Optimization of a Genetic Algorithm for the Functionalization of Fullerenes

Abstract

We present the optimization of a genetic algorithm (GA) that is designed to predict the most stable structural isomers of hydrogenated and hydroxylated fullerene cages. Density functional theory (DFT) and density functional tight binding (DFTB) methods are both employed to compute isomer energies. We show that DFTB and DFT levels of theory are in good agreement with each other and that therefore both sets of optimized GA parameters are very similar. As a prototypical fullerene cage, we consider the functionalization of the C20 species, since for this smallest possible fullerene cage it is possible to compute all possible isomer energies for evaluation of the GA performance. An energy decomposition analysis for both C20Hn and C20(OH)n systems reveals that, for only few functional groups, the relative stabilities of different structural isomers may be rationalized simply with recourse to π-Hückel theory. However, upon a greater degree of functionalization, π-electronic effects alone are incapable of describing the interaction between the functional groups and the distorted cage, and both σ- and π-electronic structure must be taken into account in order to understand the relative isomer stabilities.

Universal Structure Conversion Method for Organic Molecules: From Atomic Connectivity to Three‐Dimensional Geometry

“…Hence, we impose constraints on adjacency matrix elements by allowing bond formation only between C and O, as depicted in Figure (b). Table shows the numbers of the isomers of C 20 (OH) n for n ≤ 10; these numbers are consistent with the previous results (for n ≤ 4) obtained using the genetic algorithm …”

“…Table 4 shows the numbers of the isomers of C 20 (OH) n for n ≤ 10; these numbers are consistent with the previous results (for n ≤ 4) obtained using the genetic algorithm. 43 Table 4 also shows computational time required to search for molecular isomers. It took 51 s and 50 min to find 58 and 1642 isomers of C 20 (OH) 4 and C 20 (OH) 10 , respectively, in serial calculations on an Intel® Core™ i5-2500 CPU @ 3.30 GHz processor.…”

Stochastic structure determination for conformationally flexible heterogenous molecular clusters: Application to ionic liquids

“…Increasingly, therefore, the question of which configuration to study has become the bottleneck in computational approaches. Several algorithms have been applied to this structure search problem, such as genetic algorithms, basin hopping, simulated annealing, Monte Carlo, particle swarm optimization, and scaled hypersphere . Yet one of the most widely used algorithms remains one that is conceptually quite simple; a straightforward stochastic search which generates and optimizes many hundreds or thousands of randomized structures.…”

Pure and Hybrid Evolutionary Computing in Global Optimization of Chemical Structures: from Atoms and Molecules to Clusters and Crystals

“…Do et al [184] identified the energy minima of water, methanol, water + methanol, protonated water, and protonated water + methanol clusters with DFT combined with basin hopping. Addicoat et al [185] optimized a GA in order to identify the minimum energy structure of arbitrarily hydrogenated and hydroxylated fullerenes, and implemented the method for exhaustive calculations on all possible isomers. They suggested that crossover operator did not have significant effect on the search efficiency of GA and hence the most efficient of their GA does not employ crossover, thereby reducing it to an Evolutionary Algorithm (EA).…”