Current density functional framework for spin–orbit coupling

Relativistic two-component density functional calculations are carried out in a non-collinear formalism to describe spin–orbit interactions, where the exchange–correlation functional is constructed as a generalization of the non-relativistic density functional approximation. Contrary to non-relativistic density functional theory (DFT), spin–orbit coupling, however, leads to a non-vanishing paramagnetic current density. Density functionals depending on the kinetic energy density, such as meta-generalized gradient approximations, should therefore be constructed in the framework of current DFT (CDFT). The latter has previously exclusively been used in the regime of strong magnetic fields. Herein, we present a consistent CDFT approach for relativistic DFT, including spin–orbit coupling. Furthermore, we assess the importance of the current density terms for ground-state energies, excitation energies, nuclear magnetic resonance shielding, and spin–spin coupling constants, as well as hyperfine coupling constants, $\Delta$g-shifts, and the nuclear quadrupole interaction tensor in electron paramagnetic resonance (EPR) spectroscopy. The most notable changes are found for EPR properties. The impact of the current-dependent terms rises with the number of unpaired electrons, and consequently, the EPR properties are more sensitive toward CDFT. Considerable changes are observed for the strongly constrained and appropriately normed functionals, as well as the B97M family and TASK. The current density terms are less important when exact exchange is incorporated. At the same time, the current-dependent kernel ensures the stability of response calculations in all cases. We, therefore, strongly recommend to use the framework of CDFT for self-consistent spin–orbit calculations

Calculations of current densities and aromatic pathways in cyclic porphyrin and isoporphyrin arrays

Magnetically induced current density susceptibilities have been studied for a number of cyclic ethyne and butadiyne-bridged porphyrin and isoporphyrin arrays. The current density susceptibilities have been calculated using the gauge-including magnetically induced current (GIMIC) method, which is interfaced to the TURBOMOLE quantum chemistry code. Aromatic properties and current pathways have been analyzed and discussed by numerical integration of the current density susceptibilities passing selected chemical bonds yielding current strength susceptibilities. Despite the interrupted p-framework, zinc(II) isoporphyrin sustains a ring current of ca. 10 nA T-1. Porphyrin and isoporphyrin dimers sustain a significant current strength at the linker, whereas the larger porphyrinoid arrays sustain mainly local ring currents. Isoporphyrin dimers with saturated meso carbons have strong net diatropic ring-current strengths of 20 nA T-1 fulfilling Huckels aromaticity rule. Porphyrin trimers and tetramers exhibit almost no current strength at the linker. The porphyrin moieties maintain their strong net diatropic ring current.Peer reviewe

φ-Aromaticity in prismatic {Bi6_6}-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 {Bi$_6$} 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}$_3$Bi$_6$]–, based on a regular prismatic {Bi$_6$} unit, displays aromatic behaviour; according to quantum chemical calculations, the corresponding hypothetical Bi$_6$$^{2−}$ prism shows a similar behaviour. By contrast, [{(cod)Ir}$_3$Bi$_6$] features a distorted Bi$_6$ moiety that inhibits φ-aromaticity

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

Herein, the synthesis of new low-valent Group 14 phosphinidenide complexes [({SIDipp}P)2M] exhibiting P–M pp–pp 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

Stabilizing a metalloid Zn12_{12} unit within a polymetallide environment in [K2_{2}Zn20_{20}Bi16_{16}]6−^{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 K$_{5}$Ga$_{2}$Bi$_{4}$ with ZnPh2 at room temperature yields the heterometallic cluster anion [K$_{2}$Zn$_{20}$Bi$_{16}$]$^{6-}$. A 24-atom polymetallide ring embeds a metalloid {Zn$_{12}$} 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

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 (CuI, AgI and AuI) are described. All coinage metal centres are in tetrahedral coordination environments in the solid state and are exclusively coordinated by four neutral SnII donors. 119Sn 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

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

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, 3974-3994 (2021)] 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, i.e. the one-component treatment is not sufficient for tin compounds featuring a few heavy halogen atoms

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 nuclear magnetic resonance (NMR) shieldings and electron paramagnetic resonance (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 strongly constrained and appropriately normed (SCAN) functional families. Thus, we strongly recommend to use the current density generalized τ in paramagnetic NMR and EPR calculations with meta-GGAs