Exploring the Born-Oppenheimer surface of small and medium-sized Si clusters using the dual minima hopping method

Silicon is the most important semiconducting material in the microelectronics industry. The determination of the structure of silicon clusters is an important task since current trends of the semiconductor industry have led to a dramatic decrease of the device features. The properties of silicon clusters are peculiar and differ strongly with size. Since direct tetermination of the structure of clusters is not possible, Si clusters have been extensively studies using a combination of computational simulation and experimental techniques such as ion mobility measurements, polarizability measurements, Raman or IR spectroscopy. Nevertheless, agreement about the structure of the most promising global minimum candidate has been found only for silicon clusters Si n with n </= 7. Though existing global optimization methods were successful in correctly predicting the presence of structural motifs such as Si 6, Si 7 and Si 10 subunits in low energy isomers of silicon clusters with more than 10 atoms, they were not always able to predict structures that would reproduce all the experimentally observed properties.
In this dissertation, we present a new global optimization method which we shall call the dual minima hopping method (DMHM). The method was implemented in collaboration with Stefan Goedecker. The DMHM allows us to find the global minumum of the potential energy surface (PES) within density functional theory (DFT) for systems for which a less accurate calculation of the PES is possible. The DMHM does not involve thermodynamics and can rapidly find the ground state configuration within DFT by performing a systematic search. It is based on the recently developed minima hopping method (MHM). The DMHM couples a fast approximate method such as fore field or tight binding scheme with the slow but accurate DFT method. the DMHM is very efficient since it requires only an affordable number of DFT geometry optimizations for reasonable configurations which were obtained by the geometry optimization with a fast method and for which the DFT programs converge without problems.
We apply the new method to silicon clusters Si n in the range 7 </= n </= 19 by choosing a tight-binding scheme as fast approximate method and find a number of new low energy isomers within DFT for Si 13, Si, 16, Si 17, Si 18 and Si 19. We challenge the unique ground state structure for certain Si clusters Si n with n >/= 13 by performing DFT calcualtions using the DMHM and by comparing the DFT results with the Quantum Monte Carlo (QMC) calculations done by Richard Hennig. We show on the basis of the DFT calculations which are done using the PBE exchange-correlation functional that the lowest ten isomers coexist within a tiny energy interval. In particular, for Si 13 the lowest pure isotope-free isomers coexist within less than 10 mHa. Besides, we find more than 150 different pure isotope-free low energy isomers for Si 13. The presence of the 29-Si isotope increases this number even further. We observe that the low-lying isomers for silicon clusters Si n in the range 13 </= n </= 19 can be both prolate, oblate and spherical. For some clusters the DFT and QMC energy differences are so mall that entropy effects can change the energetic ordering. In particular, pure isotope-free configurations with rotational symmetry are disfavored by the entropy effects as compared to non-symmetric pure isotope-free configurations. Symmetric configurations containing one 29-Si isotope are disfavored by the entropy effects as compared to non-symmetric configurations containing one 29-Si isotope. From these observations we conclude that for silicon clusters Si n in the range 13 </= n </= 19 a mixture of several configurations with different shapes is to be expected at room temperature, and that interpretation of any experimental data should therefore be handled with great care.