What Electronic Structure Method Can Be Used in the Global Optimization of Nanoclusters?

The problem of obtaining the spatial structure of nanoclusters is known to be very difficult due to the large number of local minima associated with their potential energy surfaces (isomers). In global optimization approaches, such as basin hopping and genetic algorithms, the problem is normally tackled by first using a low-level and affordable method to evaluate the energy. Afterward, the putative global minimum (and often a few others) is refined with calculations using higher level methods and larger basis sets. There is no guarantee, however, that the structure obtained at the lower level method will be the global minimum at the refined one. In this work, we have performed benchmark coupled cluster calculations at the complete basis set limit for a large number of different isomers of representative clusters of third row elements. Such calculations are then employed to check the hypothesis that lower level methods can be used in the global optimization with reliable results. For this, we have developed a methodology that allows us to compare a large number of minima obtained at different calculation levels. The results indicate that, if the global optimization is capable of reaching not only the global minimum but also a reduced number of low lying structures, most of the tested density functional theory (DFT) functionals are good choices, with emphasis on TPSSh. Besides giving a more solid ground to this commonly used approach, this work helps guiding such global optimizations. The use of the MP2 method and several scaled variants is also assessed, from where it is concluded that the scaled variants yield better results than standard MP2 or DFT approaches, except for one system where a large number of van der Waals structures exist.