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, Au39(PR3)14X6 ؊ , Au 11(PR3)7X3, and Au13(PR3)10X2 3؉ , where X is either a halogen or a thiolate. Attributable to a compact, symmetric core and complete steric protection, each compound has a filled spherical electronic shell and a major energy gap to unoccupied states. Consequently, the exceptional stability is best described by a ''noble-gas superatom'' analogy. The explanatory power of this concept is shown by its application to many monomeric and oligomeric compounds of precisely known composition and structure, and its predictive power is indicated through suggestions offered for a series of anomalously stable cluster compositions which are still awaiting a precise structure determination.density functional theory ͉ monolayer-protected cluster

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 and systematic convergence properties. However, as a unique feature GPAW also facilitates a localized atomic-orbital basis set in addition to the grid. The efficient atomic basis set is complementary to the more accurate grid, and the possibility to seamlessly switch between the two representations provides great flexibility. While DFT allows one to study ground state properties, time-dependent density-functional theory (TDDFT) provides access to the excited states. We have implemented the two common formulations of TDDFT, namely the linear-response and the time propagation schemes. Electron transport calculations under finite-bias conditions can be performed with GPAW using non-equilibrium Green functions and the localized basis set. In addition to the basic features of the real-space PAW method, we also describe the implementation of selected exchange-correlation functionals, parallelization schemes, ΔSCF-method, x-ray absorption spectra, and maximally localized Wannier orbitals.

The atomic simulation environment (ASE) is a software package written in the Python programming language with the aim of setting up, steering, and analyzing atomistic simulations. In ASE, tasks are fully scripted in Python. The powerful syntax of Python combined with the NumPy array library make it possible to perform very complex simulation tasks. For example, a sequence of calculations may be performed with the use of a simple 'for-loop' construction. Calculations of energy, forces, stresses and other quantities are performed through interfaces to many external electronic structure codes or force fields using a uniform interface. On top of this calculator interface, ASE provides modules for performing many standard simulation tasks such as structure optimization, molecular dynamics, handling of constraints and performing nudged elastic band calculations.

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.