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In this article we provide an overview of the most common ways of treating electron correlation effects in 3D-periodic systems with some emphasize on wavefunction-based correlation methods such as the method of increments and the local MP2 method implemented in the Cryscor program. We discuss strengths and weaknesses of the different approaches and give examples for their application. Additionally, for the method of increments we discuss recent developments for its application to open shell systems and problems related to the treatment of graphene sheets.
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Müller et al. (2012) studied this question.
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