Segmented Contracted Error-Consistent Basis Sets of Double- and Triple‑ζ Valence Quality for One- and Two-Component Relativistic All-Electron Calculations

Segmented contracted Gaussian basis sets optimized at the one-electron exact two-component (X2C) level – including a finite size model for the nucleus – are presented for elements up to Rn. These basis sets are counterparts for relativistic all-electron calculations to the Karlsruhe “def2” basis sets for nonrelativistic (H–Kr) or effective core potential based (Rb–Rn) treatments. For maximum consistency, the bases presented here were obtained from the latter by modification and reoptimization. Additionally we present extensions for self-consistent two-component calculations, required for the splitting of inner shells by spin–orbit coupling, and auxiliary basis sets for fitting the Coulomb part of the Fock matrix. Emphasis was put both on the accuracy of energies of atomic orbitals and on the accuracy of molecular properties. A large set of more than 300 molecules representing (nearly) all elements in their common oxidation states was used to assess the quality of the bases all across the periodic table

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

Error-Balanced Segmented Contracted Basis Sets of Double‑ζ to Quadruple‑ζ Valence Quality for the Lanthanides

For lanthanides, segmented contracted Gaussian basis sets of double-ζ valence to quadruple-ζ valence quality are presented, with two different polarization sets for each level of quality. The bases are designed for use in connection with small-core Wood–Boring effective core potentials. A set of compounds representing most lanthanides in their common oxidation states is used to assess the quality. Parameters investigated were atomization energies, dipole moments, and structure parameters for Hartree–Fock, density functional, and correlated (Møller–Plesset) methods. So, the “def2” basis set series is extended to lanthanides with errors that are very similar to those previously obtained for the other elements with this type of basis set. Furthermore, for lanthanides, auxiliary bases for density fitting of Coulomb and Hartree–Fock exchange matrices are presented and tested

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

Zinc Chalcogenolate Complexes as Precursors to ZnE and Mn/ZnE (E = S, Se) Clusters

The ternary clusters (tmeda)₆Zn_{14–<i>x</i>}Mn_<i>x</i>S₁₃Cl₂ (<b>1a</b>–<b>d</b>) and (tmeda)₆Zn_{14–<i>x</i>}Mn_<i>x</i>Se₁₃Cl₂ (<b>2a</b>–<b>d</b>), (tmeda = <i>N,N,N′,N′</i>-tetramethylethylenediamine; <i>x</i> ≈ 2–8) and the binary clusters (tmeda)₆Zn₁₄E₁₃Cl₂ (E = S, <b>3</b>; Se, <b>4</b>;) have been isolated by reacting (tmeda)­Zn­(ESiMe₃)₂ with Mn­(II) and Zn­(II) salts. Single crystal X-ray analysis of the complexes confirms the presence of the six “(tmeda)­ZnE₂” units as capping ligands that stabilize the clusters, and distorted tetrahedral geometry around the metal centers. Mn­(II) is incorporated into the ZnE framework by substitution of Zn­(II) ions in the cluster. The polynuclear complexes (tmeda)₆Zn_12.3Mn_1.7S₁₃Cl₂ <b>1a</b>, (tmeda)₆Zn_12.0Mn_2.0Se₁₃Cl₂ <b>2a</b>, and (tmeda)₆Zn_8.4Mn_5.6Se₁₃Cl₂ <b>2d</b> represent the first examples of “Mn/ZnE” clusters with structural characterization and indications of the local chemical environment of the Mn­(II) ions. The incorporation of higher amounts of Mn into <b>1d</b> and <b>2d</b> has been confirmed by elemental analysis. Density functional theory (DFT) calculations indicate that replacement of Zn with Mn is perfectly feasible and at least partly allows for the identification of some sites preferred by the Mn­(II) metals. These calculations, combined with luminescence studies, suggest a distribution of the Mn­(II) in the clusters. The room temperature emission spectra of clusters <b>1c</b>–<b>d</b> display a significant red shift relative to the all zinc cluster <b>3</b>, with a peak maximum centered at 730 nm. Clusters <b>2c</b>–<b>d</b> display a peak maximum at 640 nm in their emission spectra

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

Luminescence in Phosphine-Stabilized Copper Chalcogenide Cluster MoleculesA Comparative Study

The electronic properties of a series of eight copper chalcogenide clusters including [Cu₁₂S₆(dpppt)₄] (dpppt = Ph₂P­(CH₂)₅PPh₂), [Cu₁₂Se₆(dppo)₄] (dppo = Ph₂P­(CH₂)₈PPh₂), [Cu₁₂S₆(dppf)₄] (dppf = Ph₂PCpFeCpPPh₂), [Cu₁₂S₆(PPh₂Et)₈], [Cu₁₂S₆(PEt₃)₈], [Cu₂₄S₁₂(PEt₂Ph)₁₂], [Cu₂₀S₁₀(PPh₃)₈], and [Cu₂₀S₁₀(P^<i>t</i>Bu₃)₈] were investigated by absorption and photoluminescence (PL) spectroscopy as well as time-dependent density functional theory calculations. Major features of the experimental electronic absorption spectra are generally well-reproduced by the spectra simulated from the calculated singlet transitions. Visualization of the nonrelaxed difference densities indicates that for all compounds transitions at higher energies (above ∼2.5 eV, i.e., below ∼495 nm) predominantly involve excitations of electrons from orbitals of the cluster core to ligand orbitals. Conversely, the natures of the lower-energy transitions are found to be highly sensitive to the specifics of the ligand surface. Bright red PL (centered at ∼650–700 nm) in the solid state at ambient temperature is found for complexes with all ‘Cu₁₂S₆’ (E = S, Se) cores as well as the dimeric ‘Cu₂₄S₁₂’, although in [Cu₁₂S₆(dppf)₄], the PL appears to be efficiently quenched by the ferrocenyl groups. Of the two isomeric ‘Cu₂₀S₁₀’ complexes the prolate cluster [Cu₂₀S₁₀(PPh₃)₈] shows a broad emission that is centered at ∼820 nm, whereas the oblate cluster [Cu₂₀S₁₀(P^<i>t</i>Bu₃)₈] displays a relatively weak orange emission at ∼575 nm. The emission of all complexes decays on the time scale of a few microseconds at ambient temperature. A very high photostability is quantitatively estimated for the representative complex [Cu₁₂S₆(dpppt)₄] under anaerobic conditions

Slow Magnetic Relaxation in Trigonal-Planar Mononuclear Fe(II) and Co(II) Bis(trimethylsilyl)amido ComplexesA Comparative Study

Alternating current magnetic investigations on the trigonal-planar high-spin Co²⁺ complexes [Li­(15-crown-5)] [Co­{N­(SiMe₃)₂}₃], [Co­{N­(SiMe₃)₂}₂(THF)] (THF = tetrahydrofuran), and [Co­{N­(SiMe₃)₂}₂(PCy₃)] (Cy = −C₆H₁₃ = cyclohexyl) reveal that all three complexes display slow magnetic relaxation at temperatures below 8 K under applied dc (direct current) fields. The parameters characteristic for their respective relaxation processes such as effective energy barriers <i>U</i>_eff (16.1(2), 17.1(3), and 19.1(7) cm^–1) and relaxation times τ₀ (3.5(3) × 10^–7, 9.3(8) × 10^–8, and 3.0(8) × 10^–7 s) are almost the same, despite distinct differences in the ligand properties. In contrast, the isostructural high-spin Fe²⁺ complexes [Li­(15-crown-5)] [Fe­{N­(SiMe₃)₂}₃] and [Fe­{N­(SiMe₃)₂}₂(THF)] do not show slow relaxation of the magnetization under similar conditions, whereas the phosphine complex [Fe­{N­(SiMe₃)₂}₂(PCy₃)] does, as recently reported by Lin et al. (Lin, P.-H.; Smythe, N. C.; Gorelsky, S. I.; Maguire, S.; Henson, N. J.; Korobkov, I.; Scott, B. L.; Gordon, J. C.; Baker, R. T.; Murugesu, M. <i>J. Am. Chem. Soc.</i> <b>2011</b>, <i>135</i>, 15806.) Distinctly differing axial anisotropy <i>D</i> parameters were obtained from fits of the dc magnetic data for both sets of complexes. According to density functional theory (DFT) calculations, all complexes possess spatially nondegenerate ground states. Thus distinct spin–orbit coupling effects, as a main source of magnetic anisotropy, can only be generated by mixing with excited states. This is in line with significant contributions of excited determinants for some of the compounds in complete active space self-consistent field (CASSCF) calculations done for model complexes. Furthermore, the calculated energetic sequence of d orbitals for the cobalt compounds as well as for [Fe­{N­(SiMe₃)₂}₂(PCy₃)] differs significantly from the prediction by crystal field theory. Experimental and calculated (time-dependent DFT) optical spectra display characteristic d–d transitions in the visible to near-infrared region. Energies for lowest transitions range from 0.19 to 0.35 eV; whereas, for [Li­(15-crown-5)]­[Fe­{N­(SiMe₃)₂}₃] a higher value is found (0.66 eV). Zero-field ⁵⁷Fe Mößbauer spectra of the three high-spin iron complexes exhibit a doublet at 3 K with small and similar values of the isomer shifts (δ), ranging between 0.57 and 0.59 mm/s, as well as an unusual small quadrupole splitting (Δ<i>E</i>_Q = 0.60 mm/s) in [Li­(15-crown-5)]­[Fe­{N­(SiMe₃)₂}₃]

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