Potential field, reliable description

Molecular mechanics methods are also omitted from the present discussion for similar reasons. Although very sophisticated force fields are available for water (including polarizable models), most force fields for weakly bound clusters are essentially 2-body (dimer) potentials that have been adjusted empirically to reproduce bulk-phase properties. This procedure leads to very reliable descriptions of liquid water, but diminishes the quality of results for small clusters. Although force fields that include 3-body interactions are beginning to appear, ° the effects of higher order interactions (4-body, 5-body, etc.) are still untested. Furthermore, the composition of a weakly bound cluster, not just its size, is a major concern with molecular mechanics force fields. The highly refined potentials that have been developed for water are not necessarily transferable to other weak noncovalent systems (methanol, acetone, etc.). 

Roth and coworkers41 42 have chosen carefully recalibrated force fields to predict reliable heats of formation with errors intended by the authors to be as small as 0.5 kcal mol"1. They started with the MM2 force field of Allinger98 and added to this parameters for the C(sp2)—C(sp2) and the C(cyclopropyl)—C(sp2) single bonds of reference compounds such as substituted 1,3-butadienes and vinylcyclopropanes41. Particular care was given to the correct description of the torsion potential of the reference compounds. The modified MM2 force field (MM2ERW) developed by Roth and coworkers describes polyenes and cyclopolyenes in terms of localized bond structures without any reference to quantum chemical methods such as the Pariser-Parr-Pople (PPP) approach (see Section II.C)41. 

The enormous potential of this technique is evident from the above brief descriptions, which highlighted the many ideal properties of such encoding in terms of ease, reliability, inertness and robustness, automation, complete compatibility with any biological assay, and so on. No apparent drawbacks can be found, except maybe for the lack of expertise in this field by combinatorial and organic chemists and their reluctance in getting involved in material science. Examples of applications of these, or of similar approaches where the solid support is intrinsically and nonchemically encoded, to real large encoded organic molecule libraries should appear in the near future, and will hopefully increase the interest of the combinatorial community toward these techniques. 

Future research work wiU concentrate on the description of potential parallel damage causes. The long-term goal is the determination and comprehensive description of serial, parallel and overlapping damage structures of complex components. Furthermore, current research work in cooperation with the automotive industry is the development of new methods to determine the necessary field sample size of damaged components. The approaches and results will be a contribution for a comprehensive reliable de sign of complex technical products, components and systems, respectively. 

The crystal field is defined in Equation (1) as an infinite summation. The mathematical techniques which attempt to allow for the overall potential of the infinite crystal do not meet the above expressed requirement of using simple methods which are not specific of the solid state theories and moreover these methods preliminarily need some simplifications of the expression of the y s. Thus it turns out to be convenient to proceed with finite specimens of the crystal, and to check the reliability of the description of the crystal field obtained in such a way by varying the dimensions of the specimen. 

The interatomic potentials define the force field parameters that contribute to the lattice energy of a relaxed or energy minimized structure. The fundamental question is how reliable is a force field The force field used in evaluating a potential function must be consistent and widely applicable to all similar systems. It must be able to predict the crystal properties as measured experimentally. Two main approaches, namely empirical and semi-empirical, are usually employed in the derivation of potential parameters. Empirical derivations involve a least square fitting routine where parameters are chosen such that the results achieve the best correlation with the observed properties. The semi-empirical approach uses an approximate formulation of the quantum mechanical calculations. An example of such an approximation is the electron gas method [57] which treats the electron density at any point as a uniform electron gas. The following is the analytical description of the potential energy function and interatomic potentials we recommend for use in simulation of zeolites and related system. 

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