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Basic theory behind first-principles simulations has been reviewed by many authors, e.g. Jung & Oganov (2005b) in this volume, or by Oganov et al. (2002) and Cohen (1999); the main focus of this chapter is on applications of such simulation techniques, illustrating the power of modern simulation approaches. There are two main problems thatsimulations have to be able to solve in order to be useful:

  1. prediction of crystal structure topology, i.e. of the structure type of the stable and possible metastable phases for a given chemical composition;

  2. once structural topology is known, optimisation of the structure for given PT conditions and calculation of physical properties.

While the second problem is practically solved for most properties, the first problem still poses great challengesand has no general practical solution. In principle, one should explore the entire energy surface and locate all local minima and the global minimum. However, the dimensionality of this surface is so overwhelmingly high that it is difficult to explore it efficiently. Nevertheless, there have been some recent successes in this direction and it seems that soon this problem may become tractable.

The method of Martonak et al. (2003) seems promising and using it Oganov et al. (inprep.) have been able to predict, at a fully ab initio level, several highpressure forms of MgSiO3. Since the problem of structure type prediction is still far from its solution, here we review what can be done once the structure type is known – e.g., how accurate the theoretically optimised structures are, how accurate the predicted simulations helped to resolve several important problems in mineral sciences.

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