One-Electron Energies from the Two-Component GW Method

The two-component extension of the G₀W₀ method for closed-shell systems based on the previously implemented one-component version in TURBOMOLE that uses localized basis functions is presented. In this way, it is possible to account for spin–orbit effects on one-electron energies of isolated molecular systems at the G₀W₀ level. We briefly sketch the derivation of the underlying equations, give details about the implementation, and apply the method to several atomic and diatomic systems. The influence of spin–orbit coupling changes calculated first ionization energies by up to 0.7 eV, leading to maximum errors smaller than 0.3 eV. Virtually the same results are obtained with an economic extrapolation scheme based on the one-component G₀W₀ and the two-component reference state calculation. Furthermore, for binding energies of core levels, two-component G₀W₀ is very accurate, as demonstrated for mercury and zinc atoms as well as for ZnF₂

Implementation of Two-Component Time-Dependent Density Functional Theory in TURBOMOLE

We report the efficient implementation of a two-component time-dependent density functional theory proposed by Wang et al. (Wang, F.; Ziegler, T.; van Lenthe, E.; van Gisbergen, S.; Baerends, E. J. <i>J. Chem. Phys.</i> <b>2005</b>, <i>122</i>, 204103) that accounts for spin–orbit effects on excitations of closed-shell systems by employing a noncollinear exchange–correlation kernel. In contrast to the aforementioned implementation, our method is based on two-component effective core potentials as well as Gaussian-type basis functions. It is implemented in the TURBOMOLE program suite for functionals of the local density approximation and the generalized gradient approximation. Accuracy is assessed by comparison of two-component vertical excitation energies of heavy atoms and ions (Cd, Hg, Au⁺) and small molecules (I₂, TlH) to other two- and four-component approaches. Efficiency is demonstrated by calculating the electronic spectrum of Au₂₀

Calculation of Magnetic Shielding Constants with meta-GGA Functionals Employing the Multipole-Accelerated Resolution of the Identity: Implementation and Assessment of Accuracy and Efficiency

We present a highly efficient implementation for density functional calculations of chemical shielding constants. It employs the multipole-accelerated resolution of the identity for the calculation of the Coulomb part, which complements the usage of low order scaling routines for the evaluation of the exchange-correlation part and the Hartree–Fock exchange part. Introduced errors for shifts of chemical shielding constants of H, C, F, and P are evaluated for respective test sets of molecules and are related to the accuracy of shifts obtained with hybrid and nonhybrid functionals of the generalized gradient approximation type as well as for meta-GGA functionals themselves. Efficiency is demonstrated for α-d-glucose chains with more than 2500 atoms on a single CPU as well as with an OpenMP parallelized version

Superatomic Orbitals under Spin–Orbit Coupling

The Au₂₅(SR)₁₈^– cluster has been the poster child of success in applying the superatom complex concept and remains the most studied system of all of the monolayer-protected metal clusters. In this Letter, we try to solve a mystery about this cluster: the low-temperature UV–vis absorption spectrum shows double peaks below 2.0 eV while simulation by scalar relativistic time-dependent density functional theory (TDDFT) shows only one peak in this region. Using a recently implemented two-component TDDFT, we show that spin–orbit coupling (SOC) leads to those two peaks by splitting the 1P superatomic HOMO orbitals. This work highlights the importance of SOC in understanding the electronic structure and optical absorption of thiolated gold nanoclusters, which has not been realized previously

A <i>N</i>‑Heterocyclic Carbene-Stabilized Coinage Metal-Chalcogenide Framework with Tunable Optical Properties

A new class of coinage-metal chalcogenide compounds [Au₄M₄(μ₃-E)₄(IPr)₄] (M = Ag, Au; E = S, Se, Te) has been synthesized from the combination of <i>N</i>-heterocyclic carbene-ligated gold­(I) trimethyl­silyl­chalcogenolates [(IPr)­AuESiMe₃] and ligand-supported metal acetates. Phosphorescence is observed from these clusters in glassy 2-methyl­tetra­hydro­furan and in the solid state at 77 K, with emission energies that depend on the selection of metal/chalcogen ion composition. The ability to tune the emission is attributed to electronic transitions of mixed ligand-to-metal-metal-charge-transfer (IPr → AuM₂) and interligand (IPr → E) phosphorescence character, as revealed by time-dependent density functional theory computations.N-heterocyclic carbenes (NHCs) have been applied as ancillary ligands in the synthesis of luminescent gold­(I) chalcogenide clusters and this approach allows for unprecedented selectivity over the metal and chalcogen ions present within a stable octanuclear framework

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@GeII4(GeIV4Se10)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 techniquesespecially for heavy alkali metal ions that pose environmental challenges

A <i>N</i>‑Heterocyclic Carbene-Stabilized Coinage Metal-Chalcogenide Framework with Tunable Optical Properties

A new class of coinage-metal chalcogenide compounds [Au₄M₄(μ₃-E)₄(IPr)₄] (M = Ag, Au; E = S, Se, Te) has been synthesized from the combination of <i>N</i>-heterocyclic carbene-ligated gold­(I) trimethyl­silyl­chalcogenolates [(IPr)­AuESiMe₃] and ligand-supported metal acetates. Phosphorescence is observed from these clusters in glassy 2-methyl­tetra­hydro­furan and in the solid state at 77 K, with emission energies that depend on the selection of metal/chalcogen ion composition. The ability to tune the emission is attributed to electronic transitions of mixed ligand-to-metal-metal-charge-transfer (IPr → AuM₂) and interligand (IPr → E) phosphorescence character, as revealed by time-dependent density functional theory computations.N-heterocyclic carbenes (NHCs) have been applied as ancillary ligands in the synthesis of luminescent gold­(I) chalcogenide clusters and this approach allows for unprecedented selectivity over the metal and chalcogen ions present within a stable octanuclear framework