Optical absorption of magnesia-supported gold clusters and nanoscale catalysts: Effects due to the support, clusters, and adsorbants
Polarization-resolved optical spectra of magnesia-supported gold clusters ${\mathrm{Au}}_{N}∕\mathrm{Mg}\mathrm{O}$ $(N=1,2,4,8)$, bound at a surface color center ${F}_{s}$ of the MgO(100) face, are calculated from the time-dependent density functional theory. The optical lines for $N=1,2$ are dominated by transitions that involve strong hybridization between gold and ${F}_{s}$ states whereas for $N=4,8$ intracluster transitions dominate. The theoretical optical spectra are sensitive to cluster structure and adsorbants (here CO and ${\mathrm{O}}_{2}$ molecules on ${\mathrm{Au}}_{8}∕{F}_{s}@\mathrm{Mg}\mathrm{O}$) which suggests polarization-resolved optical spectroscopy as a powerful tool t…
A 58-electron superatom-complex model for the magic phosphine-protected gold clusters (Schmid-gold, Nanogold®) of 1.4-nm dimension
We have re-investigated the structural identity of the famous gold-phosphine-halide Au:PR3:X compound having 55–69 gold atoms and core size of 1.4 nm (similar to “Schmid gold” or Nanogold®) from the viewpoint of the Superatom-Complex (SAC) model for ligand protected metal clusters, and in consideration of the ligand-adatom groups observed previously for the structurally known 39-atom cluster [Au39(PR3)14Cl6]−1. Density functional theory is used to define the formation energy of various compositions and structures, enabling a comparison of the stability of different cluster-sizes. In agreement with the SAC model, we find a strong correlation between optimal energy and delocalized electron sh…
A hollow tetrahedral cage of hexadecagold dianion provides a robust backbone for a tuneable sub-nanometer oxidation and reduction agent via endohedral doping.
We show, via density functional theory calculations, that dianionic Au16(2-) cluster has a stable, hollow, Td symmetric cage structure, stabilized by 18 delocalized valence electrons. The cage maintains its robust geometry, with a minor Jahn-Teller deformation, over several charge states (q = -1,0,+1), forming spin doublet, triplet and quadruplet states according to the Hund's rules. Endohedral doping of the Au16 cage by Al or Si yields a geometrically robust, tuneable oxidation and reduction agent. Si@Au16 is a magic species with 20 delocalized electrons. We calculate a significant binding energy for the anionic Si@Au16/O2- complex and show that the adsorbed O2 is activated to a superoxo-s…
A unified view of ligand-protected gold clusters as superatom complexes
Synthesis, characterization, and functionalization of self-assembled, ligand-stabilized gold nanoparticles are long-standing issues in the chemistry of nanomaterials. Factors driving the thermodynamic stability of well documented discrete sizes are largely unknown. Herein, we provide a unified view of principles that underlie the stability of particles protected by thiolate (SR) or phosphine and halide (PR 3 , X) ligands. The picture has emerged from analysis of large-scale density functional theory calculations of structurally characterized compounds, namely Au 102 (SR) 44 , Au 39 (PR 3 ) 14 X 6 − , Au 11 (PR 3 ) 7 X 3 , and Au 13 (PR 3 ) 10 X 2 3+ , where X is either a halogen or a thiol…
Cross-sections for (e, 3e) collisions on helium: the DS6C wavefunction
A dynamically screened product of six pairwise Coulomb functions (DS6C) is used as an analytic approximation to describe the four-body Coulomb continuum state produced by electron-impact full fragmentation of helium. Good agreement is obtained with experimental data close to threshold, where four-body effects are expected to be important. Even for the high impact energy of 640 eV, four-body effects still play a role in deciding the shape of multi-differential cross-sections.
Synthesis of a Fullerene[60] Cryptate and Systematic Langmuir-Blodgett and Thin-Film Investigations of Amphiphilic Fullerene Derivatives
The synthesis of the first fullerene cryptate 7 with a sodium ion bound to a benzo[2.2.2]cryptand covalently attached to a methanofullerene[60] is described. The amphiphilic properties of 7 as well as of a variety of other covalent fullerene derivatives with polar functional groups and the ability of these compounds to form Langmuir monolayers at the air-water interface were investigated in a systematic study. Among these derivatives are Diels-Alder adducts of C60 and methanofullerenes, four of which are fullerene C-glycosides. The films at the water surface were characterized by their surface pressure versus molecular area isotherms, compression and expansion cycles, and optical light micr…
On the Structure of Thiolate-Protected Au25
Density functional theory is used to explore the structure of Au25(RS)18. The preferred structure consists of an icosahedral Au13 core protected by 6 RS-Au-RS-Au-RS units. The enhanced stability of the structure as an anion is found to originate from closure of an eight-electron shell for delocalized Au(6s) electrons. The evaluated XRD pattern and optical spectra are in good agreement with experimental data.
Time-dependent density-functional theory in the projector augmented-wave method
We present the implementation of the time-dependent density-functional theory both in linear-response and in time-propagation formalisms using the projector augmented-wave method in real-space grids. The two technically very different methods are compared in the linear-response regime where we found perfect agreement in the calculated photoabsorption spectra. We discuss the strengths and weaknesses of the two methods as well as their convergence properties. We demonstrate different applications of the methods by calculating excitation energies and excited state Born–Oppenheimer potential surfaces for a set of atoms and molecules with the linear-response method and by calculating nonlinear e…
Electronic structure calculations with GPAW: a real-space implementation of the projector augmented-wave method.
Electronic structure calculations have become an indispensable tool in many areas of materials science and quantum chemistry. Even though the Kohn-Sham formulation of the density-functional theory (DFT) simplifies the many-body problem significantly, one is still confronted with several numerical challenges. In this article we present the projector augmented-wave (PAW) method as implemented in the GPAW program package (https://wiki.fysik.dtu.dk/gpaw) using a uniform real-space grid representation of the electronic wavefunctions. Compared to more traditional plane wave or localized basis set approaches, real-space grids offer several advantages, most notably good computational scalability an…
Nodes of entangledN-particle wave functions
In a recent paper [Bressanini et al. Phys. Rev. Lett. 95, 110201 (2005)] it was pointed out that ``the nodes of even simple wave functions are largely unexplored.'' Here we show that for $N$-particle wave functions nodal surfaces arise from the spin and orbital entanglement of constituent two-particle wave functions and derive, for two-electron atoms, 11 exact nodal rules applicable in $LS$ coupling. In addition, the ``higher symmetry'' identified numerically in the above paper is shown to be an approximate dynamical symmetry described by a molecular model or a classical unstable periodic orbit. We show that the analysis is readily extended to four-particle wave functions and consider the c…
The effect of dynamical screening on helium (e, 3e) differential cross-sections
A simplified derivation of dynamic screening in the case of three Coulomb-interacting particles in the continuum is given and applied to describe the shapes of multi-differential cross-sections for the (e, 3e) process on the helium atom in which the incident fast electron is treated in first-order Born approximation. A very good agreement with experimental multi-differential cross-sections is obtained for two slow ejected electrons (specifically both electrons have 5 eV) but the strategy appears to be breaking down at intermediate emission energies.
Symmetry-induced long-lived excited state inAu6−
We present time-resolved photoelectron spectra in combination with quantum chemical calculations based on time-dependent density functional theory for the study of the long-lived excited state of ${\mathrm{Au}}_{6}^{\ensuremath{-}}$. The experimental spectra indicate an excited state lifetime of at least $90\phantom{\rule{0.3em}{0ex}}\mathrm{ns}$. It is shown that the orbital symmetry of the photoexcited state as well as the planarity of ${\mathrm{Au}}_{6}^{\ensuremath{-}}$ are responsible for the unusual long lifetime. A possible decay mechanism is the fluorescence of a photon which is estimated to take place on a time scale of $730\phantom{\rule{0.3em}{0ex}}\mathrm{ns}$.
Electronic structure of MgO-supported Au clusters: quantum dots probed by scanning tunneling microscopy.
We investigate via density functional theory (DFT) the appearance of small MgO-supported gold clusters with 8 to 20 atoms in a scanning tunneling microscope (STM) experiment. Comparison of simulations of ultrathin films on a metal support with a bulk MgO leads to similar results for the cluster properties relevant for STM. Simulated STM pictures show the delocalized states of the cluster rather than the atomic structure. This finding is due to the presence of s- derived delocalized states of the cluster near the Fermi energy. The properties of theses states can be understood from a jellium model for monovalent gold.
Quantum Well States in Two-Dimensional Gold Clusters on MgO Thin Films
The electronic structure of ultra-small Au clusters on thin MgO/Ag(001) films has been analyzed by scanning tunneling spectroscopy and density functional theory. The clusters exhibit two-dimensional (2D) quantum well states, whose shapes resemble the eigen-states of a 2D electron gas confined in a parabolic potential. From the symmetries of the HOMO and LUMO of a particular cluster, its electron filling and charge state is determined. In accordance to a DFT Bader-charge analysis, aggregates containing up to twenty atoms accumulate one to four extra electrons due to a charge transfer from the MgO/Ag interface. The HOMO - LUMO gap is found to close for clusters containing between 70 and 100 a…
Plasma and fibroblasts of Tangier disease patients are disturbed in transferring phospholipids onto apolipoprotein A-I
Plasmas of patients with Tangier disease (TD) lack lipid-rich α-HDL which, in normal plasma, constitutes the majority of high density lipoprotein (HDL). Residual amounts of apolipoprotein (apo)A-I in TD plasma occur as lipid-poor or even lipid-free preβ-HDL. By contrast to normal plasma, TD plasma does not convert preβ-HDL into α-HDL. Moreover, fibroblasts of TD patients were found to be defective in secreting cholesterol or phospholipids in the presence of lipid-free apoA-I. We have therefore hypothesized that both defective conversion of preβ-HDL into α-HDL and defective lipid efflux from TD cells onto lipid-free apoA-I result from a disturbance in phospholipid transfer occurring in both …
Photoelectron spectra from first principles: from the many-body to the single-particle picture
We derive a many-body method to evaluate photoelectron spectra of atoms, molecules and clusters from first principles. The excitation energies and the spectroscopic factors are calculated from the linear-response time-dependent density functional theory. The method is applied to noble metal anions, anionic clusters and to neutral small molecules. Our approach shows significant improvement over a simple single-particle treatment and gives an insight into the necessary conditions under which the single-particle picture holds. The consideration of the spectroscopic factor is shown to be crucial for the correct description of inner valence photoelectron peaks.