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Local correlation methods

It is possible to apply quantum-chemical correlation methods to extended systems when using the idea of local excitations (the property, that the correlation hole, i.e. the region, where the electrons interact instantaneously, is fairly local). For a solid it is useful, therefore, to switch from the description with delocalized Bloch states to localized Wannier orbitals [16]. This is the starting-point for the so-called local correlation methods. The historically first method of this type is the Local Ansatz (LA) developed by Stollhoff and Fulde [17], [18], [19]. Whereas e.g. the coupled cluster approach [20], [21], [22], [23] uses all possible single and double excitations (CCSD), the LA uses only a subset of these excitations, relying on a physical picture of the material examined. Therefore this method can easily yield an insight into the mechanism of the correlations, but an error estimation is difficult. Another possibility to restrict the excitation space is the local correlation method of Pulay [24], where for each occupied localised orbital an excitation domain is constructed. One more method, the method of increments [25] developed by Stoll, combines Hartree-Fock (HF) calculations for periodic systems with correlation calculations for finite embedded clusters, and the total correlation energy per unit cell of a solid is written as a cumulant expansion in terms of contributions from localized orbital groups of increasing size. In contrast to the method of Pulay, here an a priori truncation of the virtual space is not necessary due to the partitioning of the correlation energy into correlation-energy increments. But of course a combination of the method of increments with the local correlation method of Pulay is possible to reduce the computational effort even further [26], [27]. Due to the computational savings with the restriction of the excitation space it is now possible to extend the local correlation method according to Pulay to solids. First attempts are made by Pisani and Schütz to extend the program package CRYSTAL [28] to correlations obtained with the local MP2 method resulting in the program code CRYSCOR [29], [30], [31], [32], [33], [34], [35], [36], [37], [38]. Note, however, that up to now CRYSCOR treatment is limited to non-metals.

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This page was last modified on April 22, 2009, at 03:56 PM