Multidimensional potential energy surfaces for systems larger than about 15 atoms are so complex that interpreting their topographies and the consequent dynamics requires statistical analyses of their minima and saddles. Sequences of minimum-saddle-minimum points provide a characterization of such surfaces. Two examples, Ar 19 and (KCI) 32 , illustrate how topographies govern tendencies to form glasses or “focused” structures, for example, crystals or folded proteins. Master equations relate topographies to dynamics. The balance between glass-forming and structure-seeking characters of a potential energy surface seems governed by sawtooth versus staircase topography and the associated collectivity of the growth process after nucleation.

The phases and phase transitions of bulk matter differ in several important ways from the phases or phase-like forms of small systems, notably atomic and molecular clusters. However, understanding those differences gives insights into the nature of bulk transitions, as well as into understanding the behaviour of the small systems. Small systems exhibit dynamic phase equilibria, large fluctuations and size-dependent behaviour in ways one cannot see with macroscopic systems. The Gibbs phase rule loses its applicability, the distinction between first-order and second-order transitions reveals a size dependence, and one can see phases in equilibrium (as minority populations) that are never the most stable thermodynamically. Introduction: phases of clusters and of macroscopic systemsThis review addresses the relations between phases and phase changes exhibited by bulk, macroscopic systems and their counterparts in small systems, atomic and molecular clusters and nanoscale particles. The differences between the phase behaviour of bulk matter and of clusters can, for the most part, be attributed to two factors. The more important is the enormous free energy differences between phases of bulk matter, which make only the most favoured phase observable, compared with the small free energy differences for clusters, which make less favoured phases nearly as observable as more favoured or most favoured phases [1]. The other is the relative contribution of the surface in a macroscopic and a small system. In a d-dimensional system containing N atoms, approximately N (d−1)/d of atoms will be on the surface; for large N the relative fraction N −1/d is very small and the surface effects on the bulk properties of the system are commonly neglected. In contrast, a high proportion of atoms or molecules are in surface layers of clusters which makes the surface as important for many cluster properties as the interior part is. In the spherical approximation used above to estimate the surface contribution one finds that about one half of the particles are on the surface of a cluster containing 500 particles. Because the ratio of surface area to bulk is large for small

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We have used density functional theory (DFT) to study adsorption of H2S molecules onto defective graphene as a function of vacancy concentration. The calculations are performed with the Quantum Espresso code, a plane‐wave realization of the DFT with norm‐conserving pseudopotentials. The Perdew et al. generalized gradient approximation to the density functional for exchange correlation energy of a many‐electron system is used. The computations show that a hydrogen sulfide molecule interacts stronger with the carbon atoms surrounding the vacancy than with the carbon atoms in a perfect arrangement. The most favorable energetically configuration is the one with the sulfur atom heading the center of the vacancy. Such a configuration facilitates covalent binding of the sulfur atom with three carbon atoms with unsaturated bonds. The density of states of perfect, defective graphene and defective graphene with chemisorbed sulfur demonstrate that the systems change their conductivity. The chemisorption is followed by a release of the hydrogen atoms, which form a H2 molecule. In the presence of more isolated vacancies per unit cell, more H2S molecules are chemisorbed. This process opens very interesting applications in the environmental and energy research. © 2012 Wiley Periodicals, Inc.