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2.1. THEORETICALDESCRIPTIONSOFMATTER 17 the overlap and the d orbital energy. The ρLF parameter is used to describe the exponential distance dependence of the overlap S = exp (−r/ρLF ) . (2.4) The AOM is described in more detail in Woodley et al. [121]. 2.1.1.2 Using genetic algorithms to find the globally optimal FF While FFs can be used to successfully model structures and properties of materi- als, a chief difficulty exists in the parametrization of the FF. Typically, this process requires chemical insight and several attempts before yielding values that achieve the desired accuracy. This is the case even when using partially automatic meth- ods, such as those where the potential parameters are varied to minimize the force on, e.g., the experimental structure that is used as the “target structure” for the parameters. While such deterministic methods facilitate the fitting of interatomic potentials, they still require that the initial parameters are well chosen. Further- more, if a successful FF is not found, with this method it is not possible to make certain that the failure is because there simply is no set of FF parameters that would be successful, or if it is due to a failure on the part of the investigator in exploring the complete parameter space. In such a situation, to make sure that the complete parameter space has been searched, a global optimization method is needed. One such optimization method is optimization by use of a suitably designed genetic algorithm (GA)[122]. Genetic algorithms are similar to the Monte Carlo method[123] or the method of simulated annealing[124, 125], both of which invoke thermodynamic arguments for explor- ing a parameter space in a way that is more efficient than a random search. As the name implies, GAs are inspired by natural evolution. The GA works in the follow- ing way. First, a number of chromosomes, e.g. in the present case an array of FF parameters, is generated randomly. These chromosomes are then evaluated using a fitness function, which ranks the quality of all chromosomes, e.g. based on their ability to model a certain structure accurately. The fittest chromosomes are carried over to the next generation. However, a crossover operator is usually also applied. This crossover operator combines the chromosomes with the highest fitnesses in the population to generate a new chromosome that possibly can exceed the quality of the “parent” chromosomes. Furthermore, a mutation operator is usually also applied, which e.g. changes one value in the chromosome of a certain individual randomly. This process is then repeated for a certain number of generations, and the chromosome with the highest fitness after the conclusion of this process is then taken as the globally optimal solution. Some challenges in the application of this method are immediately obvious. First off, there is no guarantee that the search has converged to the actual global opti-PDF Image | Studies of Electrode Processes in Industrial Electrosynthesis
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