by an order of magnitude without sacrificing accuracy. This allows for an efficient calculation of core ionization energies. The improved computational efficiency is used to provide benchmarks for core ionized states, comparing the performance of 15 density functional approximations as Kohn-Sham starting points for GW calculations on a set of 65 core ionization energies of 32 small molecules. Contrary to valence states, GW calculations on core states prefer functionals with only a moderate amount of Hartree-Fock exchange. Moreover, modern ab initio local hybrid functionals are also shown to provide excellent generalized Kohn-Sham references for core GW calculations. Furthermore, the core-valence separated Bethe-Salpeter equation (CVS-BSE) is outlined. CVS-BSE is a convenient tool to probe core excited states. The latter is tested on a set of 40 core excitations of eight small inorganic molecules. Results from the CVS-BSE method for excitation energies and the corresponding absorption cross sections are found to be in excellent agreement with those of reference damped response BSE calculations.

Practical Post-Kohn-Sham Methods for Time-Reversal Symmetry Breaking References

The applicability of reduced scaling algorithms based on auxiliary subspace methods for the correlation energy from the random phase approximation (RPA) as well as the correlation part of the self-energy obtained from the GW method is outlined for time-reversal symmetry breaking Kohn-Sham (KS) references. The updated algorithms allow for an efficient evaluation of RPA energies and GW quasiparticle energies for molecular systems with KS references that break time-reversal symmetry. The latter occur, for example, in magnetic fields. Furthermore, KS references for relativistic open-shell molecules also break time-reversal symmetry due to the single determinant ansatz used. Errors of the updated reduced-scaling algorithms are shown to be negligible compared to reference implementations, while the overall computational scaling is reduced by 2 orders of magnitude. Ionization energies obtained from the GW approximation are shown to be robust even for the electronically complicated group of trivalent lanthanoid ions. Starting from GW quasiparticle energies, it is subsequently shown that light-matter interactions of these systems can be calculated using the Bethe-Salpeter equation (BSE). Using the combined GW-BSE method, the absorption and emission spectra of a molecular europium(III) complex can be obtained including spin-orbit coupling.

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.

Ion-Selective Assembly of Supertetrahedral Selenido Germanate Clusters for Alkali Metal Ion Capture and Separation

Supertetrahedral chalcogenido (semi)metalate cluster-based frameworks possess high selectivity for alkali metal cations, matching the specific charge density of their inner surfaces, which enables their use as ion-exchange materials. Aggregates of the supertetrahedral chalcogenido metalate cluster offer even new perspectives for metal ion capture and separation. Herein, we report on ionothermal preparation of two corresponding model compounds, (C₂C₁Im)₇[Cs@Ge^II₄(Ge^IV₄Se₁₀)₄] (1) and (C₂C₁Im)₁₀[Na₅(CN)₆@Cu₆(Ge₄Se₁₀)₄(Cu)] (2). Their formation is reliant on one specific cation type each, Cs⁺ for 1 and Na⁺ for 2, thus providing promising separation potential during crystallization. Compound 1 is based on the largest discrete binary selenido germanate cluster reported to date and the first mixed-valent chalcogenido germanate(II/IV) supertetrahedron. Moreover, it adds to the few examples of chalcogenides capable of capturing Cs⁺ ions. Its high selectivity for Cs⁺ compared to that of Li⁺, Na⁺, K⁺, and Rb⁺ was confirmed by single-crystal X-ray diffraction, energy-dispersive X-ray spectroscopy, and electrospray ionization mass spectrometry. Quantum chemical studies indicate that smaller ions, K⁺ and Rb⁺, could also be embedded in an isolated cluster assembly, but as the cluster aggregate slightly distorts for crystallization, the selectivity for Cs⁺ becomes exclusive in the salt. The anionic substructure of compound 2 is based on a two-dimensional network of supramolecular assemblies and exhibits an exclusive preference for Na⁺. This work thus provides the first comprehensive insight into the selective incorporation of specific alkali metal ions into supramolecular aggregates of supertetrahedral chalcogenide clusters, as a promising basis for new ion trapping techniques─especially for heavy alkali metal ions that pose environmental challenges.

A Computational Study on Closed-Shell Molecular Hexafluorides MF6 (M=S, Se, Te, Po, Xe, Rn, Cr, Mo, W, U) - Molecular Structure, Anharmonic Frequency Calculations, and Prediction of the NdF6 Molecule

Quantum chemical methods were used to study the molecular structure and anharmonic IR spectra of the experimentally known closed-shell molecular hexafluorides MF₆ (M=S, Se, Te, Xe, Mo, W, U). First, the molecular structures and harmonic frequencies were investigated using Density Functional Theory (DFT) with all-electron basis sets and explicitly considering the influence of spin-orbit coupling. Second, anharmonic frequencies and IR intensities were calculated with the CCSD(T) coupled cluster method and compared, where available, with IR spectra recorded by us. These comparisons showed satisfactory results. The anharmonic IR spectra provide means for identifying experimentally too little studied or unknown MF₆ molecules with M=Cr, Po, Rn. To the best of our knowledge, we predict the NdF₆ molecule for the first time and show it to be a true local minimum on the potential energy surface. We used intrinsic bond orbital (IBO) analyses to characterize the bonding situation in comparison with the UF₆ molecule.

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.

Modeling Nonresonant X-ray Emission of Second- and Third-Period Elements without Core-Hole Reference States and Empirical Parameters

Nonresonant X-ray emission (XE) energies and oscillator strengths are obtained using the effective potential of the generalized Kohn-Sham semi-canonical projected random phase approximation (GKS-spRPA) method. XE energies are estimated as a difference between the valence and core ionization eigenvalues, while the oscillator strengths are obtained within a frozen orbital approximation. This straightforward approach provides accurate XE energies without any need for core-hole reference states, empirical shifting parameters, or tuning of density functionals. To account for relativistic corrections to the core orbitals, we have formulated a scalar relativistic (sr) GKS-spRPA approach based on the spin-free X2C one-electron Hamiltonian. The sr-GKS-spRPA method provides highly reliable XE energies using uncontracted basis-sets on atoms where the core-hole is created prior to emission. For the largest basis-sets used in our study, using completely uncontracted polarized core-valence Dunning basis-sets, the mean absolute errors (MAEs) are within 0.7 eV compared to experimental reference values for a test-set consisting of 27 valence-to-core XE energies of molecules with second- and third-period elements. Considering a balance of accuracy and computational effort, we recommend the use of s-uncontracted def2-TZVP for second-period and all-uncontracted def2-TZVP for third-period elements. For this recommended basis-set, the MAE is 0.2 eV. The analytically continued sr-GKS-spRPA approach, with an O(N4) computational cost, enables efficient computation of XE spectra of molecules such as S₈ and C₆₀ with several core-hole states.

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.

Communication: Impact of the current density on paramagnetic NMR properties

Meta-generalized gradient approximations (meta-GGAs) and local hybrid functionals generally depend on the kinetic energy density τ. For magnetic properties, this necessitates generalizations to ensure gauge invariance. In most implementations, τ is generalized by incorporating the external magnetic field. However, this introduces artifacts in the response of the density matrix and does not satisfy the iso-orbital constraint. Here, we extend previous approaches based on the current density to paramagnetic NMR shieldings and EPR g-tensors. The impact is assessed for main-group compounds and transition-metal complexes considering 25 density functional approximations. It is shown that the current density leads to substantial improvements-especially for the popular Minnesota and SCAN functional families. Thus, we strongly recommend to use the current density generalized τ in paramagnetic NMR and EPR calculations with meta-GGAs.

Investigation of Molecular Iridium Fluorides IrFn (n=1-6): A Combined Matrix-Isolation and Quantum-Chemical Study

The photo-initiated defluorination of iridium hexafluoride (IrF6 ) was investigated in neon and argon matrices at 6 K, and their photoproducts are characterized by IR and UV-vis spectroscopies as well as quantum-chemical calculations. The primary photoproducts obtained after irradiation with λ=365 nm are iridium pentafluoride (IrF5 ) and iridium trifluoride (IrF3 ), while longer irradiation of the same matrix with λ=278 nm produced iridium tetrafluoride (IrF4 ) and iridium difluoride (IrF2 ) by Ir-F bond cleavage or F2 elimination. In addition, IrF5 can be reversed to IrF6 by adding a F atom when exposed to blue-light (λ=470 nm) irradiation. Laser irradiation (λ=266 nm) of IrF4 also generated IrF6 , IrF5 , IrF3 and IrF2 . Alternatively, molecular binary iridium fluorides IrFn (n=1-6) were produced by co-deposition of laser-ablated iridium atoms with elemental fluorine in excess neon and argon matrices under cryogenic conditions. Computational studies up to scalar relativistic CCSD(T)/triple-ζ level and two-component quasirelativistic DFT computations including spin-orbit coupling effects supported the formation of these products and provided detailed insights into their molecular structures by their characteristic Ir-F stretching bands. Compared to the Jahn-Teller effect, the influence of spin-orbit coupling dominates in IrF5 , leading to a triplet ground state with C4v symmetry, which was spectroscopically detected in solid argon and neon matrices.

Intersystem Crossings in Late-Row Elements: A Perspective

Intersystem crossing (ISC), a vital component of the electronic and nuclear transitions that compose photophysics, has been successfully simulated in light elements and transition metal complexes. Derived from the Z-dependent spin-orbit coupling (SOC), ISC is expected to be of greater importance in heavier elements, but few attempts have been made at the simulation of ISC in lanthanides or actinides. In this work, we explore several of the challenges that will need to be overcome in order to treat ISC in late-row elements, including the loss of spin as a good quantum number, the need to include SOC variationally via two- or four-component electronic structure, and the high density of states present in late-row complexes. Density functional theory (DFT) calculations are used to illustrate several of these effects, while a model Hamiltonian is used to illustrate the importance of momentum rescaling in surface hopping simulations of strongly coupled states.

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.

Studies of the First Electronically Excited State of 3-Fluoropyridine and Its Ionic Structure by Means of REMPI, Two-Photon MATI, One-Photon VUV-MATI Spectroscopy and Franck-Condon Analysis

3-Fluoropyridine (3-FP) has been investigated by means of two-photon resonance-enhanced multi photon ionization (REMPI), mass-analyzed threshold ionization (MATI) and one-photon vacuum-ultraviolet (VUV) MATI spectroscopy. The aim was the determination of the effect of m-fluorine substitution on the vibronic structure of the first electronically excited and ionic ground state. The S₁ excitation energy has been determined to be 35 064 ± 2 cm^-1 (4.3474 ± 0.0002 eV). Strong evidence of a distinct vibronic coupling via ν_16b and ν_{[Wag.out.,16a]} to one or both of the lowest ¹ππ* states has been found, which results in a warped S₁ minimum structure with C₁ symmetry. The adiabatic ionization energy of the ionic ground state (14a', n_N-LP orbital) has been determined to be 76 579 ± 6 cm^-1 (9.4946 ± 0.0007 eV), which is the first value reported for this state. The origin of the D₁ state (4a'', π-orbital) is located close by at 77 129 cm^-1 (9.5628 eV). As a result of the D₀-D₁ vicinity, the ionic ground state is coupled to the D₁ state via ν_{[Wag.out.,16a]} and ν_10a, which induces a twisted D₀ geometry with C₁ symmetry. Furthermore, for the first time two-photon and one-photon MATI spectra are presented together, which yield a much better understanding of the ionic vibronic structure in comparison to either of these experiments alone.

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.

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-.

Investigation of the complex vibronic structure in the first excited and ionic ground states of 3-chloropyridine by means of REMPI and MATI spectroscopy and Franck-Condon analysis

3-Chloropyridine (3-CP) has been investigated by means of resonance-enhanced multi-photon ionization (REMPI) and mass-analyzed threshold ionization (MATI) spectroscopy to elucidate the effect of m-chlorine substitution on the vibronic structure of the first electronically excited and ionic ground states. The S₁ excitation energy has been determined to be 34 840 ± 2 cm^-1 (4.3196 ± 0.0002 eV) with a difference of less than 0.2 cm^-1 between both isotopomers, which is the first reported value for this transition in the gas phase so far. The S₁ state has been assigned to the ¹π* ← n transition. It is subject to strong vibronic coupling via ν_16b to one or both of the lowest ¹ππ* states. In addition, strong coupling via at least one more non-totally symmetric vibration is very likely to exist but the vibration could not be identified yet. Overall, the coupling results in a minimum S₁ structure with C₁ symmetry. The adiabatic ionization energy of the n_N-LP orbital (14a') has been determined to be 75 879 ± 6 cm^-1 (9.4078 ± 0.0007 eV) with a difference of less than 2 cm^-1 between the two isotopomers, which is the first value reported for this state so far. The ionic ground state exhibits a distinct vibronic coupling via ν_16a and ν_10a to either the D₁ state (4a'') and/or D₂ state (3a''), which results in a twisted D₀ geometry with C₁ symmetry. As a consequence of the warped geometry in both S₁ and D₀ states, very complicated MATI spectra were obtained when exciting S₁ states at higher wavenumbers.

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.

NMR Indirect Spin-Spin Coupling Constants in a Modern Quasi-Relativistic Density Functional Framework

A quasi-relativistic implementation of NMR indirect spin-spin coupling constants is presented. The exact two-component (X2C) Hamiltonian and its diagonal local approximation to the unitary decoupling transformation (DLU) are utilized together with the (modified) screened nuclear spin-orbit approach. In a restricted kinetic balance, the finite nucleus model is available for both the scalar and vector potentials. The implementation supports density functionals up to the fourth rung of Jacob's ladder, i.e., (range-separated) hybrid and local hybrid functionals based on a seminumerical ansatz. We assess the quality of our quasi-relativistic X2C approach by comparison with "fully" relativistic four-component results for small main-group molecules and alkynyl compounds. The mean absolute error introduced by the DLU scheme is less than 0.05 × 10¹⁹ T J^-2 of the reduced coupling constant for the small main-group molecules and 0.5 Hz for the alkynyl compounds. Thus, the error is significantly smaller than finite nucleus size effects for heavy elements. The basis set convergence and the impact of different density functional approximations are further studied. We propose a simple scheme to develop segmented-contracted relativistic all-electron basis sets for NMR spin-spin couplings. Our implementation allows us to perform calculations of extended molecules with reasonable computational effort, which is illustrated for the ¹J(¹¹⁹Sn, ³¹P) coupling constant of a low-valent tin phosphinidenide complex. The corresponding results are in good agreement with the experimental findings.

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.

Structures of Small Tantalum Cluster Anions: Experiment and Theory

We present a study of the structural evolution of tantalum cluster anions Ta_n^-, 6 ≤ n ≤ 13 using a combination of trapped ion electron diffraction (TIED) experiments with a variety of electronic structure methods. A genetic algorithm has been employed to establish a set of likely structures for each cluster, their geometries and energetics have been studied by density functional theory (DFT), random phase approximation, and two-component (2C) DFT methods, which include spin-orbit coupling. We find octahedral structures for Ta₆^- and Ta₈^- as well as structures based on the pentagonal bipyramid (Ta₇^- and Ta₉^-). Ta₁₀^--Ta₁₂^- are defective icosahedral structures and Ta₁₃^- is a distorted icosahedron. For most clusters, we find a good agreement between the theoretically predicted ground-state structures, especially those determined by the 2C method and the TIED results.

Using a Porphyrin Diacid Cation to Stabilize a Square-Pyramidal BiX5 (X = Br, Cl/Br) Unit

Main-group halogenido metalates are a diverse class of compounds with an intricate structural chemistry and a wide range of applications. Here, we present an unprecedented anion motif in the structural chemistry of halogenido bismuthates, a square-pyramidal BiX₅ unit. We show how the porphyrin diacid used as our compounds' counterion is templating the formation of this new motif, suggesting that other strong anion receptors may be able to stabilize unique metalate anions in future work.

Substantial π-aromaticity in the anionic heavy-metal cluster [Th@Bi12]4

The concept of aromaticity was originally defined as a property of unsaturated, cyclic planar organic molecules like benzene, which gain stability by the inherent delocalization of 4n + 2 π-electrons over the ring atoms. Since then, π-aromaticity has been observed for a large variety of organic and inorganic non-metal compounds, yet, for molecules consisting only of metal atoms, it has remained restricted to systems with three to five atoms. Here, we present the straightforward synthesis of a metal 12-ring that exhibits 2π-aromaticity and has a ring current much stronger than that of benzene (6π) and equivalent to that of porphine (26π), despite these organic molecules having (much) larger numbers of π-electrons. Highly reducing reaction conditions allowed access to the heterometallic anion [Th@Bi₁₂]^4-, with interstitial Th⁴⁺ stabilizing a Bi₁₂^8- moiety. Our results show that it is possible to design and generate substantial π-aromaticity in large metal rings, and we hope that such π-aromatic heavy-metal cycles will eventually find use in cluster-based reactions.

Stabilizing a metalloid {Zn12} unit within a polymetallide environment in [K2Zn20Bi16]6

The access to molecules comprising direct Zn–Zn bonds has become very topical in recent years for various reasons. Low-valent organozinc compounds show remarkable reactivities, and larger Zn–Zn-bonded gas-phase species exhibit a very unusual coexistence of insulating and metallic properties. However, as Zn atoms do not show a high tendency to form clusters in condensed phases, synthetic approaches for generating purely inorganic metalloid Zn_x units under ambient conditions have been lacking so far. Here we show that the reaction of a highly reductive solid with the nominal composition K₅Ga₂Bi₄ with ZnPh₂ at room temperature yields the heterometallic cluster anion [K₂Zn₂₀Bi₁₆]^6–. A 24-atom polymetallide ring embeds a metalloid {Zn₁₂} unit. Density functional theory calculations reveal multicenter bonding, an essentially zero-valent situation in the cluster center, and weak aromaticity. The heterometallic character, the notable electron-delocalization, and the uncommon nano-architecture points at a high potential for nano-heterocatalysis.

Low-valent zinc clusters, though exceedingly rare, are appealing synthetic targets because there is evidence that they may show unconventional chemical and physical behavior. Here, the authors obtain a large heterometallic zinc-bismuth cluster anion and discover that it bears a metalloid {Zn₁₂} core with four-center bonding and essentially zero-valent character.

Synthesis of a Molecule with Five Different Adjacent Pnictogens

The first molecular compound with all five pnictogens was obtained by a multi-step reaction. Lithiation of the (bisamido)diazadiarsetidine (tBuNAs)2 (tBuNH)2 in aliphatic solvents leads to the dimeric metallated species [(tBuNAs)2 (tBuNLi)2 ]2 (12 ). Upon reactions with AsCl3 , SbCl3 and BiCl3 the polycyclic compounds [(tBuNAs)2 (tBuN)2 ]PnCl (Pn=As (2), Sb (3), Bi (4)) can be obtained. Conversion of 2-4 with [tBu2 SbP(tBu)Li(OEt2 )]2 leads to the remarkable interpnictogens [(tBuNAs)2 (tBuN)2 ]PnP(tBu)SbtBu2 (Pn=As (5), Sb (6), Bi (7)), whereby 7 is the first example of a molecule containing all five Group 15 elements. The compound with adjacent AsNBiPSb-chains is surprisingly stable and does not show high sensibility against light as the labile Bi-P bond might suggest.

TURBOMOLE: Modular program suite for ab initio quantum-chemical and condensed-matter simulations

TURBOMOLE is a collaborative, multi-national software development project aiming to provide highly efficient and stable computational tools for quantum chemical simulations of molecules, clusters, periodic systems, and solutions. The TURBOMOLE software suite is optimized for widely available, inexpensive, and resource-efficient hardware such as multi-core workstations and small computer clusters. TURBOMOLE specializes in electronic structure methods with outstanding accuracy-cost ratio, such as density functional theory including local hybrids and the random phase approximation (RPA), GW-Bethe-Salpeter methods, second-order Møller-Plesset theory, and explicitly correlated coupled-cluster methods. TURBOMOLE is based on Gaussian basis sets and has been pivotal for the development of many fast and low-scaling algorithms in the past three decades, such as integral-direct methods, fast multipole methods, the resolution-of-the-identity approximation, imaginary frequency integration, Laplace transform, and pair natural orbital methods. This review focuses on recent additions to TURBOMOLE's functionality, including excited-state methods, RPA and Green's function methods, relativistic approaches, high-order molecular properties, solvation effects, and periodic systems. A variety of illustrative applications along with accuracy and timing data are discussed. Moreover, available interfaces to users as well as other software are summarized. TURBOMOLE's current licensing, distribution, and support model are discussed, and an overview of TURBOMOLE's development workflow is provided. Challenges such as communication and outreach, software infrastructure, and funding are highlighted.

Low-Valent Group 14 Phosphinidenide Complexes [({SIDipp}P)2 M] Exhibit P-M pπ-pπ Interaction (M=Ge, Sn, Pb)

Herein, the synthesis of new low-valent Group 14 phosphinidenide complexes [({SIDipp}P)2 M] exhibiting P-M pπ-pπ interactions (SIDipp=1,3-bis(2,6-diisopropylphenyl)-imidazolidin-2-ylidene, M=Ge, Sn, Pb), is presented. These compounds were investigated by means of structural, spectroscopic, and quantum-chemical methods. Furthermore, the monosubstituted compounds [(SIDippP)MX]2 (M=Sn, X=Cl; M=Pb, X=Br) are presented, which show dimeric structures instead of multiple bonding interaction.

Density Functional Calculations of Electron Paramagnetic Resonance g- and Hyperfine-Coupling Tensors Using the Exact Two-Component (X2C) Transformation and Efficient Approximations to the Two-Electron Spin-Orbit Terms

A two-component quasirelativistic density functional theory implementation of the computation of hyperfine and g-tensors at exact two-component (X2C) and Douglas-Kroll-Hess method (DKH) levels in the Turbomole code is reported and tested for a series of smaller 3d¹, 4d¹, and 5d¹ complexes, as well as for some larger 5d⁷ Ir and Pt systems in comparison with earlier four-component matrix-Dirac-Kohn-Sham results. A main emphasis is placed on efficient approximations to the two-electron spin-orbit contributions, comparing an existing implementation of two variants of Boettger's "scaled nuclear spin-orbit" (SNSO) approximation in the code with a newly implemented atomic mean-field spin-orbit (AMFSO) approximation. The different variants perform overall comparably well with the four-component data. The AMFSO approximation has the added advantage of being able to include the spin-other-orbit contributions arising from the Gaunt term of relativistic electron-electron interactions. These are of comparably larger importance for the 3d complexes than for their heavier homologues. The excellent agreement between X2C and four-component electron paramagnetic resonance parameter results provides the opportunity to treat large systems efficiently and accurately with the computationally more expedient two-component quasirelativistic methodology.