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 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.

We review the GPAW open-source Python package for electronic structure calculations. GPAW is based on the projector-augmented wave method and can solve the self-consistent density functional theory (DFT) equations using three different wave-function representations, namely real-space grids, plane waves, and numerical atomic orbitals. The three representations are complementary and mutually independent and can be connected by transformations via the real-space grid. This multi-basis feature renders GPAW highly versatile and unique among similar codes. By virtue of its modular structure, the GPAW code constitutes an ideal platform for the implementation of new features and methodologies. Moreover, it is well integrated with the Atomic Simulation Environment (ASE), providing a flexible and dynamic user interface. In addition to ground-state DFT calculations, GPAW supports many-body GW band structures, optical excitations from the Bethe–Salpeter Equation, variational calculations of excited states in molecules and solids via direct optimization, and real-time propagation of the Kohn–Sham equations within time-dependent DFT. A range of more advanced methods to describe magnetic excitations and non-collinear magnetism in solids are also now available. In addition, GPAW can calculate non-linear optical tensors of solids, charged crystal point defects, and much more. Recently, support for graphics processing unit (GPU) acceleration has been achieved with minor modifications to the GPAW code thanks to the CuPy library. We end the review with an outlook, describing some future plans for GPAW.

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 emission spectra using the time-propagation method.

Vacuum hydrogen annealing of TiO₂ leads to increased visible light absorption. The origin thereof was revealed by ab initio calculations and X-ray photoelectron spectroscopy.