Quantum mechanics, of clusters

Bawendl M G, Stelgerwald M L and Brus L E 1990 The quantum mechanics of larger semiconductor clusters ( quantum dots ) Ann. Rev. Phys. Chem. 41 477... 

The accurate quantum mechanical first-principles description of all interactions within a transition-metal cluster represented as a collection of electrons and atomic nuclei is a prerequisite for understanding and predicting such properties. The standard semi-classical theory of the quantum mechanics of electrons and atomic nuclei interacting via electromagnetic waves, i.e., described by Maxwell electrodynamics, turns out to be the theory sufficient to describe all such interactions (21). In semi-classical theory, the motion of the elementary particles of chemistry, i.e., of electrons and nuclei, is described quantum mechanically, while their electromagnetic interactions are described by classical electric and magnetic fields, E and B, often represented in terms of the non-redundant four components of the 4-potential, namely the scalar potential and the vector potential A. 

The cluster model approach assumes that a limited number of atoms can be used to represent the catalyst active site. Ideally, one would like to include a few thousands atoms in the model so that the cluster boundary is sufficiently far from the cluster active site thus ensuring that edge effects are of minor importance and can be neglected. Unfortunately, the computational effort of an ab initio calculation grows quite rapidly with the number of atoms treated quantum mechanically and cluster models used in practice contain 20 to 50 atoms only. It is well possible that with the advent of the N-scaling methods " this number can dramatically increase. Likewise, the use of hybrid methods able to decompose a very large system in two subsets that are then treated at different level of accuracy, or define a quantum mechanical and a classical part, are also very promising. However, its practical implementation for metallic systems remains still indeterminate. 

Calculations by semi-empirical quantum mechanics of the INS of water on nickel clusters also refer to the riding modes [10,11]. The cluster Niii(H20), comprising a single layer of 11 nickel atoms with the water molecule bound to the central nickel atom, was modelled. The water molecule on top of the central nickel atom was at an optimised distance of 0.22 nm it was not dissociated. The INS of nickel particles with adsorbed water molecules was assigned with the aid of the computed spectrum peaks above 350 cm, to two external and two internal vibrations of the adsorbed water molecules peaks below 350 cm, to adsorbent (i.e. nickel) vibrations enhanced by hydrogen atoms... 

M. G. Bawendi, M. L. Steigerwald, L. E. Brus, The Quantum Mechanics of Lcffger Semiconductor Clusters ( Quantum Dots ). Annual Review of Physical Chemistry 1990,41,477-496. 

Pisani C 1993 Embedded-cluster techniques for the quantum-mechanical study of surface reactivity J. Mol. Catal. 82 229... 

Clusters are intennediates bridging the properties of the atoms and the bulk. They can be viewed as novel molecules, but different from ordinary molecules, in that they can have various compositions and multiple shapes. Bare clusters are usually quite reactive and unstable against aggregation and have to be studied in vacuum or inert matrices. Interest in clusters comes from a wide range of fields. Clusters are used as models to investigate surface and bulk properties [2]. Since most catalysts are dispersed metal particles [3], isolated clusters provide ideal systems to understand catalytic mechanisms. The versatility of their shapes and compositions make clusters novel molecular systems to extend our concept of chemical bonding, stmcture and dynamics. Stable clusters or passivated clusters can be used as building blocks for new materials or new electronic devices [4] and this aspect has now led to a whole new direction of research into nanoparticles and quantum dots (see chapter C2.17). As the size of electronic devices approaches ever smaller dimensions [5], the new chemical and physical properties of clusters will be relevant to the future of the electronics industry. 

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