Quantum mechanical studies future directions

The clearest results have been obtained for classical relaxation in bound systems where the full machinery of classical ergodic theory may be utilized. These concepts have been carried over empirically to molecular scattering and decay, where the phase space is not compact and hence the ergodic theory is not directly applicable. This classical approach is the subject of Section II. Less complete information is available on the classical-quantum correspondence, which underlies step 4. This is discussed in Section III where we introduce the Liouville approach to correspondence, which, we believe, provides a unified basis for future studies in this area. Finally, the quantum picture is beginning to emerge, and Section IV summarizes a number of recent approaches relevant for a quantum-mechanical understanding of relaxation phenomena and statistical behavior in bound systems and scattering. 

In 1985, Car and Parrinello published a seminal article on an Unified approach for molecular dynamics and density functional theory Phys. Rev. Lett. 5S (1985) 2471). This paper established a basis for parameter-firee molecular dynamics simulations in which all the interactions are calculated on the fly via a first-principles quantum mechanical method. In the 15 years of its existence, the Car-Parrinello method has found widespread applications that expanded rapidly from physics to chemistry and, most recently, even into biology. In this article, the foundations of the method in its most common implementation, the one based on density functional theory, plane wave basis sets and pseudopotentials are described and extensions to the original scheme are outlined. The current power of Car-Parrinello simulations is illustrated by presenting selected case studies and possible future directions are sketched in the final outlook. 

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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