Breakdown of the pseudopotential approximation for magnetizabilities and electric multipole moments: test calculations for Au, AuF, and Sn(n) cluster (n ≤ 20).

The response of the electronic wavefunction to an external electric or magnetic field is widely considered to be a typical valence property and should, therefore, be adequately described by accurately adjusted pseudopotentials, especially if a small-core definition is used within this approximation. In this paper we show for atomic Au and Au(+), as well as for the molecule AuF and tin clusters, that in contrast to the case of the static electric dipole polarizability or the electric dipole moment, core contributions to the static magnetizability are non-negligible, and can therefore lead to erroneous results within the pseudopotential approximation. This error increases with increasing size of the core chosen. For tin clusters, which are of interest in ongoing molecular beam experiments currently carried out by the Darmstadt group, the diamagnetic and paramagnetic isotropic components of the magnetizability tensor almost cancel out and large-core pseudopotentials do not even predict the correct sign for this property due to erroneous results in both the diamagnetic and (more importantly) the paramagnetic terms. Hence, all-electron calculations or pseudopotentials with very small cores are required to adequately predict magnetizabilities for atoms, molecules and the solid state, making it computationally more difficult to obtain this quantity for future investigations in heavy atom containing molecules or clusters. We also demonstrate for this property that all-electron density functional calculations are quite robust and give results close to wavefunction based methods for the atoms and molecules studied here.

Electronic properties for small tin clusters Sn(n) (n < or = 20) from density functional theory and the convergence toward the solid state.

Global minimum structures of neutral tin clusters with up to 20 atoms obtained recently from genetic algorithm simulations within a density-functional approach (Schäfer et al., J Phys Chem A 2008, 112, 12312) were used to evaluate the corresponding electronic properties. The evolution of these properties with increasing cluster size is discussed in detail and compared with the lighter silicon and germanium clusters. We also discuss the extrapolation of these properties to the bulk limit.

A systematic search for minimum structures of small gold clusters Au(n) (n=2-20) and their electronic properties.

A systematic search for global and energetically low-lying minimum structures of neutral gold clusters Au(n) (n=2-20) is performed within a seeded genetic algorithm technique using density functional theory together with a relativistic pseudopotential. Choosing the energetically lowest lying structures we obtain electronic properties by applying a larger basis set within an energy-consistent relativistic small-core pseudopotential approach. The possibility of extrapolating these properties to the bulk limit for such small cluster sizes is discussed. In contrast to previous calculations on cesium clusters [B. Assadollahzadeh et al., Phys. Rev. B 78, 245423 (2008)] we find a rather slow convergence of any of the properties toward the bulk limit. As a result, we cannot predict the onset of metallic character with increasing cluster size, and much larger clusters need to be considered to obtain any useful information about the bulk limit. Our calculated properties show a large odd-even cluster size oscillation in agreement, for example, with experimental ionization potentials and electron affinities. For the calculated polarizabilities we find a clear transition to lower values at Au14, the first cluster size where the predicted global minimum clearly shows a compact three-dimensional (3D) structure. Hence, the measurement of cluster polarizabilities is ideal to identify the 2D-->3D transition at low temperatures for gold. Our genetic algorithm confirms the pyramidal structure for Au20.

Structure and electric properties of Sn(N) clusters (N = 6-20) from combined electric deflection experiments and quantum theoretical studies.

Electric deflection experiments have been performed on neutral Sn(N) clusters (N = 6-20) at different nozzle temperatures in combination with a systematic search for the global minimum structures and the calculation of the dielectric properties based on density functional theory. For smaller tin clusters (N = 6-11), a good agreement between theory and experiment is found. Taking theoretically predicted moments of inertia and the body fixed dipole moment into account permits a quantitative simulation of the deflected molecular beam profiles. For larger Sn(N) clusters (N = 12-20), distinct differences between theory and experiment are observed; i.e., the predicted dipole moments from the quantum chemical calculations are significantly larger than the experimental values. The investigation of the electric susceptibilities at different nozzle temperatures indicates that this is due to the dynamical nature of the tin clusters, which increases with cluster size. As a result, even at the smallest nozzle temperature of 40 K, the dipole moments of Sn(12-20) are partially quenched. This clearly demonstrates the limits of current electric deflection experiments for structural determination and demonstrates the need for stronger cooling of the clusters in future experiments.

Structural and spectroscopic studies on mercury(II) tribenzylphosphine complexes.

The tribenzylphosphine (PBz3) complexes of mercury(II), [Hg(PBz3)2](BF4)2, [Hg(PBz3)2(NO3)2] and [HgX(NO3)(PBz3)](X = Cl, Br, I and SCN), have been synthesised and their structures determined by single-crystal X-ray crystallography. [Hg(PBz3)2](BF4)2 contains [Hg(PBz3)2]2+ cations with linear P-Hg-P coordination, the first example of a truly two-coordinate [Hg(PR3)2]2+ complex. The mercury coordination in [Hg(PBz3)2(NO3)2] can be described as distorted tetrahedral, with a significant deviation of the P-Hg-P angle from linearity as a result of coordination of the nitrate groups. Nitrate coordination is also observed in [HgX(NO3)(PBz3)](X = Cl, Br, I), resulting in significantly non-linear P-Hg-X coordination. The thiocyanate complex is a centrosymmetric thiocyanate-bridged dimer with distorted trigonal-pyramidal mercury coordination to the P atom of PBz3, to the S and N atoms of two bridging thiocyanate groups, and to the O atom of one nitrate group. For all the nitrato complexes, secondary mercury-nitrate interactions (Hg-O 2.7-3.1 A) effectively raise the coordination number of the Hg(II) centres to six. High-resolution 31P solid-state NMR spectra of the six tribenzylphosphine mercury(II)-complexes, obtained by combining magic-angle spinning, proton dipolar decoupling and proton-phosphorus cross-polarization (CP-MAS), have been recorded. The spectra of [Hg(PBz3)2](BF4)2 and [HgX(NO3)(PBz3)](X = Cl, Br, I and SCN) exhibit a single line, due to species that contain non-magnetic isotopes of mercury, and satellite lines, due to 1J(31P-199Hg) coupling. The asymmetric unit of [Hg(PBz3)2(NO3)2] contains two molecules with four phosphorus environments, resulting in two AB spectra with 2J(31P-31P) coupling, due to species that contain non-magnetic isotopes of mercury, and satellite lines consisting of two ABX spectra, due to 1J(31P-199Hg) coupling. These spectra have been analysed to yield all of the chemical shifts and coupling constants involved. A remarkable increase in 1J(31P-199Hg) is observed from [Hg(PBz3)2](BF4)2 to [Hg(PBz3)2(NO3)2] as a consequence of the incorporation of the nitrate group into the Hg coordination sphere in the latter case. Several of the spectra also exhibit broader satellites due to the presence of scalar spin-spin coupling between 31P and the quadrupolar 201Hg nucleus. Slow-spinning methods have been used to analyze the spinning-sideband intensities of the NMR spectra, in order to obtain the 31P shielding anisotropy and asymmetry parameters Deltasigma and eta. The 199Hg and 31P NMR shielding tensors of PMe3 models of the above six compounds have been calculated using relativistic density functional theory. The 31P results are in good agreement with experiment and assist in the assignment of some of the signals.

Solid-state 109Ag CP/MAS NMR spectroscopy of some diammine silver(I) complexes.

Solid-state cross-polarization magic-angle spinning (CP/MAS) NMR spectra were recorded for the compounds [Ag(NH3)2]2SO4, [Ag(NH3)2]2SeO4 and [Ag(NH3))]NO3, all of which contain the linear or nearly linear two-coordinate [Ag(NH3)2]+ ion. The 109Ag CP/MAS NMR spectra show centrebands and associated spinning sideband manifolds typical for systems with moderately large shielding anisotropy, and splittings due to indirect 1J(109Ag,14N) spin-spin coupling. Spinning sideband analysis was used to determine the 109Ag shielding anisotropy and asymmetry parameters Deltasigma and eta from these spectra, yielding anisotropies in the range 1500-1600 ppm and asymmetry parameters in the range 0-0.3. Spectra were also recorded for 15N and (for the selenate) 77Se. In all cases the number of resonances observed is as expected for the crystallographic asymmetric units. The crystal structure of the selenate is reported for the first time. One-bond (107, 109Ag,15N) coupling constants are found to have magnitudes in the range 60-65 Hz. Density functional calculations of the Ag shielding tensor for model systems yield results that are in good agreement with the experimentally determined shielding parameters, and suggest that in the solid compounds Deltasigma and eta are reduced and increased, respectively, from the values calculated for the free [Ag(NH3)2]+ ion (1920 ppm and 0, respectively), primarily as a result of cation-cation interactions, for which there is evidence from the presence of metal-over-metal stacks of [Ag(NH3)2]+ ions in the solid-state structures of these compounds.